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Tree wraps and microsprinkler irrigation for freeze protection of young citrus trees

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Title:
Tree wraps and microsprinkler irrigation for freeze protection of young citrus trees
Creator:
Rieger, Mark, 1960-
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[s.n.]
Publication Date:
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English
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xii, 178 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Citrus trees ( jstor )
Fiberglass ( jstor )
Freezing ( jstor )
Irrigation rates ( jstor )
Irrigation water ( jstor )
Simulations ( jstor )
Surface temperature ( jstor )
Surface water ( jstor )
Tree trunks ( jstor )
Water temperature ( jstor )
Citrus fruits -- Frost protection ( lcsh )
Dissertations, Academic -- Horticultural Science -- UF
Horticultural Science thesis Ph. D
Plants -- Winter protection ( lcsh )
Trees -- Frost protection ( lcsh )
City of Gainesville ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1987.
Bibliography:
Bibliography: leaves 165-177.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Mark Rieger.

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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17886188 ( OCLC )
AFA2032 ( NOTIS )
AA00004846_00001 ( sobekcm )

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TREE WRAPS AND MICROSPRINKLER IRRIGATION FOR
FREEZE PROTECTION OF YOUNG CITRUS TREES
BY
MARK RIEGER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987


This dissertation is dedicated to my family members
and to the loving memory of Suzanne Lynn DiCenzo


ACKNOWLEDGEMENTS
Deepest appreciation is extended to supervisory committee
chairman, Dr. F. S. Davies, and cochairman, Dr. L. K. Jackson, for
support and aid throughout the course of this project, and L. W.
Rippetoe for technical assistance and valuable moral support.
Special thanks are given to committee members Dr. G. H. Sraerage,
Dr. W. J. Wiltbank, and Dr. G. Yelenosky for participating in
examinations and reviewing the manuscript; to Jonathan Crane for acting
as a sounding board and for his constructive criticism of seminars; to
Dr. E. Chen, Prof. G. Cook, Dr. A. Datta, Dr. D. R. Farber, Dr. W.
Huber, and Dr. J. D. Martsolf for valuable assistance with simulation
programs; to Steven Hiss for assistance with graphics; to Dr. G. A.
Couvillon for providing the incentive to finish the dissertation
(nearly) on schedule; and last but not least, to my family members and
friends for support and timely diversion of my attention to the finer
things of life.
iii


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT xi
CHAPTER
I INTRODUCTION I
II REVIEW OF THE LITERATURE 4
Introduction 4
Freezing Injury, Stress, and Cold Acclimation 4
Freezing Injury, Stress, and Cold Acclimation
in Citrus 10
Freeze Protection Methodology 15
III TRUNK TEMPERATURE, FREEZE SURVIVAL AND REGROWTH
OF YOUNG CITRUS TREES AS AFFECTED BY TREE WRAPS
AND MICROSPRINKLER IRRIGATION 26
Introduction 26
Materials and Methods 27
Results and Discussion 29
Conclusions 39
IV MICROCLIMATE OF YOUNG CITRUS TREES PROTECTED BY
MICROSPRINKLER IRRIGATION DURING FREEZE CONDITIONS 43
Introduction 43
Materials and Methods 44
Results and Discussion 46
Conclusions 55
V TRUNK TEMPERATURE, LIGHT INTENSITY, AND SPROUTING OF
WRAPPED AND UNWRAPPED YOUNG 'HAMLIN' ORANGE TREES
FOLLOWING A FREEZE 56
Introduction 56
Materials and Methods 57
Results and Discussion 58
Conclusions 64
iv


VI MODELING AND SIMULATION OF TREE WRAPS AND
MICROSPRINKLER IRRIGATION FOR YOUNG CITRUS
FREEZE PROTECTION 65
Introduction 65
Model development 67
Simulation 83
VII THERMAL PROPERTIES AND SIMULATION OF FREEZE
PROTECTION PERFORMANCE OF TREE WRAPS FOR
YOUNG CITRUS TREES 88
Introduction 88
Materials and Methods 90
Results and Discussion 95
Conclusions 119
VIII SIMULATION OF PROCESSES INVOLVED IN MICROSPRINKLER
IRRIGATION FOR FREEZE PROTECTION OF YOUNG CITRUS
TREES 120
Introduction 120
Materials and Methods 122
Results and Discussion 125
Conclusions 146
IX CONCLUSIONS 148
Field Research 148
Laboratory and Computer Simulation Analyses 149
APPENDIX
A TREE WRAP SIMULATION PROGRAM 151
B TREE WRAP AND MICROSPRINKLER IRRIGATION SIMULATION
PROGRAM 156
LITERATURE CITED 165
BIOGRAPHICAL SKETCH 178
v


LIST OF TABLES
Page
Table 3-1. Effect of microsprinkler irrigation rate and spray
pattern on height of live wood, shoot dry weight,
and number of shoots per trunk on 22 April 1985 34
Table 3-2. Height of live wood of young 'Hamlin' orange trees
on 14 April 1986 as influenced by microsprinkler
irrigation rate during several freezes in Dec.-Jan.
1985-86 38
Table 3-3. Dates of freezes, minimum air temperatures, most
efficient irrigation rates, and coefficients of
determination from quadratic regressions of trunk
heating efficiency vs. irrigation rate during Dec.
-Jan. 1985-86 41
Table 5-1. Numbers and dry weights of trunk sprouts on freeze
damaged young 'Hamlin' orange trees on 13 May 1986
as influenced by various trunk wraps 62
Table 6-1. Definition of symbols used in model development 87
Table 7-1. Thermal conductivity, density, specific heat,
and thermal diffusivity of tree wraps used for
young citrus freeze protection 96
Table 7-2. Minimum trunk and air temperatures of young 'Hamlin'
orange trees wrapped-with fiberglass, fiberglass
with water containers or styrofoam wraps on 4 mild
freeze nights in 1987 100
Table 7-3. Predicted minimum trunk temperatures for the
20-cm height for simulated freezes when air
temperature decreases from 0 C_^o -5 C in 8 hr
with windspeed of 0.5 0.1 m s using either
air temperature or mean radiant in calculation
of radiant heat transfer 109
Table 7-4. Simulated minimum trunk temperatures underneath
fiberglass wraps at various heights from simulations
using different soil temperature regimes and freeze
conditions from 21 Jan. 1985 118


LIST OF FIGURES
Page
Fig. 3-1. Truak temperatures of 2-year-old 'Hamlin' orange trees
during an advective freeze of 20 Jan. 1985 as influenced
by raicrosprinkler irrigation and tree wraps 30
Fig. 3-2. Trunk temperatures of 2-year-old 'Hamlin' orange trees
during a radiative freeze of 26 Jan. 1985 as influenced
by microsprinkler irrigation and trunk wraps 31
Fig. 3-3. Effect of irrigation rate on trunk heating efficiency
of microsprinkler irrigation treatments for young
'Hamlin' orange trees 33
Fig. 3-4. Trunk temperatures of 2-year-old 'Hamlin' orange
trees and air temperatures during advective freezes
of 25-26 Dec. 1985 ayd 27-28 Jan., 1986 for 0, 12,
22, and 38 liter hr microsprinkler irrigation
treatments 37
Fig. 3-5. Trunk heating efficiency as a function of irrigation
rate for 5 freezes during Dec.-Jan. 1985-86 40
Fig. 41. Air temperature in the canopy of 2-year-old 'Hamlin'
orange trees during a severe advective freeze on
20-21 Jan. 1985 and a radiative freeze on 26-27
Jan. 1985 48
Fig. 4-2. Dewpoint temperature in the canopy of 2-year-old
'Hamlin' orange trees during a severe advective
freeze on 20-21 Jan. 1985 and a radiative freeze
on 26-27 Jan. 1985 49
Fig. 4-3. Net radiation above 2-year-old 'Hamlin' orange trees
during a severe advective freeze on 20-21 Jan. 1985
and a radiative freeze on 26-27 Jan. 1985 51
Fig. 4-4. Net radiation above 2-year-old 'Hamlin' orange trees
during a radiative freeze on 11-12 Jan. 1987 52
Fig. 4-5. Soil temperature measured 1 cm below the surface and
next to trunks of 2-year-old 'Hamlin' orange trees
during freezes on 25-26 Dec. 1985, 26-27 Dec. 1985,
and 27-28 Jan. 1986 54
vii


Fig. 5-1.
Fig. 5-2.
Fig. 6-1.
Fig. 6-2.
Fig. 6-3.
Fig. 6-4.
Fig. 7-1.
Fig. 7-2.
Fig. 7-3.
Fig. 7-4.
Fig. 7-5.
Fig. 7-6.
Fig. 7-7.
Diurnal trunk temperatures of young 'Hamlin' orange
trees underneath various trunk wraps during a typical
sunny day and a cloudy day in March, 1985 59
Diurnal photosynthetic photon flux underneath various
tree wraps on 2-year-old 'Hamlin' orange trees during
a sunny day and a cloudy day in March, 1985 61
Conceptual model of the tree wrap/microsprinkler
irrigation system for young citrus freeze protection
illustrating heat transfer processes 68
Three-dimensional representation of the model system
showing a representative finite region of heat storage ... 72
Schematic diagram of interception of irrigation
water by the tree wrap when microsprinklers were
positioned so that water sprayed above the top of
the wrap, or only on the wrap surface 80
Cross-section of the model system showing 70% coverage
of the wrap surface with water 81
Schematic representation of the device used to measure
the thermal conductivity of tree wraps in-situ 92
Observed trunk and air temperatures on 20-21 Jan.
1985, 26-27 Jan. 1985, 25-26 Dec. 1985, 26-27
Dec. 1985, and 27-28 Jan. 1986, and predicted trunk
temperatures from simulation of the freezes 102-103
Regression of predicted vs. observed minimum trunk
temperature using 1-dimensional and 2-dimensional
models 104
Predicted trunk temperatures for 4 commercially
available wraps, styrofoam, fiberglass, polystyrene,
polyethylene, during a simulated freeze where temperature
drops curvilinearly from 0^to -5 C in 8 hr, and
windspeed is 0.5 0.1 m s 106
Predicted trunk temperatures for air, a wrap with
thermal properties of dry sand, and a fiberglass
wrap Ill
Predicted trunk and air temperatures for young
citrus trees with fiberglass wraps during 6 different
simulated freezes 113
Predicted trunk temperatures as affected by variations
in trunk diameter with 13-cm diameter fiberglass
wraps, and variations in wrap diameter with 2.4-cm
diameter trunks 115
viii


Fig. 7-8. Predicted minimum trunk temperatures of young citrus
tree trunks under fiberglass wraps as influenced by
windspeed when air temperature drops from 0 to -5 C
in 8 hr 117
Fig. 8-1. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 126
Fig. 8-2. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 57 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 127
Fig. 8-3. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 87 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 128
Fig. 8-4. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 22 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986 and a radiative freeze on 26-27
Dec. 1985 130
Fig. 8-5. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986, and a radiative freeze on 26-27
Dec. 1985 131
Fig. 8-6. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 57 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986, and a radiative freeze on 26-27
Dec. 1985 132
ix


Fig. 8-7. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liter hr microsprinklers
during mild freezes on 11-12 Jan. 1987 and 23-24
Jan. 1987 133
Fig. 8-8. Predicted minimum trunk temperatures plotted against
those observed at the 20-cm height for all irrigation
rates and dates used for validation 135
Fig. 8-9. Cross-section of a wrap showing the thickness of
simulated ice on different regions of the wrap surface .. 136
Fig. 8-10. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of fraction of water intercepted
by the wrap 138
Fig. 8-11. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of water temperature 140
Fig. 8-12. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of percent coverage of the
wrap surface with water 142
Fig. 8-13. Simulated minimum trunk temperatures at the 20-cm
height for 2-cm-diameter 2-year-old citrus trees
with fiberglass tree wraps under severe advective
and radiative freeze conditions. Simulations were
run at windspeeds of 0, 1, 4.5, and 10 m s 145
Fig. 8-14. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter young citrus trees with fiberglass
tree wraps under severe advective and radiative
freeze conditions. Simulations were run using
different values relative humidity 146
x


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
FREEZE PROTECTION OF YOUNG CITRUS TREES
WITH TREE WRAPS AND MICROSPRINKLER IRRIGATION
By
Mark Rieger
August, 1987
Chairman: Frederick S. Davies
Cochairman: Larry K. Jackson
Major Department: Horticultural Science (Fruit Crops)
Tree wraps and microsprinkler irrigation provide a reliable and
economical alternative to soil banks and orchard heaters for freeze
protection of young citrus trees. Field experimentation and computer
simulation were employed to study the freeze protection capabilities of
tree wraps alone and in combination with microsprinkler irrigation.
Trunk temperatures of 2-year-old 'Hamlin' orange (Citrus sinensis (L.)
Osb.) trees during freeze conditions were greater for wrapped trees
irrigated with a 90 spray pattern than for those irrigated at the same
rate with a 360 spray pattern. An irrigation rate of 38 liters hr *
provided the greatest increase in trunk temperature per unit water
applied during several freezes. Air temperature, dewpoint and net
radiation in the tree canopy were not increased by microsprinkler
irrigation during freeze conditions, although soil temperature was 2 to
6 C higher for irrigated than for unirrigated trees.
Thermal properties of commonly used tree wraps were determined in
the laboratory. Thermal diffusivity was lowest for styrofoam wraps with
water containers, intermediate for 9-cm diameter fiberglass wraps, and
highest for thin-walled polyethylene and polystyrene wraps. Thermal
xi


diffusivity was indicative of freeze protection capability of tree
wraps.
The simulation model of the tree wrap/microsprinkler system
predicted trunk temperatures within 1 C of observed means when
simulating the effect of tree wraps alone, although predictions
generally were Io to 3 C lower than observed means when simulating the
irrigation process. The rate of air temperature decrease, wrap
thickness and trunk diameter were positively correlated with level of
freeze protection in computer simulations of fiberglass wraps; however,
freeze duration was negatively correlated with level of freeze
protection. Windspeed had little effect on trunk temperature of
unirrigated wrapped trees, but trunk temperature of irrigated wrapped
trees was reduced 5 C as windspeed increased from 0 to 10 m s
Increasing the amount of water intercepted by the wrap and coverage of
the wrap surface with water increased trunk temperature during simulated
freezes. Temperature of the irrigation water was positively correlated
with trunk temperature for radiative but not advective freeze conditions
in simulations.
xii


CHAPTER I
INTRODUCTION
Freeze damage of young citrus trees has been a problem since the
establishment of the Florida citrus industry. Young trees are
particularly prone to freeze damage due to their small size and vigorous
growth habit. Citrus growers spend $18 to $42 and 3 to 4 years bringing
a young tree into production (95). Traditionally, soil banks have been
used for freeze protection of young citrus trees (59). Soil banks
provide several degrees C protection to the lower portion of the tree,
but are labor intensive and often result in mechanical or disease damage
to the trunk. To avoid the problems associated with soil banks,
Rohrbaugh designed the first insulative tree wrap, consisting of rock
wool inside a 30-cm cylinder of asphalt felt which surrounded the lower
50 cm of a young tree (80). Results from preliminary tests with similar
wraps appeared promising; however, the types of tree wraps used
currently provide only 3 C protection in some cases, and virtually no
protection in others (68, 121).
Overhead irrigation, petroleum fuel heaters, and wind machines have
been used successfully to protect young and mature citrus trees.
However, overhead irrigation systems often are not designed to apply
water at rates necessary for protection under advective freeze
conditions (46). Heating groves or nurseries with petroleum products is
an effective means of cold protection, but rising fuel costs have
limited the use of this practice to high cash value crops (107). Wind
1


2
machines rely on Che presence of an inversion layer (45), and therefore
are ineffective under advective freeze conditions.
A reliable and economical alternative to the conventional methods
listed above for freeze protection of young citrus is low-volume
microsprinkler irrigation. This system provides protection to the lower
portion of the tree only, much like a soil bank. Previous studies have
shown that trees irrigated with microsprinkers are usually killed above
a height of 50 to 70 cm during severe freezes (30, 104). However,
freeze-damaged trees often produce several vigorous shoots from the
remaining portion of scion wood and attain heights of 1 to 2 m by the
following autumn (104). The net result is that the grower loses about 6
months' growth on the tree but saves the cost of purchasing and
resetting new trees, which is particularly important considering the
scarcity and high prices of nursery trees due to the recent outbreak of
citrus canker disease in Florida.
Microsprinkler irrigation has been reported to alter the
microclimate of citrus plantings by raising the air temperature within
the canopy (15), creating fog or mist, and/or decreasing radiant heat
loss from the irrigated area (53, 107, 108). However, the effects of
microclimatic changes on young citrus tree temperatures and subsequent
freeze survival are unclear.
Recommendations regarding irrigation rate and spray pattern are
currently lacking, although preliminary studies indicate that 76 to 84
liters hr sprayed in a 90 pattern will protect young trees under most
freeze conditions (30, 107). Davies et al. (30) suggest that
microsprinkler irrigation combined with an insulative wrap provides
greater protection for young citrus trees than irrigation or wraps used


3
separately. However, wraps left on freeze-damaged trees may reduce
trunk sprouting and delay canopy reestablishment following a severe
freeze. Further research with tree wraps and microsprinkler irrigation
is needed to determine the effects of irrigation rate, spray pattern,
and wrap type on trunk temperature, survival and sprouting of young
citrus trees.
Modeling has been used successfully to predict overhead irrigation
rates required for freeze protection of tree crops (20, 46, 112).
Hence, modeling and simulation of the tree wrap/microsprinkler
irrigation system of freeze protection may yield useful information on
system design and behavior. Analysis of a model can produce information
unobtainable from field or laboratory experiments due to uncontrolled or
unrepresentative environmental conditions. Furthermore, experiments can
be performed with a simulation model more rapidly and inexpensively than
field experiments, improving the productivity and efficiency of the
freeze protection research program.
Research objectives of this dissertation were
1. to study the effects of tree wraps combined with various
microsprinkler irrigation rates and spray patterns on trunk temperature,
survival and regrowth of young citrus trees;
2. to determine whether microsprinkler irrigation alters the
microclimate of a young citrus tree during freeze conditions;
3. to determine the influence of various tree wraps on trunk
temperature and sprouting of freeze-damaged trees;
4. to model the dynamic behavior of trunk temperature during
freeze conditions as influenced by tree wraps and microsprinkler
irrigation


CHAPTER II
REVIEW OF THE LITERATURE
Introduction
Man's efforts to protect crops from freezing injury began at least
2000 years ago (83). In addition, the causes of freezing injury in
plants have been studied and speculated upon for well over 100 years
(124). Impetus for continued research in these areas stems from the
huge economic losses of agricultural commodities that occur annually due
to late spring or early fall frosts, or midwinter freezes. Literature
on freezing injury, protection and related topics is voluminous.
Several reviews (18, 75, 86, 91, 98, 116, 124, 135, 157, 167) and books
edited by Levitt (76) Olien and Smith (99), and Li and Sakai (78) have
covered various aspects of freezing stress and injury, and cold
acclimation and hardiness. The intent of this review is to discuss
general aspects freezing injury, resistance to freezing stress, and cold
acclimation in woody plants with special attention to citrus.
Herbaceous plants, with the exception of winter grasses (82), have
little or no resistance to freezing stress or ability to acclimate and
are therefore omitted. In addition, methods of freeze protection will
be reviewed.
Freezing Injury, Stress, and Cold Acclimation
Freezing Injury
Freezing injury results from ice formation in plant tissues and not
low temperatures per se (92). Manifestations of freezing injury include
4


5
sunscald and bark splitting of tree trunks, blackheart in trunks and
stems, death and abscission of leaves, flowers, and fruits, frost rings
on fruits, midwinter kill of dormant flower buds and stem cambia, and
death of the entire vegetative structures of cold tender plants (18,
135, 136). These visual symptoms ultimately result from processes which
occur at the cellular level.
Plant cells are injured or killed by either intracellular or
extracellular ice formation (75). It is widely accepted that
intracellular ice formation is always fatal to plant cells, although how
intracellular freezing kills the cell remains unanswered (124). It
follows that cells which survive freezing do so by tolerating
extracellular ice formation. Therefore, much attention has been devoted
to processes which occur during extracellular ice formation and the
resulting consequences.
Extracellular freezing may be summarized as follows. As
temperature decreases below 0 C, water in plant tissues initially
supercools few to several degrees (18, 86). Heterogenous nucleation
occurs in cell walls and extracellular spaces and ice crystals grow in
these areas at the expense of water inside the cells (91, 92). As long
as exosmosis of intracellular water keeps pace with the reduction in
external vapor pressure with decreasing temperature, equilibrium between
the intracellular solution and the external phase is maintained, and
intracellular freezing is avoided by colligative freezing point
reduction (86). However, supercooling and intracellular freezing are
favored at rapid cooling rates (> 10 C min ^), especially if the
permeability of the plasma membrane to water is low (85).


6
Extracellular freezing is tolerated to varying degrees in plant
tissues depending on species, time of year, preconditioning, plant part,
freezing rate and water content (135). Several hypotheses attempt to
explain causes of cell death due to extracellular freezing. Levitt (74)
hypothesized that intermolecular disulfide bonds formed among proteins
with exposed sulfhydryl groups during freeze dehydration of cells by
external ice. He stated that this resulted from the close proximity of
proteins due to the reduced volume of cytoplasm. Williams (140)
hypothesized that there was a minimum volume that cells attained during
freeze dehydration below which cell death occurred. This minimum volume
was the same for acclimated and unacclimated cells, but the temperature
at which minimum volume was reached was lower for acclimated cells due
to higher solute and bound water contents. Solution effects (i.e.,
concentration of toxic electrolytes, pH changes, precipitation of
compounds, salting out of proteins) may result in injury to cell
membranes and other cellular components during freeze dehydration
(86, 124). Recently, the behavior of the plasma membrane during
freezing was analyzed in isolated protoplasts (124). Apparently,
vesiculation and deletion of membrane material occurs in unacclimated
protoplasts, which causes altered osmotic behavior and cell lysis upon
thawing, whereas these processes are not observed in acclimated
protoplasts. Therefore, the plasma membrane may have an important role
in cold acclimation and tolerance of extracellular ice. However, none
of the above hypotheses are without limiting weaknesses, and no single
hypothesis applies to all plant cells and all freezing situations.


7
Resistance to Freezing Stress
Resistance to freezing stress is conferred by avoidance and/or
tolerance of ice formation within the plant (76).
Avoidance. Plants avoid freezing in low temperature environments
by desiccation, colligative freezing point depression, and supercooling
(75). Desiccation occurs in seeds and buds only, and freezing point
depression allows avoidance of freezing to about -4 C at most.
Alternatively, supercooling is a very effective avoidance mechanism, but
usually occurs in plants which also tolerate extracellular ice formation
(2, 42). One exception is shagbark hickory, which avoids freezing
injury to -40 C by supercooling of the entire volume of liquid water in
stems (18).
Tolerance. Reasons for difference in tolerance of extracellular
ice among species are unknown, although apparently, hardier plants
survive freezing of a larger amount of their osmotically active water
(1, 16, 18).
The latitudinal range of a particular plant species is related to
its relative tolerance of extracellular ice formation (17). Species
which tolerate little extracellular ice such as citrus, are limited to
southern latitudes where freeze events are less severe and occur
infrequently. Temperate woody plants such as Vitis, Prunus, and
Rhododendron tolerate extracellular ice in most tissues and avoid ice
formation in flower bud primordia via deep supercooling (4, 42, 142).
These plants are not found at latitudes where temperatures below about
-40 C occur, because deep supercooled cells freeze and die at this
temperature due to homogenous nucleation of intracellular water (17).
Species of the northern boreal forests such as Betula and Populus do not


8
deep supercool, but tolerate freezing of all their osraotically active
water outside the plasmaleraraa (18). These species are capable of
surviving immersion in liquid nitrogen (-196 C) after slow cooling to
-30 C.
Cold Acclimation
Irrespective of freezing tolerance mechanisms, temperate woody
plants acclimate to low temperatures in 2 distinct stages. Stage I
acclimation is a phytochrome-mediated response initiated by short days
and enhanced by warm temperatures (38, 58, 64, 87). Moderate increases
in hardiness occur during stage I acclimation (135). A translocatable
"cold hardiness producing substance" presumed to be abscisic acid (63)
has been shown to be involved in stage I acclimation (37, 66, 125).
Stage II acclimation is initiated by exposure to low, nonfreezing
temperatures or frost, and does not involve translocatable substances
(37, 58). Plants acclimate rapidly and to their fullest potential
during stage II acclimation.
Irving and Lanphear (64, 65) showed that woody plants would
eventually acclimate to normal levels when exposed to long days and low
temperatures, suggesting that low temperature has an overriding
influence on photoperiod in cold acclimation. Furthermore, they showed
that plants acclimate substantially before becoming dormant under long
day, low temperature (10 C) conditions (64). Apparently, dormancy and
cold hardiness are separate processes which occur coincidentally in the
natural environment in woody perennials.
Tumanov and Krasavtsev (127) discovered a third stage of hardiness
which develops during prolonged exposure to subfreezing temperatures,
and is rapidly lost upon rewarming. They stated that prolonged exposure


9
Co subfreezing temperatures allows sufficient time for water movement to
extracellular sites which prevents intracellular freezing, whereas
natural cooling rates are more rapid and result in supercooling and
intracellular freezing at higher temperatures. Similarly, Rajashekar
and Burke (118) found that prolonged exposure to subfreezing
temperatures reduced or eliminated low temperature exotherms indicative
of supercooling and intracellular freezing in Prunus flower buds.
Apparently, the permeability of the plasma membrane to water at
subfreezing temperatures and freezing rate dictate the ultimate
hardiness level a plant can achieve (85).
Several physical and biochemical changes occur in plants during
cold acclimation. Increased physical stability of the plasma membrane
observed during acclimation may result in reduced probability of
nucleation of the intracellular solution by external ice (124).
Increases in unsaturation of membrane lipids increases fluidity and
decreases the probability of membrane phase transition and subsequent
dysfunction of membrane-bound proteins (126). Permeability of the
plasma membrane to water increased during acclimation in Red-Osier
dogwood (88), but was similar in acclimated and nonacclimated
protoplasts isolated from rye leaves (34). The ratio of gibberellin to
abscisic acid-like substances decreased during stage I acclimation in
Acer leaves (63). Increases in soluble proteins, RNA, sulphydryl
compounds, sugars, amino acids, and organic acids occur during
acclimation of many plants (86). Water content, root hydraulic
conductivity, and storaatal conductance decreased in Red-Osier dogwood
during cold acclimation (54, 101, 135). As with the hypotheses of


