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Effects of weather on orange supplies

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Title:
Effects of weather on orange supplies
Creator:
Parvin, David Woodrow, 1939-
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1970
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English
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175 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Agriculture ( jstor )
Counties ( jstor )
Crops ( jstor )
Mathematical variables ( jstor )
Orange fruits ( jstor )
Production estimates ( jstor )
Rain ( jstor )
Seasons ( jstor )
Soil moisture ( jstor )
Weather ( jstor )
Agricultural Economics thesis Ph. D
Dissertations, Academic -- Agricultural Economics -- UF
Oranges ( lcsh )
City of Gainesville ( local )
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bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1970.
Bibliography:
Includes bibliographical references (leaves 158-173).
Additional Physical Form:
Also available on World Wide Web
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by David Woodrow Parvin.

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University of Florida
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EFFECTS OF WEATHER ON ORANGE SUPPLIES
















By
DAVID WOODROW PARVIN, JR.


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1970














ACKNOWLEDGMENTS


The author wishes to express appreciation to Dr. IM. R. Langham,

Chairman of the Supervisory Committee, for his guidance and encour-

agement throughout this period of graduate study. Special apprecia-

tion is also extended to the other members of the Supervisory Com-

mittee, Dr. B. R. Eddleman, Dr. E. L. Jackson, Dr. C. E. Murphree,

and Dr. Leo Polopolus.

The author is also indebted to Dr. L. C. Hammond, Mr. D. S.

Harrison, Mr. L. K. Jackson, and Mr. R. G. Leighty for providing

technical information which was otherwise unavailable. Special

appreciation is also extended to Mr. Joe Mullins, Statistlcian in

Charge, Florida Crop and Livestock Repo-tinr Service, for providing

data which were othe-wise unavailable.

The financial assistance f:r th;s stud> ,.s provided by the

Florida Citrus Ccrmission and the Department of Agr cultural Economics.

The services of the University of Florida Computing Center are also

acknowledged.















TABLE OF CONTENDS


ACKNOWLEDGMENTS . . . . . . . . . .

LIST OF TABLES . . . . . . . . . . . .


ABSTRACT . . . . . . . . . .

CHAPTER I

THE PROBLEM . . . . . . .
Introduction . . . . .
Objectives . . .
Method of Analysis . . . .
Definition of Terms . . . .
The Phenology of Fiorida Oranges
Florida Climate . . . . .
Weather Cv es . . . .
A Brief History of Oranges . .


.. ....... viii


CHAPTER 11


CHAPTER !II


THE STUDY OF WEATHER EFFECTS ON CROPS . . .
General Proble . . . . . . .
Pa-t Research . . . . . . . .
Classical Regression . . . . .
Weather Indexes . . . . . . .
Aridity Indexes . . . . . . .
Hybrid Tschniques . . . . . . .
Added Problems Associated with Forecasting
Florida Orange Production . . . . .
Recent Analytical Approaches . ..



TOWARD A THEORETICAL MODEL . . . . .
A General Model . . . . . . . .
Factors Affecting the Yield of an
Orange Tree . . . . . . . .
Physical F tors . . . . . .
Age . . . . . . . ..
Soils . . . . . . . .
Planting density . . . .
Variety and -ootstock . . . ..
Weather Factors . . . . . . .








Page


Rainfall . . . . . . . 47
Temperature . . . . . ... 48
Management and Cultural Practices . 53
Nutrition . . . . . ... 54
Irrigation . . . . . . 54
General Models Suggested by
Other Researchers . . . . . 56
Kuznets . . . . . . . 56
Stout . . . . . . . . 56
Others . . . . . . . 59
A Concluding Remark . . . . . 60

CHAPTER IV

ANALYTICAL METHOD AND THE DATA . . . ... 63
The Model Estimated . . . . . . 63
The Data . . . . . . . . . 69
The Estimation Technique . . . . . 84
Stage I . . . . . . . . 84
Stage II . . . . . . . . 88
Model Assumptions . . . . ...... 93

CHAPTER V

RESULTS OF ANALYSIS . . . . ... . 99
Estimated Average Yields . . . . .. 99
Weather Indexes . . . . . . . . 105
Weather Equations.. . . . . . 105
By Counties and VerietiCes . . ... 105
Early and Midseasor .. . . . 15
Valencia . . . . . .. . 1!9
By Groups of Counties and Variecy . .. 136

CHAPTER VI

CONCLUSIONS AND IMPLICATIONS ........ !47
Summary and Conclusions .. . . . .. 47
Implications . . . . . . ... 15i
For Citrus Industry .. . . . .. 15i
For Research . . . . . .. 152
Limitations . . . . . . . . 153
Suggestions for Further Research ... . . 154

LITERATURE CITED . . . . . . . . . . . 158

ADDITIONAL READINGS . . . . . . . . .. 166

BIOGRAPHICAL SKETCH . . . . . . . . .. . 174













LIST OF TABLES


Table Page


S Relative importance of factors affecting
average annual change in Florida's Valencia
orange production . . . . . . . 34

2 Relative importance of factors affecting
average annual change in Early and
Midseason orange production . . . ... 34

3 Florida Oranges Average production per
tree by age classes, 1965-66 to 1968-69 . . 42

4 Estimated average yield per tree by age
and variety, Florida . . . . . . 44

5 Counties currently producing Florida
oranges and seasons for which production
data were available . . ... . . . . 70

6 Weather stations and tiie interval for
which data viere a nailabl. . . . . . 73

7 Total orange production fcr the stace of
Florida and the amount and percentayu
For the study area by variety and by
seasons, 1548-49 through 1967-68 . . .. 75

8 Specific weather variables used in study ... 77

9 Root depth, water in root zone at field capacity,
and moisture available for plant use in soils
by counties in the Florida c;trus belt . . 80

10 Average daily evapotranspiration of Florida
citrus groves . . . . . . . ... 81

11 Mixed fertilizers commonly applied to
citrus. . . . . . . .. . . 83

12 Fertilizer materials commonly applied
to citrus . . . . . . . . ... . 83







Table


13 Simple correlation coefficients for the
variables included in equation [15] when
fitted to data for the Early and Midscason
variety, by selected counties . . . ... 96

14 Estimated yields in boxes per tree of Florida
Early and Midseason oranges by county and
age . . . . . . . . . ... . 100

15 Estimated yields in boxes per tree of Florida
Valencia oranges by county and age . . .. 102

16 Signed constants added to Chern's state
estimates of average yield per tree to
estimate average yields by counties and
orange variety . . . . . . ... 104

17 "Weather" indexes for Early and Midseason
oranges, by Florida counties and seasons,
1951-52 through 1967-68 ........... 106

18 "Weather" indexes for Valencia oranges, by
Florida counties and by seasons, 1951-52
through 1967-68 . . . . . . ... 107

19 "Weather" indexes for orange production for
counties in the study area by variety and
by seasons, 1951-52 through 167-68 ..... 10

20 Estimated regression coefficient:, standard
errors, uncorrected coefficient of multiple
determination, and Durbin-Watson "d"
statistic for the Stage II equation for
Early and Midseason orange by Fiorida
counties . . . . . . . ... .109

21 Estimated regression coefficients, standard
errors, uncorrected coefficient of multiple
determination, and Durbin-Watson "d"
statistic for the Stage II equation for
Valencia oranges by Florida counties .... 112

22 Counties included in the study by areas ... 116

23 Signs of estimated regression coefficients
for Stage II equations by varieties, areas,
and counties . . . . . . . . 17

24 Actual and estimated production of Early and
Midseason oranges by Florida counties and
by seasons, 1951-52 through !967-68 . . . 121







Table


Page


25 Actual and estimated production of Valencia
oranges by Florida counties and by seasons,
1951-52 through 1967-68 . . . . .. . 127

26 Total actual and estimated production of
Florida oranges for the study area by
variety 1951-52 through 1967-68 . . ... 133

27 Total actual and estimated production of
Florida Early and Midseason oranges for
the study area with percent errors when
actual production is estimated by Stages
I and II, by seasons 1951-52 through
1967-68 . . . . . . . .... . 134

28 Total actual and estimated production of
Florida Valencia oranges for the study
area with percent errors when actual
production is estimated by Stages I and
II, by seasons 1951-52 through 1967-68 . .. 135







Abstract of Dissertation Presented to the Graduate Council in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy


EFFECTS OF WEATHER ON ORANGE SUPPLIES

By

David Woodrow Parvin, Jr.

June, 1970




Chairman: Dr. M. R. Langham
Major Department: Agricultural Economics

A two-stage procedure was developed to estimate the relationship

between the production of Florida oranges and weather. The relation-

ship was estimated by counties for Early and Midseason, and Late

varieties. The first stage (Stags I) expressed average production

as a function of mte numbers of trees by age. The estimated overage

production frcm Stage I was used to remove that portion oF the vari-

ability in reported production data which was due to changes in

number and age of trees. The Stage I results were used to express

reported production data as the signed percentage deviation of actual

production froi; estimated average production. In the second stage

(Stage II) specified relationships between these signed percentage

deviations and weather were estimated with classical least squares

regression. The analysis was conducted on a county by country oasis.

Data were also pooled over counties and over region in alternative

specifications of the model in Stage II.

Weather indexes and average yields per tree by counties for

Early and Midseoson, and Late varieties ware estimated in Stace I.

Also, the numbers of orange trees by ages for the years 1943 through








1968 were estimated (from tree census data) for the state and for

each county for both Early and Midseason and Late varieties. These

estimates provide useful by-product information from the research.

The data covered the general period 1948 through 1968. Eighteen

counties and two varieties were included in the study. Numerous

variables were used to describe weather. Soil moisture and minimum

daily temperature explained niore of the variation in the dependent

variable of the Stage II relationship than other measures of weather

available. In general, the signs of the estimated coefficients were

reasonable. For the county equations the uncorrected coefficient of

multiple determination ranged from .12 to .84. Many of the relation-

ships estimated from pooled data were not significant. However, the

results provide reasonable bounds on the size of the effects of freez-

ing temperature and certain levels of soil moisture on the production

of Florida oranges. The estimation procedure would have benefited

from measurements of the duration of freezing temperatures and From

more accurate measurements of soil moisture. The weather index for

the state for Early and Midseason oranges varied from .68 to 1.33

indicating that unfavorable weather could reduce the crop 32 percent

and that favorable weather could increase it 33 percent. For Valencia

oranges the range of the state weather index was .60 to 1.22. This

range indicated that the effect of unfavorable weather could be

approximately twice that of favorable weather.













CHAPTER I


THE PROBLEM


Introduction


The supply of Florida oranges is quite variable. The freezes of

1957 and 1962 exerted a marked influence on the total state produc-

tion of oranges. The December estimate of the Florida Crop and Live-

stock Reporting Service for the 1962-63 season placed Florida orange

production at 120.5 million boxes. However, due to two icy nights

in December, 74.5 million boxes were ultimately harvested (iS, p. 7).

Furthermore the freeze rtoucicd the per-box ;ield of processed prcJ-

ucts. Prio- to the freeze a yield of 1.55 gallons ,per box was

estimated for that portion of the crop utilized for frozen concen-

trated orange juice. The actual yield was 1.09 ga!ions (19, p. 82).

Florida orange production fell to 58.3 million boxes the following

season (1963-64) because of the lagged effect of the freeze. It was

not ur.ti the 1966-67 season or the fifth season following the freeze

that production exceeded its 1961-62 level.

An earlier freeze in 1957 was also severe. Total production of

Florida oranges was 93.0 million boxes the season before the freeze.

The freeze dropped production to 82.5 million boxes for the 1957-58

season. And production was only 86.0 million for the 1958-59 season,

Intercounty variability in annual output aiso exis.s. Polk






county's production figures for Early and Midseason oranges during

the four seasons 1961-62 through 1964-65 were 10.7, 9.8, 4.7 and 10.2

million boxes, respectively. Polk's Valencia productions were 14.1,

8.1, 8.9, and 10.8 million boxes, respectively, for the same seasons.

However, production data did not reflect the same distribution

pattern throughout the state. For the same four seasons Valencia

production in Indian River County was 0.9, 0.8, 1.1 and 0.3 million

boxes.

The effects of other weather variables were not always reflected

by the data as clearly as freeze damage. The 1955-56 season was

shocked by severe drought (50). However, of the three major producing

counties, Polk and Orange suffered a reduction in output of Early

and Midseason oranges while Lake increased its output of these. All

three counties increased their output of Valencias. !t was not until!

the season following the drought thar its effect showed up in Valencia

production.

The Florida Crop and L;vestock Reporting Service estimated thae

Early and Midseason orange trees twenty-five years old and over

yielded 7.0 boxes per tree during the 1966-67 season. One season

later they estimated that the same age group produced only 4.0 boxes

per tree. Valencia estimates for the same two seasons were 5.7 and

3.2 boxes per tree, respectively. Sites (78) in a 1947 study of

fruit quality as related to production practices noted that weather

conditions can cause differences in fruit quality and quantity as

great or greater than differences which can be induced by any cul-

tural or nutritional treatment.

The large variations in orange supplies due to weather have not





3

only had great impact on the market for oranges but have also obscured

any relationship which may exist between orange production and other

production inputs. Detailed analysis of this latter relationship

requires that data be adjusted for the effects of weather.

The Florida orange industry is believed to face a demand curve

which is inelastic at high prices and very elastic at low prices

(18, p. 4). This demand curve creates the possibility of an industry

pricing strategy. Historically the industry (particularly the FCOJ2

portion) has tended to "overprice" and to show a definite tendency

toward price rigidity. If the Florida orange industry is to develop

an acceptable arid enduring pricing and marketing policy it is neces-

sary that the factors that affect orange supplies be understood.

Weather is a major source of orange supply variation and as such was

the concern of this study.


Objectives


The major objectives of this study wcre (1) to specify relation-

ships between weather and Florida orange production that were mean-

ingful from the point-of-view of what is known about factors affect-




For example, successful estimation of grower response to the
price of oranges requires that some variable(s) be used to reflect
the variation in output due to weather.

Frozen concentrated orange juice.

3The Federal Trade Comnission considers the Florida FCOJ indus-
try to be an oligooolistically structured industry with few firt i,
substantial barriers to ertry, little threat of outside competition,
and a high degree of vertical integration between grower and processor
(18, p. 3).





4

ing orange production and (2) to empirically measure these relation-

ships. In attempting to satisfy these major objectives certain kinds

of useful by-product information resulted from work on supporting or

minor objectives. These minor objectives were as follows:

1. To describe the groves in the state by counties, tree

numbers, ages of trees, and varieties over time.

2. To estimate county differences in the "expected" yield of

orange trees by age and variety assuming "average" weather and

average levels of other inputs.

3. To compute yearly indexes for citrus-producing counties and

the State for the 1951-52 through 1967-68 production seasons. Each

index provides a comparison between actual and "expected" orange

production. It was hypothesized that deviations of actual production

from expected production were largely ettrioutable to weather and as

a consequence estimated indexes were termed "weather" indexes.

4. To develop forecasting procedures to make long-run predic-

tions of production (under very restrictive conditions to be dis-

cussed later) and to predict the change in production should portions

of the orange belt be suddenly shocked by severe or unusual weather

patterns.


Method of Analysis


A two-stage procedure was developed to estimate the relationship

between the production of Florida oranges and weather. The relation-

ship was estimated by counties for Early and Midseason and Late

varieties. The first stage (Stage I) expressed the relationship

between average production and numbers of trees by age. It was used





5
to remove that portion of the variability in reported production data

due to changes in number and age of trees. The Stage I results were

used to express reported production data as the signed percentage

deviation of actual production from average production. In the

second stage (Stage II) specified relationships between these signed

percentage deviations and weather were estimated with classical least

squares regression.

Data were also pooled over counties and over regions in alter-

native specifications of the model in Stage II.


Definition of Terms


Weather is a collection of various conditions of the atmosphere

including such phenomena as rainfall, humidity, amount of sunshine,

length of day, light intensity, atmospheric pressure, temperature,

and other meteorological factors (81, p. 1153). It is beyond the

control of farmers. Weather influences the crop-growino environment

and affects crop yield. Some writers make a distinction between the

direct and the indirect influences of weather on production. For

example, weather affects production directly through rainfall and

temperature and indirectly through insects and diseases (81, p. il56).

For purposes of this study, weather is defined as the net effect on

production of variations in environmental factors which are neither

under the control of farmers nor in constant supply over tine (91,

p. 264). In contrast, technology is defined as the sum total of

controllable resources and how tney are utilized.

The difference between a forecast of crop production and an

annual estimate of crop production is noted as follo.s. An annual







estimate of crop production indicates a measure of an accomplished

fact at harvest time or later. A forecast of crop production refers

to an estimated future production on the basis of known facts on a

date prior to the period for which a forecast is being made.

While Florida orange trees produce a new crop each twelve

months, the harvesting of a given crop spans two calendar years.

Picking usually begins in September and continues through July of

the following year. Consequently, when discussing Florida oranges

one would not refer to the 1948 crop or 1949 crop but to the 1948-49

season.

Most commercial trees consist of two parts the rootstock which

includes the roots and trunk and the scion which is the upper frame-

work. A tree is almost two years old before it is ready to leave the

nursery. However, it may stay in the nursery a longer period. There-

fore, the convention has been adopted that the age of a commercial

tree is referenced to the year in which the tree was actually placed

in the grove (i.e. year-set).

This report is limited to round oranges. Early, Mid-Season,

and Late are the three general classes of round oranges. The terri

orange will be used in this analysis as a synonym for round oranges.

The expression "variety (macro)" will be used to refer to the

groups of Early and Midseason oranges and Late oranges. "Variety

(micro)" will be used when referring to varieties such as Hamlin,

Parson Brown, Navel, Jaffa, Pineapple, and Valencia. The term




IName is related to time of maturity or harvest.







variety will be used whenever the information being presented is

applicable to both levels of aggregation. Since Late oranges are

almost entirely Valencias, the terms Late oranges and Valencia oranges

are used interchangeably and the terms will be used as synonyms in

the analysis.


The Phenology of Florida Oranges


Commercial production of an orange tree begins at three to four

years of age, increases rapidly to ten years, levels off and reaches

a maximum at twenty-five years (94, p. 14). Plant development, flower-

ing and fruiting tend to combine into an orderly process. By fruit-

ing time many of the factors of heredity and environment which affect

the plant's capacity to produce fruit have already exerted their

influence and yield potential tends to develop unless inhibited by

abnormal growing conditions (45). For the orange tree, as with other

plants, time is relative to phenolooical development, that is, rela-

tive to the dates of flowering and the setting of fruit.

All orange varieties tend to bloom at the same tine within a

given year but with considerable year-to-year variability. Peak

bloom usually occurs around the end of March or in early April. The

blooming process usually takes about 50-60 days for the first regular

bloom. Varying weather conditions often cause a second or third bicom.

After flowering, fruit setting is a continuous process and the young




Bloom information summarized from personal conversations with
Dr. W. A. Simanton, Professor, University of Florida, Institute of
Food and Agricultural Sciences, Citrus Experiment Station. His data
will be published at a later date.




8

fruit generally reach a size of one inch or more b/ June or July (48, p.

1725). Early oranges mature from September through November, Mid-

season oranges from December through January, and Late oranges from

February through July. The Hamlin is the principal Early orange. The

Pineapple is the leading Midseason variety, and the Valencia is the

predominant Late orange (98, p. 23).


Florida Climate


The climate of the citrus-growing regions of Florida is classi-

fied as humid subtropical. From April to October temperatures are

moderately high. The highest daily temperatures in sumnier are usually

from 93 to 95 F. Higher temperatures do occur at irregular intervals

but they seldom exceed 100 F. From November through March lower

temperatures prevail and readings belo;, 32 F. are expected every

winter. The presence of the Atlantic Ocean and the Gulf of Mexico

(one of which is within 75 miles of any point in the citrus belt)

serves to moderate both summer maxina and winter minima temperatures.

The average annual rainfall within the citrus belt has been

estimated to be approximately 52 inches with a range from 37 to 84

inches (98, p. 13). Likewise, the proportion of the annual precipi-

tation which falls in any given month varies from year to year. To-

gether these annual and monthly variations give a highly variable

pattern of rainfall in Florida. A Florida Citrus Conmmissicn report

(19, p. 35) noted that, although the average interval between severe

freezing weather in Florida's citrus belt appears to be approximately

ten years, such conditions may occur at any tire, that is, they are

not regular. Butso-. and Prine (6) in a study of Florida rainfall





9

concluded that variations in rainfall frequencies are probably random

fluctuations. Frost is likely to occur anywhere on the mainland of

Florida on still, cloudless nights in winter.

Freezes, hurricanes, and other weather phenomena are discussed

in more detail in a later section.


Weather Cycles


Bean (3) noted that most crop forecasters view weather as not

predictable but considers such a view to be erroneous. Bean admitted

that weather data seem to behave like random numbers, that statistical

tests in common use fail to differentiate between series known to be

random and constructed series that are not random, and that a moving

average of time series automatically produces what looks like cyclical

movements. He contended that weather fluctuations represent law and

order and are therefore predictable He cited personal research on

rainfall, river stages, wheat, corn, cotton and potatoes Lo support

his position. Palmer (64) reported that an analysis of the meteoro-

logical record beginning in 1887 showed a surprising degree of regu-

larity in the occurrence of severe and extreme droughts in the western

third of Kansas and that an examination of the longest continuous

meteorological record in the middle United States1 indicated that

there is some statistical evidence for suspecting that serious drought

tends to occur about every twenty years in the central United States.




The St. Louis, Missouri weather record is continuous from
January 1838 to date.








However, Palmer noted that the subject requires more research in

greater detail and with more powerful methods and techniques.

Tree ring studies indicated the existence of alternate wet and

dry periods particularly in the subhumid and semiarid regions of the

United States (88, p. 26). Auer and Heady (I) using U. S. corn

production data for 1939-61 and corresponding weather data concluded

that years tended to bunch-good weather years tended to bunch to-

gether and bad weather years tended to bunch together. Tefertiller

and Hildreth (85) in an article dealing with Great Plains agriculture

also suggested the possibility of bunchiness or runs of good and bad

years. Specifically they reported a tendency for rainfall to bunch

in Oklahoma and Montana but that rainfall in Texas appeared to be

random. Shaw and Thompson (77) reported that in an iowa study

weather was found to be periodic, hut in a Kansas study the reverse

was true.

Mitchell (58) reported that most investigators ho research

weather data for ci/cles have failed to support the hypotheses of

their predecessors. Instead they turn up new hypotheses about period-

icities. Mitchell admitted the existence of two real climatic period-

icities--precipitation follows the lunar period of 25.53 days and a

cycle of approximately two years in winds and temperature at hiah

altitudesI over the tropics. However, he noted that as yet there is

no generally accepted physical explanation for either. Mitchell

(58, p. 225) wrote that variations of climate appear to be very ir-

regular.




This cycle is absent at all elevations of less than ten miles.





II

Hathaway (28, p. 492) in research devoted to the problem of the

cyclical relationship between agriculture and the non-agricultural

economy concluded that factors other than weather were needed to

explain the change in crop yields which were associated with the

cyclical change in the demand for farm products. Clawson (10) stated

that random annual variations in farm output are primarily due to

random weather conditions. Griliches (24) wrote that annual fluctua-

tions in farm output were dominated by random fluctuations in weather.

Thompson (88, p. 27) wrote that the weather cycle idea carried

the connotation of a regularity in favorable and unfavorable weather

for crops. He reported that a more acceptable interpretation is that

periodic changes in weather patterns do exist but that they do not

occur in any regular cyclical pattern. Thompson stated that the

popular notion is that wide deviations from average weather tend to

occur at random. However, in another study, Thompcon (89) cautioned

that the researcher may not be able to treat the weather variables

as random. Specifically, he found evidence that weather had not been

random but had improved for grain crops since the mid-thirties in the

central United States.

The 18 years of time series data available for this study pro-

vided no meaningful basis for assuming that departures of weather

variables from their average values occurred in a systematic and

estimable way. Therefore, such deviations were assumed to occur

randomly.


A Brief History of Oranqes


Oranges are native to the tropical regions of Asia. They have






12

spread from there to practically all regions cf the world with suitable

climates. Since their first discovery, oranges have moved westward.

From their native habitat oranges traveled to India, to the east

coast of Africa, to the eastern Mediterranean, to Italy, to Spain,

and finally to the Americas (61, p. 1021).

Oranges were probably introduced into the western hemisphere by

Columbus when he established a settlement on the island of Hispaniola

on November 22, 1493. And Ponce de Leon probably introduced oranges

to mainland North America when he discovered Florida in 1513, since

Spanish law required that each sailor carry one hundred seeds with

him (57, P. 89).

Wherever Spanish settlements were made orange plantings soon

appeared, and in Florida the Indians carried oranges with them and

dropped their seeds in the hammocks and heavily forested areas so

that years later the forests were found populated with wild sour

orange trees. In some cases these trees had beer topwcrked to sweet

oranges and constituted some of the very early groves (7, p. 6). By

1579, plantings existed in the Spanish settlement of St. Augustine

(7, p. 6).

By 1800 there were numerous groves planted by the Spanish and

other settlers along the coast south of St. Augustine, along the St.

Johns River and around Tampa Bay. With thF annexation of Florida by

the United States in 1821 settlers steadily expanded the groves.

This expansion suffered a sharp setback in 1835 when a severe freeze

killed many of the trees to the ground. After the Civil War develop-

ment was rapid. In 1886 the Florida crop reached a volume of ore

million boxes. Railroads were coming into the state and made possible





13

the development of citrus groves away from the waterways. Expansion

was steady from 1886 through 1894 (7, p. 6).

Consequently, by the latter part of the 19th century the orange

industry had been firmly established in Florida. However, in the

winter of 1894-95, a severe freeze hit Florida and practically de-

stroyed all groves. Before this freeze, production had climbed to

6 million boxes. Fourteen years passed before that level was reached

again (72).

Early plantings had been made on locations selected primarily

because of the character of the soil. The freeze of 1894 and 1895

brought to the fore the problem of cold protection and result td in a

spread of the industry to the south. By 1920 it had been discovered

that trees could be produced on the high, warm, sandy ridges of

central Florida by using rough lemon rootstock. Prior to the intro-

duction of rough lemon rootstock, sour orange and sweet orange rooe-

stock had been use' and neither was satisfartor/ or the light sandy

soils with their low fertility and irregular moisture supply. There-

fore, in a sense the industry's present size is based mainly on the

discovery of rough lemon rootstock because it made possible the use

of land not formerly suited to citrus production (7, p. 7).

By the late 1930's, production had grown to the extent that

prices were suffering. Growers and processors searched for new uses

and outlets. The development of FCOJ (frozen concentrated orange

juice) in about 1945 \;as a major breakthrough in this direction.

This new product grew at a phenomenal rate. The initial output of

226,000 gallons for the 1945-46 season grew to 30 million gallons

within 5 years, to 70 million gallons in 10 years, and to 116 million







gallons by the 1961-62 season. For the 1963-64 season, production

of FCOJ utilized more than 65 percent of the orange crop and fresh

fruit used approximately 15 percent. This figure For fresh fruit

compares to 85 percent prior to the introduction of FCOJ (18).

In the 1948-49 season, 18.2 million bearing trees produced 58

million boxes. In the 1966-67 season, 43 million bearing trees

produced 144.5 million boxes, and in December, 1967, there were an

estimated 16 million non-producing trees in Florida groves. In 1966-

67 Florida produced approximately 78 percent of the U. S. supply of

oranges and more than the combined total of the second, third, and

fourth largest producing countries-Spain, Italy and Mexico.

Commercial orange groves extend from Putnam, Marion, and Volusia

counties in tht north to Collier and Broward counties in the south

and production spans the entire breadth of the Florida peninsula.

The center of the orange belt has tended to shift south over time.

This niovement is attributed primarily to the desi r of growers to

reduce the probability of freeze damage a;d to land pressures (55).

The present center of the citrus belt is on the high pines soils of

the ridge section of Polk, Lake and Orange counties. In 1966-67

these counties produced 52 percent of the 144.5 million boxes produced

in the state -- Polk produced 34.0, Lake 24.0, and Orange county

16.5 million boxes.














CHAPTER II


THE STUDY OF WEATHER EFFECTS ON CROPS


General Problems


The cause and effect relationships between weather and crop

production have been the subject of considerable research. With the

increasing grain surpluses of the late 1950's effective agricultural

policy required that the increases in agricultural production be

separated into that attributable to favorable weather and that due

to technological improvements (2K, p. 2.2). Consequently, agricu--

tural economists have had a renewed interest in weather--particuiarly

the problem of separating the effects of weather and tecrno ogy on

production.

The biophysics of the weather-plant interaction is complex.

Most of the functional relationships between individual meteorolog-

ical variables and plant growth are not known (15, p. 81). Besides

being related to yield in some complex, unknown manner, most of the

weather variables are believed to interact with each other in varying

degrees. Yields are also affected by changing levels of technological

factors such as changes in residual soil fertility, differences in

fertilizer rates, changing insecticides, new varieties, crop densities,

mechanization, and increasess in irrigation. Other factors such as

crop diseases and insect infestation which affect yields are closely

associated with weather (15, p. SO). Because of the many factors





16

affecting yield, the estimation of an exact functional relationship

between these factors and yield has often been viewed as impossible

from an empirical point of view.

Rainfall and temperature have been used synonymously with weather,

partly because they are the dominant meteorological influences on

yields, and partly because the data on these variables are readily

available. Plants grow in the soil as well as in the air--and soil

temperature may be more important than air temperature (76, p. 3).

Likewise, rainfall is not synonymous with moisture available for

plant use. Although temperature and precipitation are the variables

usually considered, more exact indicators of the influence of metecr-

ological factors such as soil moisture and drought indexes have been

proposed. Agricultural drought should be defined on the basis of

soil moisture conditions and resultant plant behavior, rather than on

some direct interpretation of the rainfall record (92. 93). For some

years, rainfall and actual soil moisture available for plant growth

may have little correlation. Monthly average of rainfall can be

especially misleading (74, p. 224).

Problems of spatial aggregation can occur for two reasons.

First the relationship between crop yields and meteorological factors

are not monotonic (74, p. 223). Suppose a total June rainfall of 6

inches is optimal for yield end that the effect of 5 inches is the

same as the effect of 7 inches; then the average rainfall for two

counties ((5+7) / 2 = 6) is at the optimal but the true yield at this

level of rainfall will be underestimated. Secondly, a weather mea-

sure is usually accurate for only a small area, and spatial aggrega-

tion creates a problem because weather conditions at only a few







locations are available to represent rather large crop reporting

districts (76, p. 22).

Variation in agricultural output associated with variation in

weather is often greater than that associated with nonweather vari-

ables.1 While irrigation, mechanization, and improved cultural

practices have given some degree of weather-proofing to crop yields,

weather is still an important factor in determining yield (59, p. 1172).

Yields can be greatly influenced by brief periods of exception-

ally favorable or unfavorable weather. Palmer (64, p. 178) notes that

1955 was a drought year and early prospects for wheat yields were dim.

However, one or two good rains at exactly the right time produced long.

well-fitted heads and subsequently good yields. This example further

illustrates the difficulties of estimating yields directly from

meteorological data.

The initial forecast for a aiven season may he desired a con-

siderable tine in advance. Unusual weather can cause considerable

change before actual harvest.2

Since 1940 a substantial part of the variation in yields has

been attributed to technological changes (74, p. 2:9). A yield series

can be visualized as a function of weather and trend due to technol-

ogy and other factors. The economic and other factors which trend

represents will depend upon the data source used (15, p. 81). The




Some writers have classified the variation in output associated
with weather as random and that associated with other variables as
non-random (73, P. 1). This classification scheme leaves something
to be desired since it attributes all randomness to weather.

Supra, p. 1.







use of a linear time trend assumes a constant rate of technological

change and it fails to capture occasional sudden changes in technology.

Also, to assume independence of the technology variable and the

meteorological variable may be incorrect. Shaw (74, p. 222) cites

as an example the fact that in 1930 a two-inch deficiency in rainfall

cut corn yield 25 percent, but in 1960 the same deficiency cut yields

only 10 percent. It is reasonable to hypothesize that for most agri-

cultural crops weather and technology are not independent and that an

interaction exists at each point in time. Technological advances

permit man to bring more of the environment under his control.

Empirical models of weather response must of necessity be crude

abstractions of real world complexities. Howejver, there must be

justification for their form if such models are to be relevant approx-

imations of the real world. For example, if one cculd azsume that

weather variables were distributed randomly and that the effects of

all other variables were determined by trend, it tio'.'ld be feasible to

use a time trend to estimate the influence of technology and attribute

the fluctuation. in yield around the trend line to weather variables.

However, if the weather has improved during the period of study, then

a time trend overestimates the effect of technology and the other

variables (89, p. 75). Likewise, when weather is random and the rate

of technology is irregular, moving averages as discussed by Shaw and

Durost (73) provide a better estimate of the rate of technological

development than a linear time trend. In such a case, deviations

from the "technology line" may approximate deviations due to weather.

Thomosen (8), p. 75) uses hypothetical sets of yield and rainfall

data and presents a c(; e for multiple regression analysis. In his






19

model yield is estimated as a function of time (technology) and a set

of meteorological variables. He argues that the approach gives a

better estimate of the rate of technological development than simple

linear time.

Even with annual crops the problem of separating yield vari-

ability into that portion due to weather and that due to technology

can be difficult. With corn yields Thompson (88, p. 1) found that

weather was the more important variable, while Shaw and Durost (76,

p. 3) in an independent study of the same general data found the

weather effect to be negligible.


Past Research


Numerous techniques have been proposed to aid in the analysis of

the crop-weather relationship and the sometimes troublesome companion

problem of the technology-weather interaction. Each approach tends

to have a few advantages and numerous disadvantages. Historically,

the most frequent riethod of studying the crop-weather relationship

has been to estimate an equation using multiple regression techniques

(71, p. 219). Usually the dependent variable is yield, measured as

an average for some geographical area,and the independent variables

are trend and some collection of weather variables. Most often the

simplifying assumption that trend can be approximated by linear ti,.e

has been used. As noted by Stailings (81, p. 1155) very early studies

often regressed yield on a single meteorological variable such as

total rainfall during the growing season. Other studies, as discussed

by Morgan (59, p. 1173), have attempted to explain yield by using

monthly rainfall and/or temperature during the critical month of the

growing season, Quadratic and interaction terms have been included.








Classical multiple regression analysis has not been the only

technique proposed. Weather indexes have been constructed (75, 81).

Aridity indexes (62) have also been included in models. More direct

measures of the plant-weather relationship such as the use of evapo-

transpiration rates (46) have been proposed. Non-linear regression

has been used to iterate between a weather index generating function

and a function relating yield to the weather index and other variables

(15).

Basically, four general techniques have been used to study the

problem--classical regression, weather indexes, aridity indexes, and

an ad hoc group which has been labeled as hybrid techniques. In the

next section each of the four general procedures are reviewed and

one or more sample studies of each type are discussed in some detail.


Classical Reqression

The classical regression approach to the crop-weather relation-

ship includes studies in which classical least squares was used to

estimate crop yield or production as a function of measures of mete-

orological variables such as total monthly rainfall and/or average

monthly temperature.

Regression coefficients in such models provide an easily under-

stood method cF describing the effects of variations in meteorolog-

ical variables. However, such models are not suitable for predicting

yields over a wide range of weather conditions. The multiple re-

gression approach is most suited for studies at the micro-level of

the crop yield-weather relationships. Shaw (74, p. 218) states that

difficulties associated with statistical attempts to measure the

influence of weather, which requires detailed specification of im-







portant variables and their functional relationship to yields, are

perhaps insuperable and that conceivably the task could be equivalent

to a full project for each crop in every county or other small geo-

graphical unit where it is grown. Specifying appropriate variables

and functional relationships as well as problems of aggregation have

tended to limit the usefulness of multiple regression when data are

aggregated over geographical regions.

Most multiple regression studies have been disappointing, both

as forecasting formulae and as indicators of cause and effect relation-

ships. Even whan statistical indicators have been favorable, the

models have failed to give reliable answers (74, p. 218). A diffi-

culty with regression analysis is that researchers attempt to explain

variation due to weather by using an incomplete and poorly measured

set of weather variables.

Another criticism cenLers around the fact that with regression

analysis Lhe functional form of the relationship between yield and

the technology variable must be specified in advance. Similarly,

the assumption of independence of the technology variable and the

weather variables has been discussed as a disadvantage. While this

assumption is not necessary, the technology-weather interaction is

difficult to estimate. Shaw (74) contends that much more must ce

known about the pattern of technological change if weather is to be

studied by traditional multiple regression.

Because of the biases which may be introduced due to faulty

specification of the model and use of aggregated data plus a history

of failure in forecasting, many persons place little confidence in

any conclusions reached by multiple regression analysis of aggregate

crop yield-weather relationships.





22

Thompson (87, 88, 89) has been a heavy user of multiple regres-

sion techniques in the evaluation of the effects of weather and

technology on crop production. For a detailed look at some of his

work, the following terms are defined:

Y = Yield of corn in bushels per acre

X1 = Year

X2 = Preseason precipitation

X3 = May temperature

X4 = June rain

X5 = June temperature

X6 = July rain

X7 = July temperature

Xg = August rain

X9 = August temperature

Thompson (88) used multiple linear regression to estimate the

relationship between Y and X1, X2, ..., X9 for each of tihe five corn

belt states. He noted that while such multiple linear regression

coefficients indicate the effects of slight departures from average

rainfall or average temperature, they are not suitable for predicting

yields over a wide range of weather conditions. For example, with

linear regression it is assumed that each additional inch of rain in

a given month will have the same effect on yield as the first inch.

Such is not the case.

Thompson's multiple linear regression model tended to overesti-

mate in poor weather years and underestimate in good weather years.

A multiple curvilinear regression model including the rainfall-

temperaLure interaction terms corrected this difficulty (83, p. 5).





23

His multiple curvilinear model included the nine terms of the multiple

linear model plus X2 through X9 squared and the rainfall-temperature

interaction term for each of the three months.

Thompson was quick to caution that large numbers of variables

in multiple regression analyses may provide high correlations (R2)

even though the variables are meaningless. He noted that Robert Shaw

and Robert Dole (88, p. 9) drew random numbers within logical ranges

for rainfall and temperature, and used actual corn yield data for a

27-year period in Iowa. They had 21 variables in their equation and

obtained a multiple correlation coefficient of .86. 'However, none of

the "t" values for the weather coefficients were significant at the

95 per cent level. Therefore, Thompson noted that when large numbers

of variables are used in multiple regression analysis, the multiple

correlation coefficient may be misleading. He suggests that while

analysis of variance (ANOV) will not "correct" the problem, it should

make the difficulty of misleading structural estimates of parameters

and high R2 values easier to identify.1

Thompson used a linear trend for technology. He states that a

linear trend is more logical than any curvilinear trend (88, p. 16).

However, he notes that the data probably reflect a weather-fertilizer

interaction which his equations do not measure, interaction between

extra soil moisture and fertilizer is well known (86). However, for




Thompson is probably referring to an individual "t" test of the
regression coefficients and not to the usual ANOV table for regres-
sion which generally does not include the "t" values. Actually a
corrected R ( 23, p. 217) which penalizes functions with large
numbers of estimated coefficients might be a better statistic on
which to base such decisions.





24

the period of his data, Thompson felt technology had been adopted at

a fairly steady rate. He verified this assumption by examining the

residuals from his estimated function to see if they increased or

decreased over time. He argued that homogeneity in the residuals

supports the assumption that technology has been gradually adopted

over time. Thompson used a cubic in time for technology in his

studies on grain sorghums and wheat because the data did not reflect

a linear trend.


Weather Indexes

The weather index approach results in an index such that actual

yield figures may be adjusted to reflect yields had average weather

prevailed. This approach has been used in an attempt to avoid the

difficulties commonly associated with regression analysis.

Various techniques have been proposed for the construction of

weather indexes. The differences among these techniques are slight

and tend to depend on the data used. To measure the influence of

weather by the index approach, a time series of yields is required.

A trend is usually fitted to the data to describe the yield effect

due to changes in factors which were not controlled. The weather

index is calculated in each year as that year's actual yield as a

percentage of the computed trend.

If experimental plot data with most nonweather variables being

controlled are used to calculate the weather index, the index may be

an indicator of the weather alone. However, if a time series of

actual yields is used Lo calculate an index, then the effect of

weather may depend on the level of technology which is not controlled.

In such a case the index obtained would be an indicator of a!! un-





25

controlled factors which affect yields and which are not reflected in

trend (73, P. 7).

