EFFECTS OF WEATHER ON ORANGE SUPPLIES
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
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
TABLE OF CONTENDS
ACKNOWLEDGMENTS . . . . . . . . . .
LIST OF TABLES . . . . . . . . . . . .
ABSTRACT . . . . . . . . . .
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
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 . . . . . . .
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
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
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
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
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
13 Simple correlation coefficients for the
variables included in equation  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
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
David Woodrow Parvin, Jr.
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.
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
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
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
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.
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).
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
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
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
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
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 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.
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).
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
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.
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
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-
This cycle is absent at all elevations of less than ten miles.
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
A Brief History of Oranqes
Oranges are native to the tropical regions of Asia. They have
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
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
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.
THE STUDY OF WEATHER EFFECTS ON CROPS
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
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
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
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
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
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.
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
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.
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
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.
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).
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.
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.
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-
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
Ideal data for this approach would come from experimental plots
with everything held constant, except for weather, over the period of
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
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-
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.
Oury (63) has proposed that some aridity index be used as an
independent variable in relating weather to yield rather than such
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
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
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-
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' 
Y = b" + b" t + bA (P/1.07T) + e" 
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
 and ) 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
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  and . Likewise, Oury reported that equations
 and  gave more logical structural estimates of the parameters.
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 
Y = Yield
A through D = The number of drought-days in successive periods
through the growing season.
The coefficients of equation  were used to assign weights to
the individual drought-days which occurred during the three years of
the experiment. From experimental data with various levels of nitrogen
Y = 92.95 + .4834N .001N .5981D 0028ND 
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
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
Yt = -5.1443 + 3.7902Zt .1164Z2t + 2.1882t
158t + .0026t R = .90 F6]
Zt = -.689Xti + .0373Xt2 + .... + .0912Xt8
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
t = Time.
If Zt and Zt2 are substituted into equation , 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
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
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
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).
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,
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:
Event Descriptjon of average tree yield
A Slightly above average
B Slightly below 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
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.
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; 
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
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.
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.
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
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
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.
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,
.----------------------90 pound boxes-----------------------
(9, p. 58) and Savage (71, p. 3).
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
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.
4) High hanmock soils are best. The surface layer of this soil
type is usually thicker and darker because of higher organic matter
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.
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
The major components of weather, rainfall and temperature, are
discussed in this section. For levels of rainfall and temperature
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.
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).
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.
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
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
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
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).
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
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
from commercial groves will not reflect any variability due to such
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.
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
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
General Models Suggested by
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 (52) reported that the yield of a California orange tree
was related to:
1. Number of entirely cloudy days (December 16-February 15)
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,
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 (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."
Y = a + ZBiXi + e, i = 1, 2,..., 16 
Y = April 1 average volume per fruit in cubic inches
(i.e., harvest size).
XI = October 1 size.
X = X
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,
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
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
Y = 20.51 + 1.211X1 + .046X2 .044X [I]
.232X4 + 2.140X5
Y = Same as equation 
X = October 1 size.
X2 = Total rainfall from February I to October I.
X = Same as equation 
X = Average September temperature.
X5 = Same as equation 
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-
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.
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
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
ANALYTICAL METHOD AND THE DATA
The Model Estimated
The mathematical representation of the real world offered as a
general theoretical model in equation  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  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,
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-
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  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
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'
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,
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
 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
(macro) in sth county and tth year. And while  includes a single
yield function for each tree, equation [II] represents a production
function for each variety (macro) by county.
As with equation , 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-
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
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
EYrst = Hrs (Arst I Crs. Gs.); r =1,2; s= ...- 8, 
EY = Expected production of rth variety in sth county and
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
varieties in sth county production over all years.
Specifically, the set A included 22 variables. Variable I
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.
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;
Prst = (Yrst (as defined in equation [II]) EYrst
(as defined in equation ) 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
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
of trees in the county.
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
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
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
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
County Month(s) for which
Code Station Time interval data were missing
Bradenton Exp, Sta.