10
freezing injury, none of the above physical and biochemical changes can
singularly explain the resistance to freezing injury in plants.
Freezing Injury, Resistance and Cold Acclimation in Citrus
Freezing Injury
Freezing injury to citrus can be economically devastating because
present and future crops are affected by a single freeze event. For
example, in Texas a single freeze in Dec. 1983 reduced the production of
the 1983-84 season by 70%, and extensive tree damage resulted in no
production the following year (123). In Florida, damage was estimated
at one half billion dollars from the 1962 freeze alone (151), and the
severe freezes of Dec. 1983 and Jan. 1985 reduced commercial citrus
acreage by over 80,000 ha in north-central Florida (141).
Manifestations of freezing injury in citrus range from partial
defoliation and fruit abscission to death of entire trees (151, 153).
Watersoaking appears as dull, dark areas on the leaf surface and is
indicative of ice formation within the leaves (113, 175). However, ice
formation in citrus leaves and stems is not always lethal (147, 175).
Bark splitting is thought to result from large ice masses forming in the
bark, creating pressure sufficient to force the tissues apart (153).
At the cellular level, Young and Mann (171) observed destruction of
vacuolar, chloroplast, and mitochondrial membranes in hardened and
unhardened sour orange leaves subjected to freezing at -3.3 and -6.7
C, respectively. They suggested that the nature of freezing injury in
leaves was physical, caused by ice crystal growth and subsequent
cellular disruption. However, they offered no explanation as to why
hardened leaves undergo less cellular disruption at the same freezing
temperatures than unhardened leaves, when both types of leaves contained


11
ice. Lower water content (167) and/or higher bound water fractions
(122) in hardened leaves may reduce the amount of ice formed at a given
temperature, resulting in less physical disruption than in unhardened
leaves. Among citrus species, however, Anderson et al. (1) found no
relationship between bound water content and freeze tolerance of leaves,
and suggested that hardier species tolerate a greater amount of their
water frozen than non-hardy species.
Resistance to Freezing Stress
Citrus species can survive extracellular ice formation within their
tissues (147, 175), although changes in ice tolerance during acclimation
remain unexplained (157). In addition, citrus avoids freezing injury by
supercooling to temperatures as low as -8 C in leaves and stems (158).
Citrus leaves are killed shortly after freezing occurs in the
supercooled state (69, 158). The extent of supercooling in young citrus
trees increased with cooling rate (164), cold hardening (61), and water
stress (154), and decreased in the presence of external moisture or ice
(155, 166). Also, the extent of supercooling varies with species and
cultivar (157), but not in such a manner as to provide an index of
interspecific or varietal differences in hardiness (158). Supercooling
may not be as important a factor as ice tolerance in citrus freezing
resistance because recent studies indicate that several tree species
supercool only Io to 2 C before freezing under field conditions (2, 4).
Anderson et al. (1) suggested that negative pressure potentials
arise in citrus leaf cells during freeze plasmolysis, decreasing the
amount of ice formed at any given temperature. This is unlikely because
negative pressure potentials would have to be extremely low (< -10 MPa)
to decrease the amount of ice formed significantly (86), and the only


12
documented measurements of negative pressure potentials are much higher
(-6 kPa) (5).
Cold Acclimation
It has long been recognized that environmental conditions preceding
a freeze influence the freeze survival of citrus (94). Greater freeze
damage in Florida and Texas than in California under similar freeze
conditions has been attributed to higher winter temperatures in Florida
and Texas which reduce cold acclimation (23, 24). Several studies have
demonstrated that citrus tolerates lower freezing temperatures if
preconditioned for several weeks at low, nonfreezing temperatures (147,
163, 165, 173).
Generally, environmental conditions which result in inactivity or
lack of growth promote cold hardiness in citrus (167). Girton (50),
Fawcett (35) and Ivanov (cited in 167) were among the first to report on
the influence of cool (< 13 C) temperatures on growth and cold
acclimation of citrus. Seedlings exposed to alternating temperatures
(warm days and cool nights) developed superior hardiness to those
exposed to constant low (3 C) temperatures (96). Yelenosky (147, 151)
used hardening conditions of 2 weeks at 21.1/10 C (day/night) followed
by 2 weeks at 15.6/4.4 C in laboratory experiments which resulted in .
maximum hardiness.
Light is necessary for cold acclimation in citrus (96, 144).
Length of the light period is positively correlated with growth (115,
163) but does not affect cold hardiness (96, 163) or induce bud dormancy
(167). Light allows continued photosynthesis and carbohydrate
accumulation during exposure to low temperature which is necessary for
cold acclimation in leaves and stems (160, 166). Although


13
photosynthetic carbon uptake decreases during cold acclimation (169),
metabolism of photosynthate also decreases (52, 160) which probably
allows for net carbohydrate accumulation. Furthermore, absence or
inhibited function of leaves disfavors cold acclimation (146), and
starch hydrolysis cannot account for increased levels of sugars in
leaves and stems (160).
Water stress increases both freezing tolerance (150) and avoidance
(154) in citrus. Wilcox (138) reported that low (5 C) root
temperatures induced cold hardening in citrus seedlings by reducing root
hydraulic conductivity and leaf water potential. Davies et al. (28)
reported that 'Orlando' tngelo trees not receiving irrigation in the
fall had less leaf and fruit damage than fall irrigated trees following
a radiative freeze. Conversely, Koo (71) found that trees irrigated
during the fall had less leaf and fruit damage following a freeze.
In the acclimated condition, cold hardiness varies widely among
citrus cultivars (157), but when unacclimated and actively growing,
hardy and nonhardy types are killed at similar temperatures (151). In
the acclimated condition, citrus cultivars/relatives can be ranked for
hardiness in decreasing order as follows: trifoliate orange, kumquat,
sour orange, mandarin, sweet orange, grapefruit, lemon, citron (157).
The hardiness of a scion cultivar is affected by the
species/cultivar used as a rootstock (40, 55, 172), although hardiness
differences due to rootstock are slight by comparison to cultivar
differences (157). Generally, more hardy species/cultivars used as
rootstocks impart more hardiness to a scion cultivar, hence the above
ranking also applies to scions grafted to the species/cultivars listed.


14
Several biochemical and physiological changes occur in citrus
during cold acclimation. Levels of soluble carbohydrates in leaves
increased rapidly during the first week of acclimation in 'Valencia'
orange, although levels in stems increased gradually over a 6-week
period (149). The principal sugars that accumulated in 'Redblush'
grapefruit were glucose, fructose, and sucrose (166). Increased levels
of soluble carbohydrates may lower the freezing point of the tissue
water colligatively, decrease the amount of ice formed at a given
temperature, and decrease the rate of ice growth through the tissues
(145, 160). All amino acids except proline, valine, and glutamic acid
decreased during cold acclimation at 10 C in 'Valencia' orange (149).
Proline accumulated in unacclimated, water-stressed citrus leaves (77),
hence increases in proline during cold acclimation may be induced by
reductions in water potential which occur during hardening (149).
Proline accumulation did not correlate well with cold hardiness among
citrus cultivars/species (152).
Water soluble proteins decreased in 'Redblush' grapefruit during
hardening, contrary to behavior of woody deciduous plants which
accumulate water soluble proteins during acclimation (166). No new
proteins were identified by gel electrophoresis following cold
acclimation of 'Valencia' orange trees (162). However, protein
denaturation increased with freeze damage, and was greater for
unhardened than hardened leaves (162). Increased levels of
hydroxyproline may result from protein denaturation during cold
acclimation (159).
Levels of unsaturated fatty acids and phospholipids increased
during cold acclimation of citrus leaves, and the magnitude of increase


15
was positively correlated with the relative cold hardiness of the 3
species analyzed (97). This is consistent with the theory that
increased membrane fluidity is partially responsible for increased
freezing tolerance in plants (86).
Freeze Protection Methodology
Methods of freeze protection were first developed 2000 years ago,
when early viticulturists protected grapevines from freezing with fires
fueled by prunings and dead vines (83). Since then, many different
methods of freeze protection have emerged. The concepts behind several
freeze protection methods are described in the following section with
reference to citrus, although nearly all of the methods can be applied
to other tree crops and cropping systems.
Site Selection
Students of pomology quickly learn that site selection is one of
the most important decisions a grower makes when establishing an orchard
(136). Latitude, topography, and proximity of bodies of water affect
the frequency and severity of freezes at a given site (9). Low-lying
areas or "frost pockets" are often 5 C colder than adjacent hilltops
under radiative freeze conditions, but may be slightly warmer than
hilltops under advective freeze conditions (70, 132). In Florida,
freeze probability and severity decrease with latitude (12, 70), and
sites downwind of large lakes can be 4 C warmer than upwind sites (9).
However, climatic changes can occur and render once productive sites
unsuitable for growth of a particular crop, which has apparently
occurred in citriculture in northern Florida (21).


16
Cultural Practices
Krezdora and Martsolf (72) recently reviewed effects of cultural
practices on citrus cold hardiness and orchard temperatures. They
emphasized the importance of weed-free compact soil for increasing soil
heat storage and conduction, proper row orientation for air drainage,
maintenance of a full canopy to intercept radiant heat from the soil,
and practices which keep trees in a healthy condition and maximize cold
hardiness. Leyden and Rohrbaugh (80) observed higher temperatures and
less freezing injury on citrus trees in sites with chemical weed control
than in cultivated or sodded sites.
Orchard Heating
Orchard heating is the oldest and most reliable method of freeze
protection (48, 83, 129). Several different types of fuels and heating
devices have been used (83), although ordinances prohibit the use of
those which produce excessive smoke and residue (129). The high costs of
petroleum fuels preclude their use except for high cash value crops and
in nurseries (107).
Heaters provide protection by raising the air temperature and by
producing radiant heat (48). Smoke particles are not of appropriate
size to retard radiant heat losses from an orchard, thus no added
protection is obtained by smoke (89, 132). Radiant heat production is
particularly important during windy, advective freezes when the
convective component of heating is reduced (8, 137). Gerber (44)
compared several types of heaters and found chat radiant heat output was
highest for those with large metal chimneys or mantles. Heater
placement is an important factor because radiant heat decreases
exponentially with distance (8, 33, 80). Absorption of radiant heat by


17
crees is maximized by placing hearers within rows rather than between
rows (33, 137).
Pollution and expense are not the only problems associated with
heating. Heaters are often difficult to light and maintain at a
constant burning rate (143). Refueling heaters individually is labor
intensive, and automated pipeline systems for refueling can malfunction
due to clogged valves (8). Furthermore, heaters interfere with routine
orchard operations during the summer (83).
Four models exist which describe theory and concepts involved in
freeze protection with heaters. Martsolf (83) has reviewed the
strengths and weaknesses of these orchard heating models in detail.
Gerber's (43) model underestimates the heating requirement under most
freeze conditions, but is fairly accurate under calm, radiative freeze
conditions. Crawford's (25) model accounts for induced flow of air due
to air temperature (hence buoyancy) differences inside and outside the
orchard, which is lacking in Gerber's model, and predicts heat
requirement within 5% of field observations. The box model of Martsolf
and Panofsky is an embellishment of Crawford's model and is largely used
as a research tool (83). The orchard foliage temperature model (137) is
by far the most rigorous development of the orchard heating problem, but
adds little to the current body of knowledge on orchard heating
practices.
Wind Machines
Wind machines have been used for freeze protection since 1916
(129). Wind machines mix warmer air aloft with colder air in the
orchard when a stable inversion exists, hence they are only useful under
calm, radiative freeze conditions (132).


18
The amount of protection provided by wind machines depends
primarily upon inversion strength, power of the machine, and distance
from the machine (48). Leyden and Rohrbaugh (80) observed Io to 3 C
increases in air temperature over a 2.8 ha area on nights when a 4 C
inversion existed. Brooks et al. (14) also reported Io to 3 C air
temperature increases over an area of 4.2 ha when inversion strength was
7 C. Turrell and Austin (130) observed that wind machines provided
better protection on sites which had good air drainage than on sites
with windbreaks around the perimeter. Reese and Gerber (120) concluded
that on calm, clear nights wind machines can be expected to increase air
temperatures 1 C over a kidney-shaped area of 4 ha.
Wind machines are sometimes combined with heaters for freeze
protection, yielding results superior to those from either method used
alone (84, 130). Wind machines plus 20 heaters per ha produced higher
air temperatures than 40 heaters per ha alone (14).
Foam
Foam is an unstable mixture of liquid and gas which acts as an
insulative blanket when applied over crops (7). Bartholic (6) found a
10 C increase in temperature under foam applied to low-growing crops.
However, he found little or no elevation of leaf and air temperatures of
mature citrus trees covered with foam unless heaters were used in
conjunction with the foam. The additional cost and logistical
difficulties associated with foam application to trees make it
impractical to use (7).
Fog
Water droplets in clouds and fog are of appropriate size to cause
scattering of terrestrial radiation (133). Therefore, radiant heat loss


19
from orchards on freeze nights is minimized in the presence of fog.
Efforts to generate and maintain fog over crops for freeze protection
began about 20 years ago (129). Mee and Bartholic (90) have reviewed
the history and concepts associated with fog generation for freeze
protection. They point out that fog not only reduces radiant heat loss
from the orchard, but can also add heat through condensation and fusion
of water on plant surfaces.
With mature citrus trees, fog provided about 1.5 C more protection
than heaters during a -5 C freeze, and outperformed wind machines
during a -8 C freeze (89). However, in tests under windy conditions,
temperature increases were only 0 to 3.5 C and decreased with distance
from the fog source (36). Although operating costs are very low (89),
fogging systems are problematic due to the large number of emitters and
purity of water required for reliable operation (90).
Flooding
Flooding orchards either before or during a freeze event can
increase the temperature and heat capacity of the orchard floor (41).
Heat which radiates from the soil or water surface can increase air
temperatures 0.3 to Io C (Davies personal communication). Air
temperature was 0.5 to 10 C higher when the same volume of irrigation
water was distributed among 3 furrows than when only 1 furrow was
flooded (13). Comparable air temperature increases were obtained in
citrus orchards with combinations of wind machines plus heaters, and
wind machines plus flood irrigation (129).
Growth Regulator Sprays
Attempts to alter the hardiness of citrus trees by spray
application of growth regulators have been largely unsuccessful (151).


20
Maleic hydrazide sprays applied during the fall prevented freeze injury
to grapefruit seedlings during a controlled freeze at -6 C (168), but
in field studies trees treated with maleic hydrazide showed similar
damage to unsprayed trees 4 months following a freeze (19). Ethephon,
which increased hardiness and delayed bloom of cherry buds (117), had no
effect on citrus hardiness (168).
Soil Banks and Tree Wraps
Trunks of young citrus trees are protected from freezing injury by
mounding soil or wrapping insulative materials around them during
periods of cold weather. Following severe freezes, the entire canopy
above the bank or wrap is killed, but vigorous sprouts from the
protected portion of the trunk rapidly reestablish a new canopy (129).
Soil banks
In 1904 Hume (59) wrote "no method of protecting trunks of citrus
trees from cold is more efficacious than banking", and with the possible
exception of microsprinkler irrigation (see next section) Hume's
statement remains true to this day. Hume also discussed disease and
insect problems associated with soil banking, and recommended that banks
be removed from trees as soon as danger of freezing is past to prevent
disease damage to the trunk. Other disadvantages of banking include
high labor costs and mechanical damage to trunks from construction and
maintenance of the banks (68). However, soil banks continue to be used
for freeze protection of young trees due to their superior insulative
properties (31).
Generally, trunk temperatures under soil banks are 3 to 12 C
higher than those of unprotected trees, depending on depth within the
soil bank (31, 143). Rates of trunk temperature decrease during a


21
freeze are similar at all depths, but temperatures deeper within the
bank are initially higher and start to decline later than temperatures
at shallower depths (31, 143). The low thermal diffusivity and large
volume of a soil bank are responsible for its superior freeze protection
capability (129).
Tree wraps
Tree wraps were introduced into citriculture in the mid-1950's to
circumvent the problems associated with soil banks while still providing
freeze protection for young trees (80). Although tree wraps provide
less protection than soil banks (67, 68, 170), they have been proven
effective during freezes in Florida (121) and Texas (56). Furthermore,
tree wraps provide protection from wind,radiation and rodent damage
(129), and prevent trunk sprouting (121).
Early research in Texas (80, 170) demonstrated that the thickness
of fiberglass insulation was positively correlated with trunk
temperature, and survival of young grapefruit trees was best with the
thickest wraps. These studies and others (121) showed that trunk
temperatures decrease from top to bottom of wraps much as in a soil
bank, but the magnitude of the temperature gradient was lower than in a
soil bank.
Fucik and Hensz (39) suggested that the ratio of rates of bark to
air temperature decrease was indicative of freeze protection capability
of a tree wrap, and a ratio of 0.55 or less was considered adequate for
freeze protection in most situations. However, trunk and air
temperatures decrease at nearly the same rate with soil banks (ratio of
bark and air temperature decrease is about 1.0) (31), which are superior
to tree wraps with respect to freeze protection. Turrell (129) stated


22
that the thermal diffusivity was the primary determinant of freeze
protection performance of a tree wrap, and this statement probably holds
more often than the above suggestion of Fucik and Hensz.
Several different types of tree wraps are currently used, each with
somewhat different insulative characteristics. A styrofoam wrap which
has 2 containers of water attached to its inner surface produced higher
trunk temperatures and allowed greater tree survival than other wraps in
field studies (30, 67). In laboratory studies (156), this wrap
maintained trunk temperatures of young 'Valencia' orange trees at 0 C
when air temperatures remained at -10 C for 50 hr. Fiberglass wraps
provided 0 to 3 C protection in several field studies, and the level
of protection appeared to be dependent on the rate of air temperature
decrease (121). Thin-walled polystyrene wraps provided very little
protection, and sometimes allowed trunk temperature to fall slightly
below air temperature (30, 68). The level of protection provided by
other wraps was somewhere between that of the styrofoam wrap with water
containers and the thin-walled polystyrene wrap (30, 67, 68). Tree
wraps made of cornstalks were ineffective for freeze protection of young
citrus trees (143), but have been used to prevent wind or radiation
damage to trunks (129).
Sprinkler Irrigation
Sprinkler irrigation has been used successfully for freeze
protection of many crops and areas of the world, from peas and beans in
the Yukon territory (51) to strawberries (81) and citrus in Florida
(30). Perry (109) provides a comprehensive review of field studies
where sprinkling was used to protect various fruit and vegetable crops.
Among the many studies in her review, there were few instances where


23
sprinkler irrigacin was used unsuccessfully. The most notable failure
of sprinkler irrigation was reported by Gerber and Hendershoct (47)
where mature citrus trees were killed to the ground as a result of
insufficient application rates (0.25 cm hr *) during advective freeze
conditions (windspeed, 2 to 5 m s ; minimum air temperature,-9 C). In
their study, irrigated trees sustained more damage than unirrigated
trees due to evaporative cooling and elevation of tissue killing
temperatures by the presence of moisture (46).
Irrigation for freeze protection is often referred to as a
"two-edged sword" because freezing of water on the plant releases heat,
while evaporation extracts heat (136). The ratio of latent heats of
evaporation and fusion is about 7.5, thus if 7.5 times as much water is
frozen as evaporated, the temperature of the plant part will remain near
ambient (48). To maintain the plant part near 0 C, an ice-water film
must be constantly maintained on the surface (49). The irrigation rate
required to maintain an ice-water film depends on windspeed, air
temperature and humidity (20, 48, 109). Clear ice formation and icicles
are field indicators of sufficient application rates (47). Trees may be
damaged by excessive ice loading and limb breakage even if proper
application rates are supplied under severe freeze conditions (48).
Several sprinkler irrigation models have been developed due to the
need to determine appropriate application rates and maximum off times
for adequate freeze protection (20, 22, 46, 111, 114). In these models
the rate of heat loss due to radiation, convection and evaporation
(sublimation) is set equal to the amount of heat gained by the freezing
process, and the latter is divided by the heat of fusion of water to
obtain the required irrigation rate. Exceptions to this are as follows:


24
1) the model of Chesness et al. (22) assumes that uo freezing occurs,
and application rate is calculated by dividing the sura of the heat loss
terms by the specific heat and temperature difference between the water
and the leaf; 2) the model of Phillips et al. (114) calculates che
maximum time that a bud can be left unsprinkled before it drops to a
critical temperature, and does not calculate or depend on irrigation
rate. Predictions from the Gerber and Harrison (46) and SPAR79 (112)
models have been successfully validated in the field. A BASIC computer
program is available through North Carolina State University to predict
irrigation rates required for freeze protection, which is essentially
the SPAR79 model (110).
High- and low-volume undertree irrigation has been used to protect
young and mature citrus trees (11, 15, 27, 30, 107, 108, 139).
High-volume sprinklers used were the "pop-up" (27) and "impact" types
(105). Low-volume undertree sprinklers are variously referred to as
minisprinklers, misters, foggers, spinners, and microjets (79), but will
be referred to as microsprinklers for this discussion.
High-volume irrigation increased trunk, leaf and air temperatures,
and fruit pack-out in mature 'Orlando' trees in the lower third of the
canopy (15, 139). However, temperatures and tree damage were similar in
the upper 2/3 of the canopy. Although somewhat successful, high-volume
irrigation is only feasible for protecting limited acreages due to high
cost and consumption of water (15).
Observations show that microsprinkler irrigation can ameliorate the
effects of less severe freezes on mature trees when relatively high
irrigation rates are used (100). Microsprinkler irrigation at rates of
38 and 52 liter hr provided marginal leaf temperature increases in the


25
lower portion of the canopy of 'Orlando' tngelo trees, but provided
almost no fruit protection (15). Parsons et al. (107) obtained similar
results with 38 and 87 liter hr ^ microsprinklers with mature 'Valencia'
and 'Temple' orange trees during 2 relatively mild freezes.
Alternatively, microsprinkler irrigation is very effective for
freeze protection of young citrus trees under a wide variety of
conditions (11, 30, 104, 108). Typically, raicrosprinkler irrigation
protects the lower 50-70 cm of a tree, and as with soil banks and tree
wraps, new canopies are produced after severe freezes and trees attain
heights of 1 to 2 m by the following autumn (104).
Parsons et al. (108) observed air temperature increases of 0 to
2.8 C and fog in a young tree planting irrigated with microsprinklers
and suggested that partial protection was afforded by microclimate
modification. However, Davies et al. (30) produced opposing evidence
when they measured lower net radiation values over microspinklers that
produced higher rates per unit area than those producing lower rates.
Microsprinkler irrigation at 87 liters hr 1 sprayed in a
wedge-shaped 90 pattern protected young 'Hamlin' orange trees during
one of the most severe freezes in recent history in Florida (30). In
this study, it was found that tree wraps used in conjunction with
microsprinklers provided Io to 2 C more protection than microsprinklers
alone. In addition, irrigated-wrapped trees had higher trunk
temperatures than irrigated-unwrapped trees when irrigation was
discontinued during the night. Further studies indicated that
intermittent raicrosprinkler irrigation could be used to protect larger
acreages of wrapped young citrus trees than can be accomplished with
constant irrigation (32).


CHAPTER III
TRUNK TEMPERATURE, FREEZE SURVIVAL AND REGROWTH OF YOUNG
CITRUS TREES AS AFFECTED BY TREE WRAPS AND MICROSPRINKLER IRRIGATION
Introduction
Thousands of young, nonbearing citrus trees have been killed by
severe freezes in Florida during the last 5 years. Young trees are
particularly prone to freeze damage due to their small size and vigorous
growth habit. Traditionally, soil banks or tree wraps have been used
for cold protection of young trees. Jackson et al. (68) compared
several tree wraps with conventional soil banks and found that wrapped
trunk temperatures were 0to 1.5 C higher than those of unwrapped
trunks, but 4 to 6 C lower than those of banked trunks. Although soil
banks provide effective cold protection, they are labor intensive and
often result in mechanical and/or disease damage to the trunk (30). In
a subsequent study, wraps provided 0 to 2.5 C protection for young
'Hamlin' orange trees during several radiative freezes in Florida in
1982 (121).
Low volume, raicrosprinkier irrigation may provide an alternative to
wraps and banks for freeze protection of young citrus trees. Davies et
al. (30) successfully protected young 'Hamlin' orange trees during the
advective freeze of Christmas 1983 using a combination of tree wraps and
microsprinkler irrigation applied in a 90 pattern. They also showed
that wraps used in conjunction with irrigation provide greater
protection than either method alone. Microsprinkler irrigation without
tree wraps may be less effective under advective than radiative freeze
26


27
conditions because damage was observed on trees irrigated at 38 liter
hr ^ during the 1983 Christmas freeze (102, 103).
Because only one irrigation rate (87 liter hr *) and spray pattern
(90) were used in the study by Davies et al. (30), the objective of
this research was to study the effects of different microsprinkler
irrigation rates and spray patterns on trunk temperature of wrapped
trees during freeze conditions, and subsequent tree survival and
regrowth.
Materials and Methods
Winter 1984-83 Studies
A 0.3 ha. planting of 2-year-old 'Hamlin' orange trees (Citrus
sinensis (L.) Osb.) on trifoliate orange rootstock (Poncirus trifoliata
(L.) Raf.) located at Gainesville, Florida, was used in these studies.
Trees were spaced 4.6 x 6.2 m and were ca. 1.5 ra tall. The lower 40 cm
of all trees was wrapped with 9 cm (R-ll) foil-faced fiberglass
insulation. Irrigation treatments were applied in an incomplete
factorial combination of 4 rates (0, 38, 57, 87 liter hr ^) x 2 spray
patterns (90 and 360). Microsprinklers were placed 1 m from the trees
on the northwest side because winds are generally from this direction
during advective freezes in Florida.
A randomized complete block design with 3 replications was used
employing 3 trees per treatment per replication. Trunk temperatures of
6 of the 9 trees in each treatment were measured with copper-constantan
T-type thermocouples attached to the trunk under the wrap at a height of
20 cm. Air temperature was measured at several locations throughout the
planting by suspending thermocouples from the canopies of the trees at a
height of about 1 m above the soil surface. Data were logged hourly


28
during several freezes over Che winter of 1984-85. Irrigation was
started when air temperature reached 0 C and discontinued when air
temperature returned to 0 C. Two freezes, an advective freeze
beginning on 20 Jan. 1985, and a radiative freeze beginning on 26 Jan.
1985, were selected for discussion as results from other freezes were
similar.
The efficiency of each irrigation treatment (C increase in trunk
temperature per liter per hr) was calculated by subtracting the
temperature of an unirrigated wrapped trunk from an irrigated wrapped
trunk at the time of the lowest recorded temperature, and dividing by
the irrigation rate. The lowest possible efficiency was taken as zero,
although negative values could occur if the irrigated trunks were cooled
by evaporation below the temperature of the unirrigated trunk.
Winter 1985-86 Studies
Studies during Dec.-Jan. 1985-86 were similar in many respects to
those described in the last section. Two-year-old 'Hamlin' orange trees
on sour orange (Citrus aurantium L.) rootstock planted at the same site
were used to evaluate irrigation rates of 0, 12, 22, 38, and 57 liter
hr ^. On the basis of results of the previous winter, the 87 liter hr *
rate and all 360 spray pattern treatments were not repeated. A
completely randomized design was employed using 7 trees per treatment,
and all trees were wrapped with foil-faced fiberglass (R11) tree wraps.
Trunk temperatures and efficiency were measured as described in the last
section on 2 trees in each treatment during several freeze nights. The
maximum height of live wood on all trees was measured on 14 April 1986;
however, regrowth of the trees was not evaluated.