Stallings (81) has computed indexes for the influence of corn,

oats, barley, wheat, soybeans, cotton, and tobacco. The method he

uses has been called the experimental plot data approach. This

method is based on the assumption that if time series of yields for

a crop can be obtained From experimental plots in the areas where

the crop is grown and where as many variables as possible have been

controlled the remaining variation in yield from year to year (after

trend has been removed to account for increases or decreases in the

fertility level of the soil) will give an indication of the influence

of weather. Since the net effects of weather are measured, this

approach allows for all the influences of weather whether direct or

indirect. Stallings assumed that the yield trend due to fertilizer

applications on the plot was approximately linear and could be re-

moved by a linear regression on time.

For a given crop and a given location the technique is quite

simple. First, remove trend from each series by fitting a linear

regression line to the data. Second, compute indexes for each series

as the ratio of the actual to the computed yield of the regression

line. Third, average indexes for each series to obtain an index for

that location. Finally, if desired, indexes for larger areas can be

formed by weighing the index for each location within the area by

the percent of average production for the area that the location

represents.

Ideal data for this approach would come from experimental plots

with everything held constant, except for weather, over the period of





26

time for which indexes are to be calculated. Stallings notes, however,

that calculated trends could be partially or entirely due to improved

technology and management of the experimental plot. Also, the data

might not reflect the varieties, practices and technology level rep-

resentative of the production in the area to be represented by the

index. He stated that in cases of less than ideal data, judgment

and familiarity with the situation be used to help resolve data

problems. When using the experimental plot approach to generate

weather indexes, the data are subject to all the criticisms and short-

comings normally associated with field experiments. Researchers

often incorrectly assume that because the data come from experimental

plots their accuracy is superior to most secondary data.

Shaw and Durost (75) have modified the above procedure somewhat

for data from corn variety tests which were conducted under actual

farming conditions. They took the following steps to develop a

weather index for each location: (1) compute a 9-year moving average

as a first approximasion of the trer.d in jie!ds due to factors that

were not held constant, (2) extrapolate the moving average forward

and backward to the terminal years, (3) divide actual experimental

yields by the corresponding moving average yield. Consider any year

in which this percentage ranges from 85 to 115 as an 'average-weather"

year, and (4) regress yields in "average-years" on time, (5) compute

the weather index as actual test yield divided by estimated trend

test yield.

An advantage of the weather-index approach is that the specifi-

cation of the exact cause and effect relationship between yield and

an individual meteorological variable is avoided. Any assumed math-





27

ematical function requires more knowledge about the rate of techno-

logical change than we now possess (74, p. 227). Shaw notes that the

deflated yield series should indicate the form of the technological

relationship. One major use of weather indexes is to measure techno-

logical change indirectly by using the index as a deflator for the

influence of weather variation. The advantage of this approach to-

ward trend is that no assumption need iimit its form.

One basic weakness of the experimental plot data approach is its

assumption that factors other than fertility levels are constant over

the experimental period. Experimenters often attempt to optimize

nonexperimrental variables (65, p. 1161). It is likely that insect

control and other production practices are altered over the experi-

mental period to keep abreast of technological advances. If such is

the case, it will be reflected in the index by dirminished inoirect

effects of weather.

A final disadvantage of weather indexes is that they cannot be

used to predict yields on the basis of meteorological observations.

However, as indicated earlier they are useful if the purpose of the

analysis is to simply remove the weather effect so that other factors

affecting the yield of a crop may be studied in greater detail.


Aridity Indexes


Oury (63) has proposed that some aridity index be used as an

independent variable in relating weather to yield rather than such




Oury's term.







meteorological variables as rainfall and temperature. He stated

that the use of a composite aridity index may provide a relatively

simple approach to a difficult problem encountered in agricultural

supply analysis. The concept is simple and is not confined to a

single agricultural area and/or crop and the indexes can be calculated

whenever basic weather data, rainfall and temperature, are available.

This approach rests on the assumption that evapotranspiration is

the key weather-related variable that influences yields. Note the

following definitions:

1 = Aridity index

P = Precipitation or rainfall

T = Temperature

Recognizing that temperature is the major factor affecting evap-

oration various workers have suggested formulae substituting. trmper-

ature for evaporation. Several such formulae discussed'by Oury are

as follows:

Lang: I= P/T

De Martonne: I = P/(T + 10)

Koppen: I = 8P/(15T + 120)

I = 2P/(T + 33)

I = P/(T + 7)

Angstrom: I= P/1.07T

Lang's formula indicates that the effectiveness of rainfall

varies directly with precipitation and inversely with temperature.

De Martonne added the constant 10 to avoid negative values. Basi-

cally all three of Koppen's formulae are similar to those of Lang and

De Martonne. !n accordance with Van't Hoff's Law the denominator







of Angstrom's formula doubles with each rise of ten degrees centi-

grade.1

Oury estimated three models of crop yields by least squares to

determine the suitability of using De Martonne's and Angstrom's

aridity indexes. Oury "fitted" the following three functions:


Y = b + btt + bpP + bTT + e Cl]

Y = b' + b't + bM (P/(T + 10)) + e' [2]

Y = b" + b" t + bA (P/1.07T) + e" [3]


where:


Y = Yield per acre

t = Time

P = Precipitation during selected period

T = Temperature during selected period


Equation [l] implies that the marginal yield responsee to P and

T is constant. Agronomically the aridity index approach (equations

[2] and [3]) has more intuitive appeal. It implies that the marginal

yield response to P is not constant and is a function of T and like-

wise that the marginal yield response to T is not constant and is a

function of P and T.

Oury found P and T to be highly negatively correlated. The

"t" statistics indicated bM and bA to be significant at the 1 per-




Van't Hoff's Law states that the velocity of a chemical re-
action doubles or trebles with each rise in temperature of ten degrees
centigrade.





30

cent level and bp and bT at the 10 percent level. Similarly Oury

reported that the Durbin-Watson d-statistic indicated the superiority

of equations [2] and [3]. Likewise, Oury reported that equations

[2] and [3] gave more logical structural estimates of the parameters.


Hybrid Techniques


Knetsch (46) used the drought-day technique to study the effect

of moisture and fertilizer on Tennessee Valley corn. A drought-day

was considered to occur when the available moisture in the soil

reached a critical level as estimated from a moisture-balance compu-

tation of daily rainfall and evapotranspiration data.

The number of drought-days occurring during the growth period

does not give an appropriate index of drought effects on yield. The

effect of a drought depends on the stage of development of the plant.

Therefore, it was necessary to weight the drought in accordance with

the time of occurrence. The relative importance oF drought in the

different growth periods was unknown, so Knetsch developed the follow-

ing estimate from separate data:


Y = 99.04 .096A 1.376B + 5.232C 1.736D

-.403C2 .146CB .055CD + .042BD [4]


where:


Y = Yield

A through D = The number of drought-days in successive periods

through the growing season.

The coefficients of equation [4] were used to assign weights to

the individual drought-days which occurred during the three years of





31

the experiment. From experimental data with various levels of nitrogen

Knetsch estimated:

2
Y = 92.95 + .4834N .001N .5981D 0028ND [5]


where:


Y = Estimated yield in bushels

N = Pounds of nitrogen

D = Drought value


Knetsch's interest was in estimating the optimum level of nitro-

gen to apply. He specified a model with a drought-nitrogen interaction

term on the basis of prior agronomic research.

The important point for purposes of the present study is that

the drought-day criterion provides an alternative specification

hypothesis for weather in models used to study crop yields.

The drought-day approach requires that one know the maximum

water the soil can hold, the level or levels of soil moisture at

which growth is appreciably depressed, and the rate at which the soil

dries out due to evaporation. Daily precipitation records are also

required. Knetsch used the Thornthwaite formula to estimate evapo-

transpiration. This procedure requires that rainfall be added each

day and evapotranspiration be subtracted. Soil moisture is of course

bounded by zero and its maximum storage value. A drought-day is

defined to occur when the storage value equals zero or some critical

value (wilting point).

Doll (15) used data for the period 1930-63 for 37 Missouri

counties to estimate average corn yield for Missouri as a function of





32

weather and trend. He used an iterative non-linear regression pro-

cedure suggested by Edwards (17).

Because corn yields have increased rapidly in Missouri since

1930, a cubic time function was used to estimate trend. Doll's

results were:


Yt = -5.1443 + 3.7902Zt .1164Z2t + 2.1882t
2 R2
158t + .0026t R = .90 F6]

Zt = -.689Xti + .0373Xt2 + .... + .0912Xt8


where:

Yt = Predicted average corn yield for Missouri.

Xtk = Rainfall variable for year t for week k, k=1,...,8.

Zt = A measure of the impact of the rainfall variable in

year t.

t = Time.


If Zt and Zt2 are substituted into equation [6], the result is

an estimate of average yield given average weather for the time

period under consideration. A weather index was computed as the

ratio of predicted yield to the predicted yield given average weather.

Doll listed three advantages of the technique: (i) the index is

based on a functional relationship between yield and meteorological

variables (and two years with similar meteorological patterns will

have similar indexes), (2) the formulation of the model can allow

decreasing returns to meteorological variables within a time period

and interactions among time periods, (3) the inclusion of meteorolog-

ical variables in tne model improved the estimate of trend to the





33

extent that weather phenomena such as runs and extremes are "explained"

by the meteorological model.


Added Problems Associated with Forecasting
Florida Orange Production


Oranges are a perennial crop and the meaningful technical unit

for measuring yield is a tree rather than an acre. The yield of an

orange tree is a function of its variety, age, location (soil type

and depth), planting pattern (tree density and how they are physically

arranged), and average weather to which it is subjected.

A forecast based on bearing surface would be better than one

based on tree numbers or acreage, but such information would be

impossible to keep current (94, p. 12).

The 1940-44 period was characterized by two low and two high

solids seasons. However, Sites (78, p. 56) reported that no elenmeit

of weather was sufficiently outstanding to enable one to conclude

that it was the cause.

Generally, the more the acreage is concentrated, the more sus-

ceptible the total production is to weather variability. Usually if

spread over a large area, good and bad weather may tend to average

out. While the acreage devoted to Florida oranges is fairly concen-

trated, the same climatic conditions of rainfall and temperature

tend to have varying effects due to the vast differences that exist

among soil types, depth, and water-holding capacity. However, due to

the fact that the citrus belt is concentrated geographically freeze

effects tend to be more general in nature.

Stout (84) reported that a considerable amount of the year to

year variation in the production of oranges could be explained by the





34

folicwing factors: (1) tree numbers; (2) number of fruit per tree;

(3) size of fruit; (4) droppage rate. He considered Early and Mid-

season oranges and Valencia oranges independently and reported the

following results as given in Tables 1 and 2 below.


Table 1: Relative importance of factors affecting average annual
change in Florida's Valencia orange production.



Factor Percent variation explained


Tree Numbers 11.1

Number of fruit per tree 29.8

Size of fruit 14.4

Droppage rate 30.4

Other factors i4.3



Source: Stout (84, p. 30).



Table 2: Relative importance of Factors affecting average annual
change in Early and Midseason orange production.



Factor Percent variation explained


Tree numbers 4.3

Number of fruit per tree 44.3

Size of fruit 21.5

Droppage rate 9.5

0:her factors 20.4



Source: Stout (84, p. 30).







Stout (84, p. 10) noted that the number of fruit per tree is

related to the area of bearing surface of the tree and to freeze

damage. He reported a tendency for years with low sizes to follow

years with high sizes and vice versa (84, p. 12).

In summary, while many of the problems associated with forecasting

Florida orange production are due to the numerous factors related to

yields and the impossibility of stating the functional relationship

of these factors to yield and to each other, the major difficulty is

due to the fact that oranges are a perennial crop and a considerable

percentage of the year-to-year variation is due to the changing dis-

tribution of trees by age classes. Also, the relationship between

tree age and average production is not clearly understood (especially

differences in the relationship from one region within the state to

anoth.r).


Recent Analytical Approaches


Two recent studies have attempted long-range forecasts.

Raulerson (67), in a 1967 study, investigated the problem of fluc-

tuating orange supplies and grower profits in the frozen concentrated

orange juice (FCOJ) sector of the Florida citrus industry. Polopolus

and Lester (66), in a 1968 study devoted entirely to forecasting,

estimated Florida's orange production over a fifteen years period.

Raulerson updated an existing DYNAMO simulation model (39) of

the Florida citrus industry to appraise alternative supply control

policies which were designed to reduce the fluctuation in orange




Bearing surface is a function of the size of the root system (95).




36

supplies and grower profits. In simplest terms, Raulerson considered

a given year's production to be a function of productive trees and

boxes per trees. Boxes per tree were in part dependent on the level

of average grower profits. The level of productive trees was in-

creased by new planting and by hatracked trees coming back into

production, and decreased by a normal mortality rate and by productive

trees lost by freeze.

The author expressed the freeze effects on crop size and tree

numbers by defining three possible categories according to the

severity of the particular freeze encountered. Trees were killed

completely, hatracked, and/or suffered only yield losses. The sever-

ity of the particular freeze encountered was based on 23 seasons of

weather data, 1937-38 through 1964-65. A procedure of random sampling

with replacement was used to obtain 14 years of freeze effects. The

industry was simulated for a 20-year period, 1961-62 through 1980-81.

The actual weather for the first six years, 1961-62 through 1966-67,

was used.

Raulerson noted that a more accurate DYNAMO model of the citrus

industry would benefit from expanded research in some areas. An in-

complete list of research needs is given below:

1. Supply response of growers particularly when they are

facing declining prices.

2. Effects on yields of less intensive cultural practices -

especially if the reduced level of cultural practices existed for

only a few years and normal cultural practices were resumed.




IItems 1 and 2 are interrelated and Raulerson discussed both as
a single topic.







3. Effect of freezes upon present and future crops.

Polopolus and Lester used a random sampling technique to estimate

Florida's orange production over the next fifteen years on the basic

assumption of year to year variability in average yields per tree.

Their method of estimation considered each future year's production

to be an "event" drawn randomly from a set of six alternative events.

The "events" were defined to represent the range of yield possibilities

likely to occur in the future. Each of the six events had equal

probability of beiny selected for any given year. The six alternative

events were specified as follows:

1
Event Descriptjon of average tree yield

A Slightly above average

B Slightly below average

C High

D Low

E Average

F Related to freeze damage


Given a random drawing of a freeze, the intensity of the freeze

was defined by another random drawing of various possibilities of

freeze damage. F;ve alternative levels of freeze damage were developed

from historical records. They were as follows:








Events B, C, and D directly relate to historical tree yields
obtained in the 1965-66, 1966-67, and 1967-68 seasons, respectively.







Freeze Percent of total
possibility Tree loss Yield loss
Percent

1 11 15

2 8 35

3 0 17

4 0 10

5 0 5


The researchers assumed a net planting rate of zero except for

the years immediately following freezes. The experiment was "run"

fifty times for each of the fifteen seasons, 1968-69 through 1582-83.

For the fifty experiments the standard error of the estimate averaged

36.7 million boxes -- indicating the extreme year to year variability

in Florida orange production.

The authors cautioned their readers ':o interpret the production

estimates in a general fashion and to avoid placing undue emphasis

upon specific numbers in specific years. The biggest difficulty lies

in the fact that any random event drawn in the sample may tend in the

opposite direction from the real event. Likewise, the authors

mentioned that the net planting rate was not treated properly and

that the limited number of possible yield events with equal probabil-

ities terds to place limitations on the analysis.

Both the above studies indicated a need for a more accurate

description of the relationship between weather and orange production.













CHAPTER III


TOWARD A THEORETICAL MODEL


A General Model


The yield of a specific orange tree can be viewed as a function

of its variety, age, rootstock, density of planting, terrestrial

location, the soil in which it is planted, weather conditions prior

to bloom, weather conditions through the growing season including

maturity, plus the cultural practices and nutritional programs to

which the plant has been subjected. This relationship between the

yield of an orange tree and the many factors affecting the fVnal

level or yield is probably unique for each tree and may be repre-

sented in functional notation as.


Yit Z it, C it, G it, U it i=t,...I; [7]

t=l,...,T.

Y"it = Observed level of yield of ith tree in tth year.

Z"it = Set of variables which represent all physical attributes

of the ith tree which affect the yield in the tth year.

C it = Set of all weather variables affecting the ith ree's

yield in the tth year.




Asterisk superscript was placed on each variable to emphasize
that it differs from similar variable notations to be used later.







G"it = Set of all cultural, nutritional, and technological

variables affecting yield of the ith tree in the tth

year.

U"it = Disturbance term which represents that portion of yield

of the ith tree in the t year which was not explained

by the arguments in Z", C and G.

I = Number of trees and T represents the number of years.


The variables included in Z it should describe all the physical

characteristics and attributes of the ith tree such es variety, age,

rootstock, planting pattern and density, and type and depth of soil.

The set Cit would include such variables as the soil moisture condi-

tion experienced by the tree, temperature, and wind. Temperatures

are critical--particularly low temperatures which cause yield loss

due to freeze damage. The collection G" i would include such vari-

ables as those which measure fertilizer, pesticide, and water appli-

cations and other management practices including freeze protection.

The Q"i would not be separable functions in the three sets of

variables but would include inter- as well as intre-set interactions.

The necessary knowledge to specify the form of equation [7j for

each tree will probably never be available and if it were,the result-

ing complexity would be as intractable as the real world. Later,

assumptions will be used to abstract from the complexities of the

real world. But, now we turn to a discussion of what is known about

factors affecting the yield of an orange tree.







Factors Affecting the Yield
of an Orange Tree


The factors affecting yield can be broadly classified as physical,

weather, and management and cultural practices.


Physical Factors

The major physical factors affecting the yield of an orange tree

are age and soil depth. These factors affect the tree's bearing

surface which is a major determinant of its average yield. Since

oranges are a perennial crop, tree size and average yield increase

over time. Other physical factors affecting yield are variety, root-

stock, and planting density.

Age

The fundamental relationship between average yield and age of

tree has been developed only in a very general manner using aggregate

state figures and rather wide age group classifications. Deviations

in the effects of age among the various areas of the state have not

been studied in detail. Average production per tree by age classes

has been estimated for the entire state for selected seasons. The

results are summarized in Table 3.

This information is too aggregative to be useful on a county by

county basis since it implies that the average age of the trees within

each age group classification is the mean of that particular group.

For example, if in a given county the trees in the 4 9 age group

(mean age 6.5 years) had an average age of 5 years, then the coefficient

in Table 3 would yieid a biased estimate for that age group. Such

aggregative figures also fail to reflect county differences in

average yield by age. Two writers, Chern (9) and Savage (71),have









Table 3: Florida Oranges Average production per tree by age classes,
1965-66 to 1968-69.




Crop 4-9 10-14 15-24 25 Years
year Years Years Years S older

--------------------------90 pound boxes--------------------------

Early and Midseason

1965-66 .9 1.4 3.7 5.1

1966-67 1.I 3.0 5.7 7.0

1967-68 1.2 1.6 3.4 4.0

1968-69 1.1 2.9 4.3 5.1

Average 1.1 2.2 4.3 5.3

Valencia

1965-66 .5 1.7 3.1 4.0

1966-67 1.2 2.8 4.2 5.7

1967-68 1.0 1.8 2.6 3.2

1968-69 1.1 2.0 3.4 4.2

Average 1.0 2.1 3.4 4.3



Source: Unpublished information provided by the Florida Crop and
Livestock Reporting Service to the Departmenrt of Agricultural
Economics, University of Florida. See Polopolus and Lester
(66).






43

estimated average yield per tree in more detail. Their findings are

reported in Table 4.

Examination of these estimates reveals some rather extreme dif-

ferences between results found by the two researchers. For example,

Savage estimated that a 3-and a 4-year old Valencia tree would yield

a combined total of 1.1 boxes while Chern would expect only one-half

of a box.

Similarly, Savage estimated that a 25-year-old Valencia tree

would produce 5.5 boxes on the average, while Chern estimated 4.3.

Soils

Soil depth is an important factor affecting the average yield of

an orange tree since soil depth determines the size of the root

system which is directly related to bearing surface (20). Citrus

roots will not penetrate the hardpan found in some sections of Florida

and they will not grow below the highest level of the fluctuating

water table (21).

The root distribution of citrus planted in the coastal soils in

Florida is often restricted to a rather shallow zone. Young (95, P. 52)

in a 1953 study of citrus in the East Coast area of Florida found the

principal root zone to be in the surface twelve inches with few roots

belowv eighteen inches. The shallow water tables that have persisted

over long periods have seriously restricted root development and over-




Savage's coefficients were based on the analysis of grove rec-
ords of cooperating growers. If his sample included mostly better
than average growers or if he did not use proportional sampling from
all areas of the state, then his coefficients are not estimates of
average yield for the entire state. Chern's source was the statisti-
cal Crop and Livestcck Reporting Service. His coefficients are based
on a 100 percent sample of tne commercial groves in the state.










Table 4: Estimated average yield per tree by age and variety,
Florida.


Savage


Age Early


Savage


Chern


Early &
Midseason Midseason


Savage


Late


Chern



Late


.----------------------90 pound boxes-----------------------


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25 &
above


0.00
0.00
0.00
0.69
0.85
1.02
1.18
1.35
1.51
1.67
1.84
2.00
2.29
2.59
2,88
3.17
3.47
3.76
4.05
4.30
4.50
4.70
4.90
5.10

5.30


0.0 0.00
0.0 0.00
d.4 0.00
0.7 0.50
1.0 0.70
1.4 0.90
1.7 1.10
1.9 1.30
2.2 1.50
2.5 1.70
2.7 1.90
3.0 2.10
3,2 2.26
3.4 2.42
3.7 2.58
3.9 2.74
4.1 2.90
4.3 3.06
4.5 3.22
4.6 3.39
4.7 3.57
4.9 3.75
5.0 3.94
5.1 4.12

5.5 4.30


(9, p. 58) and Savage (71, p. 3).


___~I~ _~~_


Source: Chern






45

all plant growth. Hunziker (34) in a 1959 study found that the lower-

ing of the water table in the Indian River area of Florida from 20 to

40 inches doubled the quantity of feeder roots in four years and con-

sequently increased the size of the trees.

Koo et al. (50) divided soils planted to citrus in Florida in-

to two major groups--well-drained and imperfectly to poorly drained

soils. Sites and Hammond (79) reported that the rapid expansion of

the Florida citrus industry between 1950 and 1960 resulted in an

almost complete utilization of all well-drained land suitable for

citrus and noted that the water table fluctuates widely in the poorly

drained soils. During the wet season 10-20 inch depths are common

while 40-60 inches are generally expected in the dry season.

Lawrence (55) divided Florida soils planted to citrus into four

broad groups.

1) Flatwoods soils are the low, flat, poorly, drained areas

normally underlaid with hardpan. These lands, althou ,h somewhat more

fertile than the high pinelands, are usually considerably colder than

the surrounding better drained soils. Groves are affected by a

fluctuating water table (too wet and then too dry) and frequently

cold weather. The soils also require special preparation for oranges

-- e.g. ditching, bedding and other measures of water control.

2) Low hammock soils are better than flatwoods soils for citrus

but are often poorly drained and usually lack adequate air drainage.

3) High pinelands soils are usually light, well-drained sands

of low natural fertility which are found on higher elevations. They

contain the largest expansion of citrus and are suitable for citrus

only with cold protection through proper air drainage and close

proximity to lakes.






46

4) High hanmock soils are best. The surface layer of this soil

type is usually thicker and darker because of higher organic matter

content.

Since the bulk of Florida's orange acreage is located on the

ridge section, Florida soils planted to citrus can be generally

characterized as being of low fertility and moisture-holding capacity.

Planting density

Dow (16) has noted that planting densities for all citrus has

been steadily increasing. In 1951 new planting had an average of

72.0 trees per acre. By 1967 this average had increased to 103.0

for all citrus and to 110.0 for Early and midseason oranges. Koo

et al. (50, p. 22) found that fruit production per tree varied little

in the range of 45 to 84 trees per acre. However, they reported that

yield per tree was reduced approximately thirty percent with 80 to

116 trees per acre.

Variety and rootstock

Harding and Sunday (27) reported that the quantity of Florida

oranges was related to variety (micro) and to rcotstock. Hodgson

(31) reported size differences due to variety (micro) and rootstock.

Horanic and Gardner (32), in a Florida study, found rough lemon

rootstock to have a greater drought resistance than other rootstocks

because of its more extensive root system.

Varietal (macro) differences in yield are shown in Tables 3 and

4.


Weather Factors

The major components of weather, rainfall and temperature, are

discussed in this section. For levels of rainfall and temperature






47

that would be considered as normal the yield effect of these factors

is probably due to their interaction effect on the level of soil

moisture. Unusual levels of either variable may affect yield directly

by damaging fruit and/or plant.

Rainfall

Ziegler (96) indicated that total rainfall in Florida is suffi-

cient for citrus production but that its distribution is often bad.

Rains of 16 inches accompanying hurricanes have been expcrienced.

Hurricanes are threats to Florida citrus. Significant crop reduc-

tions due to hurricanes occurred in 1926, '28, '4i, '44, '45, '46,

'47, '48, '49, '50, '60 (68, p. 24). Such rains are harmful because

they supply more moisture than the sandy soils can hold and cause

serious leaching of soluble nutrients through percolation. May to

September is the rainy summer season and usually accounts for about

two-thirds of the precipitation in most sections of Florida. During

this period rainfall is generally sufficient for the needs of citrus

trees. From October through April and occasionally through lay or

early June rainfall is often insufficient for the needs of the trees.

The two periods in the annual growth cycle of the orange tree

when it is most sensitive to soil moisture deficiency are in the early

spring when the neu flush of growth is tender and fruit is setting

and in the late spring and early summer when the fruit is rapidly

increasing in size. The most critical period is in the spring, par-

ticularly during the months of March, April, and May especially

if the rainfall was deficient the preceding fall (98, p. 92). Defi-

ciency of soil moisture in May and June may limit fruit size. Shortage

of rainfall during October and November is not critical unless the

tree experiences severe wilting (98, p. 93).






43

Whenever the moisture content of a given soil is above its field

capacity the excess gravitational water will percolate away. Usually

an accumulation of greater than two and one-half inches within a few

days will cause such percolation (51). Koo and Sites (51) reported

wide variations in water transpired by months. In a study of 15-

year-old Marsh grapefruit trees on Lakeland fine sand average daily

transpiration was estimated to be 34.2 gallons per tree. However, in

February, 1952, it soared to 53 gallons per tree per day.

Because of the very low water holding capacities of most Florida

soils, the distribution of rainfall is more important than the total

amount (49, p. 2). Rainfalls of one-tenth inch or less are of little

use to citrus trees since the precipitated moisture evaporates from

the soil surface without affecting soil moisture. Rainfalls of from

one to three inches are ideal for Florida groves since the soil is

wet deep enough to suoply moisture over a long period. Heavier rains

usually cause percolation. Koo and Sites (5!) reported that the

quality of fruit is negatively correlated with total annual rainfall.

Temperature

Florida's freezes are produced by cold, dry polar air moving into

the state from northern areas. During the initial influx, winds are

rather strong, and high and low ground locations may be equally cold.

This is called cooling by advection. When a polar air mass remains

over the state the wind becomes light to calm at night. The surface

of the earth after sunset loses its heat to the very cold sky without

a return by radiation; this is called radiational cooling. Under

these conditions tha surface of the soil soon becomes cooler than the

lower layer of the atmosphere; the air in contact with the soil begins






49

to lose heat to the soil by conduction. This cooling is confined to

a relatively shallow surface layer of the air, the temperatures of

which may drop to critical values while the air just a few feet above

may remain much warmer. This is called temperature inversion. This

accounts for the phenomenon of damaged citrus fruit and foliage at

lower portions of a tree without damage to the upper portions of a

tree, or, damage decreasing as one goes up a slope (79, p. 8). Cold

air is more dense than warm air. When the ground is sloping, gravity

acts to move the thin layer of heavier cold air down the slope where

it gathers in depressions or frostpockets which become quite cold

(79, p. 11).

Freezes are always general, not local, because they result from

large masses of air at subfreezing temperatures. Freezes usually

have at least a three day duration in Florida. Ziegler and Wolfe

(98) describe the usual Florida freeze in the following nanner. Be-

cause the air is at the same temperature from top to bottom of the

moving mass, there is a tendency for equal temperatures on high and

low ground, at least on the first night of the freeze. The first

night is usually cold and windy but rarely causes serious damage,

although a possibility of damage exists with a period of calm shortly

before sunrise which allows the air to stratify. Usually there is

little warming of the air or trees during the second day as cold air

continues to move south. During the second night the wind usually

falls soon after sunset and the stratifying air may reach dangerously

low temperatures rather soon, especially in low areas. On the third

day cne wind usually shifts and begins to replace the cold air with

warmer air from the ocean. Therefore, under the usual conditions of







freezes in Florida, the second and/or third nights are the more

dangerous after the ground and trees have become cold and the wind

has ceased.

Freezes may occur in Florida any time from November 15 until

March 15. The most severe damage results when an early winter freeze

is followed by a period of warm weather sufficient to initiate new

growth which in turn is followed by a second freeze in the same winter.

Such a freeze occurred in the winter of 1894-95 and is still referred

to as the "big freeze" or "great freeze." An early freeze in Deces:ber

of 1894 defoliated the trees and fruit was frozen but wood damage

was slight. The weather was mild during January and trees put out

new shoots and growers generally felt that their groves were in good

shape. However, in a condition of tender growth, the trees were

killed to the ground by a second freeze in early February, 1'35.

In January, 1949, a freeze of several days' duration cause loss

of fruit and considerable injury to the branches but because there

was no additional severe cold that winter the new growth in February

following the freeze developed normally and the groves were essen-

tially back to normal by summer. The freeze in the winter of 1957-58

was one of repeated cold waves interspersed with periods of sufficient

length and warmth for renewal of growth. Damage was severe in many
I
areas.

The meteorological events leading up to the freeze of December,

1962 were numerous and complex. In simplest terms, the air mass that




1This section was summarized from Ziegler and Wolfe (98, p. 84-









caused this freeze was a product of the stagnation of air over the

snow-covered Arctic region during long winter nights. Its rapid

movement from Canada to the Gulf Coast was due to an avenue of

vigorous northwest to southeast air flow created by an intense

Atlantic coast low pressure and and great high pressure ridge in

the western United States. Temperatures fell on an average of 15-20 F

throughout peninsular Florida from 7 P.M. December 12 to 7 A.M.

December 13 at a rather uniform rate of 1-2 F per hour. This was a

classic advection freeze with effective radiative heat loss contrib-

uting very little to its severity. Record low temperatures were set

at many stations throughout Florida and it was the coldest night of

the century for high ground locations in the northern portion of the

citrus belt and for the so-called "warm locations" in the heart of

the citrus belt.l

Past freezes have greatly reduced short-run orange supplies.

Probably the most important factors which influence the susceptibility

of citrus to freezing temperatures are the degree of dormancy of the

trees at the time extreme cold arrives and the general physiological

conditions of the tree. Cold weather in itself induces a degree of

dormancy in citrus; if it comes gradually it is very effective in

increasing the trees' tolerance to freezing temperatures. Trees in

active growth are much more severely injured by cold than are those

somewhat dormant. Citrus trees, being evergreens, never become fully




This section on 1962 freeze summarized from Two Days in Decermbrr!
(19). Historical records indicate that severe freezes occurred in
Florida in the winters of 1747, 1766, 1774, 1799, 1828, 1835, 1850,
1857, 1880, 1884, 1894-5, 1916-!7, 1926-27, 1929-30, 1957-58, and
1962-63 (19, p. 129).






52

dormant and can never withstand temperatures as low as those tolerated

by deciduous trees (54). There are also wide variations in the cold

hardiness a-Tong orange varieties. Cooper (12) reported that these

differences are explained in part by the minimum temperature at which

dormancy is induced. Cooper (12, p. 83) in a study of the 1961-62

freeze on Valencia oranges also noted that each freeze differs from

other ones in the same area in one or more respects. Trees once

injured by cold are more susceptible to further cold damage and

disease For several years thereafter (19). The complicated bio-

physical relationships which explain how temperatures, varieties,

cultural practices, and the technology cf freeze protection affect

yields have not been studied and will not be a part of this research.

Some "average" effects of these factors on yield will be assumed.

The exact level of freezing temperatures seems to be critical.

Hendershott (3C) reported that leaf temperatures of 20 F and colder

kills 100 percent of maLure leaf tissue while temperatures in the

range of 20-21 F can be expected to kill between 50 to 70 percent.

At 22 F reading was found to kill only 5 percent and temperatures

in the range of 23-24 F killed only 1 percent. Commercial growers

tend to consider a hard freeze (one resulting in fruiL loss and/or

tree damage) to be characterized by temperatures of less than or equal

to 26 F for four or more hours (57, p. 49). Cooper (11) has stated

that temperatures of 28-30 F will not harm trees or fruit.

There are ac least two reasons why the 1962 freeze was less

damaging tha' if it had occurred several years earlier (19, p. 7).

Groves were in the best nutritional condition in history and there






53

was a capacity to use and process damaged fruit which did not exist

a few years previously.

Cold temperatures limit the northward expansion of the citrus

belt and are the most adverse climatic factor with which the Florida

grower must contend. However, high temperatures may result in

damage also. Reiatively high temperatures (in the 70's) during

December and January may encourage growth and make trees more easily

injured by late cold weather. In March and April, high temperatures

increase transpiration and if coupled with a lack of soil moisture

can cause permanent wilting. When such drought conditions (high

temperature and low rainfall causing a deficiency in soil moisture)

exist through May, even if not qeriuus enough for wilting, an exces-

sively heavy "June Drop' of fruit is the usual result. Warm weather

during Cctober and Novumber, particularly if nights are wari and

rainfall; is above normal, usual ly result in reduced internal qua i ty

and poor external color (98, p. 8,).


Maenaqer-.nt and Cuitural Practices

Past and present management and cultural practices can affect

a tree's yield in a given year. However, this phenomenon has not been

studied and is not well understood. Certainly year-to-year variations

in nutritional programs, pesticides and insecticides practices and

irrigation capacity are capable of causing variation in yield. How-

ever, whether or not yield data from commercial groves reflects a

variability due to these factors depends on the yield response of

these factors and the level of their inputs into the production

process. The possibility exists that if commercial groves are managed

at or near the optiral level for such inputs that reduction date





54

from commercial groves will not reflect any variability due to such

inputs.

Nutrition

Bitters and Batchelor (4) reported that fruit size was related

to: nutrition, spraying with growth regulators, moisture relatives,

and to certain pesticides and insecticides. Hodgson (31) in a study

including both Florida and California reported that size of fruit

was related to nutrition, and to magnesium, zinc, copper, and manganese

deficiencies. Harding and Sunday (27) reported a yield response to

fertilizers. Koo, Reitz, and Sites (50) found that nitrogen was the

only element directly related to fruit production in Florida. Jones

and Embleton (43) substantiated this finding in a California study.

However, Lenz (56) found that while nitrogen 'iad a beneficial effect

on fruit-set, it had a deleterious effect on fruit quality if high

nitrogen rates remained in the soil at or near maturity.

Irrigation

In Florida trees can become dormant for either of two reasons,

low temperature or lack of soil moisture (2). The greater the degree

of dormancy the less the danger from a freeze of a given severity.

Therefore an irrigation program designed to reduce soil moisture in

the winter months to induce dormancy can reduce the probability of

freeze damage (47).

Supplementing rainfall by irrigation has been practiced by

Florida citrus growers for many years. Whether irrigation has bene-

fited the grower in financial terms through increased fruit production

has not been firmly established (47). Savage (70) in a 1954 article

concluded from a survey of grove records accumulated over 21 seasons





55

that it did not pay to irrigate the average grove in the manner irri-

gation was usually practiced. At that time most growers irrigated

when trees showed signs of wilt. Koo (47) reported that the effects

of experimental irrigation on fruit production has been variable.

He noted that Sites et al. (80) reported in 1951 that irrigation

resulted in lower production two out of three years in several orange

varieties. Huberty and Richards (33) reported that improper irriga-

tion can reduce navel orange yields as much as 30 to 40 percent.

Higher yields due to irrigation were reported by Koo and Sites (5i)

and Ziegler (97) in later studies. Koo (47) reported that a recent

(1959-60 season through 1961-62 season) experiment indicated fruit

production was increased substantially by irrigation. He noted that

production was increased substantially by maintaining adequate soil

moisture in the root zone when fruit was small. He found it necessary

to maintain soil moisture at greater than 65 percent field capacity

between fruit set (February-March) and until the young fruit has

reached 1 inch in diameter (June-July) (48).

Sandy soils with very low water-holding capacity make irrigation

necessary and the unpredictable rainfall distribution makes irriga-

tion timing important. The above studies indicate a possible change

in yield due to improved irrigation and drainage practices over the

range of the data used in this study.

Reuss (68) in a recent study (1969) designed to estimate the

costs of developing and continuing irrigation for citrus production,

provided information on the effects of irrigation upon yields and

upon economic returns. He used experimental plot data supplied by

Koo (47) for most of his analysis and concluded that irrigation was

economically feasible.







General Models Suggested by
Other Researchers

Numerous researchersI have worked on the problems of forecasting

yield and of estimating harvest size. A few of the representative

models are briefly discussed in this section.

Kuznets

Kuznets (52) reported that the yield of a California orange tree

was related to:

1. Number of entirely cloudy days (December 16-February 15)

preceding bloom.

2. Average temperature (February 15-March 15).

3. Date of peak bloom.

4. Average maximum temperature the 46-75th day after bloom.

Kuznets and Jennings (53) in a California study, found that the

following weather variables affected yield:

1. Average temperature in degree F (March 16-3!).

2. Date of peak bloom from March 23.

3. Number of entirely cloudy days, December 16-February 15,

preceding bloom.

4. Average temperature, February 16-March 18.

5. Date of peak bloom.

6. Average maximum temperature, 48-60th day after bloom.

7. Average maximum temperature, 61-75 days after bloom.

Stout

Stout (83) worked with the following model in a study designed

to forecast the harvest size of Florida Valencia oranges.




See bibliography section entitled "Additional Readings."






57

Y = a + ZBiXi + e, i = 1, 2,..., 16 [8]


where

Y = April 1 average volume per fruit in cubic inches

(i.e., harvest size).

XI = October 1 size.

X = X
2 -
X3 = Rainfall in inches (February 1 October 1).

X = Number of days no rain (February 1 October 1).

5 = Rainfall in inches (July I Occober 1).

X6 = Number of days rainfall greater than .10 inches in

July, August, and September.

X = Number of days temperature greater than 900 F in July,

August and September.

x = July average temperature.

X = August average temperature.

X10 = September average temperature.

Xl = East coast (0,1).

X12 = Interior (0,1).

X13 = West coast (0,1).

X14 = September to October state average growth rate less

than 1.90 cubic inches (0,1).

X15 = September to October state average growth rate between

1.90 and 2.35 cubic inches (0,1).

X16 = September to October state average growth rate greater

than 2.35 cubic inches (0,1).


After analysis of the above mode! Stout developed two equations,






58

each with five significant (at .05 level) variables, to predict the

harvest size of Valencias on October 1.


Y = 28.81 + .070 XI + .100 X2 .055 X3

.260 X4 + 1.926 X5 [9


where:


Y = Predicted April 1 size on preceding October 1.

XI = October 1 size squared.

X2 = Total rainfall from July 1 to October 1.

X, = Number of days rainfall was .10 or more inches from

July 1 to October 1.

X, = Average August temperature.

X = One if September to October state average rate of growth

greater than 1.90 inches and less than 2.35 inches, zero

otherwise.

Y = 20.51 + 1.211X1 + .046X2 .044X [I]

.232X4 + 2.140X5


where:


Y = Same as equation [9]

X = October 1 size.

X2 = Total rainfall from February I to October I.

X = Same as equation [9]

X = Average September temperature.

X5 = Same as equation [9]







Others

Hodgson (31) in a study including both Florida and California

reported that size of fruit was related to adequacy of heat during

the growing period, atmosphere, humidity, and time of bloom. Cooper

(13) in a study of Florida, Texas, Arizona, and California concluded

that soil moisture was the principle factor affecting size. Caprio

et al. (8) in a study of California Valencia oranges concluded that

size was a function of: temperatures in fall and early winter; date

of bloom; cool temperatures in February and March; mean monthly

temperatures and temperature departures from normal. Beutel (5)

found harvest size to be related to soil moisture and maximum daily

summer temperature. Sites (78) reported that a dry period of three

months after fruit is set reduces size and subsequent irrigation

will not recover it. Jamison (38) reported that the yield of tne

Washington navel orange in California was significantly arn directly

related to the amount of heat during the growing season. However,

Furr et al. (22) noted that high temperature is an important factor

in causing abnormally heavy drop of fruit. Jones and Embleton (43)

found California orange production to be influenced by high temper-

atures in fruit-setting period. Jones and Cree found differences

in yield due to maximum temperature during the June drop period (L2)

and to harvest time (41). Harding and Sunday (27) reported that the

yield of Florida oranges was related to soil moisture. Haas (25),

in a 1949 study of Valencia orange in California, concluded that the

date of blossom opening was primarily related to yield.