Bradenton 5 ESF
Tarpon Sps. Sew. P1.
Lake Alfred Exp. Sta.
Fort LaJ'=r- ale
aSee Table 5 (p. 70) for names
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
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
IThe counties which made up the study area are the first eighteen
listed in Table 5, page 70.
-o CO r-C 04 O-f 0 m-\D r C: i- (ro, cO .0 o \ C4 0or-- C'o
4u-' = Cu
r- "I C' I N c'! C o 0 r O o o c Iii 0 m N 0
i I -: r f 4 fn CM -:t 00o M C: Mno C0 Lr\\c 04N OD -
"Q Oh J L ." it ri -u ,,-. r--.- c- O m0 (ri, cn -, ---C n r" --. o 4 .
0 kn u Ln Looo r- ooCo)o0 O 0o
QU c 00 O-
a) a ooooooooooooooooo o0000
u I Oh O r L- mr-- rV m oO L tOLn r^ ", ur--N -- L, O
U 4-M C'300\ C"I'.0 N CM C 0 '.0M0o '.0 N r'.0 3\C 1.Nj 0 '.0
cu m 0 0 C 0 040 -:rU:1- 0040 O mC 0 0
. L C U -- m -- 0 1 CO 4 C of C 0 0-mO -C
R- 0 a) a)C U OO3 OcoLn\oU0')0o0\ CUC U c (o-5%0 m )cUC oG)
0 u ~ -. o\ 0 roO o ou L.'A Ln- Li 0 -'C, ,o Coo
a) I IO
-' Ut V a) CU T 00 00o 00 Z00 w cc00.o- 0 r000 0- 0000
- C 00000000000C 00000000
4-' 0 0I0l 3 0 0 0 C j- 0C on 0 C0 0 C Lc- C0 0 00C 00 -.T
G- a c4 -t--Z t ', c-clOcUC 0C-CAc o -:-.l .o s00
00 0 A 0 D -
3- I n UL
0>- 1 ai 000 00000000000000o00
.0 0' OCCOO Crsil O L01-04- 00 C7CLnCO-t Lrn C)
an) c3 -i '\r .c o i- -0 1-0 10 r LO L- r.- CO Ln
^-. > c>- 0 c-I i-.2 LOU) rc0) oC0 -o Ni r3-0 4I\0 03-
a) (I 0 I 1 1 I I 1 I I 1 1 I 1 1 I 1 I I I I
-- *- n CU 0)0-C cICm-0 u) r 0-4cU0 0 N CmC L.\0' U
.0 II f -- r Lr U L n UI) -0- LOLT h'P. ) L 0 L 0\) \0 \f. \0 f0 O0 '. '.0
1- > I4) 1 ^ ^. ^ ^ ^.n ^ ^ ^- ^ ,- ^. ^ ^ ^ ^
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.
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
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.
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
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.
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
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)
Source: Harrison and Choate (37, p. 34).
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
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.
Source: Personal conversations with Mr. Larry K. Jackson, Instructor,
IFAS, Extension Service, University of Florida.
Table 12: Fertilizer materials commonly applied to citrus.
Nitrate of Soda-Potash
Nitrate of Potash
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_____ _ _~
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.
Bounds on estimates of the average yield per tree by age and
variety (macro) were available due to earlier work by the Florida
Crop and Livestock Reporting Service and by Savage, and Chern.
Supra, pp. 43 and 44.
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:
EY = E B .X
rst j=4 sj rst [IC]
A 1 th
EY = Expected production for the r variety (macro)
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).
Bsj = Average yield in s county for j age,
Observations were not available on rY Conceivably, an esti-
mate of equation  could be obtained with least squares smoothing
of the data on production and tree numbers by age. Equation  has
twenty-two coefficients and since only twenty observations were avail-
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
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 .
Suora, p. 7.
3See Havlicek (29) for discussion of methodology.
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 . 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.
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
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.
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.
regressors for equation . 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.