29
Results and Discussion
Winter 1984-85 Studies
The advective freeze on 20 Jan. 1985 was characterized by clear
skies, minimum temperature near -12.0 C with durations below 0 C of 39
hr, windspeed of 2 to 6 m s with gusts to 10 m s *, and dewpoint
ranging from -8.4 to -25.6 C. The radiative freeze on 26 Jan. 1985
was characterized by clear skies, minimum temperature of -5.0 C with
durations below 0 C of 12 hr, windspeed less than 1 m s ^ and dewpoint
of -5.3 to -9.0 C.
Trunk temperatures during both types of freezes generally were
higher with the 90 than 360 spray patterns at all irrigation rates,
particularly when minimum air temperatures were reached (Figs. 3-1,
3-2). Trunk temperatures during the advective freeze (Fig. 3-1) were at
or above -2.5 C for all irrigation treatments, while unirrigated (wrap
only) trunk temperatures decreased to -8.0 C and air temperature was
-12.0 C. Trunk temperatures remained above 0 C in all irrigation
treatments during the radiative freeze (Fig. 3-2) while minimum
temperatures were -2.0 C and -5.0 C for unirrigated trunks and air,
respectively.
Fiberglass tree wraps without irrigation maintained trunk
temperatures 3.0 to 4.0 C higher than air temperature under both
radiative and advective freeze conditions (Figs. 3-1, 3-2). In previous
studies (30, 121) fiberglass wraps provided only 1.0 to 3.0 C
protection. This difference may have been due to the greater trunk
diameter and/or greater rates of air temperature decrease in this study
compared to past studies. Larger trunks provide greater thermal mass
thansmaller ones, thus slowing the rate of decline in temperature.


30
20 00 04 08 12 18 20 00 04 08 12
TIME (hr)
Fig* 31. Trunk temperatures of 2-year-old 'Hamlin' orange trees during
an advective freeze of 20 Jan. 1985 as influenced by
microsprinkler irrigation and tree wraps^. Irrigation rates
were (a)_p liter hr (b), 57 liter hr 1 and (c), and 38
liter hr Spray pattern is denoted by 90 or 360. Each
point is the mean of 6 measurements.


31
Fig. 3-2. Trunk temperatures of 2-year-old 'Hamlin' orange trees during
a radiative freeze of 26 Jan. 1985 as influenced by
microsprinkler irrigation and trunk wraps. Irrigation rates
were (a)_^7 liter hr (b), 57 liter hr and (c) and 38
liter hr Spray pattern is denoted by 90 or 360. Each
point is the mean of 6 measurements.


32
Also, rapid decreases in air temperature may result in larger
differences between trunk and air temperatures (121).
Irrigation may have been unnecessary on 26 Jan. because wraps
maintained the trunk temperatures above -2.0 C. Nevertheless, when
irrigation is used, fiberglass wraps increase the surface area for water
interception and ice formation around the trunk, thereby providing a
buffer between the trunk and the environment should the irrigation
system fail. Davies et al. (30) found that large ice masses around tree
wraps maintained trunks well above air temperature for prolonged periods
when irrigation was discontinued. Wraps are particularly important when
using 360 emitters which produce several discrete streams of water that
could miss a small tree trunk due to improper placement or windy
conditions.
Trunk heating efficiency (C increase in trunk temperature per
liter per hr), decreased as irrigation rate increased, and was higher
for 90 than 360 patterns at all irrigation rates (Fig. 3-3).
Therefore, the 90-38 liter hr ^ treatment was the most efficient
pattern-rate combination. Because pumping capacity is often a limiting
factor when irrigating large acreages on a freeze night, further studies
are needed to determine if rates less than 38 liter hr might maintain
trunk temperatures above critical levels with equal or higher
efficiency. Efficiency of lower irrigation rates is discussed in the
next section.
All irrigated and wrapped trees had live scion wood as of 27 March,
and only one unirrigated, wrapped tree was killed to the bud union. The
height of live wood increased as irrigation rate increased for the 90
spray pattern (Table 3-1). Additionally, the dry weight and number of


EFFICIENCY ( C liter', hr
33
0.24
0.20
0.16
0.12
0.08
0.04
0
IRRIGATION RATE (liter hr-1)
Fig. 3-3. Effect of irrigation rate on trunk heating efficiency of
microsprinkler irrigation treatments for young 'Hamlin'
orange trees. Efficiency was determined on 21 Jan. 1985 at
0737 hr when air temperature was lowest (-12.0 C). For 90
pattern (A): y= -1.28x10.x + 0.21, r^= 0.40; for 360
pattern (o): y= -1.26x10 x + 0.18, r = 0.33. Slopes are not
significantly different, intercepts are significantly
different, 5% level.


Table 3-1. Effect of microsprinkler irrigation rate and spray
pattern on height of live wood, shoot dry weight,
and number of shoots per trunk on 22 April 1985.
Rate
(liters hr
)
0
38
57
87
Height Dry wt. New shoots
(cm) (g) (no.)
Spray Pattern
kO
o
o
360
90
360
90
360
23
.4
5
.3
6
.9
42.4
32.4
8.7
4.0
9.3
8.4
41.2
33.7
12.1
5.1
10.8
7.8
54.8
30.9
17.3
2.8
28.5
7.8
**z
ns
*
ns
k
ns
z
Regression coefficients significant at P< .01 (**), or .05 (*)


35
new shoots increased with irrigation rate only for the 90 pattern.
This may be explained by differences in the height of water application
between the 90 and 360 treatments. The 360 pattern applied water to
the wrap surface at a height of about 20 cm regardless of irrigation
rate. However, water from the 90 pattern tended to wet the canopy and
form ice at progressively higher levels as irrigation rate increased.
It was obvious from the severity of the advective freeze that the trees
would die-back to wood that was protected by either wrap and/or ice
because air temperatures remained below critical levels (ca -6.7 C) for
several hours. Hence, it is not surprising that trees irrigated with
90 patterns had greater heights of live wood than those irrigated with
the 360 pattern. Regrowth was greater in the 90 treatment probably
because more wood was present; thus more adventitious buds could be
initiated and undergo development.
Winter 1985-86 Studies
Two advective freezes on 25-26 Dec. 1985 and 27-28 Jan. 1986 were
selected for analysis of trunk temperature because these freezes were
severe enough to provide a rigorous test of the irrigation rates
studied. Freeze conditions on 25-26 Dec. 1985 were characterized by
minimum temperatures of about -7.0 C, windspeeds decreasing throughout
the night from 3 to < 1 m s ^, and dewpoints of about -10 C.
Conditions on 27-28 Jan. 1986 were characterized by minimum temperatures
of about -7.0 C, windspeeds of 1 to 4 m s and dewpoints of about
-14 C. In addition to the 2 advective freezes, data from 3 radiative
freezes on 22 Dec. 1985, 27 Dec. 1985, and 29 Jan. 1986 were used to
evaluate trunk heating efficiency, when minimum air temperatures of


36
-3.2, -4.0, and -2.5 C, respectively, occurred under calm, high
dewpoint conditions.
Trunk temperatures during advective freeze conditions increased
with irrigation rate up to 38 liters hr but were similar for the 38
and 57 liter hr treatments (Fig. 3-4). Trunk temperatures for the 38
and 57 liter hr ^ irrigation rates were maintained well above 0 C,
while those for the 12 and 22 liter hr treatments decreased to about
-1.0 and -3.0 C, respectively, on both dates. Unirrigated wrapped
trunks had temperatures just slightly below those for the 12 liter hr *
rate, hence, this irrigation rate provided little additional trunk
heating compared to the other rates. The relatively poor performance of
the 12 liter hr rate cannot be entirely attributed to the irrigation
rate per se, as droplet size was noticeably different for this
treatment. Rather than the raindrop-sized droplets of higher irrigation
rates, the 12 liter hr ^ emitters produced a fine mist, causing large
amounts of opaque ice to form on the wrap and lower limbs of the trees.
Opaque ice formation is indicative of water freezing before it reaches
the tree (46), which could be expected with mist-sized droplets that
cool rapidly as they travel through the air due to their high surface to
volume ratio and low heat capacity (20). Hence, small droplet size may
have been partially responsible for the poor protection afforded by the
12 liter hr rate.
Despite differences in trunk temperature due to irrigation rate,
height of live wood was not significantly related (linearly or
quadratically) to irrigation rate (Table 3-2). This is contrary to
results of 1984-85 studies, but may be explained by the less severe
freeze conditions during the 1985-86 winter causing less trunk damage in


37
_l I I I I I L
19 21 23 1 3 5 7
TIME (hr)
Fig. 3-4. Trunk temperatures of 2-year-old 'Hamlin' orange trees and
air temperatures during advective freezes of 25-26 Dec. 1985
(a), and 27-28 Jjn. 1986 (b) for unirrigated (UNIRR), 12, 22
and 38 liter hr (LPH) microsprinkler-^irrigation treatments.
Trunk temperatures in the 57_J.iter hr treatment were similar
to those for the 38 liter hr treatment, hence are not shown.
Trunk temperatures were measured at the 20-cm height
underneath fiberglass tree wraps on 2 trees in each treatment.


Table 3-2. Height of live wood of young 'Hamlin' orange
trees on 14 April 1986 as influenced by
microsprinkler irrigation rate during several
freezes in Dec.-Jan. 1985-86.
Rate
(liters hr )
Height of live wood
(cm)
0
54.7 + 20.1Z
12
35.9 + 12.5
22
56.9 + 15.6
38
46.1 + 15.6
57
57.3 + 12.8
Values of height of live wood are means + SD. Linear
and quadratic regression coefficients were not significant,
P < 0.05. n=7.


39
general, particularly for unirrigated trees. However, trees in the 12
liter hr ^ treatment were noticeably smaller than all other trees, and
the visually greater canopy damage may have resulted from insufficient
water application under windy conditions, i.e., evaporative cooling.
Trunk heating efficiency was calculated for 5 different freeze
nights and data were fitted most closely by a quadratic equation (Fig.
3-5). Setting the derivative of the equation equal to 0, the relative
maximum point on the curve was obtained which corresponded to the value
of the most efficient irrigation rate (position of the star in Fig.
3-5). Similar to the winter 1984-85 data, trunk heating efficiency
was highest for the 38 liter hr ^ irrigation rate (with a 90 spray
pattern) under the widely varying freeze conditions encountered on 5
nights during the winter of 1985-86 (Table 3-3). This is rather
fortunate because most citrus growers in Florida that have
microsprinkler irrigation systems use the 38 liter hr ^ rate (Davies,
personal communication), and trunk heating efficiency could be maximized
by simply changing from 360 to 90 spray patterns.
Conclusions
The 90 spray pattern was superior to the 360 spray pattern with
respect to maintenance of trunk temperature during freeze conditions,
and survival and regrowth of the trees the following spring. A
microsprinkler irrigation rate of 38 liter hr was most efficient for
maintaining trunks of wrapped young citrus trees above damaging
temperatures under a variety of freeze conditions. Twice as much
acreage can be protected using a 38 liter hr than a 87 liter hr *
microsprinkler with a 90 pattern given the same pumping capacity. Use
of irrigation rates < 38 liter hr with 90 spray patterns can provide


EFFICIENCY
40
IRRIGATION RATE (liter hr-1)
Fig. 3-5. Trunk heating efficiency as a function of irrigation rate
for 5 freezes during Dec.-Jan. 1985-86. Solid line is a
quadratic regression fitted through the data; the star
denotes the relative maximum on the fitted curve. Each point
is a single determination.


Table 3-3. Dates of freezes, minimum air temperatures, most
efficient irrigation rates, and coefficients of
determination from quadratic regressions of trunk
heating efficiency vs. irrigation rate during
Dec.-Jan. 1985-86.
Date
air
Minimum
z
temperature
(c)
Most efficient
irrigation rate^
(liters hr *)
2
r
Dec. 22
-3.2
38.5
0.76
Dec. 26
-7.0
41.0
0.48
Dec. 27
-4.0
40.4
0.51
Jan. 28
-7.3
38.6
0.54
Jan. 29
-2.5
40.6
0.32
Air temperatures are means of 7 measurements.
^ Most efficient irrigation rate was calculated
by setting the derivative of the quadratic
regression equations equal to zero and solving
for the relative maxima for each date.


42
Io to 4 C additional trunk protection over tree wraps alone and allow
even larger acreages to be protected on any given night. However,
height of live wood and regrowth of trees may be marginally greater
using higher irrigation rates.


CHAPTER IV
MICROCLIMATE OF YOUNG CITRUS TREES PROTECTED BY
MICROSPRINKLER IRRIGATION DURING FREEZE CONDITIONS
Introduction
Methods of freeze protection that use water include flood
irrigation, fog generation and sprinkler irrigation, and each influences
the microclimate of the orchard. Flooding an orchard during a freeze
can increase soil and air temperatures and upward radiant heat flux from
the orchard floor (13, 41), thereby increasing temperatures of the
trees. Pre-freeze irrigation by either flooding or sprinkling can have
similar effects, but does not present the problem of standing water in
the orchard (41). Fog retards the loss of infrared radiation from the
orchard and raises the dewpoint, which can prevent tree temperatures
from decreasing to damaging levels (89). Therefore, flood irrigation
and fog generation affect temperatures of trees primarily by modifying
the microclimate of the orchard.
Alternatively, sprinkler irrigation provides protection primarily
through direct transfer of latent heat from the ice-water mixture that
coats the tree (20, 46, 109). However, microclimate modification by
high-volume sprinkler irrigation has been observed for mature citrus
trees (15, 27, 108, 139). Leaf and air temperatures were 0 to 3 C
higher for irrigated than unirrigated 'Orlando' tngelo trees (27, 139)
and protection varied with position in the canopy and freeze conditions.
Parsons et al. (107) reported 0 to Io C differences in air temperature
43


44
between irrigated and unirrigated mature citrus canopies using
low-volume microsprinkler irrigation. Fog or mist generation by
microsprinklers may occur under high dewpoint conditions and is thought
to decrease radiant heat loss from the trees and soil surface (108).
However, canopy temperatures at the 2 and 3 m height of irrigated citrus
trees were similar to those of unirrigated trees, despite the presence
of fog or mist in the irrigated block (139). Preliminary studies
-2
indicated that net radiation above young citrus trees was about 8 W ra
more negative with high irrigation rates than low rates, but values for
unirrigated trees were not reported (30).
The effect of microsprinklers on microclimate and subsequent freeze
damage of young citrus trees is unclear. The objective of this research
was to determine the effect of microsprinkler irrigation on air
temperature, dewpoint, net radiation and soil temperature around young
citrus trees under various freeze conditions.
Materials and Methods
Plant Material, Freezes and Treatments
A 0.3-ha planting of 126 2-year-old 'Hamlin' orange (Citrus
sinensis (L.) Osb) trees on either trifoliate orange (Poncirus
trifoliata (L.) Raf.) or sour orange (Citrus aurantium L.) rootstock was
used for all experiments. Trees were spaced 4.6 x 6.2 ra and were 0.5 to
1.5 m in height. The lower 40 cm of all trees was wrapped with 9 cm
(R-ll) foil-faced fiberglass insulation. Microsprinklers were placed 1
m from the trees on the northwest side because winds are generally from
this direction during advective freezes in Florida.
Microclimate measurements during 6 freezes which had widely
variable meteorological conditions were chosen for analysis of treatment


45
effects. The advective freeze of 20-22 Jan. 1985 was characterized by
minimum temperature near -12.0 C with durations below 0 C of 39 hr,
windspeed of 2 to 6 m s ^ with gusts to 10ms ^, and dewpoint ranging
from -8.4 to -25.6 C. The radiative freeze on 26-27 Jan. 1985 was
characterized by minimum temperature of -5.0 C, windspeed < 1 m s
and dewpoint of -5.3 to -9.0 C. Freeze conditions on 25-26 Dec. 1985
were characterized by minimum temperature of -7.0 C, windspeed of 1 to
3 m s \ and dewpoint of about -10.0 C. Minimum temperature on 27-28
Jan. 1986 was about -7.0 C, windspeed was 1 to 4 m s ^, and dewpoint
was about -14.0 C. On 26-27 Dec. 1985, minimum temperature was about
-4.0 C, windspeed was 0 to 2 m s *, and dewpoint averaged -7.0 C.
Minimum temperature on 11-12 Jan. 1987 was -1.5 C, windspeed was 1 to 3
m s 1, and dewpoint was about -4.0 C.
In Jan. 1985, treatments were applied in a factorial combination
of 3 irrigation rates (38, 57, and 87 liters hr ') x 2 spray patterns
(90 and 360), plus an unirrigated control. Four irrigation rates (12,
22, 38, and 57 liters hr ^) were used with only the 90 spray pattern in
Dec.-Jan. 1985-86, plus an unirrigated control. In Jan. 1987, only a
90 pattern-38 liter hr rate irrigation treatment and an unirrigated
control were used.
Microclimate Measurements
Microclimate around young trees was measured during the freezes
described above for irrigated and unirrigated trees. Air and soil
temperature, dewpoint, and net radiation data were recorded hourly
during the freezes in Jan. 1985. Soil temperature measurements were
repeated during the 3 freezes in Dec.-Jan. 1985-86 because measurements
from the previous year were speculative. Net radiation measurements


46
were repeated on 11-12 Jan. 1987 co confirm results from 1985.
Observations on fog and mist generation by microsprinklers were made on
all dates. Relative humidity and temperature measurements were made on
all dates inside and outside the planting with a sling psychrometer.
Air temperature was measured with copper-constantan thermocouples
in the canopy of one tree in each treatment at a height of 1 m.
Relative humidity was measured with humidity sensors (Viasala
instruments, Woburn, Mass.) at the same location as air temperature for
one tree in each treatment, and dewpoint was calculated from
simultaneous measurements of air temperature and relative humidity. Net
radiation was measured with Fritschen-type net radiometers placed at a
height of 0.8 m and centered directly over the water spray, between the
tree and the microsprinkler. Preliminary experiments indicated that at
a height of 0.8 m, net radiometers were sensitive enough to measure
-2
differences in upward radiant flux of about 5-10 W m from an area of
2
about 2.8 m (data not shown). One net radiometer per treatment was
used during winters of 1984-85 and 1985-86, but in 1986-87, 4 net
radiometers per treatment were used. Soil temperature was measured with
thermocouples placed approximately 1 cm below the soil surface next to
the trunk of 1 tree in each treatment. This location was chosen because
it was suspected that soil temperature could influence trunk temperature
above the soil surface by conduction of heat vertically along the trunk.
Results and Discussion
Microsprinkler irrigation rate did not affect air temperature,
dewpoint or net radiation of the trees within either the 90 or 360
spray pattern during the winter of 1984-85 (data not shown). Hence,
data were classified as either irrigated-90, irrigated-360 or


47
unirrigated to simplify discussion of these variables. Soil temperature
data are discussed for the 90 pattern only, because thermocouple
placement for the 360 spray pattern treatments caused spurious
measurements.
Air Temperature
Air temperature in the tree canopy was similar for irrigated-90,
irrigated-360 and unirrigated treatments during severe advective and
radiative freezes (Fig. 4-1). Furthermore, air temperatures for all
trees were typically within 0.5 C of those outside the research plot
under both types of freeze conditions (data not shown). Temperature
differences between irrigated 90 and unirrigated treatments approached
1.0 C under radiative conditions for a 3-hr period in the middle of the
night on 26-27 Jan. 1985. This may have been attributable to heat
released by the irrigation water, but was more likely due to random
variation in air temperatures which is frequently observed on radiative
nights. Parsons et al. (108) observed consistent increases in air
temperature of 0.5 to 1.5 C for irrigated young trees, although their
raicrosprinklers were more closely spaced and freeze conditions were less
severe than in this study.
Dewpoint
Variations in dewpoint were typically less than Io C among
irrigated-90, irrigated-360, and unirrigated treatments under
advective and radiative freeze conditions (Fig. 4-2). As with air
temperature, there was a 3-hr period in the middle of the radiative
freeze night where values were higher for the irrigated-90 than
unirrigated trees (Fig. 4-2b). However, this may be a mathematical
artifact because air temperature was used to calculate dewpoint.


48
III' I I I I 1 I i
20 22 00 02 04 06
TIME (hr)
Fig. 4-1. Air temperature in the canopy of 2-year-old 'Hamlin' orange
trees during a severe advective freeze on 20-21 Jan. 1985
(a) and a radiative freeze on 26-27 Jan. 1985 (b). Points
are means of 3 values for the irrigated-90 (IRR,90) and
irrigated-360 (IRR,360) treatments, and single values for
unirrigated (UNIRR) treatments.


49
20 22 00 02 04 06
TIME (hr)
Fig. 4-2. Dewpoint temperature in the canopy of 2-year-old 'Hamlin'
orange trees during a severe advective freeze on 20-21 Jan.
1985 (a) and a radiative freeze on 26-27 Jan. 1985 (b).
Points are means of 3 values for the irrigated-90 (IRR,90)
and irrigated-360 (IRR,360) treatments, and single values
for unirrigated (UNIRR) treatments. Dewpoint was calculated
using simulataneous air temperature and relative humidity
measurements.


50
Mist often was observed over irrigated trees only during calm
conditions when dewpoint was close to air temperature, similar to the
observations of Parsons et al. (108). However, humidity measurements
made with a sling psychrometer above unirrigated trees were similar to
those outside the research plot (typically 60-100%), indicating that
microclimate around unirrigated trees within the plot was not influenced
by mist from neighboring irrigated trees.
-2
Net Radiation Net radiation was 10 to 20 W m more negative over
irrigated than unirrigated treatments under advective freeze conditions
(Fig. 4-3a). Higher net radiation values over unirrigated than
irrigated trees were observed again during a less severe freeze on 21-22
Jan. 1985 (data not shown). Net radiation values outside the planting
were comparable to values for unirrigated trees inside the planting.
Hence, the increase in outgoing radiation from the irrigated treatments
was localized, and probably caused by the presence of the relatively
warm irrigation water. If irrigation were favorably modifying the
microclimate of the trees, one would expect net radiation to be less
negative over irrigated trees, but the opposite situation is seen (Fig.
4-3a).
No differences in net radiation occurred between irrigated and
unirrigated treatments or among irrigated treatments under radiative
freeze conditions (Fig. 4-3b). Net radiation was measured above
irrigated (38 liter hr *-90 microsprinklers) and unirrigated trees
during a mild, radiative freeze on 11-12 Jan. 1987 to verify results
from 1985. Again, net radiation was found to be similar for irrigated
and unirrigated trees (Fig. 4-4), consistent with data in Fig. 4-3b.
Reasons for the lack of differences in net radiation between irrigated


net radiation (W-
51
TIME (hr)
Fig. 4 3. Net radiation above 2-year-old 'Hamlin' orange trees during a
severe advective freeze on 20-21 Jan. 1985 (a) and a
radiative freeze on 2627 Jan. 1985 (b). Points are means
of 3 values for the irrigated-90 (IRR.90) and irrigated-360
(IRR,360) treatments, and single values for unirrigated
(UNIRR) treatments.


(JU-M) NOIJLVIQVd 13N
52
-56
-58
-60
-62
22 00 02 04 06 08
-
0 UNIRRIGATED
8
IRRIGATED
-
0
-

- 09
2
09
-
<
o
o
o
O

-
0

1
1 1
-J I 1
TIME (hr)
. Net radiation above 2-year-old 'Hamlin' orange trees during a
radiative freeze on 11-12 Jan. 1987. Points are means of 4
values for irrigated and unirrigated treatments.
Fig. 4-4


53
and unirrigated trees under radiative conditions are unclear.
Variability in incoming radiation under calm conditions may have masked
any slight differences in upward radiant flux on both occassions.
Davies et al. (30) measured net radiation values of -61.3 and -53.1
2 1
W m above trees irrigated with 90-87 liters hr and 360-38 liters
hr ^ microsprinklers, respectively, under radiative conditions. Their
results could be explained by the presence of greater quantities of 10
to 15 C irrigation water underneath net radiometers for the higher than
the lower irrigation rate. However, it is unclear why differences
between 90 and 360 spray patterns were not detected under radiative
conditions in this study. Possibly, different net radiometer placement
(1.5 m for Davies et al. (30) and 0.8 m in this study) was responsible
for the conflicting results.
Soil Temperature
Soil temperature generally was highest for the 38 liter hr ^ rate,
intermediate for unirrigated trees, and lowest for the 12 liter hr *
rate during 3 freezes in Dec.-Jan. 1985-86 (Fig. 4-5). The soil
temperatures for the 22 and 57 liter hr ^ treatments were very similar
to those for the 12 and 38 liters hr treatments, respectively. The
mist-sized droplets in the 12 liter hr ^ treatment probably cooled to a
greater extent as they traveled through air than larger droplets in
other treatments (46) and consequently reduced soil temperature below
that for unirrigated trees. However, droplet size was comparable for 22
and 38 liters hr ^ microsprinklers, and the reduced soil temperature for
the former treatment cannot be explained by greater droplet cooling.


54
Fig. 4-5. Soil temperature measured 1 cm below the surface and uext to
trunks of 2-year-old 'Hamlin' orange trees during freezes on
25-26 Dec. 1985 (a), 26-27 Dec. 1985 (b), and 27-28 Jan.
1986 (c). Points are single values for the unirrigated (0
LPH), 12 (12 LPH) and 38 liter hr (38 LPH) treatments.