Koo (47) in research devoted to studying the effects of irrigation

on yields of orange and grapefruit concluded that optimal fruit produc-





60

tion requires adequate soil moisture during the period January through

June. Furr et al. (22), studying the Washington navel and Valencia

oranges in California, concluded that soil moisture depletion and

high temperatures were related to fruit drop. Dhillon and Singh

(14) concluded that fruit drop was primarily due to moisture stress.

The Federal Trade Commission (18) in a study on the frozen con-

centrated orange juice industry after the December, 1962 freeze

reported that the severity of a freeze was a function of: duration

of low temperatures, the time of year, weather conditions before and

after the freeze, surface winds, humidity, and recorded low tempera-

ture. They concluded that the recorded low temperature of the freeze

was probably the best single indicator of the severity of the freeze.


A Concluding Remark

The many weather variables related to the yield of orange trees

point to the importance of a measure or a few measures which could

account for most of the yield variability due to weather. Hints that

soil moisture is such a measure are scattered throughout the literature.

Many researchers have noted that some measure of soil moisture condi-

tions are related to the yield of orange trees. Oury (63) showed the

usefulness of the aridity index approach (either de Martonne's or

Angtrom's) for explaining yield variation due to weather and suggested

their use until more refined indexes such as Thornthwaite's became

operational. Knetsch (I4) demonstrated that a measure of available

soil moisture as estimated from a moisture-balance computation of




Koo recommended that growers attempt to maintain soil moisture
of 70 percent of field capacity during the January-June period.





61

daily rainfall and evapotranspiration could be useful for explaining

yield variation in Tennessee Valley corn. He estimated daily evapo-

transpiration by using Thornthwaite's empirical formula.

To calculate a measure of available soil moisture it is necessary

that the following information be available:

1. Depth of soil to hard-pan or water table (root depth).

2. Soil moisture at field capacity.

3. Soil moisture at which plant growth and development is

restricted (wilting point).

4. Daily rainfall and temperature.

Such information is not difficult to obtain for a given field

experiment. However, for this research effort (since the sampling

unit was an entire county) the lack of such information at the

county level presented considerable difficulties.

Evaporation is a component of climate that is seldom measured.

The combined evaporation from the soil surface and transpiration from

plants, called evapotranspiration, represents the transport of water

back from the earth to the atmosphere, the reverse of precipitation.

One cannot tell whether a climate is moist or dry by knowing the

precipitation alone. One must know whether precipitation is greater

than or less than the water needed for evaporation and transpiration.

The rate of evapotranspiration depends on four things: climate,

scil-moisture supply, plant cover, and land management.

Transpiration effectively prevents the plant surfaces that are

exposed to sunlight from being overheated. Most plants require sun-

light for growth. The energy of the sun combines water and carbon

dioxide in the leaves into foods, which are carried to all parts of






62

the plant for growth. This process, called photosynthesis, is most

efficient when the leaf temperatures are between 85 and 90 F. A leaf

exposed to direct sunlight would become much hotter if the energy of

the sun were not disposed of in some way. Transpiration is a heat

regulator, preventing temperature excesses in both plant and air.

Atmosphere elements which influence transpiration are solar

radiation, air temperature, wind, and atmospheric humidity. These

factors are all interrelated and although solar radiation is the basic

factor, temperature of the transpiring part is most closely related

to the rate of transpiration and air temperature is correlated to

the temperature of the transpiring part.






























The above section on evapotranspiration was summarized from
Thornthvwai e (90). See this reference for an empirical method for
estimating evppctranspiration.














CHAPTER IV


ANALYTICAL METHOD AND THE DATA


The Model Estimated


The mathematical representation of the real world offered as a

general theoretical model in equation [7] represented an impossible

estimation task due to the lack of information to specify such a

disaggregative model and because of inadequate data to fit such a

model if specified. To abstract from the detail of the real world,

trees whose yields were assumed to respond similarly to the variables

of equation [7] were grouped together. Additionally, the data avail-

able also placed constraints on the model estimated.

The most disaggregated observational unit on uhich production

data were reported were varieties (macro) by counties. Available

production data did not permit classification by such micro units as

rootstock, density of planting, or terrestrial location.

Classification by variety (micro), age, rootstock, soil depth,

and soil moisture capacity would have been desirable because yield

differences exist among the various levels of all five factors and

the various levels of each factor interact with weather. For example,

fruit loss and tree damage due to freezing temperatures differ among

varieties (micro) and some varieties (micro) are more drought resis-




ESu-ra, p. 52,





64

tant than others. Young trees are more severely injured by a given

low temperature than older trees. Differences in rootstock cause

differences in the drought resistance of trees and the minimum tem-
2
perature at which dormancy is induced. Soil depth determines the

size of the root structure which limits the bearing surface of the

tree. Soil moisture capacity fixes an upper limit on moisture

reserves. As a consequence, the same amount of rainfall may cause

different levels of wilting conditions depending on the soil moisture

capacity of the soil in which the trees are rooted.

While it would be possible to generate a set of time series data

of the orange groves in the state of Florida in which the trees were

classified by variety, age, rootstock, soil depth, and moisture

capacity, such a data set would be useless for estimation because

production data could not be sub-divided in a like rmnner.

The major factors for which observations have been recorded and

which contribute to year to year variat;cn in yield by county and

variety (macro) are changes in tree numbers, age distribution of trees,

and weather (84). Cultural practices and nutritional programs may

have varied over time. However, it is doubtful that significant

differences in management existed between counties in any given year.

By abstracting from the real world by grouping trees by variety

(macro) and by counties, equation [7] may be represented as:




S upra, p. 46.

2S.ura, p. 46.

SSupra, p. 43.

See Table 9, p. 80.








st = rs (Z rst C st Gst Urst), r = ...,R;

s = 1 ... ,s; t = I,...,T. EI ll


where:


Yrst = Observed production in 90 pound boxes of rth variety

(macro) in sth county and tth year.

Zrst = Set of variables which represent physical attributes of

all the trees of rth variety in sth county which affect

production in the tth year.

C rst Set of weather variables affecting the rth variety's

production in the sth county and the tth year.

Grst = Set of cultural, nutritional, and technological variables

affecting production of rth variety in sth county an'

tth year.

Urst = Disturance term which represenLs that portion of pro-

duction of the rth variety in the sth county and tth

year which is not explained by the arguments Z, C,

and G.


R is the number of varieties (macro), S the number of counties,

and T the number of years.


The variables and equations represented by the general equation

[7] differ from the variables and equations represented by [ll]. For

example, Y.* represents the yield of a single tree in tth year while

Y denotes the total production of all bearing trees of rth variety
rst
(macro) in sth county and tth year. And while [7] includes a single

yield function for each tree, equation [II] represents a production

function for each variety (macro) by county.








As with equation [7], the rsth Function of [II] would not be

separable. And, again because of a lack of information and data,

serious and insurmountable specification and estimation problems

remain. If in year t, county s had 100 trees of the rth variety and

in year t + 10 had 1,000 trees of rth variety, one would not expect

the same level of a particular variable, such as 15 drought days, to

bring forth the same change in Y expressed in boxes of fruit. This

is to say that there is an interaction between the number of trees

by age and the weather variables.1 And, even if information existed

to specify the form of equation [ll],it would not be possible to

estimate this stochastic function with the limited number of observa-

tions available.

As an approach to circumvent the need for estimating the inter-

actions among Zrst and C the concept of expected2 production and

a two stage estimating procedure was introduced. Expected production

was specified as a conditional function. of the number of trees and

their age distribution given average levels of all other inputs in-

cluding weather. Expected production was then used to remove a

portion of the year-to-year variation in observed production and to

estimate the percentage deviation of observed from expected production

for each variety (macro) by counties. These estimates of percentage

deviation of observed from expected production for each variety (macro)




1Similarly, there is an interaction among the number of trees by
age and the variables in set G.

2Expected as used here is not the same concept as mathematical
expectation. Rather the term expected production is used to define
production estimated by a synthesized average yield function to be
defined later.





67

and county were then expressed as a function of variables in the sets

Crst and Grst in a linear single equation model. The coefficients of

this model represent the change in this deviation resulting from a

one unit change in a variable from Crst or G.st. These coefficients

do not depend on the number of trees.

The two-stage approach which was used in an attempt to circum-

vent the need for estimating interaction among weather variables

and variables representing the number and age distribution of trees

may be summarized as follows:


Stage I: Average Production Equation

A
EYrst = Hrs (Arst I Crs. Gs.); r =1,2; s= ...- 8, [12]

t=l,...,20.


EY = Expected production of rth variety in sth county and
rst
tth year. Expected as used here is not to be confused

with the concept of mathematical expectation (see

Footnote 2, page 66).

Arst = Set of variables which describe the number of trees

of rth variety (macro) by age group, county and year.

C = Set of mean values of weather variables effecting rth
rs.
varieties in sth county production over all years.




Specifically, the set A included 22 variables. Variable I
rs 5
was the nurnber of trees 4 years of age, variable 2 was the number of
trees 5 years of age, and so on. Finally variable 22 was the number
of trees 25 years of age and older. The estimated coefficient for
a particular variable was an estimate of the average yield for trees
of that age.





68

Grs = Set of mean values of cultural, nutritional, and tech-

nological variables affecting the production of rth

variety in sth county over all years.


There were two varieties (macro), 18 counties, and 20 years

finally included in the analysis as will be described later.


Stage II: Weather Equation.

rst = Lrs (Crst, Grst U rs ); r=1,2; s=l ...,8;[13]

t=l,...20.

A
Prst = (Yrst (as defined in equation [II]) EYrst
A
(as defined in equation [12]) EYrst


Crst = Set of weather variables affecting production of

rth var-iety in the sth county and tth year.


Grst = Set of cultural, nutritional and other technological

variables affecting production of rth variety in the

sth county and tth year.


U' = Disturbance term which represents that portion of
rst
production of the rth variety in the sth county and

tth year which is not explained by the arguments of

A, C, and G.


As indicated earlier there were two varieties (macro), 18

counties, and 20 years finally included in the analysis. These

dimensions will be discussed later.

The major reason for expressing the dependent variable Prs as








percentage deviation of observed from expected production was, as

discussed earlier, to obtain a variable which was related to C

and G but which did not depend on the number and age distribution
rst
of trees in the county.


The Data


The Florida Crop and Livestock Reporting Service annually pub-

lishes county production figures in terms of boxes produced (72).

Their report also describes the groves within each county in terms

of total acres and number of trees by age group and variety (macro).

Two complete citrus inventories were conducted under their supervision

in 1956 and 1965 resulting in publications in 1957 and 1966. Produc-

tion and tree data were available from the 1948-49 season to date.

Daily weather observations for twenty-seven weather stations for

the period July 1, 1948 through June 30, 1966 were purchased fiom the

National Weather Records Center, Asheville, North Carolina. Addition-

ally, daily weather observations were hand-coded for the period July I,

1966 through December 31, 1968.

County fertilizer consumption by fertilizer types has been

published annually by the Inspection Division, Department of Agri-

culture, State of Florida (35, 36).

Table 5 indicates that data were available for 18 counties for

the 20 seasons 1948-L9 through 1967-68 and for 13 counties for at

least five seasons 1963-64 through 1967-68. These data were coded

and key punched as Yrst.




ISupra, p. 66.









Table 5: Counties currently producing Florida oranges and seasons
for which production data were available.




Code aCounty Seasons of available production data


Brevard
DeSoto
Hardee
Highlands
Hillsborough
Indian River
Lake
Manatee
Marion
Orange
Osceola
Pasco
Pinellas
Polk
Putnam
St. Lucie
Seminole
Volusia
Broward
Charlotte
Citrus
Collier
Glades
Hendry
Hernando
Lee
Martin
Okeechobee
Palm Beach
Sarasota
Sumter


1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49 through 1967-68
1948-49, 1963-64 through 1967-68
1948-49, 1963-64 through 1967-68
1963-64 through 1967-68
1963-64 through 1967-68
1963-64 through 1967-68
1948-49, 1963-64 through 1967-68
1948-49, 1963-64 through 1967-68
1948-49 through 1956-57, 1963-64
1963-64 through 1I67-68
1963-64 through 1967-68
1948-49, 1963-64 through 1967-68
1948-49, 1963-64 through 1967-68
948-, 1963-64 through 1967-68
1963-64 through 1967-68


through 1967-69


aThe numerical county codes will be used throughout this report.







Yrst = Observed production of rth variety (macro) in sth

county and th year.

r = I for Early and Midseason varieties.

r = 2 for Late varieties.

s = 1, 2, ...... 31.

t = I,.., 20; the 1948-49 season was coded 1.


In certain seasons Temples were included with the Early and

Midseason oranges but reported separately in other seasons. To make

the data comparable in all season, Temples were included with the

Early and Midseason oranges.

Information on orange trees was available by county, variety

(macro), and age group categories. As with the production data,

there were 18 counties with 20 years of available data and 13 counties

for which data were available for five or more years. Again, Temples

were included with Early and Midseason oranges. A major problem

existed in the degree of aggregation of the age group categories and

in the different ways the trees were grouped. For the years 1948

through 1956, data on tree numbers were grouped into age categories

4 through 5, 6 through 10, 11 through 15, and 16 and older. For 1957

and 1958 the age groups were 0 through 3, 4 through 9, and 10 and

older. For the period 1959 through 1961 age group categories were

4 through 9, and 10 and older. From 1962 through 1964 the three age

groups were 0 through 4, 5 through 9, and 10 and older. A complete

citrus inventory was conducted in 1965.

A matrix of tree data was generated with typical element arstj

ars = Number of trees of rth variety (macro) in sth county,

tth year, and jth age group.







r = 1, 2.

s = 1,..., 31.

t = 1,..., 20. The year 1948 was coded 1 and paired with

production for 1948-49 season.

j = 4,..., 25. Age group 25 included all trees 25 years old

and older.


For 1965 the citrus inventory was used to calculate arstj. Siice

no severe weather existed in 1966 or 1967 to reduce the number of

trees and since there was no reason to expect abandonment of groves

during those two years, the arstj's were generated for 1966 and 1967

by simply advancing the 1965 census ahead one and two years. This

was possible because the model only dealt with bearing trees (4-years-

old and older) and a two-year-old tree in 1965 for which data were

available was four years old in 1967.

For the other years the aratj's were generated by a simple

bookkeeping procedure ,,hereby the total number of trees reported in

a given year and age group category was distributed according to the

percentage in production as reported by the 1965 census. For example,

if in 1964 the 5 through 9 age group category was reported to include

200 trees and the 1965 census reported 10 six-year-old trees, 30

seven-year-old trees, 40 eight-year-old trees, 10 nine-year-old trees,

and 10 ten-year-old trees; then the 200 trees were distributed 20,

60, 80, 20, 20 for age groups 5 through 9, respectively.

Daily weather observations were available for stations in 27 of

the 31 counties studied (Table 6).

Most of the oranges (over 93 percent during the period of study)









Table 6: Weather stations and time interval for which data were
available.




County Month(s) for which
Code Station Time interval data were missing


Titusville
Arcadia
Wauchula 2N
Avon Park
Plant City
Fellsmere 4W
Vero Beach
Clermont
Bradenton Exp, Sta.
Bradenton 5 ESF
Ocala
Orlando WBAP
Kissimmee
Saint Leo
Tarpon Sps. Sew. P1.
Lake Alfred Exp. Sta.
Palatka
Fort Pierce
Sanford (7977)
Sanford (7982)
Deland 3N
Fort LaJ'=r- ale
Clewiston U.S.Eng.
Loxahatc'ee
Stuart IN


1/1949
1/1949
1/1949
1/1949
1/1949
1/1949
1/1949
1/1949
1/1949
4/1965
1/1949
S1/194
1/1949
1/1949
1/1949
1/1949
I/i949
1/1949
1/1949
6/!956
1/1949
1/1949
1/1949
1/1949
1/1949


6/1966
6/1966
6/1966
6/1966
6/1966
6/1966
3/1965
6/1966
3/1965
6/1966
6/1366
6/1966
1/1959
6/1966
6/1966
6/1966
6/1966
6/1966
5/1956
6/1966
6/1966
6/1966
6/1966
6/1966
6/1966


7/1958
7/1960
9-10/1957
11/1951

8-10/1963




4-6/1956, 3-4/1960

2/1959-6/1966




2/1951
6-7/1955

6-12/1959, 2-4/1960
8/1951, 5/1960
7/1956

9/194:9, 7/1952


aSee Table 5 (p. 70) for names
numbers.


of counties associated with code









were produced in the 18 county study area (Table 7). Since yield

data were restricted to only a few years (5 in most cases) and since

acceptable weather data could not be generated for the other 13 citrus-

producing counties, they were omitted from the analysis. The citrus

belt is shifting to the south and most of the deleted counties are in

the new expansion area. For long-range forecasting one would like to

be able to measure the effect of weather on orange production in

these counties which will undoubtedly be providing a larger proportion

of the crop. However, the limited number of observations frustrated

attempts to use historical data to do so.

Three counties, Indian River, Manatee, and Seminole required two

stations to obtain a continuous weather record and one county, Osceola,

did not have any weather observations beyond January, 1959. Therefore,

a nearby station (Clermont) in an adjacent county (Lake) was substituted

for the period February, 1959 through June 1966. Missing observations

in other data series (see Table 6) were estimated by the mean value of

the weather variable for that day for the station involved.

Daily weather observations were aggregated into quarterly obser-

vations for the 18 stations for the period July 1, 1966, through

December 31, 1968, to correspond with available production and tree

data.

The weather data consistently recorded by the stations were total

daily rainfall, minimum daily temperature and maximum daily temperature.

A critical weather variable (duration of freezing temperature) was

unobserved.




IThe counties which made up the study area are the first eighteen
listed in Table 5, page 70.


I_ _
























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The three weather measures available (daily rainfall, minimum

temperature, and maximum temperature) were used to synthesize obser-

vations on twenty-six weather variables (see Table 8) for each of the

18 stations used to represent county weather. These twenty-six

weather variables are those proposed by earlier researchers.

Those variables in Table 8 measuring soil moisture (3-10) and

minimum temperature (11-16) were believed to be of primary importance

in explaining yield variability due to weather.

A typical element in the matrix of observation or weather vari-

ables was wstqn.


where:


wstqn = Average monthly value of nth weather variable in sth

county, tth year, and qth quarter.


s = 1, ..., 18

t = 1, ..., 20

q = 1, ..., 4.

n = 1, ..., 26.


Variables 1 through 16 in Table 8 were reported as three month

totals. Variables 17 through 26 were reported as quarterly averages.

Degree days were based on heat units in excess of 55 F and the variable




The major cost in deriving observations on the weather variables
was associated with taking information from a large weather data tape.
The marginal cost of obtaining observations on additional variables was
so small in comparison with the cost of spinning the tape that observa-
tions were derived for any variable for which there was a possible need.

See Ne-man (60) for definition of degree days and heat units.









Table 8: Specific weather variables used in study.a


Vari-
able
No. Description of variable


1. Degree days
2. Degree days (adjusted)
3. Number of days soil moisture less than wilt (Thornthwaite)
4. Number of days soil moisture equal to zero (Thornthwaite)
5. Number of days soil moisture less than wilt (Harrison)
6. Number of days soil moisture equal to zero (Harrison)
7. Number of days soil moisture equal to 100% (Thornthwaite)
8. Number of days soil moisture greater than 70% (Thornthwaite)
9. Number of days soil moisture equal to 100% (Harrison)
10. Number of days soil moisture greater .han 70% (Harrison)
11. Number of days minimum temperature less than or equal to 32 F
12. Number of days minimum temperature less than or equal to 30 F
13. Number of days minimum temperature less than or equal to 28 F
14. Number of days mni mum temperature less than or equal to 26 F
15. Number of days minimum temperature less than or equal to 24 F
16. Number of days minimum temperature less han or equal to 22 F
17. Average temperature
18. Average temperature (maximum)
19. Average temperature (minimum)
20. Total rainfall
21. Total rainfall (adjusted)
22. Land aridity index
23. Koppen aridity index (1)
24. Koppen aridity index (2)
25. Koppen aridity index (3)
26. Angstrom aridity index



observations on these variables were computed from daily weather
information on rainfall and temperature.






78

referred to as degree days (adjusted) consisted of those heat units

in the range of 55 F and 90 F.

Variables 3 through 10 were calculated by using a bookkeeping

procedure discussed by Harrison and Choate (37). Two estimates of

each variables were calculated by using average daily evapotranspira-

tion as reported by Harrison and Choate and by calculating daily evapo-

transpiration by the Thornthwaite method (90).

The variable referred to as total rainfall (adjusted) was calcu-

lated by not considering any rainfall amounts in excess of the field

capacity of the soil in the root zone.

Variables 22-26 were generated by using the following standard

formulas:

Lang Aridity Index = P/T

Koppen Aridity Index (1) = 8P/(13T+120)

Kopper Aridity Index (2) = 2P/(T+33)

Koppen Aridity Index (3) = P/(T+7)

Angstrom Aridity Index = P/(l.07)T

Where P is rainfall measured in millimeters and T is temperature

in degrees centigrade.

Calculation of these weather variables associated with the level

of soil moisture required information on root depth, maximum water in

root zone at field capacity, and wilting point (percent soil moisture

at which growth is seriously depressed). Such information was un-

available by counties. Derivation of such information from soil maps

was considered. However, it would have been an enormous task to




ISupra, p. 28.








compile county estimates of root depth, maximum water in root zone

at field capacity, and wilting point from soil maps for a given year

and to weight such estimates by the year-to-year changes in the dis-

tribution of trees within a county. Therefore, the information which

was used (Table 9) was based on the opinion of experts with consider-

able experience in working with Florida soils. The data in Table 9

represent average county levels for root depth, maximum water in root

zone at field capacity, and usable soil moisture2 for all years in-

cluded in this study.

The aggregation of information on these variables into averages

for a county resulted in some loss of variation. For example, if the

average county root zone is 40 inches but some groves within the

county had only 10 inches of root depth then those groves might suffer

severe waiting conditions which the information or the county averages

would not reflect.

There were two basic difficulties associated with the weather

variables. First, there were no measures of the severity of low

temperatures since the durations of the low temperatures were unknown.

Secondly, there were no uniformly best measure of evapotranspiration

to include in the estimation of soil moisture. The average daily

evapotranspiration rates as reported by Harrison and Choate (Table 10)




Dr. L. C. Hammond in consultation with Mr. R. G. Leighty and Mr.
D. S. Harrison synthesized the information in Table 9. These scientists
are all with the University of Florida. Hammond and Leighty are Pro-
fessors of Soils and Harrison is Professor of Agricultural Engineering.

information on these three variables permitted the calculation
of wilting point as the differences between water in root zone at
field capacity and usable ro;sture.







Table 9: Root depth, water in root zone at field capacity, and
moisture available for plant use in soils by counties in
the Florida citrus belt.



Water in root Usable
zone at field moisture
Root depth capacity (inches
County County (inches of (inches of of
code soil) rainfall) rainfall)


1 Brevard 30 4.5 4.0
2 DeSoto 30 6.0 4.5
3 Hardee 30 6.0 4.5
4 Highlands 48 4.5 4.1
5 Hilisborough 48 5.0 .4.0
6 Indian River 24 4.0 3.4
7 Lake 60 5.2 4.7
8 Manatee 30 6.0 4.5
9 Marion 60 5.2 4.7
10 Orange 60 5.2 4.7
11 Osceola 30 6.0 4.5
12 Pasco 60 5.2 4.7
13 Pinellas 36 5.0 4.4
14 Polk 60 5.2 4.7
15 Putnam 36 6.9 5.3
16 St. Lucie 24 3.5 3.1
17 Seminole 48 4.5 4.1
18 Volusia 48 5.0 4.0
19 Broward 24 3.5 3.1
20 Charlotte 24 3.5 3.1
21 Citrus 60 5.2 4.7
22 Collier 24 3.5 3.1
23 Glades 24 3.5 3.1
24 Hendry 24 3.5 3.1
25 Hernando 48 4.5 4.1
26 Lee 24 3.5 3.1
27 Martin 24 4.0 3.4
28 Okeechobee 24 3.5 3.1
29 Palm Beach 24 3.5 3.1
30 Sarasota 30 6.0 4.5
31 Sumter 36 6.9 5.3



Source: Unpublished information compiled by Dr. L. C. Hammond, Mr.
R. G. Leighty, and Mr. D. S. Harrison. Hammond and Leighty
are Professors of Soils, and Harrison is Professor of
Agricultural Engineering, all at the University of Florida.






81

measure only that portion of the variability in soil moisture asso-

ciated with rainfall. Alternatively, the Thornthwaite method allows

for variation in soil moisture due to both rainfall and temperature

but it tends to overestimate evapotranspiration in the summer months

(26).

The average daily evapotranspiration of Florida citrus groves

has been estimated by Harrison and Choate (37). Their estimates were

based on historical average monthly temperature at Lake Alfred. Their

results are reported below.



Table 10: Average daily evapotranspiration of Florida citrus groves.



Month Average daily evapotranspiration (inches of rainfall)


January .08

February .08

March .10

April .11

May .14

June .17

July .17

August .18

September .17

October .13

November .10

December .03



Source: Harrison and Choate (37, p. 34).






82

A data search was initiated to locate information on variables

suitable to measure changes in levels of cultural and technological

practices by counties. Such variables might include an index of ir-

rigation capacity, an index of freeze protection, fertilizer utiliza-

tion per tree or acre, and pesticide utilization. Only fertilizer

use data were available. These data were collected and used as measures

of a proxy or representative variable for cultural and technological

factors.

Fertilizer data were reported as fertilizer consumption by counties,

but they were actually fertilizer sales by counties. The data did not

specify that portion of a county's fertilizer sales applied to citrus.

The mixed fertilizers and fertilizer materials in Tables 11 and 12

were commonly applied to citrus. These fertilizer analyses were used

to estimate the a;nount of fertilizer being used on citrus.

The typical element in the basic data matrix for fertilizer was

fstm where: fstm consumption in tons of mth type of fertilizer for

the sth county and th year.

s = 1, 2, ..., 18

t = 1, 2, .... 20

m = 1, 2, ..., 5

1 = Total county consumption of mixed fertilizer.

2 = Total county consumption of those mixed fertilizers

coded in Table 11.

3 = Total county consumption of nitrogen for these mixed

fertilizers coded in Table 11.

4 = Total county consumption of fertilizer material.

5 = Total county consumption of those fertilizer materials

coded in Table 12.








Table 11: Mixed fertilizers commonly applied to citrus.


N P-K


08-00-08
08-00-10
08-02-08
08-02-10
08-02-12
10-00-10
10-00-12
10-02-10
12-00-10
12-00-12
12-00-14
12-00-15
12-01-12
12-02-!2
14-00-12


N- P-K


14-00-14
14-00-16
14-01-14
15-00-12
15-00-14
15-00-15
15-01-15
16-00-16
16-00-17
16-00-18
17-00-17
18-00-16
18-00-18
20-00-20


Source: Personal conversations with Mr. Larry K. Jackson, Instructor,
IFAS, Extension Service, University of Florida.




Table 12: Fertilizer materials commonly applied to citrus.



Ammonium Nitrate
Nitrate of Soda-Potash
Nitrate of Potash
Nitrogen Solutions
Muriate of Potash (50-60%)
Sulfate of Fotash-Magnesia



Source: Personal conversations with Mr. Larry K. Jackson, Instructor,
IFAS, Extension Service, University of Florida.


__II_____ _ _~


~1~1~_







The fertilizer data which included fertilizer applied to all

citrus were adjusted by the percent of total citrus made up of oranges.

The data were then expressed on a per tree basis.

Since fertilizer programs are individual grower decisions the

mixed fertilizers and fertilizer materials reported in Tables 11 and

12 do not represent all fertilizer applied to citrus. Specifically

the mixed fertilizers 06-06-06, 08-08-08, and 10-10-10 were known to

be applied to young groves. But these were omitted because they were

also the dominant types used on lawns by homeowners. Other mixed

fertilizers and Fertilizer materials which were undoubtedly applied

to citrus at least in some instances were also omitted.


The Estimation Technique


For each county and each variety (macro) two equations were

estimated. The Stage I or average production equation expressed the

average relationship between production and tree age. The Stage II

equation was designed to explain the production variation due to

weather and to cultural practice and technology.

Since there were eighteen counties and two varieties (macro) in

the study and since the Stage I and Stage 11 equations were estimated

for each county-variety (macro) combination a total of thirty-six

equations were estimated.


Stage I

Bounds on estimates of the average yield per tree by age and

variety (macro) were available due to earlier work by the Florida
1
Crop and Livestock Reporting Service and by Savage, and Chern.



Supra, pp. 43 and 44.






85

The Florida Crop and Livestock Reporting Service average yield esti-

mates reported in Table 3 indicate a range of 4.0 to 7.0 boxes per

tree for Early and Midseason trees 25 years of age and older. Like-

wise, when the figures of Savage's and of Chern's (Table 4) were com-

pared, they also indicated a range for average yield per tree. Since

these estimates were for the entire state they do not form rigid upper

and lower limits for average yield per tree on a county by county

basis. However, they do provide information to enable one to specify

the general form of the relationship between average yield and age,

and within reasonable limits to enable one to fix upper and lower

bounds on the average yield function.

Estimates of the average yield per tree by age and by county were

developed in Stage 1. Hopefully, the intercounty variation in phys-

ica! factors (such as soil depth, varieties (micro) and planting den-

sities) which affect production was accounted for in these estimates.

The model assumes that such was the case.


The equation estimated in Stage I was:

A 25
EY = E B .X
rst j=4 sj rst [IC]


A 1 th
EY = Expected production for the r variety (macro)
rst
in sth county and tth year.

X rstj Number of trees of rth variety in sth county, tth

year and jth age. For j = 25, all trees 25 years

and older were included.




Not mathematical expectation (see footnote 2 page 66).








th th
Bsj = Average yield in s county for j age,


Observations were not available on rY Conceivably, an esti-
rst
mate of equation [14] could be obtained with least squares smoothing

of the data on production and tree numbers by age. Equation [14] has

twenty-two coefficients and since only twenty observations were avail-
I
able, some grouping over age was required.

Data on trees by age were grouped into two year groups and the

data were smoothed by least squares regression. A prior information

indicated that commercial production of an orange tree begins at

three to four years of age, increases rapidly to ten years, levels
2
off and reaches a maximum at twenty-five years. The least squares

estimates of the yield coefficients in many cases had older trees

bearing less than younger trees and the regression estimates of yields

in some cases were actually negative.

To avoid these problems of negative coefficients and older trees

producing less fruit than younger trees and to utilize other prior

information an effort was made to estimate yield coefficients with a

linear programming model which minimized the sum of the absolute

errors. Linear programming was selected due to the ease with which

probable bounds on the estimated coefficients could be incorporated

into the estimating procedure. First attempts at estimating by linear




Tree data werc grouped into two-year age categories so that only
eleven coefficients were estimated as opposed to the twenty--two re-
quired in equation [14].
2-
Suora, p. 7.

3See Havlicek (29) for discussion of methodology.





87

programming were carried out with the constraints that Bsj be greater

than or equal to zero and that the Bsj+, be greater than or equal to

Bsj for j=l, 2..., 10. This approach proved unsuccessful because for

most counties the linear programming estimates of the coefficients

set the first ten coefficients to zero and explained the variation in

the dependent variable only as a function of the older trees. Next,

additional constraints in the form of bounds which were based on the

previous work of the Florida State Crop and Livestock Reporting

Service, Savage, and Chern were placed on each of the coefficients.

For example, a bound of 4.0 to 7.0 boxes per tree was placed on

Early and Midseason orange trees twenty-four years of age and older.

This technique tended to underestimate the yield of younger trees,

overestimate the yield of older trees and failed to capture the

between-county variation in average yield known to exist.

An ad hoc model was finally used to estimate the coefficients of

equation [14]. The estimates of state average yield per tree by age

reported by Savage and by Chern2 were used as a base. Both sets of

estimates were modified in two ways. First, their estimates were

shifted upward or downward by a constant amount over a reasonable

range subject to the constraint that no coefficient could be negative.

Secondly, the estimates of Savage and of Chern were modified by

multiplication by constants which varied over a range of one and a half

boxes above and beaow the reported estimates.

The estimated average yield parameters were then selected which




Supra, p. 43.

2See Table 4, p. 44.






88

minimized the sum of the absolute errors between actual and estimated

production for each county. In over 95 percent of the cases, the

estimates derived by adding a constant to Chern's estimates performed

best.

Therefore, the estimates derived by modifying Chern's estimates

were used in all cases. These estimates of average yields which

resulted are presented in the next chapter.


Stage II

The Stage II equation was estimated by multiple regression.

Many admissible hypotheses existed for the specification of variables

to include in the model. The final choice of variables was somewhat

arbitrary in the sense that the specification provided a multiple

choice hypothesis. For example, twenty-six weaLher variables were

calculated for each quarter. If each were lagged one year and the

six minimum temperature variables were lagged an additional two years

there were 220 possible explanatory variables available. Likewise,

five fertilizer measures were available. If lagged effects of fertil-

izer applications were admitted,as is believed to be the case, the

number of choices would be augmented again.

Simple correlations, partial correlations, and step-down re-

gressions were used in the process of reducing the number of possible





Supra, p. 68.

2Sura, p. 77.

3_Sura, p. 82.





89

regressors for equation [13]. For the weather variables, this initial

process considered no lagged variables. Therefore 104 weather vari-

ables were considered. The five fertilizer variables listed on page

82 were expressed in pounds utilized per orange tree. For the initial

reduction process those five variables were considered plus each of

the five lagged one, two, and three years. Therefore 20 fertilizer

variables were initially considered in an effort to explain a portion

of the yield variability due to management and technology.

Of the fertilizer variables considered, none was significant in

explaining variation in deviations of actual from expected yields.

These variables were finally removed from the model.

For the weather variables, the initial reduction process was

quite successful. Results indicated that some measure of soil moisture

should be included and that of the eight possible measures of soil

moisture (four for the Thornthwaite procedure and four based on

Harrison and Choate's average evapotranspiration rates), the four




The initial reduction process was not necessarily a systematic
process and it certainly included a lot of judgmental decisions. In
this process only three of the major producing counties were included--
two from the ridge section and one from the Indian River section. This
initial reduction procedure was a very empirical process. The largest
equations estimated by step-down regression required that a matrix of
order 125 be inverted. At one point 4,500 simple correlation coeffi-
cients (125 for each variety (macro) -- county combination) were cal-
culated and searched for similar correlation patterns over counties.

Because this year's production might not be related to this year's
fertilizer consumption but to the sum of fertilizer applications over
the past several years,additional combinations of the fertilizer vari-
ables were also considered in other models.

3There were eight possible measures of soil moisture per quarter
or thirty-two per year. (Coded 3 through 10 on p. 77.)








based on Thornthwaite's procedure appeared superior in explanatory

power to Harrison and Choate's.

The six available minimum temperature variables did not explain

much of the percentage deviation of actual from expected yield which

was due to freezing weather.

By combining data over counties to avoid a degrees of freedom

problem, step-down regression was used in an effort to explain the

effect of freezes with the minimum temperature measures available.

The explanatory variables in this model were quarterly measures of

soil moisture conditions, six available minimum temperature variables,

and the six minimum temperature. variables lagged one, two, and three

years. While this model did not isolate the particular temperature

variable to be used to explain the yield variability due to freeze

damage it did provide some information which allowed the reduction of

the possible number of candidates. Specifically, this information

indicated that the variable which measured the number of days the

minimum temperature was less than or equal to 30 F need no longer be

considered as an explanatory variable.

A variable which was lagged twice and which was formed as a

weighted sum of the number of days the minimum temperature fell within

certain temperature intervals performed most satisfactorily in explain-

ing freeze damage.

With this freeze variable and the knowledge that a measure of

soil moisture based on the Thornthwaite empirical method of estimating

evapotranspiration explained more variation than other variables which'




These variables were coded 11 through 16 on p. 77.




Full Text

PAGE 1

EFFECTS OF WEATHER ON ORANGE SUPPLIES By DAVID WOODROW PARVIN, JR. A DISSERTATION PRESENTED TO THE GRADUATE COUNaL OF THE UNIVERSITY OF FLORIDA IN PARTIAI, FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1970

PAGE 2

kQRU TUR«l UNIVERSITY OF FLORIDA 3 1262 08552 3107

PAGE 3

ACKNOWLEDGMENTS The author wishes to express appreciation to Dr. H. R. Langham, Chairman of the Supervisory ConiiTiittee, for his guidance and encouragement throughout this period of graduate study. Special appreciation is also extended to the other members of the Supervisory Committee, Dr. B. R. Eddleman. Dr. E. L. Jackson, Dr. C. E. Murphree, and Dr. Leo Polopolus. The author is also indebted to Dr. L. C. ilaiT,rr,cnd ^ Mr. D. S. Harrison, Mr. L. i<. Jackson, and Mr. R. G. Leighty for providing technical information which was otherwise unavailable. Special appreciation is also extended to Mr. Joe Muilins, S tat ; s t ' ci un in Charge, Florida Croo and Livestock Repo-'tinr Serv'ca, tor providing data which ',«'ere otherwise unavailable. The financial assistance fcr this study v.gs provided by the Florida Citrus Ccrr.rni ss Ion and the Department of Agricultural Econorn; The services of the University of Florida Computing Center are also acknowledged.

