Title: Effects of weather on orange supplies
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Title: Effects of weather on orange supplies
Physical Description: 175 leaves : ill. ; 28 cm.
Language: English
Creator: Parvin, David Woodrow, 1939-
Publication Date: 1970
Copyright Date: 1970
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Subject: Oranges   ( lcsh )
Agricultural Economics thesis Ph. D
Dissertations, Academic -- Agricultural Economics -- UF
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non-fiction   ( marcgt )
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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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Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000414730
oclc - 37760605
notis - ACG1915

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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.




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