Conclusions
Microsprinkler irrigacin does not appear Co change Che
microclimace of a young cree in che same way as reporced for maCure
crees (15, 107). Macure crees have much greacer canopy volume chan
young crees, hence a greacer capacicy Co decrease radiacin loses and
reduce windspeeds wichin che canopy, and reCain heac released from
irrigacin waCer. Irrigacin may, under cerCain condicions, increase
Che long-wave radianc flux from Che vicinicy of a young Cree, buc Ches
effeces appear Co be localized and do noC affecc air cemperacures.
Irrigacin races > 38 liCers hr ^ elevaced soil Ceraperacure 2 co 6 C
while lower irrigacin races reduced soil Ceraperacure 2 Co 4 C wich
respecc Co che unirrigaced condicin. Therefore, ic is possible chac
heac conducCed along Che crunk from Che soil is parcially responsible
for elevacin of Crunk Cemperacures of wrapped young ciCrus crees
irrigaced wich 38 licer hr (or higher race) microsprinklers. This
possibiliCy is invescigaced in ChapCer VII.


CHAPTER V
TRUNK TEMPERATURE, LIGHT INTENSITY AND SPROUTING OF WRAPPED AND
UNWRAPPED YOUNG 'HAMLIN' ORANGE TREES FOLLOWING A FREEZE
Introduction
Tree wraps not only provide freeze protection for young citrus
trees during the winter (68, 121, 156) but also influence trunk
sprouting in the spring. Trunk sprouting on freeze-damaged trees may be
beneficial or deleterious, depending on the degree of injury sustained
by the canopy. Following less severe freezes, ample canopy wood may
survive and produce new shoots. In this case trunk sprouting would be
undesirable, occurring at the expense of growth of scaffold limbs.
However, severe freezes may kill a young tree nearly to the bud union,
and the development of trunk sprouts would be necessary for the
reestablishment of the tree canopy. In either case, absence or presence
of a tree wrap and the type of wrap become important factors in the
regrowth and proper training of a young citrus tree.
Sprout inhibition by wraps may be a result of a physical barrier
imposed by a close fitting wrap, and/or modification of the
environmental factors influencing sprout growth such as temperature and
light intensity. Shoot initiation and growth are strongly temperature
dependent in citrus (23, 35, 119, 163), and light is necessary for
shoots to become autotrophic and continue growth once initiated. The
temperature and light regimes underneath wraps have not been studied in
the early spring when sprout initiation and development occur.
Moreover, the influence of various trunk wraps on trunk sprouting has
56


57
not been critically examined in citrus. The objective of this study was
to monitor the temperature and light environment of young citrus tree
trunks underneath various wraps during early spring, and to examine the
relationship becween these environmental factors and trunk sprouting in
freeze damaged trees.
Materials and Methods
Two-year-old 'Hamlin' orange trees (Citrus sinensis (L.) Osb.) on
trifoliate orange rootstock (Poncirus trifoliata (L.) Raf.) located at
Gainesville, Florida were used in this study. These trees were
protected from severe freezes during the 1984-85 winter with fiberglass
tree wraps and microsprinkler irrigation, but were killed back to a
height of about 60 cm. On 26 Feb. 1985, fiberglass wraps were removed
and 6 wrap treatments applied to 36 trees in a randomized complete block
design as follows: unwrapped (UW), fiberglass (FG), styrofoam (SF),
styrofoam modified to exclude light (MSF), white polystyrene (WP) and
charcoal polystyrene (CP). These treatments were chosen to provide
separation of light and temperature effects on trunk sprouting. The
wraps covered the lower 40 cm of the trunk, of which about 35 cm was
scion wood. Most trees had sprouts above the wrapped portion of the
trunk at this time, but no sprouts were observed on the lower 40 cm.
Trunk temperature was measured with copper-constantan thermocouples
taped to the trunk at a 20-cm height. Air temperatures were measured
with thermocouples suspended on canopy wood 1 m above the ground.
Photosynthetic photon flux (PPF) was measured with Li-Cor quantum
sensors taped to the trunk near the thermocouples. Due to a shortage of
quantum sensors, PPF could only be measured on 3 of the 6 treatments
during any particular day. Therefore, temperature and PPF measurements


58
were made over a 20 day period in March, 1985, Che quantum sensors being
moved among treatments on different days. Temperatures were measured
hourly and PPF at 15 min. intervals.
Sprouts from the lower 40 cm of the trunks were removed and counted
on 13 May 1985, after treatments had been in place for 76 days, and
placed in an oven at 80 C for 24 hr for dry weight determination.
Temperature, sprout number and dry weight data were analyzed for
treatment effects using analysis of variance and Duncan's multiple range
test. Although PPF data could not be analyzed statistically, data for
any particular wrap treatment on different days with similar sky
conditions were comparable.
Results and Discussion
Generally, trunk temperatures under WP and CP wraps were highest
and those under SF and MSF wraps lowest during the daylight hours, wich
FG, UW and air temperatures intermediate (Fig. 5-1). However, in the
afternoon on cloudy days, all wrapped trunk temperatures were generally
higher than the air temperature, but differences among wrap treatments
were small and varied from hour-to-hour. In mid-afternoon on sunny
days, differences in trunk temperatures between WP and MSF treatments
approached 17 C, and temperatures under WP wraps reached 41 C. In
addition, temperatures remained above 38 C under WP wraps for 3 to 4
hr, while temperatures under MSF wraps generally remained below 29 C.
During the night, temperatures under the SF and MSF wraps were highest,
lowest for WP, CP, UW and air, and intermediate for FG. By sunrise ,
the temperatures under the MSF wraps were significantly higher (0.5 to
1.0 C) than all other treatments. This was probably a result of the
covering of black tape used to exclude light which made the wrap


59
__i i i i i : i i i i i i t
0 6 10 14 18 22 02 06
TIME (HR)
Fig 51. Diurnal trunk temperatures of young 'Hamlin' orange trees
underneath various trunk wraps during a typical sunny day (a)
and a cloudy day (b) in March, 1985. Each point is the mean
of 6 measurements. Abbreviations are as follows: white
polystyrene (WP), charcoal polystyrene (CP), styrofoam (SF),
modified styrofoam (MSF), unwrapped (UW), and fiberglass
(FG).


60
airtight, and thus a better insulator than the SF wrap which was
ventilated. Although statistically different, it is questionable
whether a 0.5 to 1.0 C difference in nighttime temperature is of
biological significance to a young tree with respect to trunk sprouting.
The range of trunk temperature encountered in this experiment (16
- 41 C) was above the 13 C threshold which qualitatively controls
budbreak (119, 163) and below the 50 C threshold which can cause tissue
damage in citrus (62, 119). Prolonged periods of relatively high trunk
temperature as observed for some wraps in this study might adversely
affect cambial activity and ultimately the growth of a young tree.
Alternatively, such wraps may induce earlier resumption of cambial
activity in the spring by raising trunk temperature to levels favorable
for growth. Further studies on the influence of tree wraps on growth of
young trees are warranted due to the widespread use of wraps for
protection from freeze, herbicide, and fertilizer damage.
Photosynthetic photon flux varied from ambient on unwrapped trunks
to undetectable levels on trunks of FG and CP treatments. The WP wrap
allowed the most PPF transmission (9-13% of ambient) followed by SF
(4-9% of ambient) and then MSF (less than 0.1% of ambient) (Fig. 5-2).
In the UW, WP and SF treatments, PPF was well above the reported light
compensation point for citrus (73) which is about 1-2% of full sunlight.
Unwrapped trunks had highest sprout numbers and dry weights of all
treatments (Table 5-1). Number of sprouts in the WP treatment was
statistically similar to the UW treatment, but sprouts in the WP
treatment were deformed and had lower dry weights than those in UW
treatment. Apparently this was due to the physical limitations on
sprout growth imposed by the wrap. All other treatments had


61
06 08 10 12 14 16 18
TIME (hr)
Fig* 5 2. Diurnal photosynthetic photon flux (PPF) underneath various
trunk wraps on 2-year-old 'Hamlin' orange trees during a
sunny day (a) and a cloudy day (b) in March, 1985. Each
point represents a single measurement. No PPF was detected
beneath CP and FG wraps. Abbreviations are as follows:
unwrapped (UW), white polystyrene (WP), styrofoam (SF), and
modified styrofoam (MSF).


62
Table 5-1. Numbers aad dry weights of trunk sprouts on
freeze damaged yoi ng 'ramiin' orange Lrees on
13 May 1986 influenced by various trunk wraps.
Wrap
Trunk
Dry
type
sprouts
wt
(no.)
(g)
Unwrapped
White polystyrene
Modified styrofoam
Styrofoam
Fiberglass
Charcoal polystyrene
8.4az
8.5a
5.8a
3.1b
1.5b
1.4b
1.3b
2.5b
0.0b
0.0b
0.0b
0.0b
Means followed by the same letter are not significantly
different, Duncan's multiple range test, 5%. n=6.


63
statistically similar sprout number and dry weight, although no sprouts
were found on any of the trunks in the FG and CP treatments. It is
possible that sprouts had developed somewhat but abscised before 13 May
in the FG and CP treatments due to the lack of PPF. Small etiolated
sprouts have been observed under fiberglass wraps (Davies, unpublished).
Jackson et al. (67) reported that sprouting occurred on 22% and 0% of
freeze damaged trees with SF and FG wraps, respectively, which is
qualitatively similar to the results in this study.
Some PPF (as low as 0.1% of ambient as in the MSF treatment) was
necessary for development of trunk sprouts on freeze damaged trees.
Furthermore, there was a direct correlation between PPF and sprout
growth. This is supported by the fact that trunks receiving the highest
PPF (UW and WP) had the highest number and dry weight of sprouts, trunks
receiving no measurable PPF (FG and CP) had no sprouts, and treatments
receiving intermediate intensities (SF and MSF) were intermediate in
sprout number and dry weight.
It is possible that a PPF-temperature interaction occurred in this
study, although unfortunately, the experiment was not designed for
statistical analysis of interaction. However, some of the results may
be explained better considering a PPF-temperature interaction. For
example, the CP/WP treatment pair and the SF/MSF treatment pair were
designed to create similar trunk thermal regimes but different PPF
regimes. The WP and CP treatments both had relatively high mean
temperatures and different PPF regimes, while the SF and MSF treatments
both had relatively low mean temperatures and different PPF regimes.
Large differences in sprouting occurred between the WP and CP
treatments, suggesting that PPF influences sprout development given a


64
relatively high trunk thermal regime. On the other hand, no statistical
differences in sprouting occurred between the SF an MSF treatments,
suggesting that PPF does not control sprout development given a
relatively low trunk thermal regime. Therefore, the effect of PPF on
sprouting was either strong or nonexistent, depending on the trunk
temperature regime.
Conclusions
In general, PPF was necessary for trunk sprouts to develop and
persist under the various wraps, and both high PPF and high temperature
favored the development of trunk sprouts. In relative terras, if the
temperature was high but PPF low (as for CP), or temperature low and PPF
high (as for SF), or both temperature and PPF were low (as MSF) then the
number and dry weight of sprouts were reduced. Therefore, wraps that
exclude light entirely are probably best for trunk sprout inhibition of
moderately damaged young citrus trees where regrowth will occur on
surviving canopy wood. If trees have been killed to the wrap, however,
removal of the wrap at the earliest reasonable date would encourage
development of trunk sprouts which will produce a new canopy.


CHAPTER VI
MODELING AND SIMULATION OF TREE WRAPS AND MICROSPRINKLER
IRRIGATION FOR YOUNG CITRUS FREEZE PROTECTION
Introduction
Freeze protection using tree wraps and microsprinkler irrigation
has been the subject of several field studies with young citrus trees
(30, 32, 104, 107, 108). These studies mainly present data on trunk,
leaf and air temperatures during freezes and resulting tree survival and
regrowth. Although these studies demonstrate the effectiveness of tree
wraps and microsprinkler irrigation for freeze protection under the
conditions encountered, one can only speculate on the relative
importance of humidity, air temperature, rate of air temperature
decrease, windspeed, freeze duration, wrap type, water temperature,
etc., on trunk temperature and subsequent tree survival. Freeze
chambers cannot accurately simulate radiation, humidity, temperature and
windspeed regimes observed in the field during freezes, hence laboratory
studies would be neither practical nor useful in yielding accurate
quantitative information. Alternatively, modeling and simulation of the
wrap/microsprinkler system may provide detailed information that is
currently lacking on system behavior, and can hasten the progress of
research on freeze protection of young citrus trees by allowing
investigators to study the problem year-round instead of only a few
nights per year.
Models of overhead sprinkling for freeze protection have been used
to predict irrigation requirements for successful freeze protection of
65


66
apple buds (109, 114) and mature citrus foliage (20, 46). Basically,
these models calculate the rate of heat loss from a plant part under
given freeze conditions, then use this to calculate the irrigation rate
required to maintain the plant part above a predetermined critical
temperature. Hence, output from sprinkler rate models consists of a
single value, i.e., the irrigation requirement for freeze protection
under a given set of environmental conditions (110). Practical
applications of these models are limited because most irrigation systems
are not designed to produce variable irrigation rates. However, concepts
and information contained in sprinkler rate models were useful in
developing a model of the tree wrap/microsprinkler irrigation system.
Rather than calculating static values of irrigation requirement, a
more heuristic approach was taken to model the dynamic behavior of trunk
temperature as influenced by the wrap/microsprinkler system given freeze
conditions and other easily determined parameters. Using this approach,
simulation experiments can be run and output, e.g., trunk temperature,
evaluated at any time, under a variety of conditions. Furthermore,
simulation can be used as a screen for hypotheses, reducing the amount
of field experimentation necessary to achieve a particular goal.
Ultimately, information can be derived that can be useful in redesigning
and improving the system.
The primary objective of this research was to develop a
process-based, dynamic heat transfer model of the wrap/microsprinkler
system of young citrus freeze protection and use simulation to study
system behavior. Simulations were run to assess the influence of
parameters and environmental conditions on trunk temperature. Trunk


67
temperature predicted within one standard error of observed data during
model validation were considered accurate.
Model Development
Description
The system under consideration consists of a young citrus tree
trunk enveloped by an insulative tree wrap 8-14 cm in diameter and 30-40
cm in height (Fig. 6-1). Water is applied by a microsprinkler
positioned 1 m from the tree, which consists of a plastic tube with an
orifice and directional cap on the end that control the flow rate and
spray pattern of the irrigation water. When the irrigation is on, the
wrap surface is partially covered by a thin layer of water and an ice
layer if conditions favor freezing. The wrap/ice mass intercepts a
fraction of the irrigation water, and sensible or latent heat is
transfered from the water to the wrap/ice surface. As ice accretes on
the wrap surface, the fraction of water intercepted becomes greater as
does the surface area over which water is distributed. In the field,
some of the irrigation water often is intercepted by the canopy above
the wrap, which in addition to protecting some of the canopy, can change
the trunk temperature by flowing down the trunk inside the wrap.
Symbols used in model development, their definitions and units are
listed in Table 6-1.
Heat Conduction within the Wrap and Trunk
The tree wrap system can be viewed as 2 main components: a cylinder
of citrus wood (trunk) of variable radius, surrounded by an annulus of
insulative material (wrap) of specified thickness and composition.
Within the confines of the outer wrap surface, temperature varies
spatially and temporally, hence the trunk/wrap composite cylinder is a


68
Fig. 6-1. Conceptual model of the tree wrap/microsprinkler irrigation
system for young citrus freeze protection illustrating heat
transfer processes; Q = heat conduction from within the trunk
and wrap to the external boundary.


69
time-continuous, distributed thermal system. The mathematical model for
the rate of change in temperature with time at any point within the
trunk/wrap composite cylinder is developed for the case of
one-dimensional (radial) heat flow in the following paragraphs.
The heat stored (h) per unit volume of a region within the
trunk/wrap composite cylinder is defined as
-3
h (cal cm ) = p c T [6-la]
where c is the specific heat, p the density, and T the temperature of
the region. In a time interval At, the change in heat content of a
region of volume= Ar rA0 Az (Fig. 6-2) can be written as
Ah AT
Ar rA0 Az = p c Ar rA0 Az [6-lb]
At At
where Ar, rA0 and Az are the infintesimal distance increments in the
radial, angular, and vertical dimensions. The rate of change in heat
content of the region must be equal in magnitude and opposite in sign to
the change in flux (j) with distance (Ar), according to the principle of
continuity (26)
A(h Ar rA0 Az) A(j Ar rA0 Az)
= [6-2a]
At Ar
The terms Ar, A0, and Az are independent of time and radius, and r is
independent of time, so [6-2a] can be rewritten as
Ah A(rj)
Ar rA0 Az = Ar A0 Az [62b]
At Ar
Cancelling like terms and taking the limit as At and Ar approach zero,


70
ah 1 3(rj)
= - [6-3]
at r 3r
The flux in the radial direction j can be defined as
3T
j = K [6-4]
ar
where 9T/9r is the temperature gradient between the inner and outer
surfaces of the region, and K is the thermal conductivity of the region.
Substituting for j in [6-3] yields
3h
1 3
9T
=
(r K )
[6-5
3t
r 9r
3r
Assuming K is constant with respect to r, and substituting [6-la] for h
3T
1 9
3T
=
a (r
)
[6-6
3t
r 3r
9r
where a= K/(p c), the thermal diffusivity of the region.
Similar derivations hold for the other 2 dimensions, resulting in
the following form for 3-dimensional heat transfer in cylindrical
coordinates (26)
3T
1 3
3T
2
1 3 T
2
3 T
=
a
(r -)
+ ~2 ~ +
3t
r 9r
3r
r 30
dz
Thus, the rate of temperature change of any region between the trunk
center and wrap surface is dependent on the thermal diffusivity and
temperature gradients in the radial, circumferencial and vertical
dimensions about the region.


71
Equation [6-7] was not solved analytically due to its complexity,
and the fact that the parameters K, p, and c change discretely with r at
the trunk/wrap interface. Instead, a finite difference version of [6-7]
was employed to calculate rates of change in temperature, where second
derivatives were approximated by second forward differences (26)
dTr,e,z = ^ (Tr+l,0,z~2Tr,0,z+Tr-l,0, z ^ + [ ^Tr+1,0,z~Tr-l,9,z^
dt Ar2 r 2Ar
1 (T -2T +T )
v r,0+l,z r,0,z r.O-l.z'
2 ,. 2
r A0
(Tr,0,z+l 2Tr,0,z+Tr,0,z-L)
Az2
[6-8]
Hence, if a and the temperatures of the 6 surrounding regions are
known or set to assumed initial conditions, the rate of temperature
change of any region within the trunk/wrap cylinder can be calculated.
In order to use [6-8] the distributed tree wrap system was divided
into concentric layers in the radial direction, pie-shaped regions in
the angular direction, and disc-shaped regions in the vertical direction
yielding a discrete model system (Fig. 6-2). Therefore, the model
system had a finite number of regions of heat storage each with a single
temperature at any time t, whereas the real system contains an infinite
number of different points and temperatures. Values of A0 and Az were
set at 0.63 radians (36) and 1.0 cm, respectively, and Ar was either
0.2 or 0.5 cm, which were the maximum achievable without affecting
simulation output, allowing the programs to run in the least amount of
time possible. Using these values there were 5200 (Ar=0.5) or 13000
(Ar=0.2) finite regions of heat storage for a typical trunk/wrap
composite cylinder 13 cm in diameter and 40 cm in height.


72
Fig. 6-2. Three-dimensional representation of the model system showing a
representative finite region of heat storage. For a typical
tree wrap 13 cm in diameter and 40 cm in height there were
5200 regions when Ar=0.5 cm, A0=O.63 radians, and Az=1.0 cm.


73
The temperatures of most interest are those corresponding to the
cambial region of the trunk, because adventitious buds arise from this
area to produce a new canopy. The cambium of a fully acclimated citrus
tree is killed at temperatures of about -6.7 C (157), and it is
important to know conditions under which the wrap/microsprinkler system
allows the temperature of the cambium to reach critical values.
After rates of change were calculated, state variables were updated
by Euler or rectangular numerical integration with respect to time
State = State + dt(Rate ) [6-9]
t t-dt t-dt
where subscripts t and t-dt denote current and previous times.
Temperature was the only state variable of interest in simulations
except for ice layer thickness, which appeared in only those runs of the
irrigation simulation which had rather severe simulated environmental
conditions.
The Euler method assumes that the rate of change of a state
variable is constant over the time period dt, hence dt must be small
enough to justify this assumption. The maximum useful time step in heat
transfer simulations is a function of thermal diffusivity and distance
increment (dx), and generally is described as (26)
(dx)2
dt < [6-10]
2 a
where the calculation is for the component in the system with the
highest a and lowest dx. Time steps of 0.3 or 0.8 seconds were used
when simulating freeze protection with wraps and irrigation or wraps
alone respectively, due to the different assumptions made in each case
(see section on simulation). Greater time steps caused unstable
oscillations of temperatures with time that were fatal to program
execution, while lower time steps did not affect output.


74
Heat Exchange at Che System Boundaries
Internal boundary
The internal boundary of the model system is the center of the
trunk, and its rate of temperature change cannot be calculated using
[6-8] because r=0 at the internal boundary, and [6-8] requires the
temperature at r1 for calculating radial heat transfer. Therefore, the
temperature of the internal boundary was assummed to equal the average
temperature of the adjacent regions, (i.e., where r=l). This assumption
is often made with cylindrical thermal systems (26).
External boundary
Energy is exchanged between the system and the environment across
the external system boundary, or outermost layer of the system, by the
following processes: irrigation (IR), radiation (R), evaporation (E),
and convection (CV) (Fig. 6-1). Conduction (Q) allows heat transfer to
and from the external boundary, and therefore provides the linkage
between heat transfer at the surface and that within the system. The
external boundary differs in composition in both space and time, being
either wrap material, water or ice, and it is necessary to determine its
state before calculating the energy balance. However, a general form of
the energy balance of the external boundary is
dT
Ar(P c) - = (Q+IR-R-CV-E) [6-11]
S dt
where the subscript s denotes the external system boundary, and Ar its
thickness. If the irrigation is on, the external boundary is a thin
water layer where water is striking the wrap surface. Field
observations indicated that the thickness of the water layer was about
0.1 cm, and this value was used in all simulations. If the irrigation


75
is off buC an ice layer is present, then IR=0 and E represents
sublimation instead of evaporation. Volume changes upon freezing of
water are assumed negligible, and Ar remains equal to 0.1 cm when the
system boundary is an ice layer. If the system boundary is wrap
material (no irrigation or ice), then IR and E equal 0 and Ar becomes
the thickness of the wrap surface layer, which was either 0.2 or 0.5 cm,
similar to other wrap layers. Use of Ar in [6-11] implicitly assumes
that temperature changes of the system boundary occur uniformly
throughout its volume, which may only be true for small values of Ar.
Process descriptions
The heat transfer processes in the right hand side of [6-11]
(Q, IR, E, CV, R) require specific mathematical descriptions, and all
-2 -1
must be in the same units (cal cm s ) to be summed as shown yielding
the rate of temperature change of the external system boundary.
The irrigation process is given by
IR- [RATE c (T T )]/AREA [6-12]
H20 H20 s
where RATE is the amount of water intercepted by the wrap in liters per
second, AREA is the surface area over which the water is uniformly
distributed, T and c are temperature and specific heat of water
rlZO HZO
respectively, and T^ is the temperature of the external boundary. In
[6-12] it is evident that as T aPProaches T IR approaches 0
regardless of RATE.
Conduction (Q) of heat to the external boundary from within is
given by (128)
Q= K(T. -T )/ [r ln(r /r. )] [6-13]
ins s s in
where T^ and r^ are the temperature and radius of a specified region
internal to the external boundary. For example, if the outer system


76
boundary is wrap material, then T and r^n are the temperature and
radius of the wrap layer beneath the wrap surface layer. Alternatively,
if the external boundary is water, then T. and r. would correspond to
in in v
the temperature and radius of the ice layer or the wrap surface layer,
depending on presence or absence of ice.
Radiative heat transfer is given by
R= 4aT 3 (T -T ) [6-14]
3 S3
3
where 4GT is the radiative heat transfer coefficient (46, 111). The
3
emmissivity of the surface is assumed to equal 1, and is therefore
omitted in [6-14], Some of the consequences of this assumption are
discussed in chapter VII.
Evaporative heat flux is calculated by multiplying the mass flux of
water vapor from the external boundary by the latent heat of
vaporization (or sublimation)
E= L [D Sh(W -W )] [6-15]
v wv s a
where D is the water vapor diffusivity of air, L is the latent heat
wv v
of vaporization (or sublimation), W and W are water vapor
S 3
concentrations of the external boundary and air, respectively, and Sh is
the Sherwood number which embodies windspeed and wrap dimensions (93).
Water vapor concentration of the air (W^) is calculated from air
temperature and relative humidity using the psychrometric equation. The
air adjacent to the external boundary is assumed to be saturated with
water vapor at the surface temperature (Wg) if the external boundary is
water or ice. Evaporative heat flux equals 0 if the external boundary
is wrap material.
Convective heat transfer was calculated using Monteith's (93)
equation for cylinders


77
Cv = (K Nu)/d (T -T ) [6-16]
3 S 3
where (K Nu)/d is Che convective heat transfer coefficient (93, 109),
a
and Nu is the Nusselt number embodying windspeed, wrap dimensions, and
kinematic viscosity of air.
Freezing of water on the external boundary invokes a boundary
condition where the temperature at the ice-water interface is 0 C. The
radius of the ice-water interface (r. ) is therefore important, and it
l-w
is determined by calculating the rate of ice accretion, dr^_w/dt. The
rate of heat conduction away from an ice-water interface (Q. ) is (61)
l-w
dr.
Qi- h l-w.
[6-17]
dt
where is the latent heat of fusion, and is the density of ice.
Latent heat produced at the interface can move in 2 directions, either
out (Q ) into the water layer or in (Q. ) towards the wrap surface,
out in
hence
and,
Q-
+
Q
w
yin
out
[6-18]
Q. = K. (T.-273)/(r. ln(r. /r.)) [6-1'
m i i l-w l-w i
Q (273-T )/r ln(r ,/r. ) (r ./r. ) [62i
out H20 wl wl wl l-w wl l-w
where T., r. and T , r are the temperatures, radii of the ice layer
i i wl wl
and water layer adjacent to the interface, respectively. Substituting
[6-19] and [6-20] into [6-17] and rearranging
dr.
l-w
dt
(Q Q. )/(L, P.)
out m f 1
[6-21]


78
The radius of Che ice-water interface is obtained by numerical
integration of [6-21] yielding ice thickness, and adding to it the
radius of the wrap.
Forcing Functions
The forcing functions or inputs required by the model are soil and
air temperatures, windspeed, and relative humidity as functions of time.
Forcing functions are independent variables that "force" the system to
change state, and their magnitudes are not affected by the state of the
system. With the exception of soil temperature, environmental variables
are readily available in the form of weather forecasts or can be
measured with hygrothermographs and anemometers. Soil temperatures must
be measured with thermocouples or similar devices near the trunk and
just below the soil surface. However, excluding the terms for vertical
heat transfer in [6-8] allows for independence of the model from soil
temperature data, which is desirable provided model behavior is not
greatly altered.
Simulated air and soil temperatures decreased with time from
initial values to desired minima by linear or negative exponential
functions. Relative humidity was either held constant, or allowed to
increase or decrease linearly with time as is often observed during a
freeze. Wind velocity oscillated around a mean value as a sinusoidal
function of time with a given amplitude and a period of about 30 min to
approximate the stochastic nature of wind velocity observed on freeze
nights.
Parameters
Most of the parameters used in the model were obtained from
handbooks (128, 134), and parameters that could not be obtained from the


79
existing literature were estimated through laboratory or field
experimentation. The latter included the thermal properties of tree
wraps and some of the characteristics of the irrigation process. The
determination of K, p, c and a of various tree wraps was rather
involved, and is left for discussion in Chapter VII. Parameters used in
the simulation programs are listed in appendices A and B.
Four characteristics of the irrigation process were required prior
to simulation: water temperature, fraction intercepted by the wrap,
amount of the wrap surface covered with water and distribution of the
water on the wrap surface.
Temperature of the water striking the wrap surface was estimated
with thermocouples on the surface of fiberglass wraps directly in the
path of the water spray. Wraps were placed around trunks of 6,
2-year-old 'Hamlin' orange trees and temperatures were recorded hourly
as trees were irrigated with 38 liter hr ^ emitters during 4 mild freeze
nights in Jan.-Feb. 1987. Similar data were collected during Dec.-Jan.
1985-86 on wrapped 'Hamlin' orange trees irrigated with 38 and 57 liter
hr ^ microsprinklers. Water temperature striking the surface ranged
from 10 to 15 C and was relatively constant over time and freeze
conditions.
To estimate the fraction of water intercepted, a fiberglass wrap
placed around 2.5 cm polyvinyl chloride pipe was hung over a bucket, and
irrigation water applied to the wrap for 20 to 30 min using 38, 57, and
87 liter hr microsprinklers. Water that dripped from the wrap was
collected and its volume measured in a graduated cylinder. The volume
intercepted was divided by the total volume of water leaving the
microsprinkler during the same time period to give the fraction


80
INTERCEPTION
6-3. Schematic diagram of interception of irrigation water by the
tree wrap when microsprinklers were positioned so that water
sprayed above the top of the wrap (left side), or only on the
wrap surface (right side). Hatching indicates areas not
covered by water.
Fig


81
0.05
0.095
MICROSPRINKLER
Fig. 6-4. Cross-secCion of the model system showing 70% coverage of the
wrap surface with water (sections 1-4,8-10). The numbers
associated with each section indicate the relative amount of
intercepted water distributed uniformly over the surface area
of the section.