PAGE 4

TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES v ABSTRACT viii CHAPTER 1 THE PROBLEM 1 Introduction 1 Objectives 3 Method of Analysis ^ Definition of Terms 5 The Phenology o-f Florida Oranges 7 Florida CI i mate , , . , 8 Weather C'./c'es A Brief History of Oranges il CHAPTER II CHAPTER ! I I THE STUDY OF WEATHER EFFECTS ON CROPS '5 General Problci^is 15 Pact Research 19 Classical Regression 20 Weather Indexes 2k Aridity Indexes 2/ Hybrid Techniques 30 Added Problems Associated vvi th Forecasting Florida Orange Productior, 33 Recent Analytical Approaches . 35 TOWARD A THEORETI CAL MODEL 39 A General Model 39 Factors Affecting the Yisld of an Orange Tree . , k] Physical Factors Hi Age k] So 11 s ^3 Planti ng densi ty '+6 Variety and rooLstocl''. kS Weather Factors ^S

PAGE 5

CHAPTER IV CHAPTER V Page Rainfal] kj Temperature , 48 Management and Cultural Practices .... 53 Nutri tion 5^ Irrigation 5^ Genera] Models Suggested by Other Researchers 55 Kuznets 55 Stout 56 Others ..... 59 A Concluding Remark 60 ANALYTICAL METHOD AND THE DATA 63 The Model Estimated 63 The Data 69 The Estimation Technique d>k Stage I Zk Stage !1 88 Model Assumptions 93 RESULTS OF ANALYSIS 99 Estimated Average Yields 35 Weather Indexes ,...., \^iWeather Equations . . ., , , . . . i 05 By CoL.'ities and VJ-rietics 105 Early and iSidseascr J!5 Valenci a ! 19 Sy Groups of Counties ^.^^d ^Jiu'lciy .... 136 CHAPTER V! CONCLUSIONS AND IMPLICATIONS ! if7 Summary and Conclusions ..... ]k7 Implications ISi For Citrus Industry ...... 15i For Research ..... 152 Limitations 153 Suggestions for Further' Research ., 15^ LITERATURE CITED , 158 ADDITIONAL READINGS 166 BIOGRAPHICAL SKETCH 17^

PAGE 6

LIST OF TABLES Table Page 1 Relative importance of factors affecting average annual change in Florida's Valencia orange production 34 2 Relative importance of factors affecting average annual change in Early and Midseason orange production 3^+ 3 Florida Oranges Average production per tree by age classes, I965-66 to I968-69 .... ^2 k Estimated average yield per tree by age and variety, Florida ^^^ 5 Counties currently producing Florida oranges and seasons for which production data were available 70 6 Wciither stations and tirae interval for which data vjera available 73 7 Total orange production Per the stace of Florida and the amount and percentage for the study area by variety and by seasons, lS^8-ir9 through 1 967-68 75 8 Specific weather variables used in study .... 77 9 Root depth, water in root zone at field capacity, and moisture available for plant use in soils by counties in the Florida citrus belt . . , . 10 Average daily evapotranspi ra t i on of Florida citrus groves ' • • • 11 Mixed fertilizers commonly applied to citrus 12 Fert i 1 i ze r materi al s commonly applied to ci trus 80 83

PAGE 7

Table Page 13 Simple correlation coefficients for the variables included in equation PlS] when fitted to data for the Early and Midscason variety, by selected counties 96 ]k Estimated yields in boxes per tree of Florida Early and Midseason oranges by county and age 100 15 Estimated yields in boxes per tree of Florida Valencia oranges by county and age !02 16 Signed constants added to Chern's state estimates of average yield per tree to estimate average yields by counties and orange variety ]0U 17 "Weather" indexes for Early and Midseason oranges, by Florida counties and seasons, 1951-5? through I967-68 106 18 "Weather" indexes for Valencia oranges, by Florida counties and by seasons, l55'-52 through 1967-68 107 19 "Weather" indexes for orange production for counties in the study area by variety end by seasons, 195'-52 through 1^67-68 ! 03 20 Estimated regression coefficients, standard errors, uncorrected coefficient of multiple determination, and Durbi n-Watson "d" statistic for the Stage il equation for Early and Midseason oranges by Florida counties 109 21 Estimated regression coefficients, standard errors, uncorrected coefficient of multiple determination, and Durbl n-Watson "d" statistic for the Stage II equation for Valencia oranges by Florida counties 112 22 Counties included in the study by areas lib 23 Signs of estimated regression coefficients for Stage M equations by varieties, areas, and counties , 117 2k Actual and estimated production of Early and Midseason canges by Florida counties and by seasovi, 1951-52 through !9d7-68 121

PAGE 8

Table Page 25 26 27 Actual and estimated production of Valencia oranges by Florida counties and by seasons, 1951-52 through I967-68 Total actual and estimated production of Florida oranges for the study area by variety 1951-52 through I967-68 . . . , 127 133 Total actual and estimated production of Florida Early and Midseasor. oranges for the study area with percent errors when actual production is estimated by Stages I and I I , by seasons 1951-52 through 1967-68 , 13^^ 28 Total actual and estimated production of Florida Valencia oranges for the study area with percent errors when actual production is estimated by Stages I and II, by seasons 195i-52 tlirough I967-68 135

PAGE 9

Abstract of Dissertation Presented to the Graduate Council ip Partiai Fulfillment of the Requirements for the Degree of Doctor of Philosophy EFFECTS OF WEATHER ON ORANGE SUPPLIES By David Wood row Parvin, Jr. June, 1970 Chairman; Dr. M, R, Langham Major Department: Agricultural Economics A two-stage procedure was developed to estimate the relationship between the production of Florida oranges and weather. The relationship was estimated by counties for Early and Midseason, and Late varieties. The first stage (Sta^s i) expressed average production as a function of me numbers of trees by age. The estimated overage production from Stage I was used to remove that portion of the variability in reported production data which was due to changes in number and age of trees. The Stage I results were used to express reported production data as the signed percentage deviation o^ actual production froir, estimated average production. In the second stage (Stage !i) specified relationships between these signed percentage deviations and weather were estlm.ated with classical least squares regression. The analysis was conducted on a county by councy basis. Data were also pooled over counties and oyer regioiTIn alternative specifications of the model in Stage II. V/eather indexes and average yields per tree by counties for Ear'y and Midseason, and Late varieties visre estimated in Stace I, Also, the numbers of orange trees by ages for the years (9-r3 through

PAGE 10

1968 vjere estimated (from tree census dcita) for the state and for each county for both Early and Midseason and Late varieties. These estimates provide useful by-product Information from the research. The data covered the general period 19^8 through I968. Eighteen counties and two varieties were included in the study. Numerous variables were used to describe weather. Soil moisture and minimum daily temperature explained niore of the variation in the dependent variable of the Stage II relationship than other measures of weather available. In general, the signs of the estimated coefficients were reasonable. For the county equations the uncorrected coefficient of multiple determination ranged from . 1 2 to .8k, Many of the relationships estimated from pooled data were not significant. However, the results provide reasonable bounds on the size of the effects of freezing temperature and certain levels of soil moisture on tfie prcduction of Florida oranges. The estimation procedure would have benefited from msasurements of the duration of freezing t-empe ra tures and From more accurate measurements of soil moisture. The weather index for the state for Early and MIdseason oranges varied from .68 to 1.33 indicating that unfavorable weather could reduce the crop 3?percent and that favorable weather could increase i c 33 percent. For Valencia oranges the range of the state weather index was .60 to 1.22. This range indicated that the effect of unfavorable weather could be approximately twice that of favorable weather.

PAGE 11

CHAPTER I THE PROBLEM I ntroduction The supply of Florida oranges is quite variable. The freezes of 1957 and 1962 exerted a marked influence on the total state production of oranges, Tne December estimate of the Florida Crop and Li vested^ Reporting Service for the I962-63 season placed Florida orange production at 120,5 million boxes. However, due to two icy nights in December, 7'+. 5 million boxes were ultimately harvested (iS, p. 7). Furthermore the freeze rfouced the p^;r-bcx /ield of pro>.;essed products. Prioto the freeze a y'eld of I.35 gallons per box w.is estimated for that po!"tion of the crop utilized for frozen concentrated orange jjice. The actu-al yield was 1,09 gal ions (19, p, 82). Florida orange production fell to 58,3 million boxes the following season (1963-6^) oecause of the lagged effect of the freeze. It was not until the I966-67 sea-;on or che fifth season following ihe freeze that production exceeded its 1961-62 level. An earlier freeze in '957 was also severe. Total production of Florida oranges was 93-0 million boxes the season before the freeze. The freeze dropped production to 82,5 million boxes for the 1957-58 season. And production was only 86,0 million for the 1958-59 season, Intercounty variability in annual oucput aisc exisi.s, Poik

PAGE 12

2 county's production figures for Early and Midseason oranges during the four seasons I96I-62 through ]3Sk-G^ were 10.7, 9-8, k.7 and 10.2 million boxes, respectively. Polk's Valencia productions v;ere 1^.1, 8.1, 8.9, and 10.8 million boxes, respectively, for the same seasons. However, production data did not reflect the same distribution pattern throughout the state. For the same four seasons Valencia production in Indian River County was 0.9, 0.8, 1.1 and O.S million boxes. The effects of other weather variables were not always reflected by the data as clearly as freeze damage. The 1955-56 season was shocked by severe drought (50). However, of the three major producing counties, Polk and Orange suffered a reduction in output of Early and Midseason oranges while Lake increased its output of these. All three counties increased their output of Vaiencias. !t was not until the season following the drought that its effect showed up in Valencia production. The Florida Crop and Livestock Reporting Service estimated that Early and Midseason orange trees twenty-five years old and over yielded 7.0 boxes per tree during the I966-67 season. One season later they estimated that the same age group produced only ^.0 boxes per tree, Valencia estimates for the same two seasons were 5-7 and 3.2 boxes per tree, respectively. Sites (78) in a 1947 study of fruit quality as related to production practices noted that weather conditions can cause differences in fruit quality and quantity as great or greater than differences which can be induced by any cultural or nutritional treatment. The large variations in orange supplies due to weather have not

PAGE 13

3 only had great impact on the market for oranges but have also obscured any relationship which may exist between orange production and other production inputs. Detailed analysis of this latter relationship requires that data be adjusted for the effects of v.'eather. The Florida orange industry is believed to face a demand curve which is inelastic at high prices and very elastic at low prices (18, p. k) . This demand curve creates the possibility of an industry 2 pricing strategy, i-ii stori cal ly the industry (particularly the FCOJ portion) has tended to "overprice" and to show a definite tendency 3 tov/ard price rigidity. If the Florida orange industry is to develop an acceptable and enduring pricing and marketing policy it is necessary that the factors that affect orange supplies be understood. Weather is a major source of orange supply variation and as such was the concern of this study, Ob jec ti yes The major objectives of this study were (1) to specify relationships bet'ween weather and Florida orange production that were meaningful from the poi nt-of-vi ew of what is known about factors affectFor example, successful estimation of grower response to the price of oranges requires that seme variable(s) be used to reflect the variation in output due to weather, 2 Frozen concentrated orange juice, ^The Federal Trade Commission considers the Florida FCOJ industry to be an ol i gopol i s t i cal 1 y structured industry with few firns, substantia! barriers to entry, little threat of outside coiripe 1 1 ;: I o--^ , and a hiafi degree of vertical integration between grov.'er and processor (13, p. 3).

PAGE 14

i ng orange production and (2) to empirically measure these relationships. In attempting to satisfy these major objectives certain kinds of useful by-product information resulted from work on supporting or minor objectives. These minor objectives v/ere as follows: 1. To describe the groves in the state by counties, tree numbers, ages of trees, and varieties over time. 2. To estimate county differences in the "expected" yield of orange trees by age and variety assuming "average" weather and average levels of other inputs. 3. To compute yearly indexes for ci trus-produc' ng counties and the State for the 1951-32 through I967-68 production seasons. Each index provides a comparison between actual and "expected" orange production. It was hypothesized that deviations of actual production from expected production were largely ettrioutabie to weather and as a consequence estimated indexes were termed "v/eather" indexes. k. To develop forecasting procedures to make long-run predictions of production (under very restrictive conditions to be discussed later) and to predict the change in production should portions of the orange belt be suddenly shocked by severe or unusual v/eather patterns. Met h od of Analysi s A two-stage procedure was developed to estimate the relatiorship between the production of Florida oranges and Vv/esther. The relationship was estimated by counties for Early and Midseason and Late varieties. The first stage (Stage I) expressed the relationship between average production and numbers of trees by age. It was used

PAGE 15

5 to remove that portion of the variability in reported production data due to changes in number and age of trees;. The Stage I resuits were used to express reported production data as the signed percentage deviation of actual production from average production. In the second stage (Stage II) specified relationships between these signed percentage deviations and weather were estimated with classical least squares regression. Data were also pooled over counties and over regions in alternative specifications of the model in Stage i|. Definition of Terms Weather is a collection of various conditions of the atmosphere including such phenomena as rainfall, huniidity, amount of sunshine, length of day, light intensity, atmospheric pressu'^e, temperature, and other meteorological factors (8), p. 1155), It is bevond the control of farmers. Weather influences the crop-grcwino environment and affects crop yield. Some writers make a distinction between the direct and the indirect influences of weather on production. For example, weather affects production directly through rainfall and temperature and indirectly through insects and diseases (81, p. il^b) For purposes of this study, weather is defined as the net effect on production of variations in envi ronm.enta 1 factors which are neither under the control of farmers nor in constant supply over time (91, p. 26'+), In contrast, technology is defined as the sum total of controllable resources and how tney are utilized. The difference between a forecast oP crop production and an annual estimate of crop production is noted as follc.\'S. An annual

PAGE 16

6 estimate of crop production indicates a meosure of an accomplished fact at harvest time or later, A forecast of crop production refers to an estimated future production on the basis of knovv/n facts on a date prior to the period for which a forecast is being made. While Florida orange trees produce a new crop each twelve months, the harvesting of a given crop spans two calendar years. Picking usually begins in September and continues through July of the following year. Consequently, when discussing Florida oranges one v;ould not refer to the ]SkB crop or 19^19 crop but to the \Sh8-kS season. Most commercial trees consist of tvjo parts— the rootstock which includes the roots and trunk and the scion which is the upper framework. A tree is almost two years old before it is ready to leave the nursery. However, it ma/ =^tay in Lhe nursery a longer period. Therefore, the convention has been adopted that the age of a commercial tree is referenced to the year in which the tree was actually placed in the grove (i.e. year-set). This report is limited to round oranges. Early, Mid-Season, and Late are ti-,s three general classes of round oranges. The tern-, orange vji 1 1 be used in this analysis as a synonym for round orar.ges. The expression "variety (macro)" will be used to refer to the groups of Early and Midseason oranges and Late oranges, "Variety (micro)" v\/i 1 1 be used when referring to varieties such as Hamlin, Parson Brown, Navel, Jaffa, Pineapple, and Valencia. The term Na.me is related to time of maturity or harvest.

PAGE 17

variety will be used whenever the information being presented is applicable to both levels of aggregation. Since Late oranges are almost entirely Valencias, the terms Late oranges and Valencia oranges are used interchangeably and the terms will be used as synonyms in the analysis. T he Phenology of Florid a Oranges Commercial production of an orange tree begins at three to four years of age, increases rapidly to ten years, levels off and reaches a maximum at twenty-five years (9^*, p. 1^), Plant development, flowering and fruiting tend to combine into an orderly process. By fruiting time many of the factors of heredity and environment which affect the plant's capacity to produce fruit have already exerted their influence and yield potential tends to develop unless inl.ibited by abnormal grcv/ing conditions (^5). For the orange tree, as with other plants, time is relative to phenoloqical development, that is, relative to the dates of flov/ering and the setting of fruit. All orange varieties tend to bloom at the same time within a given year but with considerable year-to-yesr variability. Peak bloom usually occurs around the end of March or in early April. The blooming process usually takes about 50-60 days for the first regular bloom. Varying weather conditions often cause a second or third bicom. After flovvering, fruit setting is a continuous process and the young Bloom i nfor(,-:a L i OP summarized from personal conversations with Dr. W. A. Simanton, Professor, University of Florida, institute of Food and Agricultural Sciences, Citrus Experiment Station. His data will be cub li shed at a later date.

PAGE 18

8 fruit generally reach a size of one inch or more b/ June or July (^8, p, I72.S). Early orenges mature from September through November, Midseason oranges from December through January, and Late oranges from February through July, The Hamlin is the principal Early orange. The Pineapple is the leading Midseason variety, and the Valencia is the predominant Late orange (98, p, 23), Flor ida C 1 i mate The climate of the citrus-growing regions of Florida is classified as humid subtropical. From Apri 1 to October temperatures are moderately high. The highest daily temperatures in summer are uf.ually from 93 to 95 F, Higher temperatures do occur at irregular intervals but they seldom exceed 100 F, From November through March lower temperatures prevail and readings below }2 F, are expected every winter. The presence of the Atlantic Ocean and the fuilf of Mexico (one of which is within 75 miles of any point in the citru? belt) serves to moderdts both summer m,axiir.a and winter miniiTia temperatures. The average annual rainfall within the citrus belt has been estimated to be approximately 52 inches with a renge from 37 to 84 inches (98, p. 13). Likewise, the proportion of the annual precipitation which falls in any given month varies from year to year. Together these annual and monthly variations give a highly variable pattern of rainfall in Florida, A Florida Citrus Cofi;-!! ssicn report (19, p. 35) noted that, alth.ough the average interval between severe freezing vjeLther in Florida's citrus belt appears to be approximately ten years, such conditions may occur at any time, that is, they are not regular.. Butso;-, and Prine (6) in a st^jdy of Florida rainfall

PAGE 19

9 concluded that variations in rainfall frequencies are probably random fluctuations. Frost is likely to occur anywhere on the mainland of Florida on still, cloudless nights in winter. Freezes, hurricanes, and other weather phenomena are discussed in more detail in a later section. Weather Cy c les Bean (3) noted tiiat most crop forecasters view weather as not predictable but considers such a view to be erroneous. Bean admitted that weather data seem to behave like random numbers, that statistical tests in common use fail to differentiate between series known to be random and constructed series that are not random, and that a moving average of time series automatically produces what looks like cyclical movements. He contended that weatheffluctustions represent law and order and are therefore predictable He cited personal researcii on rainfall, river stages, whe?t, corn, cottofj and potatoes to support his position. Palmer (6^) reported that an enalv:;is of the m.eteorological record beginning in 1887 showed a surprising degree of regularity in the occurrence of severe and extrems droughts in the western third of Kansas and that an examination of the longest continuous meteorological record in the middle United States indicated that there is seme statistical evidence for suspecting that serious drought tends to occur about every twenty years in the central United States, The St, Louis, Missouri v\'eaLher record Is continuous from January I838 to date.

PAGE 20

10 However, Palmer noted that the subject requires more research in greater detail and with more powerful methods and techniques. Tree ring studies indicated the existence of alLernete wet and dry periods particularly in the suhhumid and semiarid regions of the United States (8S, p, 26). Auer and Heady (1) using U, S. corn production data for 1939-61 and corresponding weather data concluded that years tended to bunch— good vjeather years tended to bunch together and bad weather years tended to bunch together, Tefertiller and Hildreth (85) in an article dealing v;i th Great Plains agriculture also suggested the possibility of bunchincss or runs of good and bad years. Specifically they reported a tendency for rainfail to bunch in Oklahoma and Montana but that rainfall in Texas appeared to be random. Shaw and Thompson (77) reported that in an i owa study weather was found to be periodic, but in a Kansas study the reverse was true. Mitchell (58) reported that most investigators who research weather data for cvcles have felled to support rhe hypotheses of their predecessors. Instead they turn up new hypotheses aboot periodicities. Mitchell admitted the existence of two real climatic periodicities precipitation follows the lunar period of 23.53 days and a cycle of approximately two years in winds and temoerature at high altitudes over the tropics, Hov;ever, he noted that as yet there is no generally accepted physical explanation for either, Mitchell (58, p. 225) wrote that variations of climate appear to be very i rregul ar. This cycle is absent a 1 all elevations of less than ten miles.

PAGE 21

II Hathaway (28, p. kSl) in research devoted to the problem of ttie cyclical relacionshlp between agriculture and the non-aqr i cul tur^l economy concluded that factors other than weather were needed to explain the change in crop yields which were associated with the cyclical change in the demand for farm products, Clawson (10) stated that random annual variations in farm output are primarily due to random weather conditions, Griliches {2k) wrote that annual fluctuations in farm output were dominated by random fluctuations in weather, Thompson (88, p. 27) wrote that the vjeather cycle idea carried the connotaLion of a regularity in favorable and unfavorable weather for crops. He reported that a more acceptaole interpretation is that periodic changes in weather patterns do exist but that they do not occur in any regular cyclical pattern. Thompson stated that the popular notion is that wide deviations from average weather tend to occur at random. However, in another study, Thompcon (£9) cautioned that the researcher may not be able to treat the weather variables as random. Specifically, he found evidence that weather had not been random but had improved for grain crops since the midthi rties in t!-:e central United States. The 18 years of tim.e series data available for this study provided no meaningful basis for assuming that departui^es of weather variables from their average values occurred in a systematic and estimable way. Therefore, such deviations were assumed to occur randoml y , A B rief Histor y of Oranges Oranges are native to the tropical regioris of Asia, They have

PAGE 22

12 spread from there to practically all regions of the world with suitable climates. Since their first discovery, oranges have moved westward. From their native habitat oranges traveled to India, to the east coast of Africa, to the eastern Mediterranean, to Italy, to Spain, and finally to the Americas (61, p, 1021), Oranges were probably introduced into the western hemisphere by Columbus when he established a settlement on the island of Hispaniola on November 22, I^S'3. And Ponce de Leon probably introduced oranges to mainland North America when he discovered Florida in 1513, since Spanish law required that each sailor carry one hundred seeds with him (57, p. 8S). Wherever Spanish settlements were made orange plantings soon appeared, and in Florida the Indians carried oranges wi tti them and dropped their seeds in the hammocks and hsavily forested areas so that years later the forests were found populated with v/i 1 d sour orange trees. In some cases these trees had beer top.^-crked to sweet oranges and constituted some of the very early groves (7, p. 6). By 1573, plantings existed in the Spanish settlement of St, Augustine (7, p. 6). By I800 there vjere numerous groves planted by the Spanish and other settlers along the coast south of St, Augustine, along the St, Johns River and around Tampa Bay, V/ith the annexation of Florida by the United States in 1821 settlers steadily expanded the groves. This expansion suffered a sharp setback in 1835 when a severe freeze killed many of the trees to the ground. After the Civil War development was rapid. !n 1886 the Florida crop reached a volume of one million boxes. Railroads vjere coming into the state and made possible

PAGE 23

13 the development of citrus groves away from the waterways. Expansion was steady from 1886 through ]B3k (7, p. 6). Consequently, by the latter part of the 19th century the orange industry had been firmly established in Florida. However, in the winter of l89^^-95, ^ severe freeze hit Florida and practically destroyed all groves. Before this freeze, production had climbed to 6 million boxes. Fourteen years passed before that level was reached again (72). Early plantings had been made on locations selected primarily because of the character of the soil. The freeze of 1894 and 1895 brought to the fore the problem of cold protection and resulted in a spread of the industry to the south, Sy 1920 it had been discovered that trees could be produced on the high, warm, sandy ridges of central Florida by using rough lemon rootstock. Prlcr to the introduction of rough lemon rootstock, sour orange and sweet oronge rootstock had been used and neither was satisfartor/ or the Ughi; sandy soils v/ith their low fertility and irregular moisture supply. Therefore, in a sense the industry's present size is based mainly on the discovery of rough lemon rootstock because it made possible the use of land not formerly suited to citrus production (7, p. 7). By the la;;e 1930'5, production had grown to the extent that prices were suffering. Grov-jers and processors searched for new uses and outlets. The development of FCOJ (frozen concentrated orange juice) in about 19^5 v,as a major breakthrough in tnis direction. This new product grew at a phenomenal rate. The initial output of 226,000 gallons for the l9-^5-i+6 season grevj to 30 million gallons within 5 years, to 70 million gallons in 10 years, and to 116 million

PAGE 24

14 gallons by tfie I9CI-62 season. For the I963-6^^ season, production of FCOJ utilized more than 65 percent of the orange crop and fresh fruit used approximately I5 percent. This figure For fresh fruit compares to 85 percent prior to the introduction of FCOJ (18). In the 1948-4S season, 18,2 million bearing trees produced 58 million boxes. In the I966-67 season, kZ million bearing trees produced ]kk.S million boxes, and in December, I967, there were an estimated 16 million non-producing trees in Florida groves. In 196667 Florida produced approximately 78 percent of the IJ. S, supply of oranges and more than the combined total of the second, third, and fourth largest producing countries — Spain, Italy and Mexico. Commercial orange groves extend from Putnam, Marion, and Volusia counties in the north to Collier and Broward counties in the south and production spans the ent' re breadth of the Florida peninsula. The center of the orange belt has tended to shift routh over time. This movement is attributed primarily to the desire of grov^ers to reduce the probability of freeze damage owd to land pressures (55), The present center of the citrus belt is on the high pines soils of the ridge section of Polk, Lake and Orange counties. In 1966-57 these counties produced 52 percent of the ]kh.5 million boxes produced in the state -Polk produced 34,0, Lake Z'+.O, and Orange county 16.5 mi 1 ! i on boxes .

PAGE 25

CHAPTER II THE STUDY OF WEATHER EFFECTS ON CROPS General Problems The causa and effect relationships between weather and crop production have been the subject of considerable research. With the increasing grain surpluses of the late 1350's effective agricultural policy required that the increases in agricultural production be separated into that attributable to favorable weather and that due to technological i niproverrients (2U, p. 282). Consequently, agrict'!tura! econoinists have had a renewed interest in v;ea ther-parti cui arly the problem of separating the effect"^ of weailicr ar:d techno !ogy on product ion. The biophysics of the v;eather-pi an t interaction is coinplex. Most of the functional relationships between individual me teorological variables and plant growth are not known (15, P8'). Besides being related to yield in some conplex, unknown manner, i-ncst of the weather variables are believed to Interact with each other in varying degrees. Yields are also affected by changing levels of technological factors such as changes in residual soil fertility, differences in fertilizer rates, changing insecticides, new varieties, crop densities rrechani zati on , and increases in irrigation. Other factors such as crop diseases and insect infestation which affect yields are closely associated with v;eather (15, p, SO). Because of the many factors 15

PAGE 26

16 affecting yield, the estimation of an exact functional relationship between these factors and yield has often been viewed as impossible from an empirical point of view. Rainfall and temperature have been used synonymously with weather, partly because they are the dominant meteorological influences on yields, and partly because the data on these variables are readily available. Plants grow in the soil as well as in the air--and soil temperature may be more important than air temperature (76, p. 3). Likewise, rainfall is not synonymous with moisture available for plant use. Although temperature and precipitation arc the variables usually considered, more exact Indicators of the influence of meteorological factors such as soil moisture and drought indexes have been proposed. Agricultural drought should be defined on the basis of soil moisture conditions and resul t=int plant behavior, rather than on some direct interpretation of the rainfall record (92, 93). Fo*" some years, rainfall and actual soil moisture available for plant growth may have little correlation. Monthly averages or rainfall can be especially misleading (7m-, p, 22^). Problems of spatial aggregation can occur for two reasons. First the relationship betvjeen crop yields and m:eteoro!ogi cal fectors are not monotonic (7^, p. 223). Suppose a total June rainfall of 6 inches is optimal for yield ?nd that the effect of 5 inches is the same as the effect of 7 inches; then the average rainfall for two counties ((5+7) / 2 = 6) is at the optimal but the true yield at this level of rainfall will be underestimated, Secoridly, a weather measure is usually accurate for only a small area, and spatial aggregation creates a probletn because weather conditions at only a few

PAGE 27

17 locations are available to represent rather large crop reporting districts (76, p. 22). Variation in agricultural output associated v^^i th variation in v/eather is often greater than that associated vnth nonweather variables. While irrigation, mechanization, and improved cultural practices have given some degree of weather-proofing to crop yields, weather is still an important factor in determining yield (53, P1172) Yields can be greatly influenced by brief periods of exceptionally favorable or unfavorable weather. Palmer {Sk , p. 178) notes that 1955 was a drought year and early prospects for v;hoat yields were din. Hovvever, one or two good rains at exactly the right time produced long, well-fitted heads and subsequently good yields. This example further illustrates the difficulties of estimating yields directly from meteo^'ologi cal data. The initial forecast for a given season may be desired a considerable tine in advance. Unusual weather can cause copsiderable 2 change before actual harvest. Since 19^0 a substantia' part of the variation in yields has been attributed to technological changes (7^, p. 219). A yield series can be visualised as a function of weather and trend due to technology and other factors. The economic and other factors which fend represents will depend upon the data source used (15, p. 81;. The Some writers have classified the variation in output associated with weather as random and that associated with other variables as non-random (73, p. 1). This classification scheme leaves something to be desired since it attributes all randomness to weather. 2 _Su j3r_a , p. I .

PAGE 28

18 use of a linear time trend assumes a constant rate of technological change and it fails to capture occasional sudden changes in techiio'ogy. Also, to assume independence of the technology variable and the meteorological variable may be incorrect. Shaw (7^, p. 222) cites as an example the fact that in 1930 a two-inch deficiency in rainfall cut corn yield 25 percent, but in I96O the same deficiency cut yields only 10 percent. It is reasonable to hypothesize that for m.ost agricultural crops weather and technology are not independent and that an interaction exists at each point in time. Technological advances permit man to bring more of the environment under his control. Empirical models of weather response must of necessity be crude abstractions of real world complexities. Hovyever, there must be justification for their form if such models are to be relevant approximations of the real v/orld. Tor example, if one ecu Id assume that weather variables 'w^re distributed randomly and tha^ the effects of all other variables were determined by trend, it 'io::]d be feasible co use a time trend to estimate the influence of technology and atiribiite the fluctuation in yield around the trend line to weather variables. However, if the weather has improved during the period of study, the;-, a time trend overestimates the effect of technology and the other variables (89, p. 75). Likewise, when weather is random and the rate of technology is irregular, moving averages as discussed by Shaw and Durost (73) provide a better estimate of the rate of tecnnologi ca 1 development than a linear tim.e trend. In such a case, deviations from the "technology line" miay approximate deviations due co weather, Thompscti (89, p, 75) uses hypothetical sets of yield and rainfall data and prfcsenis a c^je for multiple regression analysis, !n his

PAGE 29

19 model yield is estimated as a function of time (technology) and a set of meteorological variables. He argues that the approach gives a better estimate of the rate of technological development than simple 1 i near ti me. Even with annual crops the problem of separating yield variability into that portion due to weather and that due to technology can be difficult. With corn yields Thompson (88, p, 1) found that weather was the more important variable, while Shaw and Durost (76, p, 3) in an independent study of the same general data found the weather effect to be negligible. Past Research Numerous techniques have been proposed to aid in the analysis of the crop-weather relationship and the sometimes troublesome companiofi problem of the technology-weather interaction. Each approach tends to have a few advantages and numerous disadvantages. Historically, the most frequent method of studying the crop-weather relationship has been to estimate an equation using multiple regression techniques (71, p. 219). Usually the dependent variable Is yield, measured as an average for some geographical area, and the independent variables are trend and some collection of weather variables. Most often the simplifying assumption that trend can be approximated by linear tiire has been used. As noted by Stai lings (81, p, 1155) very early studies often regressed yield on a single meteorological variable such as total rainfall curing the growing season. Other studies, as discussed by Morgan (59, p. 1173), have attempted to explain yield by using monthly rainfall a'id/or temperature during the critical month of the growing season, Quadratic and interaction terms have been Included.

PAGE 30

20 Classical multiple regression analysis has not been the only techniq'je proposed. Weather indexes have been constructed (75, Bl). Aridity indexes (62) have also been included in models. More direct measures of the plant-weather relationship such as the use of evapotranspi ration rates (m-6) have been proposed. Non-linear regression has been used to iterate betv/een a weather index generating function and a function relating yield to the v/eather index and other variables (15). Basically, four general techniques have been used to study the problem--cl assi cal regression, weather indexes, aridity indexes, and an ad hoc group which has been labeled as hybrid techniques, !n the next section each of the four general procedures are reviewed and one or more sample studies of each type are discussed in some detail. Clas sic a l Regression The classical regression approach to the crop-vv'eather relacioriship includes studies in which classical least squares was used to estimate crop yield or production as a function of measures of meteorological variables such as total monthly rainfall and/or average monthly temperature. Regression coefficients in such models provide ^n easily understood method of describing the effects of variations in meteorological variables. Hovjever, such models are not suitable for predicting yields over a wide t"
PAGE 31

21 portant variables and their functional relationship to yields, are perhaps insuperable and that conceivably tlie task could be eqiiivalent to a full project for each crop in every county or other small geographical unit where it is grown. Specifying appropriate variables and functional relationships as well as problems of aggregation have tended to limit the usefulness of multiple regression when data are aggregated over geographical regions. Most multiple regression studies have been disappointing, both as forecasting formulae and as indicators of cause and effect relationships. Even whsn statistical indicators have been favorable, the models have failed to give reliable ansvjers (7^, p. 218), A difficulty with regression analysis is that researchers attempt to explain variation due to weather by using an incomplete and poorly misasured set of weather variables. Another criticism centers around the fact that with regression analysis the functirnal form of the relationship between yield and the technology variable must be specified in advance. Similarly, the assumption of i ndepender-ce of the technology variable and the weather variables has been discussed as a disadvantage. While this assumption is not necessary, the technology-weather interaction is difficult to estimate. Shavj (7^) contends that miich more must ce known about the pattern of technological change if weather is to be studied by traditional multiple regression. Because of the biases which may be introduced due to faulty specification of the model and use of aggregated data plus a history of failure in forecasting, many persons place little confidence in any conclusions reached by multiple regression analysis of aggregate crop yield-weather relationships.

PAGE 32

22 Thompson (87, 88, 89) has been a heavy user of multiple regression techniques in the evaluation of the effects of weather and technology on crop production. For a detailed look at some of his work, the follov^/ing terms are defined: Y = Yield of corn in bushels per acre X, = Year X2 = Preseason precipitation X, = May temperature X/^ = June rain Xr = June temperature Xg = July rain Xy = July temperature Xg = August rain Xq = August temp'i''atL're Thompson (88) used multiple linear regression to estimate the relationship between Y and X], X2, ..-, Xq for each of tne five corn belt states. He noted th?t v/hile such mu'tiple linear regression coefficients indicate the effects of slight departures from average rainfall or average temperature, they are not suitable for predicting yields over a wide range of weather conditions, ^or example, with linear regression it Is assumed that each additional inch of rain in a given month vji 1 1 have the same effect on yield as the first inch. Such is not the case. Thompson's multiple linear regression miodel tended to overestimate in poor weather years and underestimate in gcod weather years. A multiple curvilinear regression model including the rainfalltemperaLure interaction terms corrected this difficulty (88, p. 5),

PAGE 33

23 His multiple curvilinear model included the nine terms of the multiple linear model plus X2 through Xq squcjred and the ra i nfa 1 1 -temperature interaction term for each of the three months. Thompson was quick to caution that large numbers of variables in multiple regression analyses may provide high correlations (R ) even though tne variables are meaningless. He noted that Robert Shaw and Robert Dole (88, p, 9) drew random numbers within logical ranges for rainfall and temperature, and used actual corn yield data for a 27-year period in Iowa. They had 21 variables in their equation and obtained a multiple correlation coefficient of ,86, "However, none of the "t" values for the weather coefficients were significant at the 95 psr cent level. Therefore, Thompson noted that when large numbers of variables are used in multiple regression analysis, the multiple correlation coefficient may be m.isleading. He suggests that while analysis of variance (AMOV) will not "correct" the problem, it should make the difficulty of misleading structural estimates of parameters 2 1 and high R values easier to identify. Thompson used a linear trend for technology. He states that a linear trend is more logical than any curvilinear trend (88, p, 16), Hovjever, he notes that the data pi'obably reflect a wea ther-ferti 1 i zer interaction which his equations do noL measure. inceraction between extra soil moisture and fertilizeris well known (86), However, for Thompson is probably referring to an individual "t" test of the regression coefficients and not to the usual ANOV table for regression which generally does not include the "t" values. Actually a corrected R ( 23, p. 217) whicii penalizes functions with large numbers of estimated coefficients might be a better statistic on wnich to base such decisions.

PAGE 34

2k t\\c period of his data, Thompson felt technology had been adopted at a fairly steady rate. He verified this assumption by examining the residuals from his estimated functioti to see if they increased or decreased over time. He argued that homogeneity in the residuals supports the assumption that technology has been gradually adopted over time. Thompson used a cubic in time for technology in his studies on grain sorghums and wheat because the data did not reflect a 1 i near trend. W eather Indexe s The weather index approach results in an index such that actual yield figures may be adjusted to reflect yields had average weather prevailed. This approach Pias been used in an attempt to avoid the difficulties commonly associated with regression analysis. Various techniques have been proposed for the construction of weather indexes. The differences among these techniques are slight and tend to depend on the data used. To measure the influence of weather by the index approach, a time series of yields is required. A trend is usually fitted to the data to describe the yield effect due to changes in factors which were not controlled. The vjeather index is calculated in each year as that year's actual yield as a percentage of the computed trend. If experimental plot data with most nonweather variables being controlled are used to calculate the weather index, the index may be an indicator of the weather alone. However, if a time series of actual yields is used to calculate an index, then the effect of weather may depend on the level of technology which is not controlled, In such a case the index obtained vMOuid be an indicator of all un-

PAGE 35

25 controlled factors which affect yields and which are not reflected in trend (73, p. 7). Stallings (8l) has computed indexes for the influence of corn, oats, barley, wheat, soybeans, cotton, and tobacco. The method he uses has been called the experimental plot data approach. This method is based on the assumption that if time series of yields for a crop can be obtained froni experimental plots in the areas where the crop is grovjn and where as many variables as possible have been controlled the remaining variation in yield from year to year (after trend has been removed to account for increases or decreases in the fertility Isvel of the soil) will give an indication of the influence of weather. Since the net effects of weather are measured, thi'^ approach allows for all the influences of weather v\'hether direct or indirect. Stallings assumed that the yield trend due Lo fertilizer applications on the plot was approximately linear and could be removed by a linear regression on timic. For a given c'"op and a given location the technique is quite simple. First, remove trend from each series by fitting a linear regression line to the data. Second, coihpute indexes for each series as the ratio of the actual to the computed yield of the regression line. Third, average indexes for each series to obtain an Index for that location. Finally, if desired, indexes for larger areas can be formed by v.eighing the index for each location within the area by the percent of average production for t\.e area that the location represents. Ideal data for this approach would coma from experimental plots with everything held constant, except for weather, over the period of

PAGE 36

26 time for which Indexes are to be calculated. Stal lings notes, however, that calculated trends could be partially or entirely due to improved technology and management of the experimental plot. Also, the data might not reflect the varieties, practices and technology level representative of the production in the area to be represented by the index. He stated that in cases of less than ideal data, judgment and familiarity with the situation be used to help resolve data problems. When using the experimental plot approach to generate weather indexes, the data are subject to all the criticisms and shortcomings normally associated with field experiments. Researchers often incorrectly assume that becaiise the data come from experimental plots their accuracy Is superior Lc most secondary data. Shaw and Durost (75) have modified the above procedure somevvhat for data from corn variety tests v/hich were conducted under actual farming conditions. They took the following steps to develop a weather index for each location: (1) compute a g-y-ar nicving average as a first appi oxi mo cion of the trend In yields due to factors that were not held constant, (2) extrapolate the moving average forw^'-rd and backv;ard to the terminal years> (3) divide actual experimental yields by the corresponding moving average yield. Consider any year in which this percentage ranges from 85 to 115 as an "average-weather" year, and {k) regress yields in "average-years" on time, (5) compute the weather Index as actual test yield divided by estimated trend test yield. An advantage of the weatherI ndex approach is that the specification of the exact cause and effect relationship between yield sr.d. an individual meteorological variable is avoided. Any assumed math-

PAGE 37

27 etnatical function requires more knowledge about the rate of technological change than we now possess (7^, p. 227). Shaw notes that the deflated yield series should indicate the form of the technological relationship. One major use of weather Indexes is to measure technological change indirectly by using the index as a deflator for the influence of weather variation. The advantage of this approach toward trend is that no assumption need limit its form. One basic weakness of the experimental plot data approach is its assumption that factors other than fertility levels are constant over the experimental period. Experimenters often attempt to optimize nor.experi mental variables (65, p. II6I). It Is likely that insect control and other production practices are altered over the experimental period to keep abreast of technoiogi ca! advances. If such is the cc"se, 1 t wi 1 1 be reflected in the index by u inii n; shed Inoirsct effects of weather. A final disadvantage of 'weather indexes is that they cannot be used to predict yields on the basis of meteorological observations. However, as indicated earlier they are useful if the purpose of the analysis is to simply remove the weather effect so that other factors affecting the yield of a crop may be studied in greater detail. Aridity Indexes Oury (63) has proposed that some aridity index be used as an independent variable in relating weather to yield rather than such Oury's terrri,

PAGE 38

28 meteorological variables as rainfall and temperature. He stated that the use of a composite aridity Index may provide a relatively simple approach to a difficult problem encountered in agricultural supply analysis. The concept is simple and is not confined to a single agricultural area and/or crop and the indexes can be calculated whenever basic weather data, rainfall and temperature, are available. This approach rests on the assumption that evapotranspi ration is the key weather-related variable that influences yields. Note the following definitions: I = Aridity index P = Precipitation or rainfall T = Temperature Recognizing that temperature is the major factor effecting evaporation vario'js vjorkers have suggested formulae sub? ti tut i nc; temperature for evaporation. Several such formulae discussed by Oury aie as fol lovjs : = P/T = P/(T + 10) = 8P/(15T + 120) = 2P/(T + 33) = P/(T + 7) = P/1,07''" Lang's formula indicates that the effectiveness of rainfall varies directly with precipitation and inversely with temperature, De Martonne added the constant 10 to avoid negative values. Basically all three of Koppen's formulae are similar to those of Lang and De Martonne. in accordance with Van't h'ofr's Law the denominator Lang: De Martonne: Koppen: Angstrom:

PAGE 39

of Angstrom's formula doubles with each rise of ten degrees centi, I grade. Oury estimated three models of crop yields by least squares to determine the suitability of using De Martonne's and Angstrom's aridity indexes. Oury "fitted" the following three functions: Y Y Y whe re: Y t P T b + b^t + bpP + b^T + e b' + b^t + b^ (P/(T + 10)) + b" + b"^t + b^ (P/1.07''") + e' Yield per acre Time Precipitation during selected period Temperature during be lee ted period [I] [2] [3] Equation [1] implies that the marginal yield .-esponse to P and T is constant. Agronomi ca 1 1 y the aridity index approach (equations [2] and [3]) has more intuitive appeal. It implies that the marginal yield response to P is not constant and is a function of T and likewise that the marginal yield response to T is not constant and is a function of P and T. Oury found P and T to be highly negatively correlated. The "t" statistics indicated b and b, to be significant at the 1 perVan't Hoff's Law states that the velocity of a chemical reaction doubles or trebles with each rise in temperature o[ ten degrees cent i grade.

PAGE 40

30 cent level and bp and b^. at the ]0 percent level. Similarly Oury reported that the Durbln-V/atson d-statistic indicated the superiority of equations [2] and Q3j. Lil
PAGE 41

31 the experiment. From experimental data with various levels of nitrogen Knetsch estimated: 2 Y = 92,35 + .it83^N .OOIN ,598lD 0028ND [.5] where: Y = Estimated yield in bushels N = Pounds of nitrogen D = Drought value Knetsch's interest was in estimating the optimum level of nitrogen to apply. He specified a model with a drought-nitrogen interaction term on the basis of prior agronomic research. The important point for purposes of the present study is that the drought-day criterion provides an alternative specification hypothesis for weather in models used to study crop yields. The drought-day approach require? that one kno\; the maximum water the soil can hold, the level or levels of soil moisture at which growth is appreciably depressed, and tfie rate at which the soil dries out due to evaporation. Daily precipitation records are also required. Knef:ch used the Thornthwaite formula to estimate evapo-transpi ration. This procedure requires that rainfall be added each day and evapotranspl rat i on be subtracted. Soil moisture is of course bounded by zero and its maximum storage value, A drought-day is defined to occur vjhen the storage value equals zero or some critical value (wilting point), Doll (15) used data for the period 1930-63 for 37 Missouri counties to estimate average corn yield for Missouri as a function of

PAGE 42

32 weather and trend. He used an iterative non-linear regression procedure suggested by Edwards (17). Because corn yields have increased rapidly in Missouri since 1930, a cubic time function was used to estimate trend. Doll's resul ts were: Y^ = -5.1^3 + 3.7902Z^ .]]SkZ^^ + 2.l882t 2 3 9 .!158t + .0026t^ R^ = .90 [6] z^ = --.eagx^, + .0373x^2 "^ "*" -0912x^.8 where: Y = Predicted average corn yield for Missouri. ^'tk ~ Rainfall variable for year t for week k, k=l,.,.,8. Z^ A measure of the impact of the rainfall variable in year t. t T i me . 2 If Z and Z^ are substituted into equation [_6~], the result is an estimate of average yield given average weather for the time period under consideration. A weather index was computed as the ratio of predicted yield to the predicted yield given average weather. Doll listed three advantages of the technique: (i) the index is based on a functional relationship between yield and meteorological variables (and tvjo years with similar meteorological patterns will have similar indexes), (2) the formulation of the model can a]]ovi decreasing returns to meteorological variables within a time period and interactions among time periods, (3) the inclusion of meteorological variables in tne model improved the estimate of trend to the

PAGE 43

33 extent that weather phenomena such as runs and extremes are "explained' by the meteorological model. Added Problems Associated with Forecasting Florida Orange Production Oranges are a perennial crop and the meaningful technical unit for measuring yield is a tree rather than an acre. The yield of an orange tree Is a function of Its variety, age, location (soil type and depth), planting pattern (tree density and how they are physically arranged), and average v^eather to which it is subjected. A forecast based on bearing surface would be better than one based on tree numbers or acreage, but such information would be impossible to keep current (9^, p. 12). The \SkO-k'-\period was characterized by two low and two high solids seasons. However, Sites (73, p. 56) reported that no elemeiit of v-jeather was sufficiently outstanding to enable one to conclude that it was tlie causa. Generally, the more the acreage is concentrated, the more susceptible th3 total production is to vjeather variability. Usually if spread over a large area, good and bad weather may tend to average out, V/hile the acreage devoted to Florida oranges Is fairly concentrated, the same climatic conditions of rainfall and temperature tend to have varying effects due to the vast differences that exist among soil types, depth, and water-holding capacity. However, due to the fact that the citrus belt Is concentrated geographically freeze effects tend to be more general In nature. Stout (8'+) reported that a considerable amount of the year to year variation in the production of oranges could be explained by the

PAGE 44

3h foilcvving factors: (]) tree numbers; (2) number of fruit per tree; (3) size of fruit; {k) droppage rate. He considered Early and Midseason oranges and Valencia oranges independently and reported the following results as given in Tables 1 and 2 below. Table 1: Relative importance of factors affecting average annual change in Florida's Valencia orange production. Factor Percent variation explained Tree Numbers Number of fruit per tree Si ze of f rui t Droppage rate Other factors n.i 29.8 30.^ 14.3 Source: Stout (Sk, p. 30). Table 2: Relative importance of factors affecting average annual change in Early and Midseason orange production. Factor Percent variation explained Tree numbers Number of fruit per tree Si z:e of f rui t Droppage rate 0:her factors 4.3 kk.3 21.5 9.5 20.4 Source; Stout (84, p, 30),.

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35 Stout (8h, p. 10) noted that the number of fruit per tree is related to the area of bearing surface of the tree and to freeze damage. He reported a tendency for years with low sizes to follow years with high sizes and vice versa (84, p. 12), In summary, while many of the problems associated with forecasting Florida orange production are due to the numerous factors related to yields and the impossibility of stating trie functional relationship of these factors to yield and to each other, the major difficulty is due to the fact that oranges are a perennial crop and a considerable percentage of the year-to-year variation is due to the changing distribution of trees by age classes. Also, the relationship between tree age and average production is not clearly understood (especially differences in the relationship from one recion within the state to another) , Recent An alyti cal Ap proaches Two recent studies have attempted long-range forecasts. Raulerson (67), in a I967 study, investigated the problem of fluctuating orange supplies and grower profits in the frozen concentrated orange juice (FCOJ) sector of the Florida citrus industry. Polopolus and Lester (66), in a I968 study devoted entirely to forecasting, estimated Florida's orange production over a fifteen years period. Raulerson updated an existing DYNAMO simulation model (39) of the Florida citrus industry to appraise alternative supply control policies vjhich v^ere designed to reduce the fluctuation in orange Bearing surface is a function of the size of the root system (95)

PAGE 46

36 supplies and grower profits. In simplest terms, Raulerson considered a given year's production to be a function of productive trees and boxes per trees. Boxes per tree were in part dependent on the level of average grower profits. The level of productive trees was increased by new planting and by hatracked trees coming back into production, and decreased by a normal mortality rate and by productive trees lost by freeze. The author expressed the freeze effects on crop size and tree numbers by defining three possible categories according to the severity of the particular freeze encountered. Trees were killed completely, hatracked, and/or suffered only yield losses. The severity of the particular freeze encountered was based on 29 seasons of weather data, 1937-38 through 190^-65. A procedure of random sampling with replacement was used to obtain l^i years of freeze effects. The industry was simulated for a 20-year period, I96I-62 through 198G~Sl. The actual weather for the first six years, 1961-62 through I966-67, was used. Raulerson noted that a more accurate DYNAMO model of the citrus industry would benefit from expanded research in some areas. An incomplete list of research needs is given belov-7: 1. Supply response of growers — particularly when they are facing declining prices. 2. Effects on yields of less intensive cultural practices — especially if the r-educed level of cultural practices existed for only a few years and normal cultural practices were resumed. Items I and 2 are interrelated and Raulerson discu'^sed both as a single topic.

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37 3. Effect of freezes upon present and future crops. Polopolus and Lester used a random sampling technique to estimate Florida's orange production over the next fifteen years on the basic assumption of year to year variability in average yields per tree. Their method of estimation considered each future year's production to be an "event" drawn randomly from a set of six alternative events. The "events" were defined to represent the range of yield possibilities likely to occur in the future. Each of the six events had equal probability of being selected for any given year. The six alternative events were specified as follov.s: 1 Event A B C D E F Descript ion of average tree yield Slightly obove average Slightly belov/ average High Low Average Related to freeze damiaae Given a random dravjing of a freeze, the intensity of the freeze was defined by another random drav;ing of various possibilities of freeze damage. Five alternative levels of freeze damage were developed from historical records. They were as follows: Events B, C, and D directly relate to historical tree yields obtained in the I965-66, IS66-67, and I967-68 seasons, respectively.

PAGE 48

38 Freeze pos si bi 1 i ty 1 2 3 k 5 Percent of total Tree loss Yield loss Percent 15 35 17 10 5 The researchers assumed a net planting rate of zero except for the years immediately following freezes. The experiment was "run" fifty times for each of the fifteen seasons, I968-69 through I582-83. For the fifty experiments the standard error of the estimate averaged 36.7 million boxes -indicating the extreme year to year variability in Florida orange production. The authors cautioned their readers ':o interpret the production estimates in a general fashion and to avoid placing undue emphasis upon specific numbers in specific years. The biggest difficulty lies in the fact that any random event drawn in the sample may tend in the opposite direction from the real event. Likewise, the authors mentioned that the net planting rate was not treated properly and that the limited number of possible yield events with equal probabilities tends to place limitations en the analysis. Both the above studies indicated a need for a more accurate description of the relationship between weather and orange production.

PAGE 49

CHAPTER I I I TOWARD A THEORETICAL MODEL A Genera] Mode] The yie]d of a specific orange tree can be viewed as a function of its variety, age, rootstock, density of planting, terrestria] location, the soi i in which it is planted, weather conditions prior to bloom, weather conditions cnrough the growing season including maturity, plus the cultural practices and nutritional prGgrams to which the plant has beer, subjected. This relationship between the yield of an orange tree and the many factors affecting the f'na) level or yield is probably unique for each tree and may be represented in functional notation as. t=l,..,,T. Y".. = Observed level of yield of i tree in t year, Z"jj. = Set of variables which represent all physical attributes of the i' tree which affect the yield in the t year, C'.^ = Set of all weather variables affecting the i tree's yield in the t^ year. Asterisk superscript v;2s placed on each variable to emphasize that it differs froin similar variable notations to be used later.

PAGE 50

ko ^"i t ~ ^^^ °^ ^'' cultural, nutritional, and technological variables affecting yield of the i tree in the t year. U".^ = Disturbance term which represents that portion of yield It of the i tree in the t year which v;as not explained by the arguments in Z", C", and G . I = Number of trees and T represents the number of years. The variables included in 2.\^ should describe all the physical characteristics and attributes of the i ^" tree such as variety, age, rootstock, planting pattern and density, and type and depth of soil. The set C"-^^ vjould include such variables as the soil moisture condition experienced by the tree, temperature, and wind. Temperatures are critical — particularly low temperatures which cause yield loss due to freeze damage. The collection G"j ^ would include such variables as those which measure fertilizer, pesticide, and water applications and other management practices including freeze protection. The Q." J would not be separable functions in the three sets of variables but would include interas well as intr?-set interactions, The necessary knov.'ledge to specify the form of equation [7j for each tree will probably never be available and if it were, the resulting complexity would be as intractable as the real world. Later, assumptions will be used to abstract from the complexities of the real world. But, novy we turn to a discussion of what is known about factors affecting the yield of an orange tree.

PAGE 51

k] Factor s Affec ting the Yie ld of an Orange Tree The factors affecting yield can be broadiy classified as physical, weather, and management and cultural practices. Phy sical Fact ors The major physical factors affecting the yield of an orange tree are age and soil depth. These factors affect the tree's bearing surface v;hich is a major determinant of its average yield. Since oranges are a perennial crop, tree size and average yield increase over time. Other physical factors affecting yield are variety, rootstock, and planting density. The fundamental relationship between average yield and age of tree has been developed only in a very general manner using aggregate state figures and rather wide age group classi f i ca ti ens. Deviations in the effects of age among the various areas of the state have not been studied in detail. Average production per tree by age classes has been estimated for the entire state for selected seasons. The results are summarized in Table 3This information is too aggregative to be useful on a county by couniy basis since it implies that the average age of the trees within each age group classification is the mean of that particular group. For exer.ple, if in a given county the trees in che U 9 age group (mean age 6.5 years) had an average age of 5 years, then the coefficient in Table 3 would yieic a biased estimate for that age group. Such aggregative figure^ also fail to reflect county differences in average yield by age. Two v/riters, Chern (S) -^'-^^ Savage (71 ), have

PAGE 52

42 Table 3Florida Oranges Average production per tree by age classes, 1965-66 to 1968-63. Crop

PAGE 53

^3 estimated average yield per tree in more detail. Their findings are reported in Table k. Examination of these estimates reveals some rather extrem.e differences between results found by the two researchers. For example, Savage estimated that a > and a 4~year old Valencia tree would yield a combined total of 1.1 boxes while Chern would expect only one-half of a box. Similarly, Savage estimated that a 25-year-old Valencia tree 1 would produce 5-5 boxes on the average, while Chern estimated 4.3. Soi 1 s Soil depth is an important factor affecting the average yield of an orange tree since soil depth determines the size of the root system which is directly related to bearing surface (20). Citrus roots will not penetrate the hardpan found in some sections of Florida and they will riot grow below the highest level of the fluctuating water table (21). The root distribution of citrus planted in the coastal soils in Florida is often restricted to a rather shallow zone. Young (95, p. 52) in a 1953 study of citrus in the East Coast area of Florida found the principal root zone to be in the surface twelve inches with few roots below eighteen inches. The shallow water tables that hav2 persisted over long periods have seriously restricted root deve 1 oprrient and overSavage's coefficients were -.ased on the analysis of grove records of cooperating growers. If his sample included mostly better than average growers or if he did nor use proportional sampling from all areas of the stale, then his coe Ff i cients are not estimates of average yield for the entire state. Chern's source was the statistical Crop and Livestock Reporting Service, His coefficients are based on a 100 percent sample of the commercial groves in the state.

PAGE 54

kk Table if: Estimated average yield per tree by age and variety, Florida.

PAGE 55

all plant growth. Hunziknr {Ik) in a 1959 study found that the lowering of the water table in the Indian River area of Florida from 20 to kO inches doubled the quantity of feeder roots in four years and consequently increased the size of the trees. Koo et a 1 . (50) divided soils planted to citrus in Florida into two rnajor groups—we 1 1-drai ned and imperfectly to poorly drained soils. Sites and Hammond (79) reported that the rapid expansion of the Florida citrus industry between 1950 and I96O resulted in an almost complete utilization of all well-drained land suitable for citrus and noued that the water table fluctuates widely in the poorly drained soils. During the wet season 10-20 inch depths are common while 40-60 inches are generally expected in the dry season, Lawrence (55) divided Florida soils planted to citrus into four broad groups, 1) Flatwoods soils are the low, flat, pocrl/ drained area= normally underlaid with hardpan. These lands, although somewhat more fertile than the high pinelands, are usually considerably colder than the surrounding better drained soils. Groves are affected by a fluctuating water table (too wa t and then too dry) and frequently cold v;eather. The soils also require special preparation for oranges — e.g. ditching, bedding and other measures of watercontrol, 2) Low hammock soils are better than flatwoods soils for citrus but are often poorly drained and usually lack adequate air drainage, 3) HigH pinelands soils are usually light, we 1 1 -drai ned sands of low natural fertility which are found on higher elevations. They contain the largest expansion of citrus and are suitable for citrus only v.'i th cold protection through proper air drair.oge and close prcximi ty to lakes.

PAGE 56

k) High haniniock sells are best. The surface layer of this soil type is usually thicker and darker because of higher organic matter content. Since the bulk of Florida's orange acreage is located on the ridge section, Florida soils planted to citrus can be generally characterized as being of low fertility and moisture-holding capacity. Planting de nsity Dow (16) has noted that planting densities for all citrus has been steadily increasing. In 1951 new planting had an average of 72.0 trees per acre. By 196/ this average had increased to 103.0 for all citrus and to 110.0 for Early and HIdseason oranges, Koo et al . (50, p, 22) found that fruit production per tree varied little in the range of kS to 8^ trees per acre. However, they reported that yield per tree was reduced approximately thirty percent with 80 to 1 16 trees per acre. Variety and rootstock Harding and Sunday (27) reported that the quantity of Florida oranges vjas related to variety (micro) and to rootstock. Hodgson (31) reported size differences due to variety (micro) and rootstock, Koranic and Gardner (32), in a Florida study, found rough lemon rootstock to have a greater drought resistance than other rootstocks because of Its more extensive root system. Varietal (macro) differences in yield are shown in Tables 3 and k. Weather F 3_c t o r_3 The major components of weather, rainfall and teiTiOe ra ture , are discussed In this section. For levels of rainfall and temperature

PAGE 57

^7 that would be considered as normal the yield effect of these factors is probably due to their interaction effect on the level of soil moisture. Unusual levels of either variable may affect yield directly by damaging fruit and/or plant. Rainfal 1 Ziegler (96) indicated that total rainfall in Florida is sufficient for citrus production but that its distribution is often bad. Rains of 16 inches accompanying hurricanes have been experienced. Hurricanes are threats to Florida citrus. Significant crop reductions due to hurricanes occurred in 1926, '28, '^i, ' kk , ' hS , '^6, 'kj, 'i+8, 'kS, '50, '60 (68, p, 24). Such rains ere harmful becau-.e they supply more moisture than the sandy soils can hold and cause serious leaching of soluble nutrients through percolation. May to September is the rainy summer season and usually accounts for about two-thirds cf the precipitation in most sections of Flo'ida, During this period rainfall is generally sufficient for the needs of citrus trees. From October through April and occasionally through May or early June rainfall is often insufficient for the needs of the trees. The two periods in the annual growth cycle of the orange tree when it is most sensitive to soil moisture deficiency are in the early spring when the new flush of growth is tender and fruit is setting and in the late spring and early summer when the fruit is rapidly increasing in size. The most critical period is in the spring, particularly during the months of March, April, and May — especially if the rainfall was deficient the preceding fall (98, p. 92), Deficiency of soil moisture in May and June may limit fruit size. Shortage of rainfall during October and November is not critical unless the tree experiences sevsre wilting (98, p. 93).

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k3 Whenever the moisture content of a given soil is above its field capacity the excess gravitational water will percolate away. Usually an accumulation of greater than two and one-half inches within a few days will cause such percolation (51). Koo and Sites (5!) reported wide variations in water transpired by months. In a study of 15year-oid Marsh grapefruit trees on Lakeland fine sand average daily transpiration was estimated to be 3^.2 gallons per tree, Hovjever, in February, 1952, it soared to 53 gallons per tree per day. Because of the very low water holding capacities of most Florida soils, the distribution of rainfall is more important than the total amount (49, p, 2), Rainfalls of onetenth inch or less are of little use to citrus trees since the precipitated rnoisture evaporates from the soil surface without affecting soil m.oisture. Rainfalls of from one to three inches are ideal for Florida groves since the soil is wet deep enough to supply moisture over a long period. Heavier rains usually cause percolation. Koo and Sites (5!) reported that the quality of fruit is negatively correlated vjith total annual rainfall. Temperature Florida's freezes are produced by cold, dry polar air moving into the state from northern areas. During the initial Influx, winds are rather strong, and high and low ground locations may be equally cold. This is called cooling by advection. When a polar air mass renains over the state the wind becomes light to calm at nig'nt. The surface of the earth after sunset loses its heat to the very cold sky without a return by radiation; this is called radiational cooling. Under these conditions the surface of the soil soon becomes cooler than the Icv/er layer of the atmosphere; the air in contact with the soil begins

PAGE 59

^9 to lose heat to the soil by conduction. This cooling is confined to a relatively shallow surface layer of the air, the temperatures of which may drop to critical values while the air just a few feet above may remain much warmer. This is called temperature inversion. This accounts for the phenomenon of damaged citrus fruit and foliage at lower portions of a tree vjithout damage to the upper portions of a tree, or, damage decreasing as one goes up a slope (79. P. 8). Cold air is more dense than warm air. When the ground is sloping, gravity acts to move the thin layer of heavier cold air down the slope where it gathers in depressions or f rostpockets V'^hich become quite cold (79, p. n). Freezes are always general, not local, because t[iey result from large masses of air at subfreezing temperatures. Freezes usually have at least a three day duration in Florida. Ziegler and V.'clfe (98) describe the usual Florida freeze in the following nar.ner. Because the ai' is at the same temperature from top to bottom of the moving mass, there is a tendency for equal temperatures on high and low ground, at least on the first night of the freeze. The first night is usually cold and windy but rarely causes serious damage, although a possibility of damage exists with a period of calm shortly before sunrise which allows the air to stratify. Usually there is little warming of the air or trees during the second day as cold air continues to move south. During the second night the wind usually falls soon after sunset and the stratifying air msy reach dangerously low temperatures rather soon, especially in low areas. On the third day the w' nd usually shifts and begins to replace the cold air with warmer air from the ocean. Therefore, under the usual conditions oF

PAGE 60

o so freezes in Florida, the second and/or third nights are the more dangerous after the ground and trees have become cold and the wind has ceased. Freezes may occur in Florida any time from November 15 until March 15. The most severe damage results when an early winter freeze is followed by a period of warm weather sufficient to initiate new growth which in turn is followed by a second freeze in the same winter, Such a freeze occurred in the winter of l89if-95 and is still referred to as the "big freeze" or "great freeze." An early freeze in Decen^ber f 189^ defoliated the trees and fruit vjas fi'ozen but wood damage was slight. The weather was mild during Jan-jary and trees put out nev7 shoots and growers generally felt that their groves were in good shape. However, in a condition of tender growth, the trees were killed to the ground by a second freeze in early February, 1895. In January, 19'6, a freeze of several days' duration causeo loss f fruit and considerable itijury to the branches bi.it because there s no additional severe cold that winter the new growth in February following the freeze developed normally and the groves were essentially back to normal by summer. The freeze in the winter of 1957-58 was one of repeated cold waves interspersed wiih periods of sufficient length and vKirmth for renewal of growth. Damage was severe in many 1 areas. The meteorological events leading up to the freeze of December, 1962 were numerous and complex. In simplest terms, the air mass that This section was summarized fror.i Zieqler and Wolfe (qB, p. 8k87). o wa

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51 caused this freeze was a product of the stagnation of air over the snow-covered Arctic region during long winter nights. Its rapid movement from Canada to the Gulf Coast was due to an avenue of vigorous northwest to southeast air flov/ created by an intense Atlantic coast low pressure and and great high pressure ridge in the western United States, Temperatures fell on an average of 15~?0 F throughout peninsular Florida from 7 P.M. December 1 2 to 7 A.M. December 13 at a rather uniform rate of 1-2 F per hour. This was a classic advecticn freeze with effective radiative heat loss contributing very little to its severity. Record low temperatures were set at many stations throughout Florida and it was the coldest night of the century for high ground locations in the northern portion of the citrus belt and for the so-called "warm locations" in the heart of the ci trus bel t. Pact freezes have greatly reduced short-run orange supfjlies. Probably the most important factO'-s v
PAGE 62

52 dormant, and can never v-'ithstand temperatures as low as those tolerated by deciduous trees (5'0There are also wide variations in the cold hardiness a-iiOng orange varieties. Cooper (12) reported that these differences are explained in part by the minimum temperature at which dormancy is induced. Cooper (12, p. 83) in a study of the 1361-62 freeze on Va;eiicia oranges also noted that each freeze differs frora other ones in the same area in one or more respects. Trees once injured by cold are more susceptible to further cold damage and disease For severe! years thereafter (19). The complicated biophysical relationships which explain how temperatures, varieties, cultural practices, and the techr.olony cf freeze protection affect yields have not been studied and will not be a part of this research. Some "average" effects of these factors on yield will be assumed. The exact level of freezing temperatures seen.s to be critical. Hendershott (3C) reported that I:2af teniperaiures of 20 F and colder kills 100 percent cr ma Lure leaf tissue while temperatures in the rarige of 20-21 F can be expected to kill between 50 to 70 percent. At 22 F reading was found to kill only 5 percent and temperatures in the range of 23-2^+ F killed only ! percent. Cofrimercial growers tend to consider a hard freeze (one resulting in fruit loss and/or tree damage) to be characterized by temperatures of less than or equal to 26 F for four or more hours (57, p. kS) . Cooper (11) has stated that temperatures of 28-30 F will not harm trees or fruit. There are ac least two reasons v.'hy the I962 freeze was less damaging than if it had occurred several years earlier (19. P. 7). Groves were in the best nutritional condition in h* story and there

PAGE 63

53 was a capacity to use and process damaged fruit whicli did not exist a few years previously. Cold tenperaturts limit the northward expansion of the citrus belt and are the most adverse climatic factor with which the Florida grower must contend. Howevei", high temperatures may result in damage also. Reiatively high temperatures (in the 70' s) during December and January nay encourage growth and make trees m.ore easily injured by late cold weather. In March and April, high tempera tLires increase transpiration and if coupled with a lack of soil moisture can cause permat.ent wilting, V/hen such drought conditions (high temperature and ]ovi rainfall causing a deficiency in soil moisture) exist throucjri May, even if not serious enoi'gh for wilting, an excessively heavy "June Drop'' of Trui t is the usjal result. Warm weather duf-ing Cctobe;r^nd Novi;mb'T, particularly if niglits are warm and rainfai; ii above nor^.a! , usually result in reduced interna: ^vja i i ty and poor external color (58, p. 8,'). Manaqei-tnt an:!. Cultural Practices Past and presen-: management and cultural pracrlcss can affect a tree's yield in a given year. However, this pFienomenon has not been studied and Is not well understood. Certainly /ear-to-year variations in nutritional programs, pesticides and insecticides practices and irrigation capacity are capable of causing variation in yield. Hewever, whether or not yield data from commercial groves reflects a variability due to these factors depends on the yield response of these factors and the level of their inputs into the production process. The possibility exists that if commercial groves are managed at or near the opiima! level for such inpu'.s that production dati

PAGE 64

5^ from commercial groves will not reflect any variaLiillty due to sucli i nputs. N utr i tio n Bitters and Batchelor (k) reported that fruit size was related to: nutrition, spraying with growtfi regulators, moisture relatives, and to certain pesticides and insecticides. Hodgson (31) in a study including both Florida and California reported that size of fruit was related to nutrition, and to magnesium, zinc, copper, and manganese deficiencies, Harding and Sunday (27) reported a yield response to fertilizers. Koo, Reitz, and Sites (50) found that nitrogen was the only element directly related to fruit production in Florida, Jones and Enbleton (43) substantiated this finding in a California study. However, Lenz (5^) found that whi!e nitrogen '-\ad a beneficial effect on fruit-set, it had a deleterious effect on fruit quality if hig'i nitrogen rates remained in the soil at or near maturity, I rriqation In Florida trees can become dormant for either of two reasons, low temperature or lack of soil moisture (2). The greater the degree of dormancy the less the danger from a freeze of a given severity. Therefore an irrigation program, designed to reduce soil moisture in the winter months to induce donnancy can reduce the probability of freeze damage (kj) . Supplementing rainfall by irrigation has been practiced by Florida citrus growers for many years. Whether irrigation has benefited the grovjer in financial terms through increased fruit production' has not been firmly established (^7) , Savage (70) in a IQS^f article concluded from a survey of grove records accumulated over 21 seasons

PAGE 65

55 that it did not pay to irrigate the average grove in the manner irrigation vjas usually practiced. At that time most growers irrigated when trees showed signs of wilt. Koo (^7) reported that the effects of experimental irrigation on fruit production has been variable. He noted that Si tes e_t _aj_. (80) reported in I95I that irrigation resulted in lower production tvjo out of three years in several orange varieties. Huberty and Richards (33) reported that improper irrigation can reduce navel orange yields as much as 30 to kO percent. Higher yields due to irrigation were reported by Koo and Sites (50 and Ziegler (97) in later studies. Koo (^7) reported that a recent (1959-60 season through 1961-62 season) experiment indicated fruit production was increased substantially by irrigation. He noted that production v/as increased substantially by maintaining adequate soil moisture in the root zone when fruit was small. He found it nocessaiy to maintain soil moisture at greater than 65 percent field capacity between fruit set (February-March) and until the young fruit has reached 1 inch in diameter (June-July) (^8). Sandy soils with very low water-holding capacity make irrigation necessary and the unpredictable rainfall distribution makes irrigation timing important. The above studies indicate a possible change in yield due to improved irrigation and drainage practices over the range of the data used in this study. Reuss (68) in a recent study (I969) designed to estimate the costs of developing and continuing irrigation for citrus production, provided information on the effects of irrigation upon yields and upon economic returns. He used experimental plot data supplied by Koo ('17) for most of his analysis and concluded that irrigation was economically feasible.

PAGE 66

56 Genera] Models Su g gested by Other Researchers Numerous researchers have worked on the problems of forecasting yield and of estimating harvest size. A fevj of the representative models are briefly discussed in this section. Kuznets Kuznets (52) reported that the yield of a California orange tree was related to: 1. Number of entirely cloudy days (December 16-February 15) precedi ng bloom. 2. Average temperature (February 15-March 15). 3. Date of peak bloom. k. Average maximum temperature the /46-75th day after bloom. Kuznets and Jennings (53) in a California study, found that the following weather variables affected yield: 1. Average temperature in degree F (March 16-3'). 2. Date of peek bloom from March 23. 3. Number of entirely cloudy days, December 16-February 15, preceding bloom. k. Average temperature, February 16-March 18. 5. Date of peak bloom. 6. Average maximum temperature, if8-60th day after bloom, 7. Average maximum temperature, 61-75 days after bloom. Stout Stout (83) worked with the follov;ing model in a study designed to forecast the harvest size of Florida Valencia oranges. See bibliography section entitled "Additional Readings."

PAGE 67

Y = a + ZB.X. + e, I = 1 , 2,,,., 16 57 [8] where Y = April 1 average volume per fruit in cubic inches (i.e., harvest si ze) . X, = October 1 si ze. X, = Rainfall in inches (February 1 October 1). X, = Number of days no rain (February 1 October 1), Xr = Rainfall in inches (July 1 Occober 1). Xg = Number of days rainfall greater than .10 inches in July, August, and September. X^ = Number of days temperature greater than 90° F in July, August and September. Xo = July average temperature, X = August average temperature. Xj„ = September average temperature, X. , = East coast (0,1). X|2 = interior (0,1). Xj , = West coast (0,1) . X,^, = September to October state average growth rate less than 1.90 cubic inches (0,1), X, = September to October state average growth rate between 1.90 and 2.35 cubic inches (0,1), X,/= September to October state average growth rate greater than 2,35 cubic inches (0,1). After analysis of the -Jbove model Stout developed two equations

PAGE 68

58 each with five significant (at .05 level) variables, to predict the harvest size of Valenclas on October 1. Y = 28.81 + .070 X, + .100 X2 .055 X .260 X, + 1.926 X [9] where: Y = Predicted April 1 size on preceding October 1. X. = October 1 size squared. X_ = Total rainfall from July 1 to October 1. X_ = Number of days rainfall was ,10 or more inches from July 1 to October 1 , X, = Average August temperature. X = One if September to October state average rate of growth greater than 1,90 inches and less than 2.33 inches, ,-^ero otherwi se. Y = 20.51 + 1.2nx, + .OkSX .OkkX [10] 2 3 232X, + 2.1it0X^ 4 5 where ; Y = Same as equation L9li X = October 1 size. X„ = Total rainfall from February 1 to October 1 X = Same as equation TqU X, = Average September temperature, X = Same as equation [9]

PAGE 69

5S Others Hodgson (31) in a study including both Florida and California reported that size of fruit was related to adequacy of heat during the growing period, atmosphere, humidity, and time of bloom. Cooper (13) in a study of Florida, Texas, Arizona, and California concluded that soil moisture was the principle factor affecting size. Caprio et al . (8) in a study of California Valencia oranges concluded that size was a function of: temperatures in fall and early winter; date of bloom; cool temperatures in February and March; mean n.onthly temperatures and tem.perature departures from normal.' Beutei (5) found harvest size to be related to soil moisture and maximum daily summer temperature. Sites (78) reported that a dry period of tiirec months after fruit is set reduces size and subsequent irrioaiion will not recover it, Jamison (38) reported that the yieid of tne Washington nave] orange in California was significantly and directly related to the amount of heat during the growing season. However, Furr et a ] . (22) noted that high temperature is an important factor in causing abriormally heavy drop of fruit. Jones and Embleton ('43) found California orange production to be influenced by high temperatures in fruit-setting period. Jones and Cee found differences in yield due to maximum, temperature during the June drop period (^2) and to harvest time (41). Harding and Sunday (27) reported that the yield of Florida oranges was related to soil moisture, Haas (25). in a IS'+S study of Valencia orange in California, concluded that the date of blossom opening was primarily related to yield. Koo (^7) in research devoted to studying the effects of irrigation on yields of orange and grapefruit concluded cfiat optimal fruit produc-

PAGE 70

60 tion requires adequate soil moisture during the period January through June. Fur r et a1 . (22), studying the Washington navel and Valencia oranges in California, concluded that soil moisture depletion and high temperatures vjere related to fruit drop. Dhillon and Singh (14) concluded that fruit drop was primarily due to moisture stress. The Federal Trade Commission (18) in a study on the frozen concentrated orange juice industry after the December, 1962 freeze reported that the severity of a freeze was a function of: duration of low temperatures, the time of year, weather conditions before and after the freeze, surface winds, humidity, and recorded low temperature. They concluded that the recorded low temperature of the freeze was probably the best single indicator of the severity of the freeze. A Concluding Rema rk The many v.ieather variables related to the yield of orance trees point to the importance of a measure or a fe\-i m.easures v/hich could account for most of the yield variability due to weather. Hints that soil moisture is such a measure are scattered throughout the literature. Many researchers have noted that some measure of soil moisture conditions are related to the yield of orange trees. Oury (63) showed the usefulness of tne aridity index approach (either de Martonne's or Angtrom's) for explaining yield variation due to weather and suggested their use until more refined Indexes such as Thornthwai te ' s became operatio.ial . Knetsch (^to) demonstrated that a measure of available soil moisture as estimated from a moisture-balance computation of Koo recommended that growers attempt to maintain soil moisture of 70 percent of field capacity during the January-June period.

PAGE 71

61 daily rainfall and evapotranspi ration could be userul for explaining yield variation in Tennessee Valley corn. He estirnaLed daily evapotranspi ration by using Thorn thwai te ' s empirical forrriula. To calculate a measure of available soil moisture it is necessary that the following information be available: 1. Depth of soil to hard-pan or water table (root depth). 2. Soil moisture at field capacity. 3. Soil moisture at which plant growth and development is restricted (wilting point). k. Daily rainfall and temperature. Such information is not difficult to obtain for a given field experiment, Hov;ever, for this researcti effort (since the sampling unit was an entire county) the lack of such information at the county level presented considerable difficulties. Evaporation is a component of climate that is seldoni measured. The combined evaporation from the soil surface and transpiration from plants, called evapotranspi ?-at ion , represents the transport of water back from the earth to the atmosphere, the reverse of precipitation. One cannot tell whether a climate is moist or dry by knowing the precipitation alone. One must know whether precipitation is greater than or less than the water needed for evaporation and transpiration. The rate of evapotranspi rat i on depends on four things: climate, sci l-moi s ture supply, plant cover, and land management. Transpiration effectively prevents the plant surfaces that are exposed to sunlight from being overheated. Most plants require sunlight for grcvrh. The energy of the sun combines water and carbon dioxide in the liaves into foods, which are carr'ed to all parts of

PAGE 72

62 the plant for growth. This process, called photosynthesis, is most efficient when the leaf temperatures are between 85 and 90 F. A leaf exposed to direct sunlight would become much hotter if the energy of the sun were not disposed of in some way. Transpiration is a heat regulator, preventing temperature excesses in both plant and air. Atmosphere elements which influence transpiration are solar radiation, air temperature, wind, and atmospheric humidity. These factors are all interrelated and althoLigh solar radiation is the basic factor, temperature of the transpiring part is most closely related to the rate of transpiration and air temperature is correlated to the temperature of the transpiring pai t. The above section on evapotranspi rat ion was summarized from Thornthwai ce (90). See this reference for an empirical method for estimating evTpctranspi rati on.

PAGE 73

CHAPTER IV ANALYTICAL METHOD AND THE DATA The Mode] Estinia ted The mathema Liceil representation of the real world offered as a general theoretical model in equation f?!] represented an impossible estimation task due to the lack of information to specify such a di saggrega ti ve model and because of iiiad3qL;aie data to fit such a m-odel if specified. To abstract from the detail of the reai vjorld, trees whose yields v;ere assumed to respond similarly to the variables of equation [711 vjere Qfoupcd together. Additionally, the data available also placed constraints on the model estimated. The most disaggregated observational unit on which production data were reported were varieties (macro) by counties. Availabie production data did not permit classification by such micro units as rootstock, density of planting, or terrestrial locotion. Classification by variety (micro), age, rootstock, soil depth, and soil moisture capacity would have been desirable because yield differences exist among the various levels of all five factors and the various levels of each factor interact with weather. For example, fruit loss and tree damage due to freezing temperatures differ among varieties (m.icro) and some varieties (micro) are more drought resisS u p r a , p . 52. 63

PAGE 74

6^ tant than others. Young trees are more severely injured by a given low temperature than older trees. Differences in rootstock cause differences in the drought resistance of trees and the minimum tem2 perature at which dormancy is induced. Soil depth determines the size of the root structure which limits the bearing surface of the 3 tree. Soil moisture capacity fixes an upper limit on moisture reserves. As a consequence, the same amount of rainfall may cause different levels of wilting conditions depending on the soil moisture capacity of the soil in which the trees are rooted. While It would be possible to generate a set of time series data of the orange groves in the state of Florida in which the trees were classified by variety, age, rootstock, soil depth, and moisture capacity, such a data set would be useless 1'or estimation because production data could not be sub-divided in a like n^-jnner. The major factors for which observations have ceen recorded and which contribute to year to year variation In yield by county and variety (macro) are changes In tree numbers, age distribution of trees, and weather (8^). Cultural practices and nutritional programs may have varied over time. However, it is doubtful that significant differences in management existed between counties in any given year. By abstracting from the real v;orld by grouping trees by variety (macro) and by counties, equation |l7j may be represented as: Supra , p, 46. 2 Supra, p. i+5, 3c Supra , p , /f 3 , k See Table 9, p. 80.

PAGE 75

Vst = '^rs (^3f ^st' ^st• ^st^' '' = ^'••'^' s = 1,...,S; t = 1,...,T. 65 Dl] where : rst Tst Observed production in 90 pound boxes of r^h variety (macro) in s^^ county and t'-'^ year. = Set of variables which represent physical attributes of all the trees of r*^*^ variety in s*^^ county which affect production in the t^ year. Vst ^' ^®'°^ weather variables affecting the V^h variety's production in the s^^county and the t^^ year. Vst " ^®^ "^ cultural, nutritional, and technological variable affecting oroduction of r^^ variety in s^^ county and t*^*^ year. 'rst "^ Disturbance term which represents that portion of production of the r^^ variety in the s'^'^ county and t year which is not explained by the arguments Z, C, and G. th R is the number of varieties (macro), S the number of counties, and T the number of years. The variables and equations represented by the general equation [71! differ from the variables and equations represented by [ll]. For example, Y.'^ represents the yield of a single tree in t*^^ year while Y^^^ denotes the total production of all bearing trees of r^H variety (macro) in s^h county and t^" year. And while [7] includes a single yield function for each tree, equation [ll] represents a production function for each variety (macro) by county.

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66 As vj\th equation T^H, the rs^" function of CnH 'would not be separable. And, again because of a lack oF information and data, serious and insurmountable specification and estimation problems remain. if in year t, county s had 100 trees of the r^'^ variety and in year t + 10 had 1,000 trees of r variety, one would not expect the same level of a particular variable, such as 15 drought days, to bring forth the same change in Y expressed in boxes of fruit. This is to say tliat there is an interaction between the number of trees by age and the weather variables. And, even if information existed to specify the form of equation CilH.it would not be possible to estimate this stochastic function with the limited numiber of observations aval lable. As an approach to circumvent the need for estimating the interactions among Z . and C ^ the concept otexoected production and •' rst rst ' a two stage estimating procedure vias introduced. Expected production was specified as a conditional function of the number of trees and their age distribution given average levels of all other inputs including weather. Expected production was then used to remove a portion of the year-to-year variation In observed production and to estimate the percentage deviation of observed from expected production for each variety (macro) by counties. These estimates of percentage deviation of observed from expected production for each variety (macro) ^Similarly, there is an interaction among the number of trees by age and the variables in set G. Expected as used here is not the same concept as mathematical expectation. Rather the term expected production Is used to define production estimated by a synthesized average yield function to be defined later.

PAGE 77

67 and county were then expressed as a function of variables in the sets ^rst ^^'^ "^rst '" ^ linear single equation iv.ode]. The coefficients of this mode] represent the change in this deviation resulting from a one unit change in a variable from 0^^^ or G .. These coefficients do not depend on the number of trees. The tv/o-stage approach which was used in an attempt to circumvent the need for estimating interaction among weather variables and variables repressnting the number and age distribution of trees may be summarized as follows: Stage I: Average Production Equation A EY ^ rst ^s (^rst I ^s.' ^s.): •=''2' s=l,...,l8, [12] t=l ,...,20. EY = Expected production of r variety ins ' county and rst t^ year. Expected as used here is not to be confused with the concept of mathematical expectation (see Footnote 2, page 66). A . = Set of variables which describe the number of trees of r^" variety (macro) by age group, county and year. C = Set of mean values of weather variables effecting rs. varieties in s county production over all years, ,-th Specifically, the set A included 22 variables. Variable ] was the nurnber of trees k years of age, variable 2 was the number of trees 5 years of age, and so on. Finally variable 22 was the number of trees 25 years of age and older. The estimated coefficient for a particular variable was an estimate of the average yield for trees of that age.