82
intercepted. Values ranged from 0.05-0.11 depending on orientation of
the microsprinkler, being lowest when some water sprayed above 40 cm
(top of the wrap) and highest when water sprayed no higher than 40 cm
(Fig. 6-3). Interception values were adjusted accordingly in
simulations as ice accreted on the wrap and produced a larger surface
for interception.
The percentage of wrap surface covered by water and/or ice and the
distribution of water around the wrap surface are closely related.
These parameters vary with freeze conditions and canopy morphology, and
are difficult to measure in the field. The surface layer of the wrap
was equally divided into 10 sections, and each section was treated
separately in order to vary the coverage and distribution of water
around the wrap surface (Fig. 6-4). On the surface towards the
microsprinkler, all sections were assumed to be covered with water, with
distribution was highest for the section 1, intermediate for sections 10
& 2, and lowest for peripheral sections 9 & 3. Values of distribution
on the surface towards the microsprinkler are proportional to the area
of a plane normal to the streamlines of the irrigation water in each
section. Water can reach the surface opposite the microsprinkler
(sections 4-8) after being deflected or dripped from the canopy,
allowing some or all of these sections to be covered with water and/or
ice. Field observations suggested that only sections 8 and 4 received
any water except during severe freezes when all sections could be
covered with ice and water. Therefore, the total amount of wrap surface
covered by water/ice was estimated to be 70% for most simulations, but
provisions were made in simulation programs for varying this value
between 50-100% in increments of 10%. The volume of water distributed


83
on che wrap surface away from Che microsprinkler was uncercain as well,
buc like percenc coverage, ic could be varied in simulacin programs.
Wacer deflecced or dripped from Che canopy onco Che wrap surface
creaCes variabiliCy in characCerisCics of che irrigacin waCer by
increasing inCercepCion, changing discribuCion, and lowering waCer
CemperaCure due Co concacc wich lower cemperaCure objeecs and longer
disCances Craveled. While Chis may noC be a facCor on Che wrap surface
Cowards Che microsprinkler where direcC inCercepCion prevails, ic is an
imporcanc consideracin for Che wrap surface opposiCe Che microsprinkler
because Che only waCer reaching Chis area is Chac deflecced or dripped
from Che canopy. AddiCionally, wacer scriking Che canopy has been
observed Co flow down Che Crunk underneaCh wraps in Che field and reduce
crunk cemperaCure by as much as 6o C ac che 20-cm heighc on mild freeze
nighcs. The same process probably increases Crunk CemperaCures on severe
freeze nighcs when Crunk CemperaCure normally would drop below 0 C in
che absence of liquid wacer inside Che wrap. There is no provision in
Che model Co accounC for wacer flowing down Che Crunk and changing ics
CemperaCure. This faccor, along wich Che degree of uncerCainCy wich
which Che above characCerisCics of irrigacin wacer are known, decreases
Che likelihood of accurace Crunk CemperaCure prediccions in irrigacin
simulaCions.
Simulacin
Simulacin programs for Che model syscem were wriCCen in FORTRAN
and run on a Digical Vax-11 compuCer. SeparaCe programs were developed
for cree wraps alone and for irrigacin and wraps cogecher, because
differenc simplifying assumpcions were made in each case.


84
Simulacin of Freeze Protection with Tree Wraps
Heat transfer in the angular direction was disregarded when
simulating tree wraps alone, which assumes that temperature does not
vary with position around the system at any given radius r and height z.
This is a reasonable assumption because temperatures at various
positions around the trunk and wrap surfaces at a given height are
observed to be nearly equivalent in the field. Additionally, it was
found that trunk surface temperatures predicted when considering only
radial heat transfer were within +_ 0.3 C of those predicted for the
20-cm height when considering both radial and vertical heat transfer
(See Fig. 7-3). Trunk temperatures at the 20-cm height were roughly
averages of those for the 1 and 40-cm heights, and disregarding vertical
heat transfer resulted in prediction of a single average trunk
temperature. Disregarding the vertical dimension allowed independence
from soil temperature data if trunk temperatures corresponding to the
20-cm height only were desired, and the simplified program for
1-dimensional (radial) heat transfer ran in 95% less computer time than
the 2-dimensional (radial and vertical) program.
In both the 1- and 2-dimensional simulations, the rate of
temperature change at the wrap surface was calculated using equation
[6-11] (disregarding terms for irrigation and evaporation) after
obtaining values of Q, CV, and R. The terras for angular heat transfer
(and vertical heat transfer for 1-dimensional simulation) were deleted
from [6-8] to calculate rates of temperature change throughout the wrap
and trunk. Distance increments in the radial (Ar) and vertical (Az)
directions were set as high as possible without sacrificing accuracy,


85
which after many simulation trials, were determined to be 0.2 cm and 1.0
cm, respectively.
Simulation of Freeze Protection with Microsprinkler Irrigation and Tree
Wraps
Heat transfer in the vertical direction was disregarded when
simulating wraps and irrigation together, which assumes that vertical
heat transfer has no effect on temperature in the model system. This is
a reasonable assumption because omitting vertical heat transfer in the
wrap simulation resulted in prediction of an average trunk temperature,
or that for the 20-cm height (see Chapter VII). Furthermore, the
3-dimensional heat transfer simulation used 8 hr of computer time for
each hr of time simulated, hence heat transfer in one dimension had to
be disregarded to allow the simulation to run in a managable time
period. The vertical dimension was the obvious choice for omission
because temperature gradients were lower and distances greater than the
other dimensions, and simulations ran about 50 times as fast without
vertical heat transfer calculations.
The outer system boundary was either water, ice or wrap material,
depending on water distribution and the point on the wrap surface being
considered. The rate of temperature change of the system boundary was
calculated using [6-11], omitting terms E and IR for areas of the wrap
surface not covered by water. Heat transfer in Che ice and water layers
was assumed to occur in only the radial direction which simplified
calculations of energy transfer for the outer system boundary. A
subroutine for ice accretion using equations [617][621] was accessed
if the temperature of the water layer was < 0 C or if an ice layer was
already present.
i


36
Equation [6-8] without terms for vertical heat transfer was used to
calculate rates of temperature change throughout the wrap and trunk.
The radial (Ar) and angular (A9) distance increments were set at 0.5 cm
and 0.63 radians (36) respectively, which were the maximum achievable
without affecting model output. As for the tree wrap simulations, Ar
and A9 were determined after many simulation trials to increase speed of
program execution.


87
Table 6-1. Definition of symbols used in model development,
Symbol
Definition
AREA
c
Cv
d
D
E
h
IR
j
K
L
Nu
Q
R
RATE
r
Sh
T
t
W
z
a
P
a
0
A
*K l)
surface area of wrap_^cm )
specific heat (cal g K ) 0
convective heat flux (cal cm s ;
characteristic dimension £cm)^
diffusion coefficient (cm s
evaporative heat flux^(cal cm s )
heat content (cal cm )
sensible heat flux^froip irrigation water (cal cm
heat flux (cal cm s ;
thermal conductivity (cal cm s
latent heat (cal g )
Nusselt number (dimensiones^)
heat conduction (cal cm s_?)
radiative heat flux (cal_ym s
irrigation rate (liter s )
radius (cm)
Sherwood number (dimensionless)
temperature (K or C)
time (s)
water vapor concentration (g cm
vertical distance (cm)
~2 In
s )
-1.
-3,
2 -1
thermal diffus^vity (cm s )
density (g cm ) _2
Stephan-Boltzmann constant (cal cm s
angular distance (radians)
"change in"
k"4)
Subscripts
a
f
h2o
i
in
i-w
out
r
s
t
v
wl
wv
z
air
fusion
water
ice
interior region
ice-water interface
outer or exterior region
radial coordinate
system boundary
time
vaporization
water layer
water vapor
vertical coordinate
0
angular coordinate


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1 \,í ,1

TREE WRAPS AND MICROSPRINKLER IRRIGATION FOR
FREEZE PROTECTION OF YOUNG CITRUS TREES
BY
MARK RIEGER
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987

This dissertation is dedicated to my family members
and to the loving memory of Suzanne Lynn DiCenzo

ACKNOWLEDGEMENTS
Deepest appreciation is extended to supervisory committee
chairman, Dr. F. S. Davies, and cochairman, Dr. L. K. Jackson, for
support and aid throughout the course of this project, and L. W.
Rippetoe for technical assistance and valuable moral support.
Special thanks are given to committee members Dr. G. H. Sraerage,
Dr. W. J. Wiltbank, and Dr. G. Yelenosky for participating in
examinations and reviewing the manuscript; to Jonathan Crane for acting
as a sounding board and for his constructive criticism of seminars; to
Dr. E. Chen, Prof. G. Cook, Dr. A. Datta, Dr. D. R. Farber, Dr. W.
Huber, and Dr. J. D. Martsolf for valuable assistance with simulation
programs; to Steven Hiss for assistance with graphics; to Dr. G. A.
Couvillon for providing the incentive to finish the dissertation
(nearly) on schedule; and last but not least, to my family members and
friends for support and timely diversion of my attention to the finer
things of life.
iii

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT xi
CHAPTER
I INTRODUCTION I
II REVIEW OF THE LITERATURE 4
Introduction 4
Freezing Injury, Stress, and Cold Acclimation 4
Freezing Injury, Stress, and Cold Acclimation
in Citrus 10
Freeze Protection Methodology 15
III TRUNK TEMPERATURE, FREEZE SURVIVAL AND REGROWTH
OF YOUNG CITRUS TREES AS AFFECTED BY TREE WRAPS
AND MICROSPRINKLER IRRIGATION 26
Introduction 26
Materials and Methods 27
Results and Discussion 29
Conclusions 39
IV MICROCLIMATE OF YOUNG CITRUS TREES PROTECTED BY
MICROSPRINKLER IRRIGATION DURING FREEZE CONDITIONS 43
Introduction 43
Materials and Methods 44
Results and Discussion 46
Conclusions 55
V TRUNK TEMPERATURE, LIGHT INTENSITY, AND SPROUTING OF
WRAPPED AND UNWRAPPED YOUNG 'HAMLIN' ORANGE TREES
FOLLOWING A FREEZE 56
Introduction 56
Materials and Methods 57
Results and Discussion 58
Conclusions 64
iv

VI MODELING AND SIMULATION OF TREE WRAPS AND
MICROSPRINKLER IRRIGATION FOR YOUNG CITRUS
FREEZE PROTECTION 65
Introduction 65
Model development 67
Simulation 83
VII THERMAL PROPERTIES AND SIMULATION OF FREEZE
PROTECTION PERFORMANCE OF TREE WRAPS FOR
YOUNG CITRUS TREES 88
Introduction 88
Materials and Methods 90
Results and Discussion 95
Conclusions 119
VIII SIMULATION OF PROCESSES INVOLVED IN MICROSPRINKLER
IRRIGATION FOR FREEZE PROTECTION OF YOUNG CITRUS
TREES 120
Introduction 120
Materials and Methods 122
Results and Discussion 125
Conclusions 146
IX CONCLUSIONS 148
Field Research 148
Laboratory and Computer Simulation Analyses 149
APPENDIX
A TREE WRAP SIMULATION PROGRAM 151
B TREE WRAP AND MICROSPRINKLER IRRIGATION SIMULATION
PROGRAM 156
LITERATURE CITED 165
BIOGRAPHICAL SKETCH 178
v

LIST OF TABLES
Page
Table 3-1. Effect of microsprinkler irrigation rate and spray
pattern on height of live wood, shoot dry weight,
and number of shoots per trunk on 22 April 1985 34
Table 3-2. Height of live wood of young 'Hamlin' orange trees
on 14 April 1986 as influenced by microsprinkler
irrigation rate during several freezes in Dec.-Jan.
1985-86 38
Table 3-3. Dates of freezes, minimum air temperatures, most
efficient irrigation rates, and coefficients of
determination from quadratic regressions of trunk
heating efficiency vs. irrigation rate during Dec.
-Jan. 1985-86 41
Table 5-1. Numbers and dry weights of trunk sprouts on freeze
damaged young 'Hamlin' orange trees on 13 May 1986
as influenced by various trunk wraps 62
Table 6-1. Definition of symbols used in model development 87
Table 7-1. Thermal conductivity, density, specific heat,
and thermal diffusivity of tree wraps used for
young citrus freeze protection 96
Table 7-2. Minimum trunk and air temperatures of young 'Hamlin'
orange trees wrapped-with fiberglass, fiberglass
with water containers or styrofoam wraps on 4 mild
freeze nights in 1987 100
Table 7-3. Predicted minimum trunk temperatures for the
20-cm height for simulated freezes when air
temperature decreases from 0° C_^o -5° C in 8 hr
with windspeed of 0.5 0.1 m s using either
air temperature or mean radiant in calculation
of radiant heat transfer 109
Table 7-4. Simulated minimum trunk temperatures underneath
fiberglass wraps at various heights from simulations
using different soil temperature regimes and freeze
conditions from 21 Jan. 1985 118

LIST OF FIGURES
Page
Fig. 3-1. Truak temperatures of 2-year-old 'Hamlin' orange trees
during an advective freeze of 20 Jan. 1985 as influenced
by raicrosprinkler irrigation and tree wraps 30
Fig. 3-2. Trunk temperatures of 2-year-old 'Hamlin' orange trees
during a radiative freeze of 26 Jan. 1985 as influenced
by microsprinkler irrigation and trunk wraps 31
Fig. 3-3. Effect of irrigation rate on trunk heating efficiency
of microsprinkler irrigation treatments for young
'Hamlin' orange trees 33
Fig. 3-4. Trunk temperatures of 2-year-old 'Hamlin' orange
trees and air temperatures during advective freezes
of 25-26 Dec. 1985 ayd 27-28 Jan., 1986 for 0, 12,
22, and 38 liter hr microsprinkler irrigation
treatments 37
Fig. 3-5. Trunk heating efficiency as a function of irrigation
rate for 5 freezes during Dec.-Jan. 1985-86 40
Fig. 4-1. Air temperature in the canopy of 2-year-old 'Hamlin'
orange trees during a severe advective freeze on
20-21 Jan. 1985 and a radiative freeze on 26-27
Jan. 1985 48
Fig. 4-2. Dewpoint temperature in the canopy of 2-year-old
'Hamlin' orange trees during a severe advective
freeze on 20-21 Jan. 1985 and a radiative freeze
on 26-27 Jan. 1985 49
Fig. 4-3. Net radiation above 2-year-old 'Hamlin' orange trees
during a severe advective freeze on 20-21 Jan. 1985
and a radiative freeze on 26-27 Jan. 1985 51
Fig. 4-4. Net radiation above 2-year-old 'Hamlin' orange trees
during a radiative freeze on 11-12 Jan. 1987 52
Fig. 4-5. Soil temperature measured 1 cm below the surface and
next to trunks of 2-year-old 'Hamlin' orange trees
during freezes on 25-26 Dec. 1985, 26-27 Dec. 1985,
and 27-28 Jan. 1986 54
vii

Fig. 5-1.
Fig. 5-2.
Fig. 6-1.
Fig. 6-2.
Fig. 6-3.
Fig. 6-4.
Fig. 7-1.
Fig. 7-2.
Fig. 7-3.
Fig. 7-4.
Fig. 7-5.
Fig. 7-6.
Fig. 7-7.
Diurnal trunk temperatures of young 'Hamlin' orange
trees underneath various trunk wraps during a typical
sunny day and a cloudy day in March, 1985 59
Diurnal photosynthetic photon flux underneath various
tree wraps on 2-year-old 'Hamlin' orange trees during
a sunny day and a cloudy day in March, 1985 61
Conceptual model of the tree wrap/microsprinkler
irrigation system for young citrus freeze protection
illustrating heat transfer processes 68
Three-dimensional representation of the model system
showing a representative finite region of heat storage ... 72
Schematic diagram of interception of irrigation
water by the tree wrap when microsprinklers were
positioned so that water sprayed above the top of
the wrap, or only on the wrap surface 80
Cross-section of the model system showing 70% coverage
of the wrap surface with water 81
Schematic representation of the device used to measure
the thermal conductivity of tree wraps in-situ 92
Observed trunk and air temperatures on 20-21 Jan.
1985, 26-27 Jan. 1985, 25-26 Dec. 1985, 26-27
Dec. 1985, and 27-28 Jan. 1986, and predicted trunk
temperatures from simulation of the freezes 102-103
Regression of predicted vs. observed minimum trunk
temperature using 1-dimensional and 2-dimensional
models 104
Predicted trunk temperatures for 4 commercially
available wraps, styrofoam, fiberglass, polystyrene,
polyethylene, during a simulated freeze where temperature
drops curvilinearly from 0°^to -5° C in 8 hr, and
windspeed is 0.5 0.1 m s 106
Predicted trunk temperatures for air, a wrap with
thermal properties of dry sand, and a fiberglass
wrap Ill
Predicted trunk and air temperatures for young
citrus trees with fiberglass wraps during 6 different
simulated freezes 113
Predicted trunk temperatures as affected by variations
in trunk diameter with 13-cm diameter fiberglass
wraps, and variations in wrap diameter with 2.4-cm
diameter trunks 115
viii

Fig. 7-8. Predicted minimum trunk temperatures of young citrus
tree trunks under fiberglass wraps as influenced by
windspeed when air temperature drops from 0° to -5° C
in 8 hr 117
Fig. 8-1. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 126
Fig. 8-2. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 57 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 127
Fig. 8-3. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 87 liters hr microsprinklers
during an advective freeze on 20-21 Jan. 1985,
and a radiative freeze on 26-27 Jan. 1985 128
Fig. 8-4. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 22 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986 and a radiative freeze on 26-27
Dec. 1985 130
Fig. 8-5. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986, and a radiative freeze on 26-27
Dec. 1985 131
Fig. 8-6. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 57 liters hr microsprinklers
during advective freezes on 25-26 Dec. 1985 and
27-28 Jan. 1986, and a radiative freeze on 26-27
Dec. 1985 132
ix

Fig. 8-7. Predicted and observed trunk temperatures at the
20-cm height and air temperatures for 2-year-old
'Hamlin' orange trees wrapped with fiberglass tree
wraps and irrigated with 38 liter hr microsprinklers
during mild freezes on 11-12 Jan. 1987 and 23-24
Jan. 1987 133
Fig. 8-8. Predicted minimum trunk temperatures plotted against
those observed at the 20-cm height for all irrigation
rates and dates used for validation 135
Fig. 8-9. Cross-section of a wrap showing the thickness of
simulated ice on different regions of the wrap surface .. 136
Fig. 8-10. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of fraction of water intercepted
by the wrap 138
Fig. 8-11. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of water temperature 140
Fig. 8-12. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter 2-year-old citrus trees with
fiberglass tree wraps under severe advective and
radiative freeze conditions. Simulations were run
using different values of percent coverage of the
wrap surface with water 142
Fig. 8-13. Simulated minimum trunk temperatures at the 20-cm
height for 2-cm-diameter 2-year-old citrus trees
with fiberglass tree wraps under severe advective
and radiative freeze conditions. Simulations were
run at windspeeds of 0, 1, 4.5, and 10 m s 145
Fig. 8-14. Simulated trunk temperatures at the 20-cm height
for 2 cm-diameter young citrus trees with fiberglass
tree wraps under severe advective and radiative
freeze conditions. Simulations were run using
different values relative humidity 146
x

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
FREEZE PROTECTION OF YOUNG CITRUS TREES
WITH TREE WRAPS AND MICROSPRINKLER IRRIGATION
By
Mark Rieger
August, 1987
Chairman: Frederick S. Davies
Cochairman: Larry K. Jackson
Major Department: Horticultural Science (Fruit Crops)
Tree wraps and microsprinkler irrigation provide a reliable and
economical alternative to soil banks and orchard heaters for freeze
protection of young citrus trees. Field experimentation and computer
simulation were employed to study the freeze protection capabilities of
tree wraps alone and in combination with microsprinkler irrigation.
Trunk temperatures of 2-year-old 'Hamlin' orange (Citrus sinensis (L.)
Osb.) trees during freeze conditions were greater for wrapped trees
irrigated with a 90° spray pattern than for those irrigated at the same
rate with a 360° spray pattern. An irrigation rate of 38 liters hr *
provided the greatest increase in trunk temperature per unit water
applied during several freezes. Air temperature, dewpoint and net
radiation in the tree canopy were not increased by microsprinkler
irrigation during freeze conditions, although soil temperature was 2° to
6° C higher for irrigated than for unirrigated trees.
Thermal properties of commonly used tree wraps were determined in
the laboratory. Thermal diffusivity was lowest for styrofoam wraps with
water containers, intermediate for 9-cm diameter fiberglass wraps, and
highest for thin-walled polyethylene and polystyrene wraps. Thermal
xi

diffusivity was indicative of freeze protection capability of tree
wraps.
The simulation model of the tree wrap/microsprinkler system
predicted trunk temperatures within 1° C of observed means when
simulating the effect of tree wraps alone, although predictions
generally were Io to 3° C lower than observed means when simulating the
irrigation process. The rate of air temperature decrease, wrap
thickness and trunk diameter were positively correlated with level of
freeze protection in computer simulations of fiberglass wraps; however,
freeze duration was negatively correlated with level of freeze
protection. Windspeed had little effect on trunk temperature of
unirrigated wrapped trees, but trunk temperature of irrigated wrapped
trees was reduced 5° C as windspeed increased from 0 to 10 m s ^.
Increasing the amount of water intercepted by the wrap and coverage of
the wrap surface with water increased trunk temperature during simulated
freezes. Temperature of the irrigation water was positively correlated
with trunk temperature for radiative but not advective freeze conditions
in simulations.
xii

CHAPTER I
INTRODUCTION
Freeze damage of young citrus trees has been a problem since the
establishment of the Florida citrus industry. Young trees are
particularly prone to freeze damage due to their small size and vigorous
growth habit. Citrus growers spend $18 to $42 and 3 to 4 years bringing
a young tree into production (95). Traditionally, soil banks have been
used for freeze protection of young citrus trees (59). Soil banks
provide several degrees C protection to the lower portion of the tree,
but are labor intensive and often result in mechanical or disease damage
to the trunk. To avoid the problems associated with soil banks,
Rohrbaugh designed the first insulative tree wrap, consisting of rock
wool inside a 30-cm cylinder of asphalt felt which surrounded the lower
50 cm of a young tree (80). Results from preliminary tests with similar
wraps appeared promising; however, the types of tree wraps used
currently provide only 3° C protection in some cases, and virtually no
protection in others (68, 121).
Overhead irrigation, petroleum fuel heaters, and wind machines have
been used successfully to protect young and mature citrus trees.
However, overhead irrigation systems often are not designed to apply
water at rates necessary for protection under advective freeze
conditions (46). Heating groves or nurseries with petroleum products is
an effective means of cold protection, but rising fuel costs have
limited the use of this practice to high cash value crops (107). Wind
1

2
machines rely on Che presence of an inversion layer (45), and therefore
are ineffective under advective freeze conditions.
A reliable and economical alternative to the conventional methods
listed above for freeze protection of young citrus is low-volume
microsprinkler irrigation. This system provides protection to the lower
portion of the tree only, much like a soil bank. Previous studies have
shown that trees irrigated with microsprinkers are usually killed above
a height of 50 to 70 cm during severe freezes (30, 104). However,
freeze-damaged trees often produce several vigorous shoots from the
remaining portion of scion wood and attain heights of 1 to 2 m by the
following autumn (104). The net result is that the grower loses about 6
months' growth on the tree but saves the cost of purchasing and
resetting new trees, which is particularly important considering the
scarcity and high prices of nursery trees due to the recent outbreak of
citrus canker disease in Florida.
Microsprinkler irrigation has been reported to alter the
microclimate of citrus plantings by raising the air temperature within
the canopy (15), creating fog or mist, and/or decreasing radiant heat
loss from the irrigated area (53, 107, 108). However, the effects of
microclimatic changes on young citrus tree temperatures and subsequent
freeze survival are unclear.
Recommendations regarding irrigation rate and spray pattern are
currently lacking, although preliminary studies indicate that 76 to 84
liters hr * sprayed in a 90° pattern will protect young trees under most
freeze conditions (30, 107). Davies et al. (30) suggest that
microsprinkler irrigation combined with an insulative wrap provides
greater protection for young citrus trees than irrigation or wraps used

3
separately. However, wraps left on freeze-damaged trees may reduce
trunk sprouting and delay canopy reestablishment following a severe
freeze. Further research with tree wraps and microsprinkler irrigation
is needed to determine the effects of irrigation rate, spray pattern,
and wrap type on trunk temperature, survival and sprouting of young
citrus trees.
Modeling has been used successfully to predict overhead irrigation
rates required for freeze protection of tree crops (20, 46, 112).
Hence, modeling and simulation of the tree wrap/microsprinkler
irrigation system of freeze protection may yield useful information on
system design and behavior. Analysis of a model can produce information
unobtainable from field or laboratory experiments due to uncontrolled or
unrepresentative environmental conditions. Furthermore, experiments can
be performed with a simulation model more rapidly and inexpensively than
field experiments, improving the productivity and efficiency of the
freeze protection research program.
Research objectives of this dissertation were
1. to study the effects of tree wraps combined with various
microsprinkler irrigation rates and spray patterns on trunk temperature,
survival and regrowth of young citrus trees;
2. to determine whether microsprinkler irrigation alters the
microclimate of a young citrus tree during freeze conditions;
3. to determine the influence of various tree wraps on trunk
temperature and sprouting of freeze-damaged trees;
4. to model the dynamic behavior of trunk temperature during
freeze conditions as influenced by tree wraps and microsprinkler
irrigation.

CHAPTER II
REVIEW OF THE LITERATURE
Introduction
Man's efforts to protect crops from freezing injury began at least
2000 years ago (83). In addition, the causes of freezing injury in
plants have been studied and speculated upon for well over 100 years
(124). Impetus for continued research in these areas stems from the
huge economic losses of agricultural commodities that occur annually due
to late spring or early fall frosts, or midwinter freezes. Literature
on freezing injury, protection and related topics is voluminous.
Several reviews (18, 75, 86, 91, 98, 116, 124, 135, 157, 167) and books
edited by Levitt (76) Olien and Smith (99), and Li and Sakai (78) have
covered various aspects of freezing stress and injury, and cold
acclimation and hardiness. The intent of this review is to discuss
general aspects freezing injury, resistance to freezing stress, and cold
acclimation in woody plants with special attention to citrus.
Herbaceous plants, with the exception of winter grasses (82), have
little or no resistance to freezing stress or ability to acclimate and
are therefore omitted. In addition, methods of freeze protection will
be reviewed.
Freezing Injury, Stress, and Cold Acclimation
Freezing Injury
Freezing injury results from ice formation in plant tissues and not
low temperatures per se (92). Manifestations of freezing injury include
4

5
sunscald and bark splitting of tree trunks, blackheart in trunks and
stems, death and abscission of leaves, flowers, and fruits, frost rings
on fruits, midwinter kill of dormant flower buds and stem cambia, and
death of the entire vegetative structures of cold tender plants (18,
135, 136). These visual symptoms ultimately result from processes which
occur at the cellular level.
Plant cells are injured or killed by either intracellular or
extracellular ice formation (75). It is widely accepted that
intracellular ice formation is always fatal to plant cells, although how
intracellular freezing kills the cell remains unanswered (124). It
follows that cells which survive freezing do so by tolerating
extracellular ice formation. Therefore, much attention has been devoted
to processes which occur during extracellular ice formation and the
resulting consequences.
Extracellular freezing may be summarized as follows. As
temperature decreases below 0° C, water in plant tissues initially
supercools few to several degrees (18, 86). Heterogenous nucleation
occurs in cell walls and extracellular spaces and ice crystals grow in
these areas at the expense of water inside the cells (91, 92). As long
as exosmosis of intracellular water keeps pace with the reduction in
external vapor pressure with decreasing temperature, equilibrium between
the intracellular solution and the external phase is maintained, and
intracellular freezing is avoided by colligative freezing point
reduction (86). However, supercooling and intracellular freezing are
favored at rapid cooling rates (> 10° C min ^), especially if the
permeability of the plasma membrane to water is low (85).

6
Extracellular freezing is tolerated to varying degrees in plant
tissues depending on species, time of year, preconditioning, plant part,
freezing rate and water content (135). Several hypotheses attempt to
explain causes of cell death due to extracellular freezing. Levitt (74)
hypothesized that intermolecular disulfide bonds formed among proteins
with exposed sulfhydryl groups during freeze dehydration of cells by
external ice. He stated that this resulted from the close proximity of
proteins due to the reduced volume of cytoplasm. Williams (140)
hypothesized that there was a minimum volume that cells attained during
freeze dehydration below which cell death occurred. This minimum volume
was the same for acclimated and unacclimated cells, but the temperature
at which minimum volume was reached was lower for acclimated cells due
to higher solute and bound water contents. Solution effects (i.e.,
concentration of toxic electrolytes, pH changes, precipitation of
compounds, salting out of proteins) may result in injury to cell
membranes and other cellular components during freeze dehydration
(86, 124). Recently, the behavior of the plasma membrane during
freezing was analyzed in isolated protoplasts (124). Apparently,
vesiculation and deletion of membrane material occurs in unacclimated
protoplasts, which causes altered osmotic behavior and cell lysis upon
thawing, whereas these processes are not observed in acclimated
protoplasts. Therefore, the plasma membrane may have an important role
in cold acclimation and tolerance of extracellular ice. However, none
of the above hypotheses are without limiting weaknesses, and no single
hypothesis applies to all plant cells and all freezing situations.

7
Resistance to Freezing Stress
Resistance to freezing stress is conferred by avoidance and/or
tolerance of ice formation within the plant (76).
Avoidance. Plants avoid freezing in low temperature environments
by desiccation, colligative freezing point depression, and supercooling
(75). Desiccation occurs in seeds and buds only, and freezing point
depression allows avoidance of freezing to about -4° C at most.
Alternatively, supercooling is a very effective avoidance mechanism, but
usually occurs in plants which also tolerate extracellular ice formation
(2, 42). One exception is shagbark hickory, which avoids freezing
injury to -40° C by supercooling of the entire volume of liquid water in
stems (18).
Tolerance. Reasons for difference in tolerance of extracellular
ice among species are unknown, although apparently, hardier plants
survive freezing of a larger amount of their osmotically active water
(1, 16, 18).
The latitudinal range of a particular plant species is related to
its relative tolerance of extracellular ice formation (17). Species
which tolerate little extracellular ice such as citrus, are limited to
southern latitudes where freeze events are less severe and occur
infrequently. Temperate woody plants such as Vitis, Prunus, and
Rhododendron tolerate extracellular ice in most tissues and avoid ice
formation in flower bud primordia via deep supercooling (4, 42, 142).
These plants are not found at latitudes where temperatures below about
-40° C occur, because deep supercooled cells freeze and die at this
temperature due to homogenous nucleation of intracellular water (17).
Species of the northern boreal forests such as Betula and Populus do not

8
deep supercool, but tolerate freezing of all their osraotically active
water outside the plasmaleraraa (18). These species are capable of
surviving immersion in liquid nitrogen (-196° C) after slow cooling to
-30° C.
Cold Acclimation
Irrespective of freezing tolerance mechanisms, temperate woody
plants acclimate to low temperatures in 2 distinct stages. Stage I
acclimation is a phytochrome-mediated response initiated by short days
and enhanced by warm temperatures (38, 58, 64, 87). Moderate increases
in hardiness occur during stage I acclimation (135). A translocatable
"cold hardiness producing substance" presumed to be abscisic acid (63)
has been shown to be involved in stage I acclimation (37, 66, 125).
Stage II acclimation is initiated by exposure to low, nonfreezing
temperatures or frost, and does not involve translocatable substances
(37, 58). Plants acclimate rapidly and to their fullest potential
during stage II acclimation.
Irving and Lanphear (64, 65) showed that woody plants would
eventually acclimate to normal levels when exposed to long days and low
temperatures, suggesting that low temperature has an overriding
influence on photoperiod in cold acclimation. Furthermore, they showed
that plants acclimate substantially before becoming dormant under long
day, low temperature (10° C) conditions (64). Apparently, dormancy and
cold hardiness are separate processes which occur coincidentally in the
natural environment in woody perennials.
Tumanov and Krasavtsev (127) discovered a third stage of hardiness
which develops during prolonged exposure to subfreezing temperatures,
and is rapidly lost upon rewarming. They stated that prolonged exposure

9
Co subfreezing temperatures allows sufficient time for water movement to
extracellular sites which prevents intracellular freezing, whereas
natural cooling rates are more rapid and result in supercooling and
intracellular freezing at higher temperatures. Similarly, Rajashekar
and Burke (118) found that prolonged exposure to subfreezing
temperatures reduced or eliminated low temperature exotherms indicative
of supercooling and intracellular freezing in Prunus flower buds.
Apparently, the permeability of the plasma membrane to water at
subfreezing temperatures and freezing rate dictate the ultimate
hardiness level a plant can achieve (85).
Several physical and biochemical changes occur in plants during
cold acclimation. Increased physical stability of the plasma membrane
observed during acclimation may result in reduced probability of
nucleation of the intracellular solution by external ice (124).
Increases in unsaturation of membrane lipids increases fluidity and
decreases the probability of membrane phase transition and subsequent
dysfunction of membrane-bound proteins (126). Permeability of the
plasma membrane to water increased during acclimation in Red-Osier
dogwood (88), but was similar in acclimated and nonacclimated
protoplasts isolated from rye leaves (34). The ratio of gibberellin to
abscisic acid-like substances decreased during stage I acclimation in
Acer leaves (63). Increases in soluble proteins, RNA, sulphydryl
compounds, sugars, amino acids, and organic acids occur during
acclimation of many plants (86). Water content, root hydraulic
conductivity, and storaatal conductance decreased in Red-Osier dogwood
during cold acclimation (54, 101, 135). As with the hypotheses of

10
freezing injury, none of the above physical and biochemical changes can
singularly explain the resistance to freezing injury in plants.
Freezing Injury, Resistance and Cold Acclimation in Citrus
Freezing Injury
Freezing injury to citrus can be economically devastating because
present and future crops are affected by a single freeze event. For
example, in Texas a single freeze in Dec. 1983 reduced the production of
the 1983-84 season by 70%, and extensive tree damage resulted in no
production the following year (123). In Florida, damage was estimated
at one half billion dollars from the 1962 freeze alone (151), and the
severe freezes of Dec. 1983 and Jan. 1985 reduced commercial citrus
acreage by over 80,000 ha in north-central Florida (141).
Manifestations of freezing injury in citrus range from partial
defoliation and fruit abscission to death of entire trees (151, 153).
Watersoaking appears as dull, dark areas on the leaf surface and is
indicative of ice formation within the leaves (113, 175). However, ice
formation in citrus leaves and stems is not always lethal (147, 175).
Bark splitting is thought to result from large ice masses forming in the
bark, creating pressure sufficient to force the tissues apart (153).
At the cellular level, Young and Mann (171) observed destruction of
vacuolar, chloroplast, and mitochondrial membranes in hardened and
unhardened sour orange leaves subjected to freezing at -3.3° and -6.7°
C, respectively. They suggested that the nature of freezing injury in
leaves was physical, caused by ice crystal growth and subsequent
cellular disruption. However, they offered no explanation as to why
hardened leaves undergo less cellular disruption at the same freezing
temperatures than unhardened leaves, when both types of leaves contained

11
ice. Lower water content (167) and/or higher bound water fractions
(122) in hardened leaves may reduce the amount of ice formed at a given
temperature, resulting in less physical disruption than in unhardened
leaves. Among citrus species, however, Anderson et al. (1) found no
relationship between bound water content and freeze tolerance of leaves,
and suggested that hardier species tolerate a greater amount of their
water frozen than non-hardy species.
Resistance to Freezing Stress
Citrus species can survive extracellular ice formation within their
tissues (147, 175), although changes in ice tolerance during acclimation
remain unexplained (157). In addition, citrus avoids freezing injury by
supercooling to temperatures as low as -8° C in leaves and stems (158).
Citrus leaves are killed shortly after freezing occurs in the
supercooled state (69, 158). The extent of supercooling in young citrus
trees increased with cooling rate (164), cold hardening (61), and water
stress (154), and decreased in the presence of external moisture or ice
(155, 166). Also, the extent of supercooling varies with species and
cultivar (157), but not in such a manner as to provide an index of
interspecific or varietal differences in hardiness (158). Supercooling
may not be as important a factor as ice tolerance in citrus freezing
resistance because recent studies indicate that several tree species
supercool only Io to 2° C before freezing under field conditions (2, 4).
Anderson et al. (1) suggested that negative pressure potentials
arise in citrus leaf cells during freeze plasmolysis, decreasing the
amount of ice formed at any given temperature. This is unlikely because
negative pressure potentials would have to be extremely low (< -10 MPa)
to decrease the amount of ice formed significantly (86), and the only

12
documented measurements of negative pressure potentials are much higher
(-6 kPa) (5).
Cold Acclimation
It has long been recognized that environmental conditions preceding
a freeze influence the freeze survival of citrus (94). Greater freeze
damage in Florida and Texas than in California under similar freeze
conditions has been attributed to higher winter temperatures in Florida
and Texas which reduce cold acclimation (23, 24). Several studies have
demonstrated that citrus tolerates lower freezing temperatures if
preconditioned for several weeks at low, nonfreezing temperatures (147,
163, 165, 173).
Generally, environmental conditions which result in inactivity or
lack of growth promote cold hardiness in citrus (167). Girton (50),
Fawcett (35) and Ivanov (cited in 167) were among the first to report on
the influence of cool (< 13° C) temperatures on growth and cold
acclimation of citrus. Seedlings exposed to alternating temperatures
(warm days and cool nights) developed superior hardiness to those
exposed to constant low (3° C) temperatures (96). Yelenosky (147, 151)
used hardening conditions of 2 weeks at 21.1/10° C (day/night) followed
by 2 weeks at 15.6/4.4° C in laboratory experiments which resulted in .
maximum hardiness.
Light is necessary for cold acclimation in citrus (96, 144).
Length of the light period is positively correlated with growth (115,
163) but does not affect cold hardiness (96, 163) or induce bud dormancy
(167). Light allows continued photosynthesis and carbohydrate
accumulation during exposure to low temperature which is necessary for
cold acclimation in leaves and stems (160, 166). Although

13
photosynthetic carbon uptake decreases during cold acclimation (169),
metabolism of photosynthate also decreases (52, 160) which probably
allows for net carbohydrate accumulation. Furthermore, absence or
inhibited function of leaves disfavors cold acclimation (146), and
starch hydrolysis cannot account for increased levels of sugars in
leaves and stems (160).
Water stress increases both freezing tolerance (150) and avoidance
(154) in citrus. Wilcox (138) reported that low (5° C) root
temperatures induced cold hardening in citrus seedlings by reducing root
hydraulic conductivity and leaf water potential. Davies et al. (28)
reported that 'Orlando' tángelo trees not receiving irrigation in the
fall had less leaf and fruit damage than fall irrigated trees following
a radiative freeze. Conversely, Koo (71) found that trees irrigated
during the fall had less leaf and fruit damage following a freeze.
In the acclimated condition, cold hardiness varies widely among
citrus cultivars (157), but when unacclimated and actively growing,
hardy and nonhardy types are killed at similar temperatures (151). In
the acclimated condition, citrus cultivars/relatives can be ranked for
hardiness in decreasing order as follows: trifoliate orange, kumquat,
sour orange, mandarin, sweet orange, grapefruit, lemon, citron (157).
The hardiness of a scion cultivar is affected by the
species/cultivar used as a rootstock (40, 55, 172), although hardiness
differences due to rootstock are slight by comparison to cultivar
differences (157). Generally, more hardy species/cultivars used as
rootstocks impart more hardiness to a scion cultivar, hence the above
ranking also applies to scions grafted to the species/cultivars listed.

14
Several biochemical and physiological changes occur in citrus
during cold acclimation. Levels of soluble carbohydrates in leaves
increased rapidly during the first week of acclimation in 'Valencia'
orange, although levels in stems increased gradually over a 6-week
period (149). The principal sugars that accumulated in 'Redblush'
grapefruit were glucose, fructose, and sucrose (166). Increased levels
of soluble carbohydrates may lower the freezing point of the tissue
water colligatively, decrease the amount of ice formed at a given
temperature, and decrease the rate of ice growth through the tissues
(145, 160). All amino acids except proline, valine, and glutamic acid
decreased during cold acclimation at 10° C in 'Valencia' orange (149).
Proline accumulated in unacclimated, water-stressed citrus leaves (77),
hence increases in proline during cold acclimation may be induced by
reductions in water potential which occur during hardening (149).
Proline accumulation did not correlate well with cold hardiness among
citrus cultivars/species (152).
Water soluble proteins decreased in 'Redblush' grapefruit during
hardening, contrary to behavior of woody deciduous plants which
accumulate water soluble proteins during acclimation (166). No new
proteins were identified by gel electrophoresis following cold
acclimation of 'Valencia' orange trees (162). However, protein
denaturation increased with freeze damage, and was greater for
unhardened than hardened leaves (162). Increased levels of
hydroxyproline may result from protein denaturation during cold
acclimation (159).
Levels of unsaturated fatty acids and phospholipids increased
during cold acclimation of citrus leaves, and the magnitude of increase

15
was positively correlated with the relative cold hardiness of the 3
species analyzed (97). This is consistent with the theory that
increased membrane fluidity is partially responsible for increased
freezing tolerance in plants (86).
Freeze Protection Methodology
Methods of freeze protection were first developed 2000 years ago,
when early viticulturists protected grapevines from freezing with fires
fueled by prunings and dead vines (83). Since then, many different
methods of freeze protection have emerged. The concepts behind several
freeze protection methods are described in the following section with
reference to citrus, although nearly all of the methods can be applied
to other tree crops and cropping systems.
Site Selection
Students of pomology quickly learn that site selection is one of
the most important decisions a grower makes when establishing an orchard
(136). Latitude, topography, and proximity of bodies of water affect
the frequency and severity of freezes at a given site (9). Low-lying
areas or "frost pockets" are often 5° C colder than adjacent hilltops
under radiative freeze conditions, but may be slightly warmer than
hilltops under advective freeze conditions (70, 132). In Florida,
freeze probability and severity decrease with latitude (12, 70), and
sites downwind of large lakes can be 4° C warmer than upwind sites (9).
However, climatic changes can occur and render once productive sites
unsuitable for growth of a particular crop, which has apparently
occurred in citriculture in northern Florida (21).

16
Cultural Practices
Krezdora and Martsolf (72) recently reviewed effects of cultural
practices on citrus cold hardiness and orchard temperatures. They
emphasized the importance of weed-free compact soil for increasing soil
heat storage and conduction, proper row orientation for air drainage,
maintenance of a full canopy to intercept radiant heat from the soil,
and practices which keep trees in a healthy condition and maximize cold
hardiness. Leyden and Rohrbaugh (80) observed higher temperatures and
less freezing injury on citrus trees in sites with chemical weed control
than in cultivated or sodded sites.
Orchard Heating
Orchard heating is the oldest and most reliable method of freeze
protection (48, 83, 129). Several different types of fuels and heating
devices have been used (83), although ordinances prohibit the use of
those which produce excessive smoke and residue (129). The high costs of
petroleum fuels preclude their use except for high cash value crops and
in nurseries (107).
Heaters provide protection by raising the air temperature and by
producing radiant heat (48). Smoke particles are not of appropriate
size to retard radiant heat losses from an orchard, thus no added
protection is obtained by smoke (89, 132). Radiant heat production is
particularly important during windy, advective freezes when the
convective component of heating is reduced (8, 137). Gerber (44)
compared several types of heaters and found that radiant heat output was
highest for those with large metal chimneys or mantles. Heater
placement is an important factor because radiant heat decreases
exponentially with distance (8, 33, 80). Absorption of radiant heat by

17
crees is maximized by placing hearers within rows rather than between
rows (33, 137).
Pollution and expense are not the only problems associated with
heating. Heaters are often difficult to light and maintain at a
constant burning rate (143). Refueling heaters individually is labor
intensive, and automated pipeline systems for refueling can malfunction
due to clogged valves (8). Furthermore, heaters interfere with routine
orchard operations during the summer (83).
Four models exist which describe theory and concepts involved in
freeze protection with heaters. Martsolf (83) has reviewed the
strengths and weaknesses of these orchard heating models in detail.
Gerber's (43) model underestimates the heating requirement under most
freeze conditions, but is fairly accurate under calm, radiative freeze
conditions. Crawford's (25) model accounts for induced flow of air due
to air temperature (hence buoyancy) differences inside and outside the
orchard, which is lacking in Gerber's model, and predicts heat
requirement within 5% of field observations. The box model of Martsolf
and Panofsky is an embellishment of Crawford's model and is largely used
as a research tool (83). The orchard foliage temperature model (137) is
by far the most rigorous development of the orchard heating problem, but
adds little to the current body of knowledge on orchard heating
practices.
Wind Machines
Wind machines have been used for freeze protection since 1916
(129). Wind machines mix warmer air aloft with colder air in the
orchard when a stable inversion exists, hence they are only useful under
calm, radiative freeze conditions (132).

18
The amount of protection provided by wind machines depends
primarily upon inversion strength, power of the machine, and distance
from the machine (48). Leyden and Rohrbaugh (80) observed Io to 3° C
increases in air temperature over a 2.8 ha area on nights when a 4° C
inversion existed. Brooks et al. (14) also reported Io to 3° C air
temperature increases over an area of 4.2 ha when inversion strength was
7° C. Turrell and Austin (130) observed that wind machines provided
better protection on sites which had good air drainage than on sites
with windbreaks around the perimeter. Reese and Gerber (120) concluded
that on calm, clear nights wind machines can be expected to increase air
temperatures Io C over a kidney-shaped area of 4 ha.
Wind machines are sometimes combined with heaters for freeze
protection, yielding results superior to those from either method used
alone (84, 130). Wind machines plus 20 heaters per ha produced higher
air temperatures than 40 heaters per ha alone (14).
Foam
Foam is an unstable mixture of liquid and gas which acts as an
insulative blanket when applied over crops (7). Bartholic (6) found a
10° C increase in temperature under foam applied to low-growing crops.
However, he found little or no elevation of leaf and air temperatures of
mature citrus trees covered with foam unless heaters were used in
conjunction with the foam. The additional cost and logistical
difficulties associated with foam application to trees make it
impractical to use (7).
Fog
Water droplets in clouds and fog are of appropriate size to cause
scattering of terrestrial radiation (133). Therefore, radiant heat loss

19
from orchards on freeze nights is minimized in the presence of fog.
Efforts to generate and maintain fog over crops for freeze protection
began about 20 years ago (129). Mee and Bartholic (90) have reviewed
the history and concepts associated with fog generation for freeze
protection. They point out that fog not only reduces radiant heat loss
from the orchard, but can also add heat through condensation and fusion
of water on plant surfaces.
With mature citrus trees, fog provided about 1.5° C more protection
than heaters during a -5° C freeze, and outperformed wind machines
during a -8° C freeze (89). However, in tests under windy conditions,
temperature increases were only 0° to 3.5° C and decreased with distance
from the fog source (36). Although operating costs are very low (89),
fogging systems are problematic due to the large number of emitters and
purity of water required for reliable operation (90).
Flooding
Flooding orchards either before or during a freeze event can
increase the temperature and heat capacity of the orchard floor (41).
Heat which radiates from the soil or water surface can increase air
temperatures 0.3° to Io C (Davies personal communication). Air
temperature was 0.5° to 10 C higher when the same volume of irrigation
water was distributed among 3 furrows than when only 1 furrow was
flooded (13). Comparable air temperature increases were obtained in
citrus orchards with combinations of wind machines plus heaters, and
wind machines plus flood irrigation (129).
Growth Regulator Sprays
Attempts to alter the hardiness of citrus trees by spray
application of growth regulators have been largely unsuccessful (151).