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68 G = Set of mean values of cultural, nutritional, and techno logical variables affecting the production of r^" variety in s county over all years. There were two varieties (macro), 18 counties, and 20 years finally included in the analysis as will be described later. Stage I I : Weather Equation, ^st = "-.s (Cpst'^sf U'rst)' -1'2; s=l,...,l8; [13: t=l,,,.20. ''rst " ^^rst ^^^ defined in equation [||J) EY^ ^ (as defined in equation [12]) ^ -^rst ' Cp.^^ = Set of weather variables affecting production of r variety in the s^*"' county and t year. G . = Set of cultural, nutritional and other technological variables affecting production of r" variety in the s "^ county and t year. U' = Disturbance term which represents that portion of rst production of the r'-'' variety In the s^" county and t year which Is not explained by the arguments of A, C, and G. As indicated earlier there were two varieties (macro), 18 counties, and 20 years finally Included in the analysis. These dimensions v/i 1 I be discussed later. The major reaicon for expressing the dependent variable P^-j. as

PAGE 79

69 percentage deviation of observed from expected production was, as discussed earlier, to obtain a variable which was related to C ' rst and G but which did not depend on the number and aqe distribution rst ^ of trees in the county. The Data The Florida Crop and Livestock Reporting Service annually publishes county production figures in terms of boxes produced (72). Their report also describes the groves within each county in terms of total acres and number of trees by age group and variety (macro),. Two complete citrus inventories were conducted under their supervision in 1956 and I965 resulting in publications in 1957 and I9S6. Production and tree data were available from the 19^8-49 season to date. Daily weather observations for twenty-seven weather stations for the period July 1, 19'48 through June 30, I966 were purc^^ased from the National V/eather Records Csnter, Asheville, North Carolina. Add'tio-^ally, daily weather observations v.'ere hand-coded for the period July 1 1966 through December 3I, I968, County fertilizer consumption by fertilizer types has been published annually by the Inspection Division^ Department of Agriculture, State of Florida (35, 36). Table 5 indicates that data were available for 18 counties for the 20 seasons 19^+8-^^9 through I967-68 and for 13 counties for at least five seasons 1963-6^+ through I967-68. These data were coded and key punched as Y,.cr' Supra, p. 66.

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70 Table 5: Counties currently producing Florida oranges and seasons for which production data were available. Code County Seasons of available production data 1 2 3 k 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Zk 25 26 27 28 29 30 31 Brevard DeSoto Hardee Hi ghlands Hi 1 1 sborough I ndian Ri ver Lake Manatee Marion Orange Osceola Pasco Pinellas Polk Putnam St. Lucie Semi nole Vol us ia Broward Charlotte Ci trus Col 1 ier Glades Hendry Hernando Lee Marti n Okeeciiobee Palm Beach Sarasota Sumter 1948-'+9 ] 948-^9 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-49 1948-^:9 1948-49 19^:8-49 1948-49 1948-43 1948-49 1963-64 1963-64 1963-64 1948-49 1948-49 19^8-49 1963--64 1963-64 1948-49 1948-49 1963-64 through through through through through through through through through through through through through through tiirough through through through , 1963-64 , 1963-64 through ! through 1 through 1 1963-64 i963--64 through I through 1 through I 1963-64 1963-64 through 1 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 967-68 through through ]3t'/ 967-68 967-68 967-68 through I967-68 through I967-68 956-57, 1963-64 967-68 967-68 through 1967-63 1967-68 68 tnrough ]967'-68 h rough 967-68 1967-68 The numerical county codes will be used throughout this report.

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71 rst Observed production of r variety (macro) in s county and t year, r = 1 for Early and Midseason varieties. r =2 for Late varieties. s =1,2, , 31. t = 1,,.,, 20; the 19it8-^9 season was coded 1. th in certain seasons Temples were included with the Early and Midseason oranges but reported separately in other seasons. To make the data comparable in all season, Temples were Included with the Early and Midseason oranges. Information on orange trees was available by county, variety (macro), and age group categories. As with the production data, there were 18 counties with 20 years of available data and 13 ccuntie; for which data were available for five or more years, /^gain. Temples were included with Early and Midseason oranges, A major problem existed in the degree of aggregation of the age gro'.ip categories and In the different ways the trees were grouped. For the years 19^8 through 1956, data on tree numbers were grouped into age categories k through 5, 6 through 10, 11 through 15, and 16 and older. For 1957 and 1958 the age groups v;ere through 3, ^ through 9, 2nd 10 and older. For the period 1959 through I96I age group categories ware k through 9, and 10 and older. From I962 through 196^ the three age groups were through k, 5 through 9, •^nd 10 and older. A complete citrus inventory was conducted in I365. A matrix of tree data was generated with tvpical element a^_.^.. -' ' "^ rs Lj a ^. = Number of trees of r variety (macro) in s^" county. th . th t^n year, and j age group.

PAGE 82

72 r = 1,2. s = 1,..., 31. t = 1,..., 20. The year 19^8 was coded 1 and paired with production for 19^8-^9 season, j = k,..., 25, Age group 25 Included all trees 25 years old and older. For 1965 the citrus inventory was used to calculate a-et"* Sii.ce no severe weather existed in I966 or 19^7 to reduce the number of trees and since there was no reason to expect abandonment of groves during those two years, the a ..'s were generated for I966 and I967 by simply advancing the 19^5 census ahead one and two years. This was possible because the model only dealt with bearing trees (4-yearsold and older) and a twc-year-old tree in I965 for which data were available was four years old in 19b7. For the other years the a ^^-'s were generated by a simple bookkeeping procedure whereby the total number of trees reported in a given year and age group category was distributed according to the percentage in pi-oduction as reported by the 19^5 census. For example, If in 1964 the 5 through 9 age group category was reported to include 200 trees and the I965 census reported 10 six-year-o'd trees, 30 seven-year-old trees, 40 eight-year-old trees, 10 nine-year-old trees, and 10 ten-year-old trees; then the 200 trees were distributed 20, 60, 80, 20, 20 for age groups 5 through 9, respectively. Daily weacher observations were available for stations in 27 of the 31 counties studied (Table 6). Most of the oranges (over 93 percent during the period of study)

PAGE 83

73 Table 6; Weather stations and time interval for which data were avai lable. County

PAGE 84

74 were produced in the 18 county study area (Table 7). Since yield data were restricted to only a few years (5 In most cases) and since acceptable weather data could not be generated for the other I3 citrusproducing counties, they were omitted from the analysis. The citrus belt is shifting to the south and most of the deleted counties are in the new expansion area. For long-range forecasting one would like to be able to measure the effect of weather on orange production in these counties which will undoubtedly be providing a larger proportion of the crop. However, the limited number of observations frustrated attempts to use historical data to do so. Three counties, Indian River, Manatee, and Seminole required two stations to obtain a continuous weather record and one county, Osceola, did not have any weather observations beyond January, 1959. Therefore, a nearby station (Clermont) In an adjacent, county (Lake) was substituted for the period February, 1939 through June 1966. Missing observations in other data series (see Table 6) were estimated by the mean value of the weather variable for that day for the station involved. Daily weather observations were aggregated Into quarterly observations for the 18 stations for the period July 1, I966; through December 3I, 1968, to correspond with available production and tree data. The weather data consistently recorded by the stations were total daily rainfall, minimum daily temperature and maximum daily temperature. A critical v;eather variable (duration of freezing tempera -cure) was unobserved. The counties whicii made up the study area are the first elgFiteen listed in Table 5, page 70.

PAGE 85

75 i-i

PAGE 86

76 The three weather measures available (daily rainfall, minimum temperature, and maximum temperature) were used to synthesize observations on twenty-six v;eather variables (see Table 8) for each of the 18 stations used to represent county vjeather. These twenty-six weather variables are those proposed by earlier researchers. Those variables in Table 8 measuring soil moisture (3-10) and minimum temperature (11-16) were believed to be of primary importance in explaining yield variability due to vjeather. A typical element In the matrix of observation or weather varlabl es was vj„ . . stqn where: w . = Average monthly value of n~ weather variable in s^ stqn ^ ' 4.th th county, t year, anc q quarter. s

PAGE 87

77 Table 8: Specific v;eather variables used in study. Variable No. Description of variable 1. Degree days 2. Degree days (adjusted) 3. Number of days soil moisture less than wilt (Thornthwai te) k. Number of days soil moisture equal to zero (Thornthwai te) 5. Number of days soil moisture less than wilt (Harrison) 6. Number of days soil moisture equal to zero (Harrison) 7. Number of days soil moisture equal to 100% ( rhornthwai te) 8. Number of days soil moisture greater than 70/{, (Thornthwai te) 9. Number of days soil moisture equal to 100% (Harrison) 10. Number of days soil moisture greater chan 70% (Harrison) 11. Number of days minimum temperature less than or equal to 32 F 12. Number of days minimum temperature ^ess than or equal to 30 f" 13. Number of days minimum temperature less than or equal to 28 F 1^. Number of days minimum temperafjre less tha.T or equal to 26 F 15Number of days minimum temperature less than or equal to 2k F 16. Number of days minimum temperature less than or equal to 22 r 17. Average temperature 18. Average temperature (maximum) 19. Average temperature (minimum) 20. Total rainfall 21. Total rainfall (adjusted) 22. Land aridity index 23. Koppen aridity index (1) 2k. Koppen aridity index (2) 25. Koppen aridity index (3) 26. Angstrom aridity index ^Observations on these variables were computed from daily weather information on rainfall and temperature.

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78 referred to as degree days (adjusted) consisted of those heat units In the range of 55 F and 90 F. Variables 3 through 10 were calculated by using a bookkeeping procedure discussed by Harrison and Choate (37). Two estimates of each variables were calculated by using average daily evapotranspi ration as reported by Harrison and Choate and by calculating daily evapotranspi ration by the Thornthwaite method (90). The variable referred to as total rainfall (adjusted) was calculated by not considering any rainfall amounts in excess of the field capacity of the soil in the root zone. Variables 22-26 were generated by using the following standard formulas : Lang Aridity Index = P/T Koppen Aridity Index (1) = 8P/(13T+120) Kopper Aridity Index (2) = 2P/(T+33) Koppen Aridity Index (3) = P/(T+7) Angstrom Aridity Index = P/(1.07)^ Where P is rainfall measured In millimeters and T is temperature . ^ . , 1 in degrees centigrade. Calculation of these weather variables associated with the level of soil moisture required information on root depth, maximum water in root zone at field capacity, and vnlting point (percent soil moisture at which growth is seriously depressed). Such information was unavailable by counties. Derivation of such information from soil maps was considered. Hovjever, it would have been an enormous task to 'Supra, p. 28.

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79 compile county estimates of root depth, maximum water in root zone at field capacity, and wilting point from soil maps for a given year and to weight such estimates by the year-to-year changes in the distribution of trees within a county. Therefore, the information which was used (Table 9) was based on the opinion of experts with considerable experience in working with Florida soils. The data in Table 9 represent average county levels for root depth, maximum water in root 2 zone at field capacity, and usable soil moisture for all years included in this study. The aggregation of information on these variables into averages for a county resulted in some lo^s of variation. For example, if the average county root zone is kO inches but some groves v;ithin the county had only 10 inches of root depth then those groves might suffer severe wMting conditions which the information or the county averages would not reflect. There were two basic difficulties associated with the weather variables. First, there were no n;easures of the severity of low temperatures since the durations of the low tem.peratures were unk.nov;n. Secondly, there vjere no uniformly best measure of evapotranspi rat ion to include in the estimation of soil moisture. The average dally evapotranspi ration rates as reported by Harrison and Choate (Table 10) Dr. L. C, Hammond in consul tat ioii with Mr. R, G. Leighty and Mr. D. S. Harrison synthesized trie information in Table 9. These scientists are all with the University of Florida. Hammond and Leighty are Professors of Soils and Harrison is Professor of Agricultural Engineering. 2 information on these tliree variables permitted the calculation of wilting point as the differences betvjeen water in root zone at field capacity and usable '^oisture.

PAGE 90

80 Table S: Root depth, water in root zone at field capacity, and moisture available for plant use in soils by counties in the Florida citrus belt.

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81 measure only that portion of the variability in soil moisture associated with rainfall. Alternatively, the Thornthv.'ai te method allows for variation in soil moisture due to both rainfall and temperature but it tends to overestimate evapotranspi ration in the summer months (2b). The average daily evapotranspi rat ion of Florida citrus groves has been estimated by Harrison and Choate (37). Their estimates were based on historical average monthly temperature at Lake Alfred. Their results are reported below. Table lOi Average daily evapotranspi rat i on of Florida citrus groves. Month Average daily evapotranspi rat ion (inches of rainfall) January .08 February .08 March .10 April .11 May ,1^ June . 1 7 July .17 August .18 September . ] 7 October .13 November , 10 December .08 Source: Harrison and Choate (37, p. 3^0

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82 A data search was initiated to locate information on variables suitable to measure changes in levels of cultural and technological practices by counties. Such variables might include an index of irrigation capacity, an index of freeze protection, fertilizer utilization per tree or acre, and pesticide utilization. Only fertilizer use data were available. These data were collected and used as measures of a proxy or representative variable for cultural and technological factors. Fertilizer data were reported as fertilizer consumption by counties, but they were actually fertilizer sales by counties. The data did not specify that portion of a county's fertilizer sales applied to citrus. The mixed fertilizers and fertilizer materials in Tables 11 and 12 were commonly applied to citrus. These fertilizer analyses were used to estimate the amount of fertilizer being used en citrus. The typical element in the basic data matrix for fertilizer was ^stm w'^^''^^stm " consumption in tons of m type of fertilizer for *u th , . ,th the s county and t year. s =1,2, ..., 18 t = 1 , 2 , . . , , 20 m =1,2, ..., 5 1 = Total county consumption of mixed fertilizer, 2 = Total county consumption of those mixed fertilizers coded i n Tab 1 e 11. 3 = Total county consumption of nitrogen for those mixed fertilizers coded In Table il. k = Total county consumption of fertilizer material, 5 = Total county consumption of those fertilizer materials coded 1 n Table 1 2.

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83 Table 11: Mixed fertilizers commonly applied to citrus. P K 08-00-08 14-00-14 08-00-10 14-00-16 08-02-08 14-01-14 08-02-10 15-00-12 08-02-12 15-00-14 10-00-10 15-00-15 10-00-12 15-01-15 10-02-10 16-00-16 12-00-10 16-00-17 12-00-12 16-00-18 12-00-14 17-00-17 12-00-15 18-00-16 12-01-12 18-00-18 12-02-12 20-00-20 14-00-12 Source: Personal conversations with Mr, Larry K, Jackson, Instructor IFAS, Extension Service, University of Florida. Table 12: Fertilizer materials commonly applied to citrus, Ammoni urn Ni trate Nitrate of SodaPotash Nitrate of Potash Ni trogen Sol uti ons Muriate of Potash (50-60%) Sulfate of Potash-Magnesia Source: Personal conversations with Mr, Larry K. Jackson, Instructor, IFAS, Extension Service, University of Florida,

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8k The fertilizer data v/hich included fertilizer applied to all citr-js were adjusted by the percent of total citrus made up of oranges, The data were then expressed on a per tree basis. Since fertilizer programs are individual grower decisions the mixed fertilizers and fertilizer materials reported in Tables 11 and 12 do not represent all fertilizer applied to citrus. Specifically the mixed fertilizers O6-O6-O6, O8-O8-O8, and 10-10-10 were known to be applied to young groves. But these were omitted because they were also the dominant types used on lawns by homeowners. Other mixed fertilizers and fertilizer materials which were undoubtedly applied to citrus at least in some instances were also omitted. The Estimation Tec h niq ue For each county and each variety (macro) tv.'O equations v;ere estimated. The Stage I or average production equation expi'essed the average relationship between production and tree age. The Stage II equation was designed to explain the production variation due to weather and to cultural practice and technology. Since there vv/ere eighteen counties and tvjo varieties (macro) in the study and since the Stage I and Stage II equations viere estimated for each county-variety (macro) combination a total of thirty-six equations were estiniated. Stage I Bounds on estimates of the average yield per tree by age and variety (macro) K-jere available due to earlier vjork by the Florida 1 Crop and Livestock Reporting Service and by Savage, and Chern, I _Sug£a, pp. '43 snd ^'4.

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85 The Florida Crop and Livestock Reporting Service average yield estimates reported in "^able 3 indicate a range of ^.0 to 7-0 boxes per tree for Early and Midseason trees 25 years of age and older. Likewise, when the figures of Savage's and of Chern's (Table k) were compared, they also indicated a range for average yield per tree. Since these estimates were for the entire state they do not form rigid upper and lov^ier limits for average yield per tree on a county by county basis. However, they do provide information to enable one to specify the general form of the relationship between average yield and age, and within reasonable limits to enable one to fix upper and lov;er bounds on the average yield function. Estimates of the average yield per tree by age and by county were developed in Stage 1. Hopefully, the intercounty variation in pnysica! factors (such as soil depth, varieties (micro) and planting densities) which affecL production was accounted for in these estimates. The model assumes that such \-jbc the case. The equation estimated in Stage I was: A 25 ^Vst = jh ^j^st Cm: A 1 -^h EY = Expected production for the r '' variety (macro) rst th , , ,th in s county and t year. 4-1 4. 1 th X = Numbeiof trees of r variety in s county, t rstj year and j age. For j = 25, all trees 25 years and older were included. Not mathematical expectation (see footnote 2 page 66)

PAGE 96

B . = Average yield in s county for j age. Observations were not available on EY . Conceivably, an estirst mate of equation [14] could be obtained with least squares smoothing of the data on production and tree numbers by age. Equation [[14] has twenty-two coefficients and since only twenty observations were availI able, some grouping over age was required. Data on trees by age were grouped into two year groups and the data were smoothed by least squares regression, A prior information indicated that commercial production of an orange tree begins at three to four years of age, increases rapidly to ten years, levels 2 off and reaches a maximum at twenty-five years. The least squares estimates of the yield coefficients in many cases had older trees bearing less than younger trees and the regression estimates of yields in some cases were actually negative. To avoid these problems of negative coefficients and older trees producing less fruit than younger trees and to utilize other prior information an effort v\;as made to estimate yield coefficients with a linear programming model v;hich minimized the sum of the absolute 3 errors. Linear programming was selected due to the ease with which probable bounds on the estimated coefficients could be inccrporeted into the estimating procedure. First attempts at estimatirig by linear Tree data were grouped into two-year age categories so that only eleven coefficients were estimated as opposed to the twenf.y-two required in equation r|4j. Supra , p , / . "See Havlicek (23) for discussion of ine thodol ogy .

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87 programming were carried out with the constraints that B^; be greater than or equal to zero and that the B . , be greater than or equal to sj + l ^ ^ B . for j=l , 2.,., 10. This approach proved unsuccessful because for most counties the linear programming estimates of the coefficients set the first ten coefficients to zero and explained the variation in the dependent variable only as a function of the older trees. Next, additional constraints in the form of bounds which were based on the previous work of the Florida State Crop and Livestock Reporting Service, Savage , and Chern were placed on each of the coefficients. For example, a bound of k.O to 7.0 boxes per tree vjas placed on Early and Midseason orange trees twenty-four years of age and older. This technique tended to underestimate the yield of younger trees, overestimate the yield of older trees and failed to capture the be tween-coun ty variation in average yield knov.'n to exist. An ad hoc model was finally used to escim.ate the coefficients of equation C 1 4 J . The estimates of state average yield per tree by age 2 reported by Savage and by Chern ' were used as a base. Both ?r;ts of estimates were modified in tvvo \-jays. First, their estimates were shifted upward or downward by a constant amount over a reasonable range subject to the constraint that no coefficient could be negative. Secondly, the estimates of Savage and of CiSern were modified by multiplication by constants which varied over a range of one and a half boxes above and ba'ow the reported estimates. The estimated average yield parameters were then selected which Supra , p. k3 . ^See Table k, p. kk.

PAGE 98

minimized the sum of the absolute errors between actual and estimated production for each county. In over 95 percent of the cases, the estimates derived by adding a constant to Chern's estimates performed best. Therefore, the estimates derived by modifying Chern's estimates were used in all cases. These estimates of average yields which resulted are presented in tlic next chapter. Stage I I 1 The Stage II equation was estimated by multiple regression. Many admissible hypotheses existed for the specification of variables to include in the model. The final choice of variables was somewhat arbitrary in the sense that the specification provided a multiple choice hypothesis. For example, twenty-six A'saiher variables were 2 calculated for each quarter. If each we'-e lagged one year and the six minimum teitiperature variables were lagged an additional two years there were 220 possible explanatory variables available. Likewise, five fertilizer measures were available. If lagged effects of fertil izer applications were admitted, as is believed to be the case, the number of choices would be augmented again. Simple correlations, partial correlations, and step-dcwn regressions were used in the process of reducing the number of possible Supra , p. 68. SjJ2_r_a, p. 77. ^ Supra , p , 82.

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I regressors for equation Q|3]. For the weather variables, this initial process considered no lagged variables. Therefore ]0k weather variables were considered. The five fertilizer variables listed on page 82 were expressed in pounds utilized per orange tree. For the initial reduction process those five variables were considered plus each of the five lagged one, two, and three years. Therefore 20 fertilizer variables were initially considered in an effort to explain a portion 2 of the yield variability due to management and technology. Of the fertilizer variables considered, none was significant in explaining variation in deviations of actual from expected yields. These variables were finally removed from the model. For the weather variables, the initial reduction process was quite successful. Results indicated that seme measure of soil moisture should be included and that of the eight possible measures of soil moisture (four for the Thornthwaite procedure and four based on Harrison and Choate's average evapotranspi ration rates), the four The initial reduction process vvas not necessarily a systematic process and it certainly included a lot of judgmental decisions. In this process only three of the major producing counties were included-two fi^om the ridge section and one from the Indian Pxiver section. This initial reduction procedure was a very empirical process. The largest equations estimated by step-down regression required that a matrix of order 125 be inverted. At one point ^,500 simple correlation coefficients (125 for each variety (macro) — county combination) were calculated and searched for similar correlation patterns over counties. 2 Because this year's production might not be related to this year's fertilizer consumption but to the sum of fertilizer applications over the past several y aars ,addi t i onal combinations oF the fertilizer variables were also considered in other models. •^There were eight possible measures of soil moisture per quarter or thirty-t'wo per year, (Coded 3 through 10 en p. 77')

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90 based on Thornthv.'ai te ' s procedure appeared superior in explanatory power to Harrison and Choate's. The six available minimum temperature variables did not explain much of the psrcentage deviation of actual from expected yield which was due to freezing weather. By combining data over counties to avoid a degrees of freedom problem, step-down regression v;as used in an effort to explain the effect of freezes with the minimum temperature measures available. The explanatory variables in this model were quarterly measures of soil moisture conditions, six available minimum temperature variables, and the six minimum temperature variables lagged one, two, and thrae years. While this model did not isolate the particular temperature variable to be used to explain the yield variability due to freeze damage it did provide some information which allowed the reduction of the possible number of candidates. Specifically, this informacion indicated that the variable which measured the number of days the minimum temperature was less than cr equal to 30 F need no longer be considered as an explanatory variable. A variable which was lagged twice and which was formed as a weighted sum of the number of days the minimum temperature fell within certain temperature intervals performed most satisfactorily in explaining freeze damage. With this freeze variable and the knowledge that a measure of soil moisture based on the Thornthv/ai te emipirical method of estiniating evapotranspi ra tion explained more variation than other variables which' These variab'es were coded 11 through I6 on p. 77.

PAGE 101

91 were admissible candidates, the final process of specifying variables to include in the second stage model was to choose from among the four measures of soil moisture based on Thornt hwa i te ' s method. However, nom; of these measures was clearly superior in terms of explanatory power. The four Thornthwaite variables under discussion are listed as numbers 3, ^, 7, and 8 in Table 8. The same model was fitted for each of the eight largest producing counties for both varieties (macro). The estimating procedure vjas repeated four times, once for each of the four measures of soil moisture. Three of the variables still remained tied to terms of predictiv-a ability. The tie was broken by selecting the variable for v.hich the most temperature signs were consistent with prior knowledge. The final form of the Stage II equation was: Prst = ^sO ^ ^sl 'sU ^ \sl ^st2 ^ ^s3 'st3 ' ^s4 ^ti. -^ ^s5 ^t5 " ^s6 ^t6 " ^s7 ^t7 [151 II ^ ^st P ^ = Signed percentage deviation of actual production of the rSt J r J r r variety in the s^ county and the t year from its corresponding expected production. V ^ ; q = ],...,h Number of days soil moisture reached field stq M ' ' / th th ^ th 3 capacity in s county, t year, and q quarter. Supra, p. 77. 2 See p. 68 for formula by which Pgj-i, was calculated. 3 Number of day; based on a soil moisture budget technique (see van Bavel (92) for description of rr.eth.od) usir.q soil moisture information furnisined by Dr. L. C. Hammond (see Table 9, p. 80) and estimate evapotranspi rat ! on by the Thornthwaite method (90).

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92 = \<=-\/p] rif frfip^F' \/PirIphlp in c t-r-,init\i an/-) I-"" st5 y = Level of freeze variable in s county and t "" year. For Early and Midseason oranges only the fourth quarter of the first year of crop season was considered. For Valencia oranges the sum of the fourth quarter of the first year of the crop season and 2 the first quarter of the second year of the crop season was used, V ^ = Level of freeze variable for previous winter. Equivalent to V as defined for Valencia oranges lagged one year. V = Level of freeze variable for winter two years removed. st7 Equivalent to V ,r as defined for Valencia oranges lagged tvjo years. B .; j = ] , . . . ,7 . = Estimeted regression coefficients for th . ^ th , , .th . ^, r variety, s county, and j variable. U'' , = Disturbance term which accounts for variations in P not accounted for by the V's. Observations for the freeze variable were calculated by summing 1.0 times the number of days the minimum temperature was less than or equal to 26 F but greater than 2k F, 2.0 t'mes the number of days the minimum temperature v;as less than or equal to 2k F but greater than 22 F, and 3-0 times number of days the minimum temperature was less than or equal to 22 F. 2 For example, if the crop season was 195^-55, for Early and Midseason oranges only October, November, and December, 195^ vjere considered. For Valencia oranges October, November, December, 195^ plus January, February, and March, 1955 were considered. The first quarter of the second year of the crop season (January, February, and i^.arch, 1955 in this example) will be referred to as the fifth quarter of the season.

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93 The estimated coefficients for equation Cl53 are presented in the next, chapter. Model Assumptions Ideally, data for the estimating equation [I4j would have i n2 eluded only those seasons affected by "average" vveather or "equal" amounts of "good" and "bad" weather years plus the "average" weather years. The criterion for selecting the estimated coefficients of equation ^14^ for each of the 36 county-variety (macro) combinations was that of minimizing the sum of the absolute errors of actual from expected production. An alternative would have been to minimize the sum of the squared errors. This latter alternative would have given more v^eight to the extreme (unusually "good" or "bad" years) observations. Both procedures vjould give identical results under the assumption that the weather data available vjere symmetrically distribu^^ed about the average, Had the 20 years of dota used to estimate equation |[|4j been An iterative procedure was set up to iterate between the Stage I and Stage II equations in the hope of improving the estimates of both equations. The scheme was to change the estimates of the Stage I equation by addition or subtraction of a small delta or by multiplication by one plus or minus a small delta, recalculate the dependent variable for the Stage li equation and fit the Stage II equation again by Ordinary Least Squares. This procedure was contiriued until the sum of the squared errors of the Stage II equation vjas a minimum. An identical procedure was also used with the objective of minimizing the sum or the absolute errors of the Stage II equation. Both schemes failed to significantly improve the estimates (i.e., neither the sum of the squared errors nor the sum of the absolute errors was reduced significantly by the procedure). 2 These very general terms, good, bad, and average, a re used only in a descriptive manner and without precise definition.

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94 generated by 10 years of "good" weather and 10 years of "average" weather or 10 years of "bad" weather and 10 years of "average" weather then the average yield coefficients would have been biased in the corresponding direction. It was assumed that such an asymmetric distribution of "good" or "bad" years did not occur. The data provided no good basis for questioning the validity of this assumption. Equation |Il5lJ was estimated by classical least squares. The estimated coefficients are best linear unbiased estimators (BLUE) under the following assumptions: 1 . E(U" J for al 1 r, s, and t. ^ rst ' ' 2. E(U" U" ,v) =P^ 6tt" where 6tt" = 1 when t = t" ^ = otherwise. 3, The V's are fixed from sample to sample for every combination of r and s, or if variable, the conditional distribution of the U's giver a set of observations on the V's has the above properties. If the U's are normally distributed the least squares estimates are equivalent to maxi mum1 i kl i hood estimates. The assumption of normality is also required to use t and F tests (kh, p. 356). However, such conventional test procedures do not appear to be sensitive to departures from normality {hk, p. 356). Before dealing specifically with the assumptions we turn to a discussion of mul ti col 1 i near i ty. In the case when two explanatory variables are perfectly related the least sq:.:ares procedure breaks down. This seldom occurs with real world data. From an empirical poi nt-of-view it is usually more relevant to discuss mul ti col 1 i near! ty in terms of its severity

PAGE 105

95 than its existence or nonexistence. Severe cases of mul tied 1 i near i ty result in estimates that are sensitive to change in the mode I specification and that have large standard errors. Empirical estimates of the pairwise relationship among variables In equation []I5] are given by some representative simple correlation coefficients in Table 13. These estimates would support the notion that mul ti col 1 i neari ty was not a serious problem. Another problem to be considered is that of autocorrelation. Specification errors may cause autocorrel a ted disturbances. This creates some anxiety because, as mentioned earlier, an empirical model of the weather effect on orange production can never be completely specified in terms of variables and/or form. The Durbi n-Wa tson d1 statistic was calculated anJ tested for each of the thirty-six "fits" of equation lI53' '" '' o^ the 36 cases, the test would accept the hypothesis that the disturbance term was non-autocorre 1 ated . In the other 25 cases, the test was Inconclusive. In no case would the test lead to a rejection of the hypothesis that the disturbances were non2 autocorrel atcd. The assumption of homoscedas t i cl ty was not tested statistically. However, he teroscedas ti ci ty probably existed. For near average levels of soil moisture and temperature one could expect the variance of each U" j^ to be finite and homoscedas ti c. However, levels of soil moisture lov; enough tc kill the ti-ee would result in the yield and its variance falling tc zero. Likewise, levels of temperature low enough to kill Text values used for d, , d were (.?S, 2.k\) . L u \ > / 2 Ourb i n-WaCson ter>t assumes that u's am normal, homoscedas t i c , and non-autocorrel aled {kk, p. 367).

PAGE 106

96 Table 13: Simple correlation coefficients for the variables included in equation TlSHv^hen fitted to data for the Early and Midseason variety, by selected counties. County code Variable

PAGE 107

97 the tree would result in the yield and its variance falling to ?.ero. Such levels were observed. While too much soil moisture (field capacity for several days) can kill a tree, it is doubtful if such a condition has ever been serious enough in the citrus belt of Florida to be reflected by the data. The existence of he teroscedas t i ci ty does not prevent OLS (ordinary least squares) estimates from being unbiased. It does reduce the efficiency of the estimators. Classical linear regression assumes that variables are measured without error. Observations on weather conditions at a single point in each county were used to represent the weather experienced by the entire county. If the weather conditions recorded by the single weather station did not accurately describe the average weather experienced by the entire county errors of measurement were encountered. Even V'^hen the regressors oF equation Q|5^ were cons^ic'ered only as proxy variables for the conditions they represent it was doubtful if the relationship between the proxy variables and the weather conditions they represent was constant over the time period considered. When data were pooled across county lines the assumption of no measurement errors is questionable for tv^JO reasons, 1. The estimates of soil depth and water-holding capacity (Table 8, p. 77) probably vary in accuracy from county to county. 2. The location of weather stations varied between counties. Some stations were located on high ground, some on low ground. Some were located many miles Inland and a few were located right on the beaches. Consequerii 1 y , the estimated relationship betv;een production and a given level of a specific weather variable varied from county

PAGE 108

to county. For example, consider two identical counties subjected to identical weather. If one county has a high ground recording station but the other a low ground recording station the observations on a particular temperature variable collected by the two stations would not be identical. Likev;ise, consider two identical coastal counties subjected to identical weather. If one of the recording stations were located on the beach and the other 15-20 miles inland one would record considerably more rainfall than the other. Efforts were made to minimize these problems when the weather stations were selected. However, due to the small number of weather stations within each county v^i th long-running continuous records the effort was not always successful . Errors of observation on the regressors result in biased structural estimates. There was no objective basis for estimating the extent to which measurement errors may have biased the results presented in the next chapter. See Johnston {hO , p. 148), Goldberger (23, p. 28?.), and Steel and Torrie (82, p. (65).

PAGE 109

CHAPTER V RESULTS OF ANALYSIS Estimated Average Yields The estimates of average yield per tree by county, variety (macro) and age are presented in Tables ]k and ]5. Such information on difference in yield by such small geographic areas was previously unavailable. The constants which were added to Chern's coefficients to derive these average yield estimates are presented in Table 16. The estimates of the average yield coefficients were consistent with expectations. The deep soils of the ridce section tenced to outyield the shallower soils of the coastal and flatwoods areas. The estimated coefficients for Marlon and Seminole counties seemed somewhat inconsistent with expectations since in both cases they indicate that Early and Midseason oranges yielded less than the state average but Valencia oranges yielded more. However, both counties produce very few Valencia oranges, and consequently their average yield coefficients for Valencia oranges were probably over-estimated. It appears that the estimated coefficients for St. Lucie county are too high when compared with the other coastal counties. The data indicated that Hardee had the highest yields on the If the constant added to Chern's coefficients was 0.0, then the particular county would be producing at the state average, 99

PAGE 110

100 Table ]k: Estimated yields in boxes per tree of Florida Early and Midseason oranges (including Temples) by county and age.^

PAGE 111

Table 1^: Continued. 101

PAGE 112

102 Table 15: Estimated yields in boxes per tree of Florida Valencia oranges by county and age. Age County code 456

PAGE 113

Table 15: Continued, 103 10 .08 .28 .48 .68 .88 2.08 2.28 2.48 2.68 2.84 3.00 3.16 3.^2 3.48 3.64 3.80 97 15 33 52 70 0.41 0,61 0.81 .01 .21 .41 .61 .81 2.01 2.17 2.33 2.49 2.65 2.81 2,97 3 12 30 48 :> 3 3 3.66 3.85 4.03 0.32 0.52 0.72 0.92 .12 .32 .52 .72 .92 2.08 2.24 2,40 2,56 2.72 2.88 3.04 3.21 3.39 3.57 3.76 3.94 4.12 County code 13 14 15 •90 pound boxes0,34 0,54 0,74 0,94 1.14 1.34 1.54 1.74 1.94 2.10 2.26 2.42 2.^8 2.74 2.90 3.06 3.23 3.41 3.59 3.78 3.96 4,14 1.15 1.35 1.55 1.75 1.95 2.15 2.35 2.55 2,75 2,91 3.07 3.23 3.39 3.55 3.7! 3.87 4,04 4.22 4,40 4.59 4.77 4.95 0.16 0.36 0.56 0.76 0.96 16 36 56 76 92 2,05 2,24 2.40 2.56 2.72 2.88 3.05 3.23 3.41 3.60 3.78 3.96 16 0.53 0.73 0.93 1.13 1.33 1.53 73 93 13 29 45 2.61 2,77 2.93 3.09 3.25 3.42 3.60 3.78 3.97 4.15 4.33 17 .07 .27 .47 .67 .87 2.07 2.27 2.47 2.67 2,83 2.99 3.15 3.31 3.47 3.63 3.79 3.96 4.14 4.32 4.51 4.69 4.87 0.31 0.51 0.71 0.91 ,11 .31 .51 .71 .91 2.07 2.23 2.39 2.55 2.71 2.87 3.03 3.20 3.38 3-56 3.75 3.95 4,11

PAGE 114

10'+ Table 16: Signed constants added to Chern's state estimates of average yield per tree to estimate average yields by counties and orange variety (macro), ^

PAGE 115

105 average in the production of Early and Kidseason oranges and that Highlands county had the highest average for the production of Valencies, This result was probably due to the fact that these counties seldom experienced the more severe freezing temperatures experienced by the counties in the more northern portions of the ridge. The results indicated that Pinellas was the lowest yielding county on the average for the production of Early and Midseason oranges and that Brevard was the lowest yielding county en the average for the production of Valencias, In both cases the low yields were probably due to a combination of shallow soils and the frequency of low temperatures. Weather I ndexes The average yield estimate? were used in conjunction with data on tree numbers to obtain an estimate of production. The ratio of total production to expected production provides a binary comparison or index. The deviation of this index from 1.0 indicates the combined effect of all factors whose influence vjcs not measured in the estin'aticn of expected production. Since weather factors were a major influence in the deviation of actual from expected yield the index provides an estimate of a weather index. These indexes (see Tables 17, 18, and 19) indicate a considerable yearco-year variation. Weather Eq i iation s By Counties an d Variet ies (Ma cro) The estimated regression coefficients for the weather equation are summarized in Tables 20 and 21, Thirty-six equations were estimated

PAGE 116

106 . m — a 1o TO L.

PAGE 117

]07 — CTv — Oa~\0-:i--a"C^. — O— -ztOOOf^vD — r-~ LA — o^, -:t LA O o^ UA CO CO 0--, 'LA vX) f~^ ' LAOvo i^r^oo r~-^o rv~,Q^, -zf CM — jr^-jr^ <^ G^ 0"\vO O O O -} P^ vD r^ vD r^ r~-~ vO t^-' o^ LAO r^cTiOcsi^v^r^r^ (v^ r-^ ,3o-i co -3^n or-~-dr^-JocsJo-^cNico-3"CO C LAr~^— CT, cNo^^^^'-• 1^00 —coco-^ coo^o--r O O O -J-3" MD LA-4" O — 00 i>l CA C", a\ 00 CO ~0 — — OOvOOoAOAOO. <>J r-^r^\£)OtA 1^^ O cv' vD -d" vD — -:t — LA cn m LA, O CA r^ -d" 00 LA — — cnrAvO^^O"^\X)o^C^I(v~^0>^^-.CO — O^J" O CTlLACnJ" LA-^ '-AfAO LAO OvO OAcn— ocrioocricMrMuA— — ooA vncri-d-o^tNcNo — cnj-lajo^cncoco-^ O^COrA — CMCNJO-d"LAO' — rA' — COvDOJ'vD OLAr^OOO-\COOOO — O'-. 1 — OLACO — — 0^ — 00 O r^r^o — cOvOvD lalao^ — o r~-co LAOO rAo~\r-^r--— r-J o^covr; o LA-:3--dCT^a^O CTAOACOvDO^OOOJ-vO r--0 O Cvl o — rA-or-^COO lArALA — t~AO\£>vDOO CTi P^COOvOr^I^OO — O-JOOCvCN — fA csj rA-d" LTiv^ r^-co 0'^0 — cN tv-v.:^ lav£> r^co LA LA LA la LA LT, LA LA O O 'X) \-0 VO O v^ VD ^D I I I I I I I I I I i I I I I I I — CM rA Jt A vD r^ CO CT\ o — rvi en cr. o~\ a^ o"v c^ o^ (j\ cr\ o^

PAGE 118

108 Table 19: "Weather" indexes for orange production for counties in the study area by variety (macro), and by seasons, 195152 through 1967-68.^

PAGE 119

109 — -o Q. C — (D '>3 — E Io

PAGE 120

110 >>Q

PAGE 121

in ,

PAGE 122

112 vO

PAGE 123

113 CS — CVJ LA OO — vO OO O ^ — CNI o o — vD LA J" JCA O -:1vO LA LA
PAGE 124

cr> o CNI LTV O VD

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115 Only 19 equations had one or more estimated coefficients significant at the .05 level (t-test). However, of the 288 coefficients estimated (eight per equation) 1^+1 had t-values greater than 1.0. Disregarding the intercept, 130 of 252 (over 50 percent) had t-values In excess of I.O. Only two equations (Orange county for Early and Midseason oranges and Brevard county for Valencia oranges) had no coefficients with tvalues greater than 1.0. The signs of the coefficients for a particular variable (see the columns of Tables 20 and 21) behave quite erratically. However, some order does exist when counties are grouped by areas. Tables 22 and 23 sre presented to aid in the discussion of these estimates by areas. When only those estimates of Table 23 with absolute values for the t statistic in excess of 1.0 are considered, the directions of the relationships are as expected in a majority of the cases. E arly and Mi d season For Early and Midseason oranges B2 was estimated positive 1! times and negative only once indicating a positive marginal response to adequate soil m.oisture in the first quarter. Only four of the eighteen coefficients for the soil moisture variable in the second quarter (B,) had t-values in excess of 1.0. This result probably indicates that normal rainfall patterns supplemented by irrigation has provided enough soil m.oisture in the second quarter over the years covered by this study so that variation in the yields of Early in the remainder of this papei" reference to t-values in excess of 1.0 refers to absolute values in excess of 1.0,

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Table 22: Counties included in the study by areas 116 Area Counties Area 1 : East Coast 1 Brevard 6 I ndian Ri ver 16 St. Lucie 18 Volusia Area 2: V/est Coast 5 Hill sborough 8 Manatee 12 Pasco 13 Pinellas Area 3Lower interior Area k: Upper interior 2

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117 Table 23: Signs of estimated regression coefficients for Stage II equations by varieties (macro), areas, and counties.^ Early and Midseason Area County (including Temples) Valencia code'' code*^ b^ b^ b^ b b^ b-, bg b^ b b^ b b^ b b Varie ty1 1 00 + + 00 0000000 l.6 0000 + + + --00 + + + 1 16 0000 + + + 0000 + 00 1 18 +000--0000-02 5 2 8 2 12 2 13 3 2 3 3 3 4 k 7 ^ 9 k 10 k 11 k ]l* k 15 4 17 ^Zeros indicate that the t statistic had an absolute value less 1. '^Area code 1 = East Coast, 2 = West Coast, 3 = Lower Interior, k = Upper ! nter i or . ''See Table 5 (p. 70) for names of counties associated with each numbe'-. +

PAGE 128

1)8 and Midseason oranges was not significantly affected by variations in soi 1 moi sture. The expected sign for the coefficients of the soil moisture variable in the third and fourth quarters was negative, V/hi le more estimates were negative than positive in both quarters, the results were inconclusive. Estimates for the variable measuring the freeze effect in the current year (Bg) appears at first glance to be reversed with eight positive and four negative. However, during the years covered in this study, only two major freezes occurred and both came after all or the majority of the Early and Midseason oranges had been harvested. The positive signs could have resulted for two reasons. First, the freezing temperatures were experienced after harvest in which case the coefficients measure a relationship which did not exist. Second, in the case of the more southern counties (note that all three counties of the lower interior section indicated a positive response) the low temperatures probably existed for only a few minutes shortly before sunrise and were not sustained for the length of time necessary to cause damage. The positive estimates of Brshould certainly not be interpreted to mean that if a freeze occurred in October or November it would have a positive effect on the current crop. It should be pointed out that the four negative estimates occurred in the northern counties of Volusia, Pinellas, Marion, and Putnam. These estimates 'would come closer to describing the true relationship between freezing temperatures and currant production since these counties probably experience low temperatures of sufficient duration tc cause damage to the current crop.