20
Maleic hydrazide sprays applied during the fall prevented freeze injury
to grapefruit seedlings during a controlled freeze at -6° C (168), but
in field studies trees treated with maleic hydrazide showed similar
damage to unsprayed trees 4 months following a freeze (19). Ethephon,
which increased hardiness and delayed bloom of cherry buds (117), had no
effect on citrus hardiness (168).
Soil Banks and Tree Wraps
Trunks of young citrus trees are protected from freezing injury by
mounding soil or wrapping insulative materials around them during
periods of cold weather. Following severe freezes, the entire canopy
above the bank or wrap is killed, but vigorous sprouts from the
protected portion of the trunk rapidly reestablish a new canopy (129).
Soil banks
In 1904 Hume (59) wrote "no method of protecting trunks of citrus
trees from cold is more efficacious than banking", and with the possible
exception of microsprinkler irrigation (see next section) Hume's
statement remains true to this day. Hume also discussed disease and
insect problems associated with soil banking, and recommended that banks
be removed from trees as soon as danger of freezing is past to prevent
disease damage to the trunk. Other disadvantages of banking include
high labor costs and mechanical damage to trunks from construction and
maintenance of the banks (68). However, soil banks continue to be used
for freeze protection of young trees due to their superior insulative
properties (31).
Generally, trunk temperatures under soil banks are 3° to 12° C
higher than those of unprotected trees, depending on depth within the
soil bank (31, 143). Rates of trunk temperature decrease during a

21
freeze are similar at all depths, but temperatures deeper within the
bank are initially higher and start to decline later than temperatures
at shallower depths (31, 143). The low thermal diffusivity and large
volume of a soil bank are responsible for its superior freeze protection
capability (129).
Tree wraps
Tree wraps were introduced into citriculture in the mid-1950's to
circumvent the problems associated with soil banks while still providing
freeze protection for young trees (80). Although tree wraps provide
less protection than soil banks (67, 68, 170), they have been proven
effective during freezes in Florida (121) and Texas (56). Furthermore,
tree wraps provide protection from wind,radiation and rodent damage
(129), and prevent trunk sprouting (121).
Early research in Texas (80, 170) demonstrated that the thickness
of fiberglass insulation was positively correlated with trunk
temperature, and survival of young grapefruit trees was best with the
thickest wraps. These studies and others (121) showed that trunk
temperatures decrease from top to bottom of wraps much as in a soil
bank, but the magnitude of the temperature gradient was lower than in a
soil bank.
Fucik and Hensz (39) suggested that the ratio of rates of bark to
air temperature decrease was indicative of freeze protection capability
of a tree wrap, and a ratio of 0.55 or less was considered adequate for
freeze protection in most situations. However, trunk and air
temperatures decrease at nearly the same rate with soil banks (ratio of
bark and air temperature decrease is about 1.0) (31), which are superior
to tree wraps with respect to freeze protection. Turrell (129) stated

22
that the thermal diffusivity was the primary determinant of freeze
protection performance of a tree wrap, and this statement probably holds
more often than the above suggestion of Fucik and Hensz.
Several different types of tree wraps are currently used, each with
somewhat different insulative characteristics. A styrofoam wrap which
has 2 containers of water attached to its inner surface produced higher
trunk temperatures and allowed greater tree survival than other wraps in
field studies (30, 67). In laboratory studies (156), this wrap
maintained trunk temperatures of young 'Valencia' orange trees at 0° C
when air temperatures remained at -10° C for 50 hr. Fiberglass wraps
provided 0° to 3° C protection in several field studies, and the level
of protection appeared to be dependent on the rate of air temperature
decrease (121). Thin-walled polystyrene wraps provided very little
protection, and sometimes allowed trunk temperature to fall slightly
below air temperature (30, 68). The level of protection provided by
other wraps was somewhere between that of the styrofoam wrap with water
containers and the thin-walled polystyrene wrap (30, 67, 68). Tree
wraps made of cornstalks were ineffective for freeze protection of young
citrus trees (143), but have been used to prevent wind or radiation
damage to trunks (129).
Sprinkler Irrigation
Sprinkler irrigation has been used successfully for freeze
protection of many crops and areas of the world, from peas and beans in
the Yukon territory (51) to strawberries (81) and citrus in Florida
(30). Perry (109) provides a comprehensive review of field studies
where sprinkling was used to protect various fruit and vegetable crops.
Among the many studies in her review, there were few instances where

23
sprinkler irrigación was used unsuccessfully. The most notable failure
of sprinkler irrigation was reported by Gerber and Hendershoct (47)
where mature citrus trees were killed to the ground as a result of
insufficient application rates (0.25 cm hr *) during advective freeze
conditions (windspeed, 2 to 5 m s ; minimum air temperature,-9° C). In
their study, irrigated trees sustained more damage than unirrigated
trees due to evaporative cooling and elevation of tissue killing
temperatures by the presence of moisture (46).
Irrigation for freeze protection is often referred to as a
"two-edged sword" because freezing of water on the plant releases heat,
while evaporation extracts heat (136). The ratio of latent heats of
evaporation and fusion is about 7.5, thus if 7.5 times as much water is
frozen as evaporated, the temperature of the plant part will remain near
ambient (48). To maintain the plant part near 0° C, an ice-water film
must be constantly maintained on the surface (49). The irrigation rate
required to maintain an ice-water film depends on windspeed, air
temperature and humidity (20, 48, 109). Clear ice formation and icicles
are field indicators of sufficient application rates (47). Trees may be
damaged by excessive ice loading and limb breakage even if proper
application rates are supplied under severe freeze conditions (48).
Several sprinkler irrigation models have been developed due to the
need to determine appropriate application rates and maximum off times
for adequate freeze protection (20, 22, 46, 111, 114). In these models
the rate of heat loss due to radiation, convection and evaporation
(sublimation) is set equal to the amount of heat gained by the freezing
process, and the latter is divided by the heat of fusion of water to
obtain the required irrigation rate. Exceptions to this are as follows:

24
1) the model of Chesness et al. (22) assumes that uo freezing occurs,
and application rate is calculated by dividing the sura of the heat loss
terms by the specific heat and temperature difference between the water
and the leaf; 2) the model of Phillips et al. (114) calculates che
maximum time that a bud can be left unsprinkled before it drops to a
critical temperature, and does not calculate or depend on irrigation
rate. Predictions from the Gerber and Harrison (46) and SPAR79 (112)
models have been successfully validated in the field. A BASIC computer
program is available through North Carolina State University to predict
irrigation rates required for freeze protection, which is essentially
the SPAR79 model (110).
High- and low-volume undertree irrigation has been used to protect
young and mature citrus trees (11, 15, 27, 30, 107, 108, 139).
High-volume sprinklers used were the "pop-up" (27) and "impact" types
(105). Low-volume undertree sprinklers are variously referred to as
minisprinklers, misters, foggers, spinners, and microjets (79), but will
be referred to as microsprinklers for this discussion.
High-volume irrigation increased trunk, leaf and air temperatures,
and fruit pack-out in mature 'Orlando' trees in the lower third of the
canopy (15, 139). However, temperatures and tree damage were similar in
the upper 2/3 of the canopy. Although somewhat successful, high-volume
irrigation is only feasible for protecting limited acreages due to high
cost and consumption of water (15).
Observations show that microsprinkler irrigation can ameliorate the
effects of less severe freezes on mature trees when relatively high
irrigation rates are used (100). Microsprinkler irrigation at rates of
38 and 52 liter hr * provided marginal leaf temperature increases in the

25
lower portion of the canopy of 'Orlando' tángelo trees, but provided
almost no fruit protection (15). Parsons et al. (107) obtained similar
results with 38 and 87 liter hr ^ microsprinklers with mature 'Valencia'
and 'Temple' orange trees during 2 relatively mild freezes.
Alternatively, microsprinkler irrigation is very effective for
freeze protection of young citrus trees under a wide variety of
conditions (11, 30, 104, 108). Typically, raicrosprinkler irrigation
protects the lower 50-70 cm of a tree, and as with soil banks and tree
wraps, new canopies are produced after severe freezes and trees attain
heights of 1 to 2 m by the following autumn (104).
Parsons et al. (108) observed air temperature increases of 0° to
2.8° C and fog in a young tree planting irrigated with microsprinklers
and suggested that partial protection was afforded by microclimate
modification. However, Davies et al. (30) produced opposing evidence
when they measured lower net radiation values over microspinklers that
produced higher rates per unit area than those producing lower rates.
Microsprinkler irrigation at 87 liters hr 1 sprayed in a
wedge-shaped 90° pattern protected young 'Hamlin' orange trees during
one of the most severe freezes in recent history in Florida (30). In
this study, it was found that tree wraps used in conjunction with
microsprinklers provided Io to 2° C more protection than microsprinklers
alone. In addition, irrigated-wrapped trees had higher trunk
temperatures than irrigated-unwrapped trees when irrigation was
discontinued during the night. Further studies indicated that
intermittent raicrosprinkler irrigation could be used to protect larger
acreages of wrapped young citrus trees than can be accomplished with
constant irrigation (32).

CHAPTER III
TRUNK TEMPERATURE, FREEZE SURVIVAL AND REGROWTH OF YOUNG
CITRUS TREES AS AFFECTED BY TREE WRAPS AND MICROSPRINKLER IRRIGATION
Introduction
Thousands of young, nonbearing citrus trees have been killed by
severe freezes in Florida during the last 5 years. Young trees are
particularly prone to freeze damage due to their small size and vigorous
growth habit. Traditionally, soil banks or tree wraps have been used
for cold protection of young trees. Jackson et al. (68) compared
several tree wraps with conventional soil banks and found that wrapped
trunk temperatures were 0°to 1.5° C higher than those of unwrapped
trunks, but 4° to 6° C lower than those of banked trunks. Although soil
banks provide effective cold protection, they are labor intensive and
often result in mechanical and/or disease damage to the trunk (30). In
a subsequent study, wraps provided 0° to 2.5° C protection for young
'Hamlin' orange trees during several radiative freezes in Florida in
1982 (121).
Low volume, raicrosprinkier irrigation may provide an alternative to
wraps and banks for freeze protection of young citrus trees. Davies et
al. (30) successfully protected young 'Hamlin' orange trees during the
advective freeze of Christmas 1983 using a combination of tree wraps and
microsprinkler irrigation applied in a 90° pattern. They also showed
that wraps used in conjunction with irrigation provide greater
protection than either method alone. Microsprinkler irrigation without
tree wraps may be less effective under advective than radiative freeze
26

27
conditions because damage was observed on trees irrigated at 38 liter
hr ^ during the 1983 Christmas freeze (102, 103).
Because only one irrigation rate (87 liter hr *) and spray pattern
(90°) were used in the study by Davies et al. (30), the objective of
this research was to study the effects of different microsprinkler
irrigation rates and spray patterns on trunk temperature of wrapped
trees during freeze conditions, and subsequent tree survival and
regrowth.
Materials and Methods
Winter 1984-83 Studies
A 0.3 ha. planting of 2-year-old 'Hamlin' orange trees (Citrus
sinensis (L.) Osb.) on trifoliate orange rootstock (Poncirus trifoliata
(L.) Raf.) located at Gainesville, Florida, was used in these studies.
Trees were spaced 4.6 x 6.2 m and were ca. 1.5 ra tall. The lower 40 cm
of all trees was wrapped with 9 cm (R-ll) foil-faced fiberglass
insulation. Irrigation treatments were applied in an incomplete
factorial combination of 4 rates (0, 38, 57, 87 liter hr ^) x 2 spray
patterns (90° and 360°). Microsprinklers were placed 1 m from the trees
on the northwest side because winds are generally from this direction
during advective freezes in Florida.
A randomized complete block design with 3 replications was used
employing 3 trees per treatment per replication. Trunk temperatures of
6 of the 9 trees in each treatment were measured with copper-constantan
T-type thermocouples attached to the trunk under the wrap at a height of
20 cm. Air temperature was measured at several locations throughout the
planting by suspending thermocouples from the canopies of the trees at a
height of about 1 m above the soil surface. Data were logged hourly

28
during several freezes over Che winter of 1984-85. Irrigation was
started when air temperature reached 0° C and discontinued when air
temperature returned to 0° C. Two freezes, an advective freeze
beginning on 20 Jan. 1985, and a radiative freeze beginning on 26 Jan.
1985, were selected for discussion as results from other freezes were
similar.
The efficiency of each irrigation treatment (°C increase in trunk
temperature per liter per hr) was calculated by subtracting the
temperature of an unirrigated wrapped trunk from an irrigated wrapped
trunk at the time of the lowest recorded temperature, and dividing by
the irrigation rate. The lowest possible efficiency was taken as zero,
although negative values could occur if the irrigated trunks were cooled
by evaporation below the temperature of the unirrigated trunk.
Winter 1985-86 Studies
Studies during Dec.-Jan. 1985-86 were similar in many respects to
those described in the last section. Two-year-old 'Hamlin' orange trees
on sour orange (Citrus aurantium L.) rootstock planted at the same site
were used to evaluate irrigation rates of 0, 12, 22, 38, and 57 liter
hr ^. On the basis of results of the previous winter, the 87 liter hr *
rate and all 360° spray pattern treatments were not repeated. A
completely randomized design was employed using 7 trees per treatment,
and all trees were wrapped with foil-faced fiberglass (R—11) tree wraps.
Trunk temperatures and efficiency were measured as described in the last
section on 2 trees in each treatment during several freeze nights. The
maximum height of live wood on all trees was measured on 14 April 1986;
however, regrowth of the trees was not evaluated.

29
Results and Discussion
Winter 1984-85 Studies
The advective freeze on 20 Jan. 1985 was characterized by clear
skies, minimum temperature near -12.0° C with durations below 0° C of 39
hr, windspeed of 2 to 6 m s * with gusts to 10 m s *, and dewpoint
ranging from -8.4° to -25.6° C. The radiative freeze on 26 Jan. 1985
was characterized by clear skies, minimum temperature of -5.0° C with
durations below 0° C of 12 hr, windspeed less than 1 m s ^ and dewpoint
of -5.3° to -9.0° C.
Trunk temperatures during both types of freezes generally were
higher with the 90° than 360° spray patterns at all irrigation rates,
particularly when minimum air temperatures were reached (Figs. 3-1,
3-2). Trunk temperatures during the advective freeze (Fig. 3-1) were at
or above -2.5° C for all irrigation treatments, while unirrigated (wrap
only) trunk temperatures decreased to -8.0° C and air temperature was
-12.0° C. Trunk temperatures remained above 0° C in all irrigation
treatments during the radiative freeze (Fig. 3-2) while minimum
temperatures were -2.0° C and -5.0° C for unirrigated trunks and air,
respectively.
Fiberglass tree wraps without irrigation maintained trunk
temperatures 3.0° to 4.0° C higher than air temperature under both
radiative and advective freeze conditions (Figs. 3-1, 3-2). In previous
studies (30, 121) fiberglass wraps provided only 1.0° to 3.0° C
protection. This difference may have been due to the greater trunk
diameter and/or greater rates of air temperature decrease in this study
compared to past studies. Larger trunks provide greater thermal mass
thansmaller ones, thus slowing the rate of decline in temperature.

30
20 00 04 08 12 18 20 00 04 08 12
TIME (hr)
Fig* 3—1. Trunk temperatures of 2-year-old 'Hamlin' orange trees during
an advective freeze of 20 Jan. 1985 as influenced by
microsprinkler irrigation and tree wraps^. Irrigation rates
were (a)_p liter hr , (b), 57 liter hr 1 and (c), and 38
liter hr . Spray pattern is denoted by 90 or 360. Each
point is the mean of 6 measurements.

31
Fig. 3-2. Trunk temperatures of 2-year-old 'Hamlin' orange trees during
a radiative freeze of 26 Jan. 1985 as influenced by
microsprinkler irrigation and trunk wraps. Irrigation rates
were (a)_^7 liter hr , (b), 57 liter hr and (c) and 38
liter hr . Spray pattern is denoted by 90 or 360. Each
point is the mean of 6 measurements.

32
Also, rapid decreases in air temperature may result in larger
differences between trunk and air temperatures (121).
Irrigation may have been unnecessary on 26 Jan. because wraps
maintained the trunk temperatures above -2.0° C. Nevertheless, when
irrigation is used, fiberglass wraps increase the surface area for water
interception and ice formation around the trunk, thereby providing a
buffer between the trunk and the environment should the irrigation
system fail. Davies et al. (30) found that large ice masses around tree
wraps maintained trunks well above air temperature for prolonged periods
when irrigation was discontinued. Wraps are particularly important when
using 360° emitters which produce several discrete streams of water that
could miss a small tree trunk due to improper placement or windy
conditions.
Trunk heating efficiency (°C increase in trunk temperature per
liter per hr), decreased as irrigation rate increased, and was higher
for 90° than 360° patterns at all irrigation rates (Fig. 3-3).
Therefore, the 90°-38 liter hr ^ treatment was the most efficient
pattern-rate combination. Because pumping capacity is often a limiting
factor when irrigating large acreages on a freeze night, further studies
are needed to determine if rates less than 38 liter hr * might maintain
trunk temperatures above critical levels with equal or higher
efficiency. Efficiency of lower irrigation rates is discussed in the
next section.
All irrigated and wrapped trees had live scion wood as of 27 March,
and only one unirrigated, wrapped tree was killed to the bud union. The
height of live wood increased as irrigation rate increased for the 90°
spray pattern (Table 3-1). Additionally, the dry weight and number of

EFFICIENCY ( C • liter', hr
33
0.24
0.20
0.16
0.12
0.08
0.04
0
IRRIGATION RATE (liter - hr-1)
Fig. 3-3. Effect of irrigation rate on trunk heating efficiency of
microsprinkler irrigation treatments for young 'Hamlin'
orange trees. Efficiency was determined on 21 Jan. 1985 at
0737 hr when air temperature was lowest (-12.0° C). For 90°
pattern (A): y= -1.28x10.x + 0.21, r^= 0.40; for 360°
pattern (o): y= -1.26x10 x + 0.18, r = 0.33. Slopes are not
significantly different, intercepts are significantly
different, 5% level.

Table 3-1. Effect of microsprinkler irrigation rate and spray
pattern on height of live wood, shoot dry weight,
and number of shoots per trunk on 22 April 1985.
Rate
(liters hr
)
0
38
57
87
Height Dry wt. New shoots
(cm) (g) (no.)
Spray Pattern
kO
o
o
360°
90°
360°
90°
360°
23
.4
5
.3
6
.9
42.4
32.4
8.7
4.0
9.3
8.4
41.2
33.7
12.1
5.1
10.8
7.8
54.8
30.9
17.3
2.8
28.5
7.8
**z
ns
*
ns
•k
ns
z
Regression coefficients significant at P< .01 (**), or .05 (*)

35
new shoots increased with irrigation rate only for the 90° pattern.
This may be explained by differences in the height of water application
between the 90° and 360° treatments. The 360° pattern applied water to
the wrap surface at a height of about 20 cm regardless of irrigation
rate. However, water from the 90° pattern tended to wet the canopy and
form ice at progressively higher levels as irrigation rate increased.
It was obvious from the severity of the advective freeze that the trees
would die-back to wood that was protected by either wrap and/or ice
because air temperatures remained below critical levels (ca -6.7° C) for
several hours. Hence, it is not surprising that trees irrigated with
90° patterns had greater heights of live wood than those irrigated with
the 360° pattern. Regrowth was greater in the 90° treatment probably
because more wood was present; thus more adventitious buds could be
initiated and undergo development.
Winter 1985-86 Studies
Two advective freezes on 25-26 Dec. 1985 and 27-28 Jan. 1986 were
selected for analysis of trunk temperature because these freezes were
severe enough to provide a rigorous test of the irrigation rates
studied. Freeze conditions on 25-26 Dec. 1985 were characterized by
minimum temperatures of about -7.0° C, windspeeds decreasing throughout
the night from 3 to < 1 m s ^, and dewpoints of about -10° C.
Conditions on 27-28 Jan. 1986 were characterized by minimum temperatures
of about -7.0 °C, windspeeds of 1 to 4 m s and dewpoints of about
-14° C. In addition to the 2 advective freezes, data from 3 radiative
freezes on 22 Dec. 1985, 27 Dec. 1985, and 29 Jan. 1986 were used to
evaluate trunk heating efficiency, when minimum air temperatures of

36
-3.2°, -4.0°, and -2.5° C, respectively, occurred under calm, high
dewpoint conditions.
Trunk temperatures during advective freeze conditions increased
with irrigation rate up to 38 liters hr but were similar for the 38
and 57 liter hr * treatments (Fig. 3-4). Trunk temperatures for the 38
and 57 liter hr * irrigation rates were maintained well above 0° C,
while those for the 12 and 22 liter hr * treatments decreased to about
-1.0° and -3.0° C, respectively, on both dates. Unirrigated wrapped
trunks had temperatures just slightly below those for the 12 liter hr *
rate, hence, this irrigation rate provided little additional trunk
heating compared to the other rates. The relatively poor performance of
the 12 liter hr * rate cannot be entirely attributed to the irrigation
rate per se, as droplet size was noticeably different for this
treatment. Rather than the raindrop-sized droplets of higher irrigation
rates, the 12 liter hr ^ emitters produced a fine mist, causing large
amounts of opaque ice to form on the wrap and lower limbs of the trees.
Opaque ice formation is indicative of water freezing before it reaches
the tree (46), which could be expected with mist-sized droplets that
cool rapidly as they travel through the air due to their high surface to
volume ratio and low heat capacity (20). Hence, small droplet size may
have been partially responsible for the poor protection afforded by the
12 liter hr * rate.
Despite differences in trunk temperature due to irrigation rate,
height of live wood was not significantly related (linearly or
quadratically) to irrigation rate (Table 3-2). This is contrary to
results of 1984-85 studies, but may be explained by the less severe
freeze conditions during the 1985-86 winter causing less trunk damage in

37
_l I I I I I L
19 21 23 1 3 5 7
TIME (hr)
Fig. 3-4. Trunk temperatures of 2-year-old 'Hamlin' orange trees and
air temperatures during advective freezes of 25-26 Dec. 1985
(a), and 27-28 J^n. 1986 (b) for unirrigated (UNIRR), 12, 22
and 38 liter hr (LPH) microsprinkler-^irrigation treatments.
Trunk temperatures in the 57_J.iter hr treatment were similar
to those for the 38 liter hr treatment, hence are not shown.
Trunk temperatures were measured at the 20-cm height
underneath fiberglass tree wraps on 2 trees in each treatment.

Table 3-2. Height of live wood of young 'Hamlin' orange
trees on 14 April 1986 as influenced by
microsprinkler irrigation rate during several
freezes in Dec.-Jan. 1985-86.
Rate
(liters hr )
Height of live wood
(cm)
0
54.7 + 20.1Z
12
35.9 + 12.5
22
56.9 + 15.6
38
46.1 + 15.6
57
57.3 + 12.8
Values of height of live wood are means + SD. Linear
and quadratic regression coefficients were not significant,
P < 0.05. n=7.

39
general, particularly for unirrigated trees. However, trees in the 12
liter hr 1 treatment were noticeably smaller than all other trees, and
the visually greater canopy damage may have resulted from insufficient
water application under windy conditions, i.e., evaporative cooling.
Trunk heating efficiency was calculated for 5 different freeze
nights and data were fitted most closely by a quadratic equation (Fig.
3-5). Setting the derivative of the equation equal to 0, the relative
maximum point on the curve was obtained which corresponded to the value
of the most efficient irrigation rate (position of the star in Fig.
3-5). Similar to the winter 1984-85 data, trunk heating efficiency
was highest for the 38 liter hr ^ irrigation rate (with a 90° spray
pattern) under the widely varying freeze conditions encountered on 5
nights during the winter of 1985-86 (Table 3-3). This is rather
fortunate because most citrus growers in Florida that have
microsprinkler irrigation systems use the 38 liter hr ^ rate (Davies,
personal communication), and trunk heating efficiency could be maximized
by simply changing from 360° to 90° spray patterns.
Conclusions
The 90° spray pattern was superior to the 360° spray pattern with
respect to maintenance of trunk temperature during freeze conditions,
and survival and regrowth of the trees the following spring. A
microsprinkler irrigation rate of 38 liter hr * was most efficient for
maintaining trunks of wrapped young citrus trees above damaging
temperatures under a variety of freeze conditions. Twice as much
acreage can be protected using a 38 liter hr ^ than a 87 liter hr *
microsprinkler with a 90° pattern given the same pumping capacity. Use
of irrigation rates < 38 liter hr * with 90° spray patterns can provide

EFFICIENCY
40
IRRIGATION RATE (liter hr-1)
Fig. 3-5. Trunk heating efficiency as a function of irrigation rate
for 5 freezes during Dec.-Jan. 1985-86. Solid line is a
quadratic regression fitted through the data; the star
denotes the relative maximum on the fitted curve. Each point
is a single determination.

Table 3-3. Dates of freezes, minimum air temperatures, most
efficient irrigation rates, and coefficients of
determination from quadratic regressions of trunk
heating efficiency vs. irrigation rate during
Dec.-Jan. 1985-86.
Date
air
Minimum
z
temperature
(°c)
Most efficient
irrigation rate^
(liters hr *)
2
r
Dec. 22
-3.2
38.5
0.76
Dec. 26
-7.0
41.0
0.48
Dec. 27
-4.0
40.4
0.51
Jan. 28
-7.3
38.6
0.54
Jan. 29
-2.5
40.6
0.32
Air temperatures are means of 7 measurements.
^ Most efficient irrigation rate was calculated
by setting the derivative of the quadratic
regression equations equal to zero and solving
for the relative maxima for each date.

42
Io to 4° C additional trunk protection over tree wraps alone and allow
even larger acreages to be protected on any given night. However,
height of live wood and regrowth of trees may be marginally greater
using higher irrigation rates.