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119 The results indicated by estimates Bt and Bn ^re quite clear. Freezing temperatures have a negative effect on the production of Early and Midseason oranges for at least two years after the freeze. Of the seven signs which were positive, four occurred in the southern counties of Indian River and St. Lucie where most of the minimum temperatures observed probably existed for only a few minutes. In such cases one would not expect a negative lagged effect. Valenci a For Valencia oranges the results were approximately the same. The estimates of B„ indicate a positive marginal response to adequate soil moisture in the first quarter with eight positive and only one negative. As with Early and Midseason oranges the results indicated by the estimates of B, were inconclusive with four positive and two negative. Again, this would seem to indicate that during the second quarter normal rainfall patterns supplemented with irrigaiiion provided sufficient soil moisture so that fruit production was not significantly affected by variations in soil moisture. As expected the results indicated a negative marginal response to the soil moisture variable in the third quarter with six negative and only one positive. However, the fact that eleven of the eighteen estimates had t-va!ucs which were less than 1.0 only provides a basis for conjecture and not for substantive argument. The expected sign for B^. was negative. However, five /.ere positive and two were negative. This seemingly inconsistent result may be traceable to a confounding of temperature -• soil moisture effects. The results indicated by the estimates of B/, B-,, and Bo were as expected. The production of Valencia oranges was negatively

PAGE 130

120 related to freezing temperatures in the current season and for at least two lagged seasons. The six estimates which were positive were all in the southern counties of Indian River, St. Lucie, Hardee and Highlands where the minimum temperature observed probably did not exist long enough for serious damage. To reduce the difficulties associated with presenting the results of weather equations the following three terms were defined. Actual production denotes reported production. Expected production refers to estimated average production from Stage I of the model, it is based on tree numbers by age and estimated average yisSld, Estimated production refers to production estimated wi i;h the additional information from Stage 11. It i s the estimcted value of actual production and is based on expected or estimated average production adjusted for weather. For ex?^mple, if the expected production for a given county was 2Q0 units and che predicted signed percentage deviation of expected from actual production was -.10 then the estimated production would be 180 units. Actual and estimated production figures are reported in Tables 2k and 25 for counties and in Table 26 for the study area. Expected (estimated average) production are also included in these later tables for purposes of comiparison. The forecasting ability of the estimating procedure is expressed in terms of percent error in Tables 27 and 28. As expected, the addition of Stage 11 and the available weather information helped to explain more of the variation in production by variety (macro) and county.

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29 ^ OCOCO — \Croc^r«->cv)-tr-.0 — O\0j" •X) — i-A CX3 m OO o> ro -:i-:f -:}• CT, O -:t -T rA -:f CM Csl CV4 CN est CNJ 04 CN CSi CM — CM CM i-vl CV-> CM X)vD-4" d" CTi CMCMC^JCMCMCM — CMCMOOOO — CMCMC*'!. — . — cNj-ur\CNifv^cou~v^— . — v£)CNi d" — ^•^ rOLAOO CTiOO r^vr-— — LAP--. ^"OO r-^00 r--JJ4J .4-d" r^ (v-( cN c^ ( .-v 3" 00 CM u-\ vI3 \0 ^ -Jvo o a-v ija fJ J" sO ^o LA o CM ra o a^ o r^ -d" o ' — o o^ o CA rri csi LA vc CO CM — r~~ r~. J--TvOi-ALA-:l"-d'-d"-d'rAv£)— r<^LAOu^ vo— ^or — d"coLAv£)cr\vDO(:)OCMo"i' — '-^-^ CM r^ cr\ c^ CM r-~^ O O <.M UA •— ^ c^ ra CM r-~ -:fCO CTv' :d" rAl^rAracv^O-d" CJ\0 CA-J'vO r<^rA(v-vj-^\£)_j(J^cOCO O LA4l^O cr^u^ -I o oor — :}" cnt^LAOO-a-dr^ro^ c^Jcococo v£) r«-^ vo en (^ 00 CM CO \D CM o .~r~-. CO -d" -T — O CM-CfOCO lA — OOO UA r-^O O — O -sO Cv| c^cArot^f^vX) LAvOvO r^oo o~\vX) r-~.o O — CX3m-:fr-~.criOOOv£>vDCMr~--CMoALAO d" u-\ CM CM — c^j r~lA o CO CO en -J" la co o f^-» oa LAOCOO~\<"At^.a'vvX)CnLACO' — O-d"-!"^ LA CA PA (A r>A vD vO LA C» 00 r-O -'t LA r-~\0 O 1-A — CM l>A _iLr\ \£> ^^ CO 0^ O — C>l OA -T" ^'\ ^O r-^ LA LA LA I A U^ '-A -A lA U\ v.o vO VO ^£> ^ ».0 VO VD c, m g^. cj^ o-. o^ o\ o\

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130 OO i-rvr~-v£)vD-d" O LACN cr\^ CVIOO CT\ CO LA — UPlOaiC^ LAj-OLACM-d" O LAMD-3"CO-:l-CM LTvr-^o o^o o o r^vo-d" LnrocTir^cnO-:!" (N C>J CN . — oocPir^r^cNi — ^-cNio^-aDOOcOMDOLn-J" i-rvCnCTit^^vDCO OCO LPv' — rovXlJr^M3vO rr\ LnrMOcMj-r--j-^o c^ooLnoo lao ocxd CM rr\ cr\ r^ c^\0 UAO^r^Oi^D — -:tOO CPiO r^ r<~iCO~-tCOr^r~~' itCTiOraOcnO — o-df^-\LA\OI^COG^-J"0"^'-£)vJ30COOOsl — OO Ld c-~! csi rsi cNi csj cs i" J-3" LTV — r-1 — en CO CO en u-\ — . — 00 r-^ -zl" v£) CM o: upi — cv-, r-~oj o cm co UACO r^vDOO LA — ' — f^OO' — LA — O^O U'\LA OACMJ-CMCMvO^.OOOOOa"lLAOLACOr^CM\Xl OCXDLAOO OOMDLAj-OO-d-OvOLAOO CMr-^O^L(^rACsluAOOCNJOOOv£) — ^•rALAO'-i O^CMvD-:fOOCMOoALACMCMvX)CMvOr^^LA OA -d" -:t -4" -:}• LA rA -:t -:! u\\X> c^ oa o.-^ la ca la LAr^t^-J-ooo — LAr^LAcoocM — oa^-T CXJLAvOCMO-d^rACMOa^CM-j-CPvvDOr^vD cr\ — -3^LAC»r~-^o^LA — o—cocsir^^ooo fA-5--d--:j-J--:tJ'-3"-:}" lavO laoa-J" -alavX) en — — LA— '— oAcocMvo^D-^tnocMocovo CM LA -4' r^ c^ cNi — 00 vo r^ r<-i r^ a"v cc c . • — la oolacmj-cM(v>(-aolao-4 o-5"oocna^ LA-Ct" lAvLALALAf^-d" LA-:}LAC-J rAj" rAU-\CM CMoA^LAvXir^COO^O — CslOA.:}-LA\£)r^CO LALALALALALALAU"\OMJVDvC^MDv£)vOv£) I I I I I I I I I I I I I I I I I — CMrAj-LP. vOf^OOCT^O' — CMrA_-} LAvOr»U> LA LA LTi LA Lr'i UA LA LA »-0 VD VD MD O VO VD vjO (7^ o^ o~\ Oi o^ en a\ o^ en cTi c~\ en cr\ m cr> en o^

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131 — CV-ifV-jJUAJ-0OCX30O — — LTvCriCO (Tiv£) CM v0-:l"r^vi)^D1^00C0O-:}'Crir<-\' j-c-J — o -d" LAf^i— vT) LTvLACO — VD LACXICO (T^Lr^— r^ Ja^L^^^o rr\\D oo ^ CO r^t>A-Jo^-nD OvDOO -:l"0OvOfMCMMD r^LACN LAOAC^LAMD CTii-AO CnOO — — CM CM r^CTiO r^f'-JCO (J\— (>-\vX) i-A 03-4 r--~ r^ -^ vri CM CO (X) -4vo o o> o~, fM ^ Lr\— oo-d" O' — — CO cr\i"^<^r-^r-~-i-r\vD cmmd CO — CM Lf\ c» LA 00 ^ CO o'^ -J" CO LA r-o u-\ en O^OOOO — OOCOCT^ CA-dJJai vDLAr^— vX)0;^--Ola--^cv1-4"LA-4 C'-tv£i rO^ — oA csi (M LA xi LA r^ -:!" — r^ CC' CO la ltv OOCX)OA~"t OCM cv-iO^LALP, — — O^COOC LACT* ooocMo — o^r-^ooor^-^-ooooovDCO-cf" COLAOOvO^-d-O^Or--V-OOCOO^CNIr'^LA O^ — CTi vn r--~ — O LC\ — MD vO "vO CO l^^ CM O vO r~-coocx3COr-^cOMDr^\Dr-~ cMCMLALAo'^ r^i — LACMrAQ>|LAr^— CSI. — CM0CC>JOCJ~vO CM LALT, CnCvlJ-J-JrnCXJCMCSl.::— LALAt^ CO cX) CX) CO o^ r^ CO r^ r-. r^ CO ^ oa c^i u-x la u-\ (J\ — OvDcAOO — lavdcolaooo. — r^ CsICO CPiLA^ LAO CTi-i" r^-r|-COMD oA — ^£ICO (j\r^ooc»r-^vX)i — comdo cM-i-r^cv, CMOA-4"LAvOr^CX)<;^0 — CMCA.J-LAvOf^0O LALTxLALALALALAUAVOvDvOvOvXJV^JvOMDVO I I I I I I I I i I I I I I I I I .— cMo~iJ-LAvi3r--cOcr>0 — cMr.-,,:}LAvDr^ LA LA U> LA U~l LA LA LA LA v£> O VO V-O ^X) ^O VD ^ CT^a^CT^c^^cAa^cJ^o^c^lcnfT^c^lC3^.
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32 -3"i^vDv£ivor^oo--tooocMr-^ — a>J' CNJroO' — r^ — 00 r--.co CnOr^vOr-^CO — CMcTvCOCTi— i-AI^CNI-dr-^ vD — CTvCOvDJ" oor^CO LAr'-iv£)vD CN O \0 CO OCO — cMCMOOvir-j-a-p^oorALPv^LAaD-d' CTi . — O OA CPi c^i O r'> 00 r^ vO '--i' oo la CO OA ^ JJ_iu-\ >,0 vO LA ••-O 00 O r^ V.O MD VO vO 0-:}-C>lr--OvDOl^Cr, OO^cs-OOJ-OJvO vT) oo 00 o^ -d" r^CQ .-vi o r--~ — -d" uj — .-v^ o -d" -T ro LA -4" W\kO rA -d" V.O vO 0~\ ("A i-A u'^ j,-^ cA LAO~\VOO — cnvOONOoA — vDOO— CXDiALA CO CO r-^ CNI o^ -^ ~"t CSi CO c^i rA 0^ — vO r~^ Lr\ j— — ^AC^^^A-d-v£l^-^voc^^'~^oo^^r^ — d"coo ^. , — , — — , — , — , — — — cslCM — Cv4CNIrA vO O^ O CO -d" CC' LA C^J — LA -4" v£) LA — J-4 -j— CN^J-LAVOLALf^-4'\£)OCMCMa^CO-J"' — o CM CM rAoAcA-4'vDMDvOOO r-^r^cocOJ' r^O _,-,— ,— _ — ^„__^__-„„_cslcvlrA Cr. -4" — LA O — CA— — \iDM3COO~\v£>cvJOfAr-^-4"-4'OA , — , — , — , — . — , — , — , — , — — CM CM C\l — CM C^J (A CM0Aj-LA\X)f^C0cr\O' — CM0A-4"LAvX)r^0C lA LA LA U^V LA L'\ LA LA VO v£) ^£! VO V£> VO VO VD VO I I i I I I I I ) i I I I I I I I — C~4rA-d-LAvri|~~~COo^O — CMCA-S'LAMDrLA LA LA LA LA LA LA LA LA s£) VD VO vO v.O VO VD O ij^, a\ c^ CTi CT\ o\ (T\ a^ (j^ cr\ o^ iT\ (T\ cT\
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133 Table 26: Total actual and estimated production of Florida oranges for the study area by variety (macro) 1951-52 through 1967-68 (in thousands of boxes). ^

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134 Table 27: Total actual and estimated production of Florida Early and Midseasori oranges (including Temples) for the study area with percent errors when actual production is estimated by Stages I and I I , by seasons 1951-52 through I967-68 (in thousands of boxes). Production Actual Estimated Percent error Season Stage 1 Stage I I Stage I Stage I i 1951-52 1952-53 1953-54 1954-55 1955-56 1956-57 1957-58 1958-59 1959-60 1960-61 1961-62 1962-63 1963-64 1964-65 1965-66 1966-67 1967-68 41,339 39,882 48,309 50,553 50,357 52,984 51,697 46 , 243 48,093 50,008 55,624 44,345 26,947 44,884 49.832 75,375 53,636 41,797 43,973 46,515 47,685 43,690 49,890 46,934 48,315 44,764 49,823 52,011 48,252 39,852 33,646 58,134 62,121 66,178 39,716 43,647 48,617 46,951 50,740 51,833 48,811 46,768 46.701 51,776 57,374 45,802 42,191 41 ,900 56,997 65,074 57,464 01

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135 Table 28: Total actual and estimated production of Florida Valencia oranges for the study area v.'i th percent errors when actual production is estimated by Stages I and 1 I , by seasons 1951-52 through I967-68 (in thousands of boxes).

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136 By Groups of Coiinties and Variety (Macr o) The estimates (particularly their signs) presented in Tables 20 and 21 indicate considerable unexplained variability betvjeen counties. The data were pooled across counties in an attempt to obtain estimates of the structural relationship between production and v;eather consistent vjith a priori expectations based on what is known about the effect of weather on orange supplies. The pooling of data across counties made it possible to include more variables in the model. Other measures of soil moisture were included with the idea that perhaps two soil moisture vari ables-one to mieasure positive response such as number of days soil moisture was greater than or equal to 70 or 100 percent of field capacity, and one to measure negative response such as number of days the level of soil moisture was less than the wilting point but greater thsri zero might be included in the model for each quarter. The possibility tliat some soil moisture variable for the fifth quarter of the growing season might be significantly related to the production of Valencies was also Investigated, Likewise, the single freeze variable used as a regressor in equation [ 1 5 J was expanded in an effort to obtain more consistent estimates of the relationship between production and freezes of varying severities. The freeze variable used as a regressor in equation Cl5] had been "arbitrarily" formed as a weighted sum of the number of days the minimum temperature was less than or equal to 26 F but greater than 2^ F, les::. than or equal to 2k F but greater than 22 F, and less than or equal to 22 F, in the expanded equation a separate coefficient for each of the three levels of freeze severity was i nc ! uded.

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137 To explore these possibilities ordinary least squares was used to fit the fojlovjing model for Valencias only, using Valencia data of the 18 counties. ^2st " -^^^^ "^ .OOOSVj .OO3IV2 + .OOISV^ .0002V^ (0.^03) (0.199) (0.83^) (0.6U0 (0.113) + .01 17V, + .0036V, .00I7V-, .0008Vq + .0005V„ 5 6 / o y (2.508) (0.598) (0,516) (0.31^) (0,301) .OlOOVjQ + .0038V J J .027^V,2 . 0097V, ^ (1.558) (0.653) (1.079) (O.362) + .OO3OV,,. .00^9V,, + .0018V,, + . 0006V, ^ [161 I H 15 Id 17 (0.123) (0.792) (l.liiS) (0.135) + . 0007V, g + . 0033V, + .OCO6V2Q + .OOO6V2, (O.IOI) (0.8^1) (0.435) (0.027) .026OV22 .3032V 23 + .0I26V2^ .0\^Gy (0.600) (5.866) (6.152) (0.336) .20if5V25 + .OO76V27 + .OI30V2g .0226V2g R = .35 (i+.02'+) (3.679) (0,117) (O.i+02) P = signed percentage deviation of actual production of Valencia 2st oranges in the s county and the t year from corresponding The estimated coefficients will be referred to as subscripted s. For example, the estimated coefflcietit for V2-7 will be referred to as B^-,. Numbers in parentheses are t-values

PAGE 148

38 expected of estimated average production. There were 306 observations-1 8 counties and 17 years. v., j=l,...,5 = number of days soil moisture was less than or equal to wilting point in j quarter of season. Vji j=6,...,10 number of days soil moisture was equal to zero in (j~5) quarter of season. Vj , j=ll,...,15 number of days soil moisture equal to field capacity in (j-10) quarter of season. V; , j = l6,...,20 = number of days soil moisture was greater than or equal to 70 percent of field capacity in (j-15) quarter of season. th v.,. = number of days mlMimurn tenipeta ture was greater than 2A f b'-'t less than or equal to 26 F during winter of growing season. V „ = number of days minimum temperature was greater than 22 F but less than or equal to 2k F during winter of growing season. V„_ = number of days minimum temperature was less than or equal to 22 F during winter of grovnng season. hk = 'li ^23 25 22 \/„/= \l „^ lagged one season, 26 23 Winter of growing season would include ^th and 5th quarters for Valenc ! as.

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139 V V lagged one season. V»o = V lagged two seasons. V-q = V_. lagged tv\/o seasons. The most surprising result f rom estimati ng equation Ci6l]v>jas that the estimated coefficient for V_, (number of days minimum temperature was greater than 2k F but less than or equal to 26 F) was not significant and had a smaller t-value than ar.y of the other variables. This result may reflect growers' use of freeze protection devices to the extent that temperatures were raised above the critical level in the groves. A second explanation is offered by the nature of the weather observation. Under normal conditions the temperature usually falls 3 to 4 F for 30 to ^fO minutes around sunrise. Consequently, one might observe a minim.um Lemperature in the --ange of 2k to 26 F when, in fact, the temperature w^as experienced for such a brief period that it had no effect on the trees or was beneficial. Such temperatures under normal conditions would exist only fora short time, rather than for the four hours required to do serious damage. The squared terms, V„, , Vj-,, and Vjq, were placed in the model because resu'ts of the simple linear model (equation []l5!])hed consistently overestimated production in the freeze years. However, the coefficients of these variables were inconsistent in sign (positive) in two cases and the one negative coefficient v;as not This brief exposure to cold might help condition the tree against future damage by inducing dormancy.

PAGE 150

significantly different from zero. The signs of the coefficients of the other freeze variables were as expected, except for B ^. 28 Of the soil moisture variables considered the ones which measured the number of days soil moisture was greater than or equal to 70 percent of field capacity had estimated coefficients which were all positive. While not exactly consistent with prior expectations, the estimated coefficients could be rationalized. Due to signs which were inconsistent with expectations, efforts to include two soil moisture variables for each quarter, one to measure a positive response and one to measure a negative response, v;ere abandoned. Based on the information obtained from estimating equation [_\6^ another model was formulated and estimated by OLS for Valencies only. The emphasis was on estimating the interactions among adequate soil moisture and freezing temperatures In the winter months. Seventeen variables were included in the model. P = ,0823 + .00i7V . + .0053V .0020V (1.396) (1.982) (1,819) (0.571) + .OOlSVjQ .0022V2Q (0.73'4) (2.566) Adequate soil moisture stimulates growth. Hov.'ever, too much soil moisture when the fruit is nearing maturity (winter months) may prohibit it frc^ reaching legal maturity standards and will increase freeze damage >. 83j. Levels of soil moisture in the winter months which do not keep the fruit from maturity and not accompanied by low temperatures could account for the signs of all the estimated coefficients being positive.

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]li] .OI38V22 .35^3V23 + .0]2k\J^^^ (0.330) (1.177) (5.2Mf) + ,0261V2^ .265^V2^ + .OO8IV27 [17] (0.590) (0,850) (3.526) .0981 v^g + .0275V29 + .ooosv^Q (1.142) (0.641) (0.159) .0007V,] + .0143V, 2 + .0004V,, (0.200) (1.127) (0.103) R^ = .29 The variables In this equation have the same meaning as they do in equation [l6j> except: V,Q = interaction between V^^ and V. V,, = interaction between V and V2Q V-„ V-^ laqued one season 32 30 V = V . lagged one season The interaction terms V_^, V,,, V,p and V were included because soil moisture tends to stimulate growth and deter dormancy during the winter months, thereby making the trees more susceptible to freezing temperatures. However, the signs of the estimated coef f i c i er.ts for interaction terms were inconsistent (positive) with a priori knowledge. The signs of the soil moisture variables became negative for the 3''d and 5th quarter. The effect of these variables may have been confounded with the interaction terms. The estin^ates of the coefficients for the squared temperature terms remained positive. This result wouid indicate that over the years studied some freezes that lasted fewer days than others actually did more damage. Some

PAGE 152

1^2 of the temperature variables reversed themselves and became positive, A problem of mul ti col 1 i near i ty betvjeen the soil moisture variables for the 5th quarter and freezing winter temperatures was expected. If adequate soil moisture during the v;inter months and low winter temperatures were positively related, the inconsistent signs on the interaction terms would be easier to explain. The largest simple correlation coefficient involved was ,30 and did indicate a positive relationship. However, its level would not lead one to suspect serious mul ti col! i near i ty problems. Because the estimated coefficient for the soil moisture variable in the 5th quarter was highly significant, the interactions variables (V^Q through V „) and the squared temperature variables (Vjk, V„^, and V2q) were removed from equation Ci7j and the model reestimated. The resul ts were: Po ^ = .139 2. -!,0017V,^ + ,0067V,-, ,0001V „ + , 0004V 2st '''16 '17 18 19 (2,308) (2.06i|) (2,201) (0.016) (O.lSC) .00i;4V2Q .O722V22 .OOO3V23 .03l1V2g [13] (5.1^8) (1.737) (0.025) (2.643) -oonv^g R^ = .15 (0.02if) The variables in this equation have the same meaning as in equation Ci5.].. The F-value for equation C'SJ indicated that the regression v^as Parentheses enclose t-value:

PAGE 153

1^3 highly significant. The significant coefficients for V.^and V.., agree with the a priori information that adequate soil moisture is important during the first six months of the year. The significant negative coefficient for \l ^n '^ probably measuring an interaction between adequate soil moisture and freeze damage rather than a simple negative response to soil mioisture. However, too much soil moisture near maturity may prevent the fruit from maturing. The signs of the temperature variables are all consistent and the magnitudes are about as expected except for the coefficient of V„^, One would expect the coefficient for \/«, to be more negative than the coefficient fo"V .2 22 Equation [^|5j provides additional information on the structural relationship betvieen production and vjeather. However, as indicated 2 by its lew R it would not be useful for forecasting total state production of Valencia oranges. Equation L 1 8 J was fit to the Early and Midseascn data with \l2C\ removed. The results were: P.st = .0015 + . 0002V, ^ , 0006V, + , 0072V, g ,00l8V, (0,033) (0.22if) (0.205) (1.975) (0,765) 2 + .O527V22 + .OO87V2, •OI82V2. + .06lOV2g R = .0'4 (0.851) (0.732) (1.62if) (1.^87) Supra , p. if 7. 2. "The difficulcy v;i th the relative size of the coefficients of V and V„-, vjss not due to their being correlated. Their simple cor'relatioi^ coefficient was ,08.

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1^4 P St is defined here for Early and Midseason oranges as it was in equation Cl63 for Valencia. The F-value for equation Cl^Hwas not significant. Equation L i 9J indicates that there has not been enough observations on freezing temperatures to estimate an unlagged relationship between the production of Early and Midseason oranges and freezes for the state as a whole. The possibility of using dummy variables to estimate regional differences in the relationship between production and weather was considered. Equation CiSJwas reformulated by adding three dummy variables to measure regional differences. The first ten variables remained as defined for equation Cl8j. V^ took on the value 1 if an observation was from the East Coast aiid zero otherwise. V^^ ^nd V were defined for the West Coast and Upper Interior in an analogous 36 manner. The average effect for the Lower interior was included in the intercept. The results were disappointing. None of the dummy variables were significant et the ,05 level and the R -va ! ue was oniy increased from ,15 to .16. The sign of the freeze variable lagged twice (V-o) was reversed, indicating a positive marginal response cc freezing temperatures two years removed. However, the estimate was not si gni f i cciitl y different from zero. Other signs were unaffected. Because the dominant weather factor explaining most of the yearto-year variability of actual from expected production seemed to be some measure of freezing conditions and since the use of all data included numerous observations without freeze damage, It was decided ^es Table 22 (p, 1 16).

PAGE 155

145 to use only the data from the Upper Interior region (the region v;hich had suffered the most freeze damage over the range of the data) to estimate equations ClSD and C 1 9] in an attempt to obtain estimates of the relationship between production and freezing temperature which were more consistent with a priori expectations. P„ is the signed percentage of actual production of Valencia 2st 3 r 3 r oranges in the s county and the t year from corresponding expected production. P]st '^ defined similarly for Early and Midseason oranges. Other variables were defined in equation ClSH. The resul ts were : ^2st " '^^Sl + 0.0004Vj^ + 0, 0138V 0. 0058V, g + O.OOQifV (l.if58) (C.289) (2.642) (0.818) (O.O'/if) o.oojbv^Q + 0.0217V22 0..3223V23 o.iieQV^g C203 (2.135) (0.331) (3.788) {].kh2) O.O378V23 K' = ,30 (0.493) Since only data from the Upper Interior region were used, there were II9 observat ions--7 counties and 17 years. The variables in this equation have the same meaning as they do in equation [!5ll. P. . = 0.0145 + 0,00G3V,, + O.OOOIV,^ + 0. 0022V, „ O.OOOSV,^ T? 1 ] ISC lb 1/ ly ]^ •-• (0.186) (0.235) (0.025) (0.376) (O.I80) "Parentheses enclose t-values.

PAGE 156

146 + 0.0121V„, 0.11it3V,, 0, 1625V , + 0,0if27V „ 22 23 26 28 (0.221) (1.611) (2.416) (0.664) R = .09 Equation [r2IJwas not significant. Equation [^20l] was highly significant. The magnitude of the extimated coefficients for the freeze variables V.^ and \/„g increased while those for ^ and \/„o decreased from the estimates of the same coefficients in equation [18].

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CHAPTER Vl CONCLUSIONS AND IMPLICATIONS Summary and Conclusions The major research objectives were to specify and estimate relationships betv.'een weather and Florida orange production. Relationships were specified and then estimated by counties. Data were also pooled over cour.ties and the relationships estimated by groups of counties and for the state. Efforts to estimate the sepcified relationships indicated that soil moisture and minimum daily temperature explained mere of tlie variation in production than the ocher measures of vMeather available. In general, the signs of the estimated coefficients v^/ere reasonable. For the county equations the uncorrected coefficient of multiple determination ranged from .12 to .8h. The estimation of the re lat ionsh i pt between orange production by counties and weather would have benefited from measurements of the duration of freezes and from more accurate measurements of soil moisture. Weather indexes and average yields per tree by counties for Early and Midseason, and Late varieties were estimated. Also, the number o? orange trees by ages for the years IS'-i-S through 1968 were estimated (from tree census data) for the state and for each county for both Early and Midseason and Late varieties. n^i

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148 Data In Tables ]k, 15, and 16 reveal that the average per tree yield of either variety (macro) can be expected to vary over 1.5 boxes between counties with the lowest and highest yields. A large part of the between county variation in average yield is due to soil depth (size of root system) and to the fact that severe freezing temperatures are not experienced with the same frequencies in all counties, The weather effect on Florida orange production has been large. The state weather index for Early and Midseason oranges for the 196465 season was 1.33, while for Valencia oranges in the I962-63 season it was .60 (Table I9). The weather effect also differs among varieties (macro) in a given season. For example, in the 1962-63 season the state index v;as .92 for Ear]y and Midseason oranges and .60 for Valencia oranges. The relative effect of favorable and unfavorable weather also varies by varieties (macro). For the years under study the state index for Early and Midseason oranges varied r-OiT: .63 co 1.33 indicating that unfavorable weather could reduce the crop 32 percent and that favorable weather could increase it 33 percent, Hov;ever, for Valencia oranges the range of the weather index was from .60 to 1.22. This range indicated that the effect of unfavorable weather could be approximately tv>jice that of favorable weather. The weather effect also differs betvjeen counties in a given season. For the 1962-63 season the weather index for Valencia oranges was .14 for Pinellas county and .19 for Putnam county while it was 1.21 for St. Lucie county and 1.23 for Indian River county (Table 18). Data in Tables 26, 27, and 28 reveal that for most years the estimated average vieid equations (Stage !) or the weather equations (Stage 1!) estimated actual production reasonably well. in years of

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1^9 unusual weather the weather equations explained more of the variation in total production than did the average yield equations. Some general comments can be made concerning the size of the coefficient for the freeze variable. Consider the variable representing the number of days the minimum temperature was less than 26 F. A particular freeze observation could range from 26 F for a few minutes to less than 10 F for several hours. The extreme situations establish bounds on the possible effect of freezing temperatures. 2 Equation [|5] for counties 5, 7, 8, 10, 11, 17 (see Tabio 21) and equation [20l] indicate that one "freeze day" could reduce Valencia orange production 6 to 38 percent. The reduction one would expect within these bounds would be a function of both the duration and level of the freezing temperature. The weather indexes for Valencia oranges (Tab'e 18) indicate that the combined effect of several "freeze days" could be as large as an 80 to 85 percent reduction in a given county. Reduction of production the following season might range from zero to 35 percent. Again weather indexes indicate that the combined effect of several "freeze days" could be as high as 70 to 75 percent the follov/ing season. The reduction of production two Temperatures of 26 F for less than k hours are not considered damaging. However, extremely low temperatures that exist for less than four hours may be damaging, 2 These counties were selected because in the opinion of the author they had the most reasonable estimates of t.he freeze effect. Equation TiSj included three freeze variables as regressors. For these six counties the estimated coefficients for all three were negative. Four other counties (12, 1^, 15, and 18) also have estimated coefficients v;hich were negative.

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150 seasons removed may range from zero to 1^ percent. The combined effect of several "freeze days" would probably not reduce production more than 25 percent the second year. For Early and Midseason oranges based on the estimates of equation [ 1 5l] for counties 5, 9, 10, 15, 17, 18 (see Table 20) and equation L2 I H one "freeze day" could reduce current production 1 to 1 1 percent. With Early and Midseason oranges the time cf the freeze and the portion of the crop already harvested are important. The weather indexes for Early and Midseason oranges (Table 17) indicate that the combined effect of several "freeze days" would not exceed a 50 percent reduction. The effect on production the season following the freeze vjould be greater. The results indicate that the reduction might range from zero to 16 percent. The weather indexes also indiccte that the combined effect of several "frseze days" could result in a 65 to 70 percent reduction the following year. The reduction two saasono remo\ed ranges from to 1 2 percent, and the combined effect of several "freeze days" would probably not exceed 25 percent the second year. The estimates presented for equations ClSH and [[201] ^^Y be viewed as additional information on the structural relationship between the production of Valencia oranges and weather conditions. All signs viere consistent vjith apriori knowledge and the magnitudes of the coefficients were reasonable. As previously mentioned strict interpretation of the estimate of the coefficient for \l 20 '^ questionable These counties v.-ere selected because in the opinion of the author they had the most reasonable estimates of the freeze effect.

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151 since the variable is probably measuring more than a simple negative response to adequate soil moisture. The estimates for the freeze variables seem to be for two different populations. The estimates for equation D SH are considerably less negative than those for equation [20j. "fhe estimates for equation [^201] seem more reasonable in magnitude. In neither case were the coefficients of the two freeze variables for the current year as expected. In equation [IlBl] relative sizes were reversed and in equation r20j the estimate of E„^ was posi ti ve. I mpl ications For Ci trus I ndustry The inter-county and inter-variety variability in production due to weather effects and the inter-county and i n ter-var I ety variations in average yields which are indicated by the results of this study have risk implications for persons making investment decisions in new tree planting. The research also furnished the industry vji Lh another method of obtaining a mean estimate of production for future years. Since the number of trees is known by variety (macro) county, and age at the beginning of each season and since a tree is riOt commercially productive until four years of age, mean estimates of the current year and the next four years may be obtained by using the average yield coefficients and tree numbers by county, variety (macro), and age. These results also provide information on the deviation of actual Published annually by Florida Crop and Livestock Reporting Service, Orlando. Florida.

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152 from expected supplies (Table 19). Such information must be considered when and if the industry considers policies of supply control and levels of carry-over from season to season. The results of this study also provide a basis for estimating the change in production if portions of the citrus belt were shocked by severe v-jeather. !n making such an adjustment care should be taken to consider the time of year and the percent of the crop already harvested. For example, if the Early and Midseason oranges have already been harvested, no adjustment need be made of their estimated level of production. Historically, after a freeze there has been extreme pressure within the industry to raise price. This pressure is im.mediate and is felt days or weeks before the Florida Crop and Livestock Reporting Service can sample the damage and generate an adjusted forecast. The estimated change in production could be useful in helping establish the new fruit prices. For Research Variations in production due to weather tend to dominate and hence obscure other sources of variation. For this reason it is necessary to know something about the effects of weather if one is interested in studying other supply shifters. For example, growers' responses to various economic conditions are reflected in their production. However, It is difficult to measure such responses since they tend to be obscured by the effects of v.'eather on production. The weather indexes provide a basis for deflating to remove the weather effect from production data. The estimates of average ^ield per tree by variety (macro), county, and age of tree snould be useful to the developers of the

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153 third generation simulation model of the Florida orange industry. The average yield estimates provide a basis to help simulate production over time. Also, the v/eather indexes, provide a basis for 2 simulating variation in production. Limi tat io ns The major difficulties encountered when studying the effect of weather on perennial crops is a combination of specification and timation. Considerable knowledge exists concerning the physiology f most plants. However, information on the plant-weather interaction usually lacking or takes the form of some poorly structured hypothEven if a model could be specified with all the weather factors influencing yield and the necessary interaction terms included it could probably never be estimated. Even when assumptions are introduced to limit the number of coefficients in the model the number often remains quite large in comparison with the nurriber of observations available on the variable(s). These problems are aggravated If data from commercial farms must be used because age of plant becomes a factor to be considered. The level of knowledge may never permit one to avoid specification errors in expressing the relationship between the production of Florida oranges and weather, A linear approximation to the desired es o i s eses Charles Powe has recently begun work on such a simulator at the University of Florida, 2 Botn county and state indexes were estimated. However, regional (groups of counties) estimates could be constructed from the results presented.

PAGE 164

154 relationship certainly restricts the predictive accuracy of the model, parti cularl y at more extreme levels of the independent variables. Errors of observation and the aggregation of data over regions may also have affected the estimates presented. Unfortunately, any measurement problems which may have resulted from observational errors and the level of aggregation are unknown and probably unknowable. The estimates reported in this study are based on an assumption of perfect knowledge of tree numbers by county, age, and variety (macro) at the beginning of each season. The problem of estimating the number of trees over time was not confronted in this study. Also, the effects on the results of stochastic elements in the information on tree numbers was not explored. Suqqes tJ_o ns for Further R esearch This study indicated that the level of soil moisture explains more yield variability than most of the usual measures of weather such as average temperature and monthly rainfall. However, this study was not completely successful in efforts to estimate the structural relationship between soil moisture and yield. More accurate measures of soil moisture are needed. Greater efforts are also needed to determine the extent and effectiveness of m.an's attempt to modify the effects of weather. For example, irrigation and freeze protection devices are used quite widely in the citrus belt, but we have very few data on how much or in what ways they are used. There is also considerable dlsagreem.ent about the effectiveness of these device;^. This disagreement is More research of the type done by Koo (if/) and recently analyzed from an economic point of view by Reuss (63) is needed..

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155 largely the result of inadequate knowledge. If such practices are effective, their use needs to be reflected in models which attempt to determine the effects of weather on yields. Reliable long-range weather forecasts would be a major breakthrough for improving crop forecasts, especially when estimates are desired several months in advance, e.g., before the fruit is set. Research to examine the phenological events such as planting, fruit emergence, and fruit counts by maturity categories and to study the mechanism of growth and development over time as related to accumulated weather factors (53) is needed. Such studies m,ay require that teams of agror,on;i s ts , plant physiologists, meteorologists, agricultural engineers, and agricultural economists work jointly. In som.e cases controlled environments may be useful to gather observations on many different weather levels in a fev^ years. Most orenges are no longer sold by the box but in terms of pounds of solids. Weither also affects this measurement of crop production. Just as there is reason to expect a logical cause and effect relationship between 'weather and the production of oranges measured in boxes, there is reason to expect a logical cause and effect relationship between weather and the production of pounds of solids. Further research should look niore closely into this relationship. Similarly, on the fresh fruit side, little is knov%'n about the relationship between v;eather and size and quality of fruit. Studies that relate v/eather to the actual units in which the crop is sold would facilitate an economic interpretation of weather effects. Sucli an interpretation would also be of use in an estimation of potential payoff from such practices as irrigation, freeze protection, and fertilization.

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156 More exact indicators of the influence of meteorological factors such as precipitation and temperature have been proposed. Soil moisture is an indicator of moisture available for plant growth. Drought indexes measure variation in soil moisture relative to the capacity of the soil or to the v.'ilting point. This study relied heavily on the empirical estimation of evapotranspi rati on by the Thornthvyai te method though it is known to overestimate evapotrarispi ration in the summer months. Additional efforts . 1 should be undertaken to measure evapotranspi ration or evaporation at several points within the citrus belt or to empirically estimate it with greater accuracy. Additional work should be undertaken to specify the form of the relationship between the production of Florida oranges and v/eaiher with greater accuracy and structural estimates of the parameters attempted. Alternative measures of freeze variables might explain more yield variation. The lowest level of freeze severity measured in this study was the number of days the minimum temperature was less than or equal to 22 F. Perhaps lower minimum temperature categories would have given results that explained more of the variation in production. The importance of the duration of freezing temperatures cannot be overs tressed , Data on the duration of damaging temperatures should be collected. More accurate estimates of the structural relationship between The majority of the weather stations in the citrus belt do not record observations on evaporation. It would be helpful if several more did. Tht Information would be useful in research efforts si miliar to this one and properly modified could be used by growers for irrigation scheduling.

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157 soil moisture and yield in all probability cannot be made until methods are developed to accurately measure the level of soil moisture in the various areas of the citrus belt. Hov^;ever, regardless of the data difficulty, future effort in the area must confront the problem that the relationship between yield, soil moisture, and freezes is not linear and that interactions do exist. Special emphasis should be placed on estimating the interaction between adequate soil moisture in the winter, warm winter temperatures, and freezes. Since the expected maturity date for Early versus Midseason oranges is fairly distinct (69) and since Savage (70) has estimated that the two varieties are expected to yield at different average rates, it might bs beneficial to separate the Early and Midseason varieties into two groups. Then if a freeze occurs after the usual harvest date ^or Early oranges a totsl forecast of Florida orange production might be improved by considering that the Early oranges are unaffected by the freeze until the next season while the Midseasor and Late varieties might be expected to suffer a direct effect as well as a lagged effect due to the freeze. Lastly, the inter-county and inter-variety difference in average yields and in production variability due to weather effects should be analyzed in an economic risk model to determine the implications on optimum decision strategies vjith regard to grove investments.

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LITERATURE CITED 1. Auer, Ludv.'ig and Heady, Earl 0, "The Contribution of Weather and Yield Technology to Changes In U.S, Corn Production 1939 to 1 9 6 1 " . Weather and Our Food Supply . Ame s , I owa : I owa State University, Center for Agricultural and Economic Development, Report 20, 1964. 2. Bain, F. M. "Ci trus and CI i mate", (Part I). Cal i fornia Citroqraph, Vol. 3k (19^9), P. 382. 3. Bean, Louis K. "The Predictability of Cycles, Trends and Annua] Fluctuations in Weather and Crops". Weathe r and Our Food Supp ly. Ames, Iowa: Iowa State University, Cente.r for Agricultural and Economic Development, Report 20, ly^^. 4. Bitters, W. P. and Eatchelor, L, D, "Effect of Rootstock or. the Size of Orange Fruits". Ameri can So ciety f or Hor Lieu! _tu raj A'li.SiLC-^L'; cceedir.qs , Vol. 57 ( 1 S ' :-6 ) , P P • 133-141. 5. Ejeutel, J. A. "Soil Moisture, Weather, and Fruit Growth". Cal i forni a C i troqrapn, Vol. kj (1964), p. 372, 6. But son, ',<.. D, a I id Pnne, G, M, Wee !< ]_y ..l^.^.i rf a 1 1 F r e o it e n c i e s in Florida. Gainesville, Florida: University of Florida Agricu!tur-al Experiment Stations, Circular S~187, April, I968, 7. Camp, A, F. Citrus Industry of Flo rida. Tallahassee, Florida: Florida State Department of Agriculture, I96O. 8. Caprio, Joseph M, ; Harding, R, B. ; and Jennings, R, F, "Orange Fruit Size and Yield in Relation to .Mean Monthly Temperatures in a California Orchard", Ameri can Society for Horticultu ral Science Proce edi ngs, Vol, 66 (1955), PP. 45-55. 9. Chern, W, "Determination of the Optimum N'uniber, Size and Location of Orange Packing and Processing Plants in Florida", Gainesville, Florida: University of Florida, Unpublished Master's Thesis, I969. 10, Clawson, Marion, "Reflections on Gross Farm Output". J ourn al of Farm Economics, Vol, 41 (May, 1939), Pp. 247-256, 11. Cooper, W. C. "Cold Hardiness in Citrus as Related to Dormancy" IUPjJ-lg._-Jlil^ Jl?±LLJ?.!lL-:l'-r jJ_S^_c_.'i; '^ y Proceedings, Vol. 72 (1959) . pp." 61-65. 153

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159 12. Cooper, W. C. "Effects of ]96l-62 f-'reeze on Valencia Oranges in Florida, Texas and California". Florida State Horticultural Society Procee d ings , Vol, 75 (19^?), pp. 82-88. 13. Cooper, W, C, "Microclimate and Pliysiology of Citrus", Agr i cultural Science Reviev N/, Vol. 2 (196^), pp. 38-50. \k. Dhillon, B, S. and Singh, J. P. "Relationship Betv-yecn Soil Moisture and Fruit Crop in Mandarin". The Indi an Journal of Ho rticulture . Vol. 22 (I965), PP. 309-313."' 15. Doll, John P. "An Analytical Technique for Estimating Weather Indexes from Meteorological Measurements". Journa l of Farm Economics , Vol. kS (February, I967) , pp. 79-88. 16. Dow, H. K. "The Impact of Mechanical Harvesting on the Demand for Labor in the Florida Citrus Industry". Gainesville, Florida: University of Florida, Department of Agricultural Economics, 1969. (To be Published). 17. !idwards, Clark. "Non-Linear Prog'-eiii:ir!i ng and Non-Linear Regression Procedures". Journal o f Fa r m Econom ics. Vol. -fi|(February, I962), pp. 100--11'!-. 18. Federal Trade Commission. Staff Report. Econom ic Report_ on the Froz en Concentrated Orange Juice Indust ry . Washington, D. C. : Federal Trade Commission, August, 1964. 19. Florida Citrus Commission. Two Da ys in Decemb er-' A Report on the Florida Freeze of I962. Lakeland, Florida; Florida Ci trus Commi 1 si on. 20. Ford, Harry W. "The Distribution of Feeder Roots of Orange and Grapefruit Trees on Rough Lemon Rootstock". C* trus Mega~i ne , Vol. 14 (July, 1952), pp. 22-23. " "' 21. Ford, Harry W, "Root Distribution in Relation to the Water Table". Florida State Horticultural Society Proceed ings. Vol. 67 (I95M, pp. 30-33. 22. Furr, J. R.; Taylor, C. A,; and Reeve, J. 0. "Fruit Set of Citrus, Effect of Spring Soil Moisture Upon the Drop of Young F r u i t " . Am erican Society f or H or ti cultural Science P roc ee d i nqs Vol. 37 (1939), pp. 152-157. 23. Goldberger, A. S. Econ o metric Theo ry. New York: John V/iley & Sons, I96U. 2k. Griliches, Zvi . "Estimates of the Aggregate U.S. Farm Supply Function". Jou rnal of Far m E conomi cs, Vol. k2 (May, I96O), pp. 282-293. 25. Haas, A. R. C. "Orange Fruiting in Relation to the Blossom Opening Period". Plant Physipioqy, Vol. 2k (I94S) , pp. ^:-8l^93.

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160 26. Hammond, Luther C. "Methods of Measuring Soil Moisture". The Citrus Indu stry, Vol. 33 (October, 1S52) , pp. 8-9. 27. Harding, P. L. and Sunday, M. B. Fore ca sting Quality and Pound Solids in Florida Oran ges. Washington, D. C: Market Quality Research Division, U. S. Agricultural Marketing Service, AMS-533, 196^. 28. Hathaway, Dale E. "Agriculture in an Unstable Economy Revisited". J ournal of Farm Economics , Vol. k] (August, 1959), pp. ^i87-'f99. 29. Havlicek, Joseph, Jr. "Use of Linear Programming for Obtaining Minimum-Deviation Estimates of Functional Relationships". Contemporary A g ricultural Mar k eting , Chapter 12. Edited by Irving Dubov. University of Tennessee Press. 30. Hendershott, C. H. "The Responses of Orange Trees and Fruits to Freezing Temperatures". Am eri can Socie ty for Horticultural Science Proceedings , Vol. 8"0~TT9o 2 ) , pp. T5 7 2 ST'. 31. Hodgson, R. V/. "The Fruit Size Problem of California and Florida". Cal if ornia Ci trograph , Vol. 32 (19^7), p. 332. 32. Horanic, George E. and Gardner, F. E. "Relative Wilting of Orange Trees on Various Rootstccks". Florida State Horticult ural S ociety Proceedings, Vol. 72 (1959), pp. 77-79. 33. Huberty, M. R. arid Richards, S. J. 'Higher Yields Obtaincc v/ith Frequent irrigation". California Citrograph , Vol. 39 (l95-i)j pp. 408-410. 34. Hunziker, R. R. "Water Damage to Citrus in the Indian River A^-.-ja i n 1959" . S^o i 1 and Cr op^ Sc i ence Soc iety of Florida Pro ceedings , Vol. 19 (195SlTpp. 357-364: 35inspection Division. Summar y Report of Fertil izer Materi als Consumed in Fl orida , PTscal Years July 1, 19'^"^-' June 30, 1945 through July 1, 19^7 " June 30, 1S68. Tallahassee, Florida: State of Florida Department of Agriculture. 36. Inspection Division. Summa ry Report o f Mi xed Fertiliz ers Consumed in Flor ida, Fisca' Years July l"^ TgW June 30, 19^ through July 1," 19''67 June 30, 1968. Tallahassee, Florida: State of Florida Department of Agriculture. 37"Irrigate by the Accounting Method". Fl orida Grov.er and R ancher, October, 1968, pp. 34-36. 38, Jamison, V. C. "Soil Moisture Relationships in Sandy Soils Planted to Citrus in Florida" Florida State Horticultural Soc i £ ty _P rcceed i ngs , Vol. 58 (1945), pp. 5-16. 39Jarmain, V/. E. "Dynamics of the Florida Froze.i Orange Concentrate Industry". Cambridge, Massachusetts: Massachusetts institute of TechnoioGy, Unpublished Mas ter's Thes i s , September, 1962.

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161 AO. k]. m. A3. he. hi. 48. hS. 50. 51. 52. Johnston, J. E conometric Methods , rk.w York: McGrav/-Hi 1 1 , I963, Jones, W. W. and Cree, Clarence B. "Harvest Time Affects Valcncias". California Agriculture , Vol. 9 January, 1355), p. 11. Jones, W. W. and Cree, Clarence B. "Environmental Factors Related to Fruiting of Washington N'avel Oranges over a 38-Year Period". American So ciety for Horticultural Science Proc eedings , Vol. 86 (1365)," pp. 267-271 . Jones, W, W. and Embleton, T. W. "Yield and Fruit Quality of 'Washington Navel Orange Trees as Related to Leaf Nitrogen and Nitrogen Fertilization". America n So ciet y for Horticultural Science Proceedings , Vol. 91 (1 9'67) TTF-"!^" 1^2. Kane , E . J . Econom i c Statistics and E conometr i cs . Nev/ York : Harper and Row, \3l>^. Kelly, Bruce \S . and Kirkbridge, John V, . "Forecasting Crop Yields". Weather and Our Food Suppl y. Ames, !ov.-a: Iowa State University, Center for Agricultural and EcononMC Development, Report 20, I96A. Knetsch, Jack L. "Moisture Uncertainties and Fertility Response Studies". Journal of Farm Eco n omics , Vol. k] (February, 1359). pp. 70-76. Koo, Robert C. J. "Effects of Frequence of Irrigations on Yield of Orange and Grapefruit". Florida State Ho rticultural So ciety Proceedings, Vol. 76 (I963) , "ppTHTs". Koo, Robert C. J. Evapotranspi rat ion and Soil Moist ur e Determ inat io n as Guides to Citrus Irrigation . Proceedings of ti''2 First International Citrus Symposium, Vol. 3 (^969), pp. 1725" 1730. Koo, Robert C. J. and Harrison, D. S. Summary of Citru s irrig ation Research in Flori d_a_. Gainesville, Florida: University of Florida Extension Agricultrual Engineering Mimeo Report 65-8, November, 1965Koo, Robert C. J.; Reitz, Herman J.; and Sites, John W. A_ Survey of th e Mineral Nutr ition Statu s of Valencia Orano c in Flor i da . Gainesville, Florida: Agricultural Experiment Station Bulletin 60A, December, 1958. Koo, Robert C. J. and Sites, John W. "Results of Research and Response of Citrus to Supplemental Irrigation". The Soil Science Society of Florida Pro ceedings , Vo 1 . 15 (1 9551 , pp. 180^190. ' Kuznets, G. M. "Weather Effects on Oranges' Agriculture, Vol. k, No. 6 (1950), p. 2. Cal i f orn I a

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162 53. Kuznets, G. M. and Jennings, Robert F. "Effect of Weather on Average Size and Yield of Oranges". California Citrograph , Vol. 35 (1950), pp. 365-368. "~ 5^. Lav;rence, Fred P. Treatment of Cold-Injured Citr us Trees . Gainesville, Florida: Agricultural Extension Service, Circular 17^, December, 1957. 55. Lawrence, Fred P. Selecting a Grove Site . Gainesville, Florida: Agricultural Extension Service, Circular 185, June, 1958. 56. Lenz, F. "Flower and Fruit Development in 'Valencia Late' Orange, as Affected by Type of Inflorescence and Nutritional Status". Horticultural Research , Vol. 6 (I966), pp. 65-78. 57. McPhee, John. Oranges . New York: Farrar, Straus and Giroux. 1967. 58. Mitchell, J. Murray, Jr. "A Critical Appraisal of Periodicities in Climate". Weather and Our Food Supply. Ames, i ow3 : !ow3 State University, Center for Agricultural and Economic i^evclopment, Report 20, 1964. 59Morgan, John J. "Use of Weather Factors in Short-Run Forecasts of Crop Yields". Jou rnal of Farm Economics, Vol. k3 (December, 1961), pp. 1172-117117 " 60. Newman, J. E. e t a 1 . "Growing Degree Days". Crop and Sons Magazine, Vol, 2r(3/ , (December , 1968),pp. g-TTl 61. "Oranges". Encycloped ia Brittancia. I969. Vol. XVI. 62. u r y , B e r n a rd . A Milk Production M odel for Wi s cons in (19-.:6-19 62) . Raleigh, North Carolina: University of North Carolina, March,, 1965. 63. Oury, Bernard. "Allowing for Weather in Crop Production Model Building". Journal of Farm Econo mics, Vol. ^7 (May, 1965), pp. 270-283. 64. Palmer, Wayne C. "Climatic Variability and Crop Production". Weather and Our Food Su pply . Am.es , Iowa: Iowa State University, Center for Aarlcultural and Economic Development, Report 20, 196'*. 65. Plaxico, James S. "Discussion: A Measure of the Influence of WeTithc on Crop Production". Journal of Farm Economics , Vol. 43 (December, I96I), pp. 1 I60-I 1627 66. Polopolus, Leo and Lester, VI. Bernard. "Estimation of Florida's Orange Production Over the Next Fifteen Years by the Random Sampling Technique". Unpublished Report, Economic Research Department, Florida Citrus Commission, University of Florida, September 3, 1968.

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163 67. Raulerson, Ricliord C. "a Study of Supply-Oriented Marketing Policies for Frozen Concentrated Orange Juice: An Application of Dynamo Simulation". Gainesville, Florida: University of Florida, Unpublished Masters Thesis, June, 1967. 68. Reuss, L. A. Yield Response and Economic Feasibili ty of Sprinkler I rrig a tion of Citrus, Central Florida . Gainesville, Florida: University of Florida, Agricultural Experiment Station, Economics Mimeo Report EC 69-IO, June, I969. 69. Reuther, Walter; Weber, Herbert John; and Batchelor, Leon Dexter, editors. The Citr us Industry, Vol. I, Berkeley: A Centennial Publication of the University of California, I967. 70. Savage, Zack. Do es Irrigatio n Pay on Your Grove ? Gainesville, Florida: Uriiversity of Floridf Agricultural Experiment Station, Economics Series No. 5^-8, 195^K 71. Savage, Zack. LLtrus Yield Per Tree By A ge. Gainesville, Florida: University of Florida Agricultural Extension Service, Economics Series 66-3, May, 19&6. 72. Schuler, Paul E., ed . Florida Agricultura l St atistics Citrus Summ ary (Prior to IS62 l-^nown as Florida Citrus Frui t Annual Summary) . Orlando, Florida: Florida Crop and Livestock Reporting Service, 19^8 through 19d7 yearly issues. 73Shaw, Lawrence H. and Durost, Donald D. Measuring the Eff ects of V/e ather on Agricultural Output . Washington, D. C: Farm Economics Division, Economic Research Service, U. S. Department of Agriculture, ERS-72, October, 1962. 7^. Shaw, Lawrence H. "The Effect of Weather on Agricultural Output: A Look at Methodology". Journal of Farm Ec o nomi cs, Vol. '+6 (February, 196^), pp. 218-230. 75Shaw, Lawrence H. and Durost, Donald D. "The Weather Index Approach". Weather and Ou r Food Supply. Ames, Iowa: Iowa State University, Center for Agricultural and Economic Development, Report 20, I96A. 76. Shaw, Lawrence H. and Durost, Donald D. The Ef fect of Weather and T ec hno 1 j2Q y on C orn Yields in the Corn Belt , 1920-62. Washington, D. C: Economic Research Service, U. S. Department of Agriculture, Agricultural Economics Report Number 80 , July. 1965. 77Shav/, Robert H. and Thompson, Louis M. "Grain Yields and Weather Fluctuations". Weath er and O ur Food Supply . Ames, Iowa: Iowa State University, Ci;nter for A"gr i cu 1 tura ) and Ecotiomic Development, Report 20, )96^.

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I6it 78. Sites, John V/. ''Internal Fruit Quality as Related to Production Practices". Florida State Horticul tural Soci ety Proceedinas, Vol. 60 (I9A7) , pp. 55-62. "~ 79. Sites, John V.'. and Hammond, Luther C. I nforma t ion to Consider in Use of Flatlands and Ma rshes f or Ci trus . Ga i nes v i 1 I e , Florida: University of Florida Agricultural Experiment Station Circular S-135, 1961. 80. Sites, John W. ; Reitz, Herman J.; and Deszych, E. J. "Some Results of Irrigation Research with Florida Citrus ". Florida Sta^te H orticultural Society Procee dings. Vol. 6^ (1351), pp. 7I-79T" 81. Stal lings, Janles L. "A Measure of the Influence of Weather on Crop Production". Journal of Farm Econ omics, Vol. k'i (December, 1961) , pp. 1153-1160; 82. Steel, R. G. D. and Torrie, J. H. Pr inciples and Procedures of Statistic s. New YorkMc Graw-Hill Book Co., 19bO'." 83. Stout, Roy. "Some Relevant Factors in Forecasting Harvest Size of Valencia Oranges". Proceedings of Florida SLci te H orti cu ltural Society, Vol. 76 (1963), pp. 57-^5. 84. Stout, Roy. Some Fac tors Co ntr i but i n g to Year to Year Va r i at ions in Florida Orange Produc tion. Gainesville, Florida: University of Florida Agricultural Experiment Station, Agricultural Economics Mimec Report FC 6^-12, April, IQS^. 85. Tefertiller, K. P.. and Hildreth, R. J. "Importance of Weather Variability on Management Decisions". Journal of Farm Economics, Vol. A3 (December, I96I), pp. 1163-1169'. 86. Thompson, L . M. Soils and So il Fertility, New York: McGrawHill Book Co, 1957.' 87. Thompson, L. M. V/eathe_r and Corn Production. Ames, Iowa: Iowa State University, Center for Agricultural and Economic Adjustmeni;, CAEA Report 12, 1962. 88. Thompson, L. M. Weath e r and Technolog y in the Reductio n o f Cor n and Soybeans . Ames, !owa: Iowa State University, Center for Acri cultural and Economic Develcoment, CAED Report 17, 1963." 89. Thompson, L. M. "Multiple Regression Techniques in the Evaluation of Weather and Technology in Crop Production". Weather and Our Foou Supoly. Ames, I ov;a : Iowa State University, Center for Agricultural and Economic Development, Report 20, 196^1.

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165 90. Thornthwai te , C. W. "An Approach Toward a Rational Classification of Climate". Geographical Reviev /, Vol. 38 (I9^l8), pp. 55-9^t. 91. Upchurch, M. L. "Consideration of Weather in Farm Program Planning". V/eat ti er and Our Food Suppl y. Ame s , I owa : I ov/a State University, Center for Agricultural and Economic Development, Report 20, 196^. 92. Van Bavel, C. H. M. "A Drought Criterion and Its Application in Evaluating Drought Incidence and Hazard". Agro no my Journa l, Vol. k5 (1953), pp. 167-172. " 93. van Bavel, C. H. M. ; Newman, J. E.; and Hilgeman, R. H. "Climate and Estimated V/ater Use by an Orange Orchard". Agr i cul tura 1 Meteorology , Vol. k (1967), pp. 27-37. """ 9^. Williams, S. R. Foreca sting Florida Citrus Production: Meth odology and its Develop ment. Gainesville, Florida: University of Florida in Cooperation with the Florida Crop and Livestock Reporting Service, January, I965. 95. Young, T. W. Soil Moisture Rel ations in the Coastal Citrus Areas of Florida. Gainesville, Florida: University of Florioa" Agricultural Experiment Station, No. 526, September, 195396. Ziegler, Louis V/. "Moisture Saturatiori of Leaf and Twig cf Certain Species and Varieties of Citrus as an indication of Soil Moisture Conditions". Gainesville, Florida: University of Florida, Unpublished Masters Thesis, June, 1950. 97. Ziegler, Louis vl . "Irrigation Studies with Marsh Grapefruit on Lakeland Fine Sand in Central Florida". Flor ida S tate Hor ticultural Soc iety P roceedin gs, Vol. 68 (1955J~ pp. JS-'kT. 93. Ziegler, Louis V.'. and Wolfe, Herbert S. Ci trus Grovying in Florida . Gainesville, Florida: University of Florida Press,

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167 Cassin, J., e t al . "The Influence of Climate Upon the Blooming of Citrus in Tropical Areas". Proceedings First international Citrus Symposium . Vol, I (I969), pp. 315-323, Cochrane, Willard W, "The I'Jature of the Race Between Food Supplies and Demand in the United States, 1951-75". Journal of Farm Economics . Vol. 35 (May, 1953), pp. 203-222. Cooper, W. C. and Peynado, A. "Winter Temperatures of Three Citrus Areas as Related to Dormancy and Freeze Injury of Citrus Trees". American Society for Horticult ural Science Pr oc eedings , Vol, fk (1959), pp. 333-3^7. Cooper, W. C. , e_t_a]_. "Tree Growth and Fruit Quality of Valencia Oranges in Relation to Climate", American Soci ety for Horticu l tural Science Proceedi ngs. Vol, 82 (1963), pp. I8O-I92. Dale, Robert F, "Discussion: Use of Weather Factors in Short-Run Forecasts of Crop Yields", Journal of Farm Economics . Vol, 43 (December, I96I), pp, 1179-1182, Dale, Robert F, "Changes in Moisture Stress Days Since 1933". Weath er and Our Food Supply . Ames, Iowa: Iowa State University, Center for Agricultural and Economic Development, Report 20, 1964, Denrr.ead, 0. T. and Shaw, Robert H. "Aval "iabi 1 i cy of Soil Water to Plants as Affected by Soi i Moisture Content and Meteorological Conditions", A qrcnomy Journal , Vol. 54 (I962), pp, 3S5-389, Erickson, L, C, "Abscission of Reproductive Structures and Leaves of Orange Trees". A me r i c an Society for Horticultural Scien ce Proceedi nas , Vol. 75 (I960), pp. 222-229. Ezekiel, Mordecal, "World Food Problems", Weather an d Ou r Food Sup ply. Ariies, I ovja : 1 ov\'5 State University, Center for Agricultural and Economic Development, Report 20, 1964. Fifte en Years o f Publications: July 1, I95O -June 30, I965 , Gainesville, Florida, Agricultural Economics Mimeo Report EC 66-12, June, 1966. Fcrd, Harry W. "Root Distribution of Chlorotic and I ron-Che 1 ateTreated Ci trus Trees", Florida State Hort ic ultural Society Proceed ill3A. V0I, 66 (1953), pp. 22-26, Fox, Karl. "Panel Discussion of Implications of Weather in Agricultural Policy Planning". V/e ather and Our F ood Su pply, Ames, Iowa: I O'wa State University, Center for Agricultural and Economic Development, Report 20, 1964. Furr, J, R, and Taylor, C, A, Gro wth of Lem on Fruits i n R elat ion to Moisture Co ntent of the Soil . Washington, D. C: United States Department of Aor i cu 1 ture , Technical Bulletin No, 640, 1939,

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168 Gerber, J, F, and Krezdorn, A. H. "Preconditioning of Plants in Relation to Cold Tolerance". Florida Agricultural Experiment Station Annual Report . Gainesville, Florida: University of Florida, I963, p. 128. Ghazaleh, M. Z. S. and Hendershott, C. H. "Effect of Drought and Low Temperature on Leaf Freezing Points, and Water-Soluble Proteins and Nucleic Acid Content of Sweet Orange Plants". American Society f or Horticultural Science Proceedings . Vol. 90 (I967), pp. 93-102, Griliches, Zvi. "The Demand for imputs in Agriculture and a Derived Supply Elasticity". Journal of Farm Economics , Vol, ^1 (May, 1959), pp. 309-322. Hales, T. A.; Moayen, R, G, ; and Rodney, D, R, "Effects of Climatic Factors on Daily 'Valencia' Fruit Volume Increases". Amer i can Soci ety for Horticultural Scien ce P roceedings , Vol, 92 (I968), pp. [85-! 90. Harding, P. L, "(Quality in Citrus Fruits". American Society for Horticultu ral Sc i ence Proceed ings , Vol. ks ( 1 Sk'/ ) , pp. 1 07115. Harding, P. L. ; Winston, F, R,; and Fisher, D, F, Seas onal Chan ges i n Florida O ranges , Washington, 0, C: United States Department of Agricul ture, Technical Bulletin No. 753, 19'-^0, Harding, R, B.; Chapman, H. u . : and Whiting, F. L. "Smaii Fruit Sizes of Valencias". Ca1 i for nia Agric ul tu re. Vol. 9 (April, 1955), p. 6. Hashemi, F, "A Mi crorneteorologi cal Approach to Estimating the Eyapotranspi rat ion of a Citrus Grove", Gainesville, Florida: University of Florida, Unpublished Ph,D, Thesis, April, I967. Hashefni , F. and Gerber, J. F, "Estimating Evapotranspi ration from a Citrus Orchard with Weather Data", American Society for Hort icultural Science Pro ceedings . Vol. 9I (I967), pp. 173-179. Hendershott, C, H. "Effect of Various Chemicals on the Induction of Fruit Abscission In 'Pineapple' Oranges". A merican Soci ety for Horticultural Science Proceedings . Vol. 85 (196^), pp. 201-209, Hield, H. Z. "Effect of Gibberellin Sprays on Fruit Set of Washington Navel Orange Trees". Hidga rdia , Vol. 36 (January, I965), pp. 297-311, Hildreth, R. J. "Influence of Rainfall on Fertilizer Profits", Journa l of Farm Economics , Vol, 39 (May, 1957), Pp. 522-524. Hilgemsn, R. H. ; Tucker, H. ; and Hales, T, A, "The Effect of Temper. ature, Precipitation, Blossom Date and Yield upon the Enlargement of Valencia Oranges", Ame rican So ciet y for Hort i cultural Scien ce Proceedings, Vol. 7^ (1959), PP26'6~279.

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169 Hilgenian, R, H, "Trunk Grcwr.h of the Valencia Orange in Relation to Soil Moisture and Climate". American Society for Hor ti cul t ural S cien c e Proceedings . Vol, 82 (I963), pp. 193'.98, Horanic, George E. and Gardner, F, E. "Relative Wilting of Orange Trees on Various Rootstocks". Florida Slate Horticultural Societ y Proceedings . Vol, 72 (1959), PP. 77-79Hurst, Rex L, "Statistical Techniques Which Might Be Useful in Further Research". Weather and Our Food Supply . Ames, Iowa: Iowa State University, Center for Agricultural and Economic Development, Report 20, 1964. Inventory of Comm ercial Citrus Acreage, December. I965 , Florida Agricultural Statistics, Orlando, Florida: Florida Crop and Livestock Reporting Service, 1965Jamison, V. C. "The Penetration of Irrigation and Rain Water Into Sandy Soils of Central Florida". So il Science Society of America Proceedings . Vol, 10 (19^+5), PP 25-29, Johnson, Paul R, "Alternative Functions for Analyzing a FertilizerYield Relationship", Journal of Farm Economics . Vol. 35 (November, 1953), pp. 519-529. Jones, V/. W. ; Embleton, T. W. ; and Cree, Clai-ence B. "Temperature Effects Acid, Brix in Washington Navel Oranges". Cal i forni a Ci trograph, Vol. kj (1962), pp. 132-13'+. Jones, W. W. ; Embleton, T. W. ; Steinacker, M. L. ; and Cree, Clarence 3. "The Effect of Fruit Harvest on Fruiting and Carbohydrate Supply in the Valencia Orange". American Society for Horticultural Sc ience Proceedings. Vol. %k (1964), pp. 152-157. Jones, W. W. and Embleton, T. W. "Influence of Amount of Fruit and Time of Harvest on Macronu Lrient Concentrations in 'Valencia' Orange Leaves". A merican Society for Horticultural Science Proceedings . Vol. 92 (1968) , pp. 191-194. Kimball, Marston H, and Gilbert, Bewayne E. "PI ante 1 i ma te Mapping: The Key 10 Conservation of Resources", Ground Level Climatolog y. Edited by Robert H. Shaw, Washington, D. C. : American Association for the Advancement of Science, I967. Koo, Robert C. J, "A Study of Soil Moisture in Relation to Absorption and Transpiration by Citrus", Gainesville, Florida: University of Florida, Unpublished Ph.D. Dissertation, June, 1953. Koo, Rcbert C. J, "Prepare Trees for Dormanc/". Ci trus World , Vol, 5 (1968), pp. 15-16, Krezdorn, A, H, "The Influence of Girdling on the Fruiting of Orlando Tangelos and Navel Oranges", Florida S tate Horticultural Socie ty Procee dings . Vol, 73 (I960), pp. 49-52.

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170 Krezdorn, A. H, "Factors Affecting Unf rui tf ul ness of 'Orlando' Ta n g e 1 o s " . Florida Agricultural Exper i ment S tati on Annual Report . Gainesville, Florida: University of Florida, I963, P. 1^0, Krezdorn, A, H. and Cohen, M. "The Influence of Chemical Fruit-Set Sprays on Yield and (Quality of Citrus". Florida State Horticultural So ciety Proceedings . Vol, 75 (1962), pp. 53-60. Lawless, W. W. "Effect of Freeze Damage on Citrus Trees and Fruit in Relation to Grove Practices". Florida State Horticultural Society Proceedings, Vol. 5^ (19^0, PP. 67-7'k Lenz, F. "Relationships between the Vegetative and Reproductive Growth of Washington Navel Orange Cuttings". Journal for Horti cultural Science. Vol. k2 (I967), Pp. 31-39. The Mand a rin Pranc e in Florida. Tallahassee, Florida: Department of Agriculture, New Series No. 69, August, 193'k McCloud, D, E. "Water Requirements of Field Crops in Florida as Influenced by Climate". Proceedings o f th e Soi l and Crop Science Soc iety of Florida, Vol. 15 (1955), PP^ 165-172. McCown, Jack T. "Additional Observations on Florida Citrus Following the 1557-58 Freezes". Flor i da S tate Horticu ltural Society Proceed jj?iis, Vol. 72 (1959), pp. 75-77. McPhersori, W. K, "Future Water l^equ: remencs of Agricultural and Forest Enterprises". Soil and Cr op Scien ce Socie t y of Florida P roceedings , Vol. 22 (1962), pp. 27^-282. Miller, Paul A. and Newman, Jai.ics E. "Conductive Heat Exclianges at Terrestrial Surfaces as Influenced by Changing Air Density". Procee ding s o f the I ndiana Ac ad e my of Science of I96 6, Vol . 76 (1967), pp. 372-376^ Monselise, S. P. and Halevy, A. H. "Chemical Inhibition and Pror.iotion of Citrus Flower Bud Induction". A meric a n Society for Horticu ltural Science P roceedings, Vol, 84 (1964), pp. I4l-Ui5. Newman, J. E,, e t a 1 . "Orange Fruit Maturity and Net Heat Accumulations". Ground Level^ Cllmatologv. Edited by Robert H, Shaw. Washington, D, C: American Association for the Advancement of Scier.ce, I967. Nijjar, G, S, and Sites, John W. "Some Effects of Day Length and Temperature on Cold Hardiness of Citrus". Flo ri da Sta t e Horticultu ral Soci ery Proceedings , Vol, 72 (1959), PP • 1 061 09 . North, C. P. and Wallace, A. "Soil Temperature and Citrus". Cal i forn i a AiiricLHt.ure, Vol. 9, No. 11 (1955), p. 13.

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171 Parker, E, R. and Jones, W, W. Effects of F ertilizers Upon the Y iel ds. S ize and Quali ty of Orange Fruits . Berkeley, California: University of California College of Agriculture, California Agricultural Experiment Station Bulletin 722, March, 1951. Patt, J.; Carmeli, D. ; and Zafrir, 1, "Influence of Soil Physical Conditions on Root Development and on Productivity of Citrus Trees". Soil Scienc e (August, 1966), pp. 82-84. Penn, J. B. ; Heagler , Arthur M. ; and Bolton, Bill. Preci pi tation Probabilities f or S ele cte d L oc ations in Louisiana. Baton Rouge, Louisiana: Louisiana State University in Cooperation with the Economic Research Service, U. S, Department of Agriculture, D.A.E. Research Report No, 392, March, 196g. Pesek, John T. ; Heady, Earl 0.; and Venesizn, Eduardo. Ferti 1 i zer P rodu c tion Functions in Relation to V/ea ther, Lo c ation, Soil a nd Crop Variables . Ames, iowa: Iowa State University Agriculture and Home Economics Experiment Station Research bulletin 55^, August, I967. Piatt, R, G. "Leaf Drop, Ffu't Drop, and Twig Die Back". Cal i f ornXa Ci troqraph. Vol. k3 (1958), pp. 192, 207-209. Porter, Charles N. How to have a n O.-ang e Grove in Florid a. Ocala, Florida: Banner-Lacon, 1882. Randh:;wa, G. 5. and Dinsa, H. S. "Tim.e of BlossomBud Differentiation in Citrus". Amei iran Society for H orti £u 1 tur al Sc i_e.nc_e_ Pro c e_e_d i rgs , Vol. 50 (19^7), pp. 165-171. Reece, Philip C, "Fruit Set in the Sweet Orange in Relation to F 1 ov^e r i ng hab it". American Society for Horticultural Sci ence Proceeding s. Vol. kS (19^5), pp. 81-86. Rcitz, Herman J. and Long, W. T, "Water Table Fluctuation and Depth of Rooting of Citrus Trees in the Indian River Area". Flo rida S tate Horticu ltural So ciety Proceedings , Vol. 68 (1955), pp. 2^^-29. Reitz, Herman J, "Fertilizing Florida Citrus". A merica n Fr u't Grower , Vol. 77 (March, 1957) , p. 15. Reuther, Walter and R i os-Cas tano , Danilo. "Comparison of Growth, Maturation and Composition of Citrus Fruits in Subtropical California and Tropical Columbia". Proceeding s First Inte rnat ional Citrus Sympos ium, Vol. 1 (I969), pp. 227-300. Savage, Zack. "Irrigated and Nonirri gated Groves". Ci trus Ma q az i r.e , (October, 195'), PP. 23-27. Savage, Zack. Est i mating the Val ue of Citru s Frui t as |t Deve lops . Gainesville, Florida: University of Florida Agricultural Extension Service, Economics Series 64-6, September, 1964.

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172 Sauer, M. R. "Flowering in the Sweet Orange". Austral i an Jou rnal of Aqricul tura] Research , Vol. 5 (195^), PP. 649-657. Score, R. W. and Newman, J. E. "A Phenological Study of the Essential Oils of the Peel of Valencia Oranges". Agricultural Mieteorolog v. Vol. k (1967), pp. 11-26. Shoemyen, Janos. "Drainage Techniques Still an Issue in Flatwoods Citrus", Citrus and Vegetable Magazine , Vol. 32 (February, I969) , pp. 8, 37. Smith, Paul F. and Rasmussen, Gordon K. "Relation of Potassium Nutrition to Size and Quality of Valencia Oranges". Ameri can Societ y fo r Horti c ultural Science Proceedings , Vol. 7^ (1959), pp. 261-265. Soost, P. K. and Burnett, R. H. "Efforts or Gibberellin on Yield and Fruit Characteristics of 'Clementine' Handariii". Ameri can Socie ty for Horticultural Scien c e Proceedings , Vol. 77 (I96I), pp. 19'+-201 , Soule, M. J. and Lawrence, Fred P. Testing Orange s for Processing . Gainesville, Florida: Agricultural Extension Station, Circular 18^1, June, 1958, Spreen, William C. "Empirically Determirted Distributions of Hourly Temperatures". J ourna i of Met eorolo gy, Vol. 13 (1956), pp. 351-355. Stal lings, James L, "Weather Indexes". Journal of Farin Econo mic s, Vol. kl (February, I96O) , pp. 130-186. Steward, Ernest H. ; Powell, David P.; and Hammond, Luther C, ilollX*-L'3'. Character! s t ics of S o me Representative Soils of Florida . W a 3 h i n a t o n , D. C. : U. S. Department of Agriculture, Agriculture Research Service, ARS itl-63, April , 1963. Stout, Roy. Size o f Fruit and Droppaqe Rates Influence Total Citru s Prod uc tion . Gainesville, Florida: Florida Agricultural Experiment Station, Agricultural Economics Report EC 62-2, I96I. Stout, Roy. Florida Citr us Fr uit and Tree Losses from the Dec ember, 1962 Fr eeze. Gainesville, Florida, Florida Agricultural Experiment Station, Agricultural Economics Mimeo Report EC 64-7, 1964. Stout, Roy . Specific Gravit y as a Means of Estim a ting Jui ce Yields of Freeze D ama ged Valenci a O ranges. Gainesville, Florida: Agricultural Extension Service, Circular S-I5O, March, 1964, Swanson, Earl R, "Problems of Applying Experimental Results to Commercial Practice", J ourna l of Farm Economics , Vol, 39 (May, iS5/), pp. 382-389. Teague, C, P, "Improve Fruit Sizes with Better Water Distribution". Calif ornia Ci trograph. Vol. 34 (1949), pp. 398-400.

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173 Thompson, Arthur T. "The Size of Grain Stocks That Should Be Maintained", Weathe r and Our Foo d Supply. Ames, lovja: Iowa State University, Center for Agricultural and Economic Development, Report 20, 196it, Thompson, C. R. "Effects of Air Pollutants on Lemons and Navel Oranges", Cal ifornia A qricul t ure. Vol. 22, No, 9 (1968), pp. 2-3. Tramel , Thomas E. "Alternative Methods of Using Production Functions For Making Recommendations". Journal of Farm Economi cs. Vol. 39 (August, 1957), pp. 790-793. Tukey, Loren D. Periodicity in the Growth of Fruits of A pples, Peaches and Sour Cherries with Some Factors Influencin g this Deveiopment . University Park, Pennsylvania: Pensyivania State University, Agricultural Experiment Station Bulletin 661, September, 1959, Wadleigh, Cecil. "The Need to Evaluate V/eather". Weather and Our F ood Su pply. Ames, Iowa: Iowa State University, Center for Agricultural and Economic Development, Report 20, 1964. Wander, I. W. "An Interpretation of the Cause of Water-Repel lent Sandy Soils Found in Citrus Groves in Central Florida". Sci ence . Vol. 110 (1949), pp. 299-300. Willet, Hurd C. "Evidence of Solar-Climatic Relationships". We a the r_ an d Our Food '^ upoiy. Ames, Iowa: lov-'a State University, Center for Agricultural and Econom.ic Development, RepcrE 20, 1964, Winston, J. R. "Vitamin C Content and Juice (Quality of Exposed anc Shaded Citrus Fruits". Florida State Hq r_LJ cultural Societ y Proceedings . Vol. 60 (1947), pp. 63-67. "Yields Affscted by Tree Age and Spacing, Records Show". Ca i i f ern! a Ci troqraph. Vol, 43 (November, 1957), p. 9. Young, T. W. "Soil Moisture and the Citrus Tree Root System". FJonde State Horticultur al Society Proceedings . Vol. 61 {]SkB) , pp. 74-79. Young, T. V/, "The Economy of Adequate Drainage for Citrus in Florida Coastal Areas". Florida Sta te Horticu l tural Society Proceedings, Vol. 64 (1951), pp. 60-64.

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This dissertation w-.s propcr^c under .he ciir^c;ior; of Lne cli3i niian or ine canci date ' s SLipervisory cor;..:.! ttee and h^is t-er. evp.-ovc. by all mei-r,bers of that coni.r.i ttee. It wciS SLibnii tied zc the Dean c' tne College of Agriculture and to me Graduate Council, and vvas approved "s partial fulfil '.-cni g' ta ric,..i re.T.ents for the degree of Doctor of Phi l-vso.-.-.y. O'JIlo, li;/u /V^ A^ juon, College of Agriculture Dein, Graduate Scnco'. Supervisory Committee: y^/h^ ^^. .^Z^^-^^^c^ ^^ una; rri,an £^L . ^iAju^^^c-^'O-'^ il_L o ^JtSJJkc^^^.^.

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