CHAPTER IV
MICROCLIMATE OF YOUNG CITRUS TREES PROTECTED BY
MICROSPRINKLER IRRIGATION DURING FREEZE CONDITIONS
Introduction
Methods of freeze protection that use water include flood
irrigation, fog generation and sprinkler irrigation, and each influences
the microclimate of the orchard. Flooding an orchard during a freeze
can increase soil and air temperatures and upward radiant heat flux from
the orchard floor (13, 41), thereby increasing temperatures of the
trees. Pre-freeze irrigation by either flooding or sprinkling can have
similar effects, but does not present the problem of standing water in
the orchard (41). Fog retards the loss of infrared radiation from the
orchard and raises the dewpoint, which can prevent tree temperatures
from decreasing to damaging levels (89). Therefore, flood irrigation
and fog generation affect temperatures of trees primarily by modifying
the microclimate of the orchard.
Alternatively, sprinkler irrigation provides protection primarily
through direct transfer of latent heat from the ice-water mixture that
coats the tree (20, 46, 109). However, microclimate modification by
high-volume sprinkler irrigation has been observed for mature citrus
trees (15, 27, 108, 139). Leaf and air temperatures were 0° to 3° C
higher for irrigated than unirrigated 'Orlando' tángelo trees (27, 139)
and protection varied with position in the canopy and freeze conditions.
Parsons et al. (107) reported 0° to Io C differences in air temperature
43

44
between irrigated and unirrigated mature citrus canopies using
low-volume microsprinkler irrigation. Fog or mist generation by
microsprinklers may occur under high dewpoint conditions and is thought
to decrease radiant heat loss from the trees and soil surface (108).
However, canopy temperatures at the 2 and 3 m height of irrigated citrus
trees were similar to those of unirrigated trees, despite the presence
of fog or mist in the irrigated block (139). Preliminary studies
-2
indicated that net radiation above young citrus trees was about 8 W ra
more negative with high irrigation rates than low rates, but values for
unirrigated trees were not reported (30).
The effect of microsprinklers on microclimate and subsequent freeze
damage of young citrus trees is unclear. The objective of this research
was to determine the effect of microsprinkler irrigation on air
temperature, dewpoint, net radiation and soil temperature around young
citrus trees under various freeze conditions.
Materials and Methods
Plant Material, Freezes and Treatments
A 0.3-ha planting of 126 2-year-old 'Hamlin' orange (Citrus
sinensis (L.) Osb) trees on either trifoliate orange (Poncirus
trifoliata (L.) Raf.) or sour orange (Citrus aurantium L.) rootstock was
used for all experiments. Trees were spaced 4.6 x 6.2 ra and were 0.5 to
1.5 m in height. The lower 40 cm of all trees was wrapped with 9 cm
(R-ll) foil-faced fiberglass insulation. Microsprinklers were placed 1
m from the trees on the northwest side because winds are generally from
this direction during advective freezes in Florida.
Microclimate measurements during 6 freezes which had widely
variable meteorological conditions were chosen for analysis of treatment

45
effects. The advective freeze of 20-22 Jan. 1985 was characterized by
minimum temperature near -12.0° C with durations below 0° C of 39 hr,
windspeed of 2 to 6 m s ^ with gusts to 10ms ^, and dewpoint ranging
from -8.4° to -25.6° C. The radiative freeze on 26-27 Jan. 1985 was
characterized by minimum temperature of -5.0° C, windspeed < 1 m s
and dewpoint of -5.3° to -9.0° C. Freeze conditions on 25-26 Dec. 1985
were characterized by minimum temperature of -7.0° C, windspeed of 1 to
3 m s \ and dewpoint of about -10.0° C. Minimum temperature on 27-28
Jan. 1986 was about -7.0° C, windspeed was 1 to 4 m s ^, and dewpoint
was about -14.0° C. On 26-27 Dec. 1985, minimum temperature was about
-4.0° C, windspeed was 0 to 2 m s *, and dewpoint averaged -7.0° C.
Minimum temperature on 11-12 Jan. 1987 was -1.5° C, windspeed was 1 to 3
m s 1, and dewpoint was about -4.0° C.
In Jan. 1985, treatments were applied in a factorial combination
of 3 irrigation rates (38, 57, and 87 liters hr ') x 2 spray patterns
(90° and 360°), plus an unirrigated control. Four irrigation rates (12,
22, 38, and 57 liters hr ^) were used with only the 90° spray pattern in
Dec.-Jan. 1985-86, plus an unirrigated control. In Jan. 1987, only a
90° pattern-38 liter hr * rate irrigation treatment and an unirrigated
control were used.
Microclimate Measurements
Microclimate around young trees was measured during the freezes
described above for irrigated and unirrigated trees. Air and soil
temperature, dewpoint, and net radiation data were recorded hourly
during the freezes in Jan. 1985. Soil temperature measurements were
repeated during the 3 freezes in Dec.-Jan. 1985-86 because measurements
from the previous year were speculative. Net radiation measurements

46
were repeated on 11-12 Jan. 1987 co confirm results from 1985.
Observations on fog and mist generation by microsprinklers were made on
all dates. Relative humidity and temperature measurements were made on
all dates inside and outside the planting with a sling psychrometer.
Air temperature was measured with copper-constantan thermocouples
in the canopy of one tree in each treatment at a height of 1 m.
Relative humidity was measured with humidity sensors (Viasala
instruments, Woburn, Mass.) at the same location as air temperature for
one tree in each treatment, and dewpoint was calculated from
simultaneous measurements of air temperature and relative humidity. Net
radiation was measured with Fritschen-type net radiometers placed at a
height of 0.8 m and centered directly over the water spray, between the
tree and the microsprinkler. Preliminary experiments indicated that at
a height of 0.8 m, net radiometers were sensitive enough to measure
-2
differences in upward radiant flux of about 5-10 W m from an area of
2
about 2.8 m (data not shown). One net radiometer per treatment was
used during winters of 1984-85 and 1985-86, but in 1986-87, 4 net
radiometers per treatment were used. Soil temperature was measured with
thermocouples placed approximately 1 cm below the soil surface next to
the trunk of 1 tree in each treatment. This location was chosen because
it was suspected that soil temperature could influence trunk temperature
above the soil surface by conduction of heat vertically along the trunk.
Results and Discussion
Microsprinkler irrigation rate did not affect air temperature,
dewpoint or net radiation of the trees within either the 90° or 360°
spray pattern during the winter of 1984-85 (data not shown). Hence,
data were classified as either irrigated-90°, irrigated-360° or

47
unirrigated to simplify discussion of these variables. Soil temperature
data are discussed for the 90° pattern only, because thermocouple
placement for the 360° spray pattern treatments caused spurious
measurements.
Air Temperature
Air temperature in the tree canopy was similar for irrigated-90°,
irrigated-360° and unirrigated treatments during severe advective and
radiative freezes (Fig. 4-1). Furthermore, air temperatures for all
trees were typically within 0.5° C of those outside the research plot
under both types of freeze conditions (data not shown). Temperature
differences between irrigated 90° and unirrigated treatments approached
1.0° C under radiative conditions for a 3-hr period in the middle of the
night on 26-27 Jan. 1985. This may have been attributable to heat
released by the irrigation water, but was more likely due to random
variation in air temperatures which is frequently observed on radiative
nights. Parsons et al. (108) observed consistent increases in air
temperature of 0.5° to 1.5° C for irrigated young trees, although their
raicrosprinklers were more closely spaced and freeze conditions were less
severe than in this study.
Dewpoint
Variations in dewpoint were typically less than Io C among
irrigated-90°, irrigated-360°, and unirrigated treatments under
advective and radiative freeze conditions (Fig. 4-2). As with air
temperature, there was a 3-hr period in the middle of the radiative
freeze night where values were higher for the irrigated-90° than
unirrigated trees (Fig. 4-2b). However, this may be a mathematical
artifact because air temperature was used to calculate dewpoint.

48
III'» I I I I 1 I i
20 22 00 02 04 06
TIME (hr)
Fig. 4-1. Air temperature in the caaopy of 2-year-old 'Hamlin' orange
trees during a severe advective freeze on 20-21 Jan. 1985
(a) and a radiative freeze on 26-27 Jan. 1985 (b). Points
are means of 3 values for the irrigated-90° (IRR,90) and
irrigated-360° (IRR,360) treatments, and single values for
unirrigated (UNIRR) treatments.

49
20 22 00 02 04 06
TIME (hr)
Fig. 4-2. Dewpoint temperature in the canopy of 2-year-old 'Hamlin'
orange trees during a severe advective freeze on 20-21 Jan.
1985 (a) and a radiative freeze on 26-27 Jan. 1985 (b).
Points are means of 3 values for the irrigated-90° (IRR,90)
and irrigated-360° (IRR,360) treatments, and single values
for unirrigated (UNIRR) treatments. Dewpoint was calculated
using simulataneous air temperature and relative humidity
measurements.

50
Mist often was observed over irrigated trees only during calm
conditions when dewpoint was close to air temperature, similar to the
observations of Parsons et al. (108). However, humidity measurements
made with a sling psychrometer above unirrigated trees were similar to
those outside the research plot (typically 60-100%), indicating that
microclimate around unirrigated trees within the plot was not influenced
by mist from neighboring irrigated trees.
-2
Net Radiation Net radiation was 10 to 20 W m more negative over
irrigated than unirrigated treatments under advective freeze conditions
(Fig. 4-3a). Higher net radiation values over unirrigated than
irrigated trees were observed again during a less severe freeze on 21-22
Jan. 1985 (data not shown). Net radiation values outside the planting
were comparable to values for unirrigated trees inside the planting.
Hence, the increase in outgoing radiation from the irrigated treatments
was localized, and probably caused by the presence of the relatively
warm irrigation water. If irrigation were favorably modifying the
microclimate of the trees, one would expect net radiation to be less
negative over irrigated trees, but the opposite situation is seen (Fig.
4-3a).
No differences in net radiation occurred between irrigated and
unirrigated treatments or among irrigated treatments under radiative
freeze conditions (Fig. 4-3b). Net radiation was measured above
irrigated (38 liter hr *-90° microsprinklers) and unirrigated trees
during a mild, radiative freeze on 11-12 Jan. 1987 to verify results
from 1985. Again, net radiation was found to be similar for irrigated
and unirrigated trees (Fig. 4-4), consistent with data in Fig. 4-3b.
Reasons for the lack of differences in net radiation between irrigated

NET RADIATION (W-
51
TIME (hr)
Fig. 4 3. Net radiation above 2-year-old 'Hamlin' orange trees during a
severe advective freeze on 20-21 Jan. 1985 (a) and a
radiative freeze on 26—27 Jan. 1985 (b). Points are means
of 3 values for the irrigated-90° (IRR.9Q) and irrigated-360°
(IRR,360) treatments, and single values for unirrigated
(UNIRR) treatments.

(¿JU-M) NOIJLVIQVd 13N
52
-56
-58
-60
-62
22 00 02 04 06 08
-
0 UNIRRIGATED
8
• IRRIGATED
-
0
-
•
- om
2
09
-
<
•o
•o
•o
O
•
-
0
•
i
1 1
-J I 1
TIME (hr)
. Net radiation above 2-year-old 'Hamlin' orange trees during a
radiative freeze on 11-12 Jan. 1987. Points are means of 4
values for irrigated and unirrigated treatments.
Fig. 4-4

53
and unirrigated trees under radiative conditions are unclear.
Variability in incoming radiation under calm conditions may have masked
any slight differences in upward radiant flux on both occassions.
Davies et al. (30) measured net radiation values of -61.3 and -53.1
—2 —1
W m above trees irrigated with 90°-87 liters hr and 360°-38 liters
hr ^ microsprinklers, respectively, under radiative conditions. Their
results could be explained by the presence of greater quantities of 10°
to 15° C irrigation water underneath net radiometers for the higher than
the lower irrigation rate. However, it is unclear why differences
between 90° and 360° spray patterns were not detected under radiative
conditions in this study. Possibly, different net radiometer placement
(1.5 m for Davies et al. (30) and 0.8 m in this study) was responsible
for the conflicting results.
Soil Temperature
Soil temperature generally was highest for the 38 liter hr ^ rate,
intermediate for unirrigated trees, and lowest for the 12 liter hr *
rate during 3 freezes in Dec.-Jan. 1985-86 (Fig. 4-5). The soil
temperatures for the 22 and 57 liter hr ^ treatments were very similar
to those for the 12 and 38 liters hr * treatments, respectively. The
mist-sized droplets in the 12 liter hr ^ treatment probably cooled to a
greater extent as they traveled through air than larger droplets in
other treatments (46) and consequently reduced soil temperature below
that for unirrigated trees. However, droplet size was comparable for 22
and 38 liters hr ^ microsprinklers, and the reduced soil temperature for
the former treatment cannot be explained by greater droplet cooling.

54
Fig. 4-5. Soil temperature measured 1 cm below the surface and uext to
trunks of 2-year-old 'Hamlin' orange trees during freezes on
25-26 Dec. 1985 (a), 26-27 Dec. 1985 (b), and 27-28 Jan.
1986 (c). Points are single values for the unirrigated (0
LPH), 12 (12 LPH) and 38 liter hr (38 LPH) treatments.

Conclusions
Microsprinkler irrigación does not appear Co change Che
microclimace of a young cree in che same way as reporced for maCure
crees (15, 107). Macure crees have much greacer canopy volume chan
young crees, hence a greacer capacicy Co decrease radiación loses and
reduce windspeeds wichin che canopy, and reCain heac released from
irrigación waCer. Irrigación may, under cerCain condicions, increase
Che long-wave radianc flux from Che viciniCy of a young Cree, buc Ches
effeces appear Co be localized and do noC affecc air cemperacures.
Irrigación races > 38 liCers hr ^ elevaced soil Ceraperacure 2° co 6° C
while lower irrigación races reduced soil Ceraperacure 2° Co 4° C wich
respecc Co che unirrigaced condición. Therefore, ic is possible chac
heac conducCed along Che crunk from Che soil is parcially responsible
for elevación of Crunk Cemperacures of wrapped young ciCrus crees
irrigaced wich 38 licer hr * (or higher race) microsprinklers. This
possibilicy is invescigaced in ChapCer VII.

CHAPTER V
TRUNK TEMPERATURE, LIGHT INTENSITY AND SPROUTING OF WRAPPED AND
UNWRAPPED YOUNG 'HAMLIN' ORANGE TREES FOLLOWING A FREEZE
Introduction
Tree wraps not only provide freeze protection for young citrus
trees during the winter (68, 121, 156) but also influence trunk
sprouting in the spring. Trunk sprouting on freeze-damaged trees may be
beneficial or deleterious, depending on the degree of injury sustained
by the canopy. Following less severe freezes, ample canopy wood may
survive and produce new shoots. In this case trunk sprouting would be
undesirable, occurring at the expense of growth of scaffold limbs.
However, severe freezes may kill a young tree nearly to the bud union,
and the development of trunk sprouts would be necessary for the
reestablishment of the tree canopy. In either case, absence or presence
of a tree wrap and the type of wrap become important factors in the
regrowth and proper training of a young citrus tree.
Sprout inhibition by wraps may be a result of a physical barrier
imposed by a close fitting wrap, and/or modification of the
environmental factors influencing sprout growth such as temperature and
light intensity. Shoot initiation and growth are strongly temperature
dependent in citrus (23, 35, 119, 163), and light is necessary for
shoots to become autotrophic and continue growth once initiated. The
temperature and light regimes underneath wraps have not been studied in
the early spring when sprout initiation and development occur.
Moreover, the influence of various trunk wraps on trunk sprouting has
56

57
not been critically examined in citrus. The objective of this study was
to monitor the temperature and light environment of young citrus tree
trunks underneath various wraps during early spring, and to examine the
relationship between these environmental factors and trunk sprouting in
freeze damaged trees.
Materials and Methods
Two-year-old 'Hamlin' orange trees (Citrus sinensis (L.) Osb.) on
trifoliate orange rootstock (Poncirus trifoliata (L.) Raf.) located at
Gainesville, Florida were used in this study. These trees were
protected from severe freezes during the 1984-85 winter with fiberglass
tree wraps and microsprinkler irrigation, but were killed back to a
height of about 60 cm. On 26 Feb. 1985, fiberglass wraps were removed
and 6 wrap treatments applied to 36 trees in a randomized complete block
design as follows: unwrapped (UW), fiberglass (FG), styrofoam (SF),
styrofoam modified to exclude light (MSF), white polystyrene (WP) and
charcoal polystyrene (CP). These treatments were chosen to provide
separation of light and temperature effects on trunk sprouting. The
wraps covered the lower 40 cm of the trunk, of which about 35 cm was
scion wood. Most trees had sprouts above the wrapped portion of the
trunk at this time, but no sprouts were observed on the lower 40 cm.
Trunk temperature was measured with copper-constantan thermocouples
taped to the trunk at a 20-cm height. Air temperatures were measured
with thermocouples suspended on canopy wood 1 m above the ground.
Photosynthetic photon flux (PPF) was measured with Li-Cor quantum
sensors taped to the trunk near the thermocouples. Due to a shortage of
quantum sensors, PPF could only be measured on 3 of the 6 treatments
during any particular day. Therefore, temperature and PPF measurements

58
were made over a 20 day period in March, 1985, Che quantum sensors being
moved among treatments on different days. Temperatures were measured
hourly and PPF at 15 min. intervals.
Sprouts from the lower 40 cm of the trunks were removed and counted
on 13 May 1985, after treatments had been in place for 76 days, and
placed in an oven at 80° C for 24 hr for dry weight determination.
Temperature, sprout number and dry weight data were analyzed for
treatment effects using analysis of variance and Duncan's multiple range
test. Although PPF data could not be analyzed statistically, data for
any particular wrap treatment on different days with similar sky
conditions were comparable.
Results and Discussion
Generally, trunk temperatures under WP and CP wraps were highest
and those under SF and MSF wraps lowest during the daylight hours, with
FG, UW and air temperatures intermediate (Fig. 5-1). However, in the
afternoon on cloudy days, all wrapped trunk temperatures were generally
higher than the air temperature, but differences among wrap treatments
were small and varied from hour-to-hour. In mid-afternoon on sunny
days, differences in trunk temperatures between WP and MSF treatments
approached 17° C, and temperatures under WP wraps reached 41° C. In
addition, temperatures remained above 38° C under WP wraps for 3 to 4
hr, while temperatures under MSF wraps generally remained below 29° C.
During the night, temperatures under the SF and MSF wraps were highest,
lowest for WP, CP, UW and air, and intermediate for FG. By sunrise ,
the temperatures under the MSF wraps were significantly higher (0.5° to
1.0° C) than all other treatments. This was probably a result of the
covering of black tape used to exclude light which made the wrap

59
__i i i i i : i i i i i i t—
0 6 10 14 18 22 02 06
TIME (HR)
Fig» 5—1. Diurnal trunk temperatures of young 'Hamlin' orange trees
underneath various trunk wraps during a typical sunny day (a)
and a cloudy day (b) in March, 1985. Each point is the mean
of 6 measurements. Abbreviations are as follows: white
polystyrene (WP), charcoal polystyrene (CP), styrofoam (SF),
modified styrofoam (MSF), unwrapped (UW), and fiberglass
(FG).

60
airtight, and thus a better insulator than the SF wrap which was
ventilated. Although statistically different, it is questionable
whether a 0.5° to 1.0° C difference in nighttime temperature is of
biological significance to a young tree with respect to trunk sprouting.
The range of trunk temperature encountered in this experiment (16°
- 41° C) was above the 13° C threshold which qualitatively controls
budbreak (119, 163) and below the 50° C threshold which can cause tissue
damage in citrus (62, 119). Prolonged periods of relatively high trunk
temperature as observed for some wraps in this study might adversely
affect cambial activity and ultimately the growth of a young tree.
Alternatively, such wraps may induce earlier resumption of cambial
activity in the spring by raising trunk temperature to levels favorable
for growth. Further studies on the influence of tree wraps on growth of
young trees are warranted due to the widespread use of wraps for
protection from freeze, herbicide, and fertilizer damage.
Photosynthetic photon flux varied from ambient on unwrapped trunks
to undetectable levels on trunks of FG and CP treatments. The WP wrap
allowed the most PPF transmission (9-13% of ambient) followed by SF
(4-9% of ambient) and then MSF (less than 0.1% of ambient) (Fig. 5-2).
In the UW, WP and SF treatments, PPF was well above the reported light
compensation point for citrus (73) which is about 1-2% of full sunlight.
Unwrapped trunks had highest sprout numbers and dry weights of all
treatments (Table 5-1). Number of sprouts in the WP treatment was
statistically similar to the UW treatment, but sprouts in the WP
treatment were deformed and had lower dry weights than those in UW
treatment. Apparently this was due to the physical limitations on
sprout growth imposed by the wrap. All other treatments had

61
06 08 10 12 14 16 18
TIME (hr)
Fig* 5 2. Diurnal photosynthetic photon flux (PPF) underneath various
trunk wraps on 2-year-old 'Hamlin' orange trees during a
sunny day (a) and a cloudy day (b) in March, 1985. Each
point represents a single measurement. No PPF was detected
beneath CP and FG wraps. Abbreviations are as follows:
unwrapped (UW), white polystyrene (WP), styrofoam (SF), and
modified styrofoam (MSF).

62
Table 5-1. Numbers aad dry weights of trunk sprouts on
freeze damaged yoi ng 'Hamlin' orange Lrees on
13 May 1986 influenced by various trunk wraps.
Wrap
Trunk
Dry
type
sprouts
wt
(no.)
(g)
Unwrapped
White polystyrene
Modified styrofoam
Styrofoam
Fiberglass
Charcoal polystyrene
8.4az
8.5a
5.8a
3.1b
1.5b
1.4b
1.3b
2.5b
0.0b
0.0b
0.0b
0.0b
Means followed by the same letter are not significantly
different, Duncan's multiple range test, 5%. n=6.

63
statistically similar sprout number and dry weight, although no sprouts
were found on any of the trunks in the FG and CP treatments. It is
possible that sprouts had developed somewhat but abscised before 13 May
in the FG and CP treatments due to the lack of PPF. Small etiolated
sprouts have been observed under fiberglass wraps (Davies, unpublished).
Jackson et al. (67) reported that sprouting occurred on 22% and 0% of
freeze damaged trees with SF and FG wraps, respectively, which is
qualitatively similar to the results in this study.
Some PPF (as low as 0.1% of ambient as in the MSF treatment) was
necessary for development of trunk sprouts on freeze damaged trees.
Furthermore, there was a direct correlation between PPF and sprout
growth. This is supported by the fact that trunks receiving the highest
PPF (UW and WP) had the highest number and dry weight of sprouts, trunks
receiving no measurable PPF (FG and CP) had no sprouts, and treatments
receiving intermediate intensities (SF and MSF) were intermediate in
sprout number and dry weight.
It is possible that a PPF-temperature interaction occurred in this
study, although unfortunately, the experiment was not designed for
statistical analysis of interaction. However, some of the results may
be explained better considering a PPF-temperature interaction. For
example, the CP/WP treatment pair and the SF/MSF treatment pair were
designed to create similar trunk thermal regimes but different PPF
regimes. The WP and CP treatments both had relatively high mean
temperatures and different PPF regimes, while the SF and MSF treatments
both had relatively low mean temperatures and different PPF regimes.
Large differences in sprouting occurred between the WP and CP
treatments, suggesting that PPF influences sprout development given a

64
relatively high trunk thermal regime. On the other hand, no statistical
differences in sprouting occurred between the SF an MSF treatments,
suggesting that PPF does not control sprout development given a
relatively low trunk thermal regime. Therefore, the effect of PPF on
sprouting was either strong or nonexistent, depending on the trunk
temperature regime.
Conclusions
In general, PPF was necessary for trunk sprouts to develop and
persist under the various wraps, and both high PPF and high temperature
favored the development of trunk sprouts. In relative terras, if the
temperature was high but PPF low (as for CP), or temperature low and PPF
high (as for SF), or both temperature and PPF were low (as MSF) then the
number and dry weight of sprouts were reduced. Therefore, wraps that
exclude light entirely are probably best for trunk sprout inhibition of
moderately damaged young citrus trees where regrowth will occur on
surviving canopy wood. If trees have been killed to the wrap, however,
removal of the wrap at the earliest reasonable date would encourage
development of trunk sprouts which will produce a new canopy.

CHAPTER VI
MODELING AND SIMULATION OF TREE WRAPS AND MICROSPRINKLER
IRRIGATION FOR YOUNG CITRUS FREEZE PROTECTION
Introduction
Freeze protection using tree wraps and microsprinkler irrigation
has been the subject of several field studies with young citrus trees
(30, 32, 104, 107, 108). These studies mainly present data on trunk,
leaf and air temperatures during freezes and resulting tree survival and
regrowth. Although these studies demonstrate the effectiveness of tree
wraps and microsprinkler irrigation for freeze protection under the
conditions encountered, one can only speculate on the relative
importance of humidity, air temperature, rate of air temperature
decrease, windspeed, freeze duration, wrap type, water temperature,
etc., on trunk temperature and subsequent tree survival. Freeze
chambers cannot accurately simulate radiation, humidity, temperature and
windspeed regimes observed in the field during freezes, hence laboratory
studies would be neither practical nor useful in yielding accurate
quantitative information. Alternatively, modeling and simulation of the
wrap/microsprinkler system may provide detailed information that is
currently lacking on system behavior, and can hasten the progress of
research on freeze protection of young citrus trees by allowing
investigators to study the problem year-round instead of only a few
nights per year.
Models of overhead sprinkling for freeze protection have been used
to predict irrigation requirements for successful freeze protection of
65

66
apple buds (109, 114) and mature citrus foliage (20, 46). Basically,
these models calculate the rate of heat loss from a plant part under
given freeze conditions, then use this to calculate the irrigation rate
required to maintain the plant part above a predetermined critical
temperature. Hence, output from sprinkler rate models consists of a
single value, i.e., the irrigation requirement for freeze protection
under a given set of environmental conditions (110). Practical
applications of these models are limited because most irrigation systems
are not designed to produce variable irrigation rates. However, concepts
and information contained in sprinkler rate models were useful in
developing a model of the tree wrap/microsprinkler irrigation system.
Rather than calculating static values of irrigation requirement, a
more heuristic approach was taken to model the dynamic behavior of trunk
temperature as influenced by the wrap/microsprinkler system given freeze
conditions and other easily determined parameters. Using this approach,
simulation experiments can be run and output, e.g., trunk temperature,
evaluated at any time, under a variety of conditions. Furthermore,
simulation can be used as a screen for hypotheses, reducing the amount
of field experimentation necessary to achieve a particular goal.
Ultimately, information can be derived that can be useful in redesigning
and improving the system.
The primary objective of this research was to develop a
process-based, dynamic heat transfer model of the wrap/microsprinkler
system of young citrus freeze protection and use simulation to study
system behavior. Simulations were run to assess the influence of
parameters and environmental conditions on trunk temperature. Trunk

67
temperature predicted within one standard error of observed data during
model validation were considered accurate.
Model Development
Description
The system under consideration consists of a young citrus tree
trunk enveloped by an insulative tree wrap 8-14 cm in diameter and 30-40
cm in height (Fig. 6-1). Water is applied by a microsprinkler
positioned 1 m from the tree, which consists of a plastic tube with an
orifice and directional cap on the end that control the flow rate and
spray pattern of the irrigation water. When the irrigation is on, the
wrap surface is partially covered by a thin layer of water and an ice
layer if conditions favor freezing. The wrap/ice mass intercepts a
fraction of the irrigation water, and sensible or latent heat is
transfered from the water to the wrap/ice surface. As ice accretes on
the wrap surface, the fraction of water intercepted becomes greater as
does the surface area over which water is distributed. In the field,
some of the irrigation water often is intercepted by the canopy above
the wrap, which in addition to protecting some of the canopy, can change
the trunk temperature by flowing down the trunk inside the wrap.
Symbols used in model development, their definitions and units are
listed in Table 6-1.
Heat Conduction within the Wrap and Trunk
The tree wrap system can be viewed as 2 main components: a cylinder
of citrus wood (trunk) of variable radius, surrounded by an annulus of
insulative material (wrap) of specified thickness and composition.
Within the confines of the outer wrap surface, temperature varies
spatially and temporally, hence the trunk/wrap composite cylinder is a

68
Fig. 6-1. Conceptual model of the tree wrap/microsprinkler irrigation
system for young citrus freeze protection illustrating heat
transfer processes; Q = heat conduction from within the trunk
and wrap to the external boundary.

69
time-continuous, distributed thermal system. The mathematical model for
the rate of change in temperature with time at any point within the
trunk/wrap composite cylinder is developed for the case of
one-dimensional (radial) heat flow in the following paragraphs.
The heat stored (h) per unit volume of a region within the
trunk/wrap composite cylinder is defined as
-3
h (cal cm ) = p c T [6-la]
where c is the specific heat, p the density, and T the temperature of
the region. In a time interval At, the change in heat content of a
region of volume= Ar rA0 Az (Fig. 6-2) can be written as
Ah AT
Ar rA0 Az — = — p c Ar rA0 Az [6-lb]
At At
where Ar, rA0 and Az are the infintesimal distance increments in the
radial, angular, and vertical dimensions. The rate of change in heat
content of the region must be equal in magnitude and opposite in sign to
the change in flux (j) with distance (Ar), according to the principle of
continuity (26)
A(h Ar rA0 Az) A(j Ar rA0 Az)
= - [6-2a]
At Ar
The terms Ar, A0, and Az are independent of time and radius, and r is
independent of time, so [6-2a] can be rewritten as
Ah A(rj)
Ar rA0 Az — = - Ar A0 Az [6—2b]
At Ar
Cancelling like terms and taking the limit as At and Ar approach zero,

70
ah 1 3(rj)
— = - - [6-3]
at r 3r
The flux in the radial direction j can be defined as
3T
j = - K — [6-4]
ar
where 9T/9r is the temperature gradient between the inner and outer
surfaces of the region, and K is the thermal conductivity of the region.
Substituting for j in [6-3] yields
3h
1 3
9T
— =
(r K —)
[6-5
3t
r 9r
3r
Assuming K is constant with respect to r, and substituting [6-la] for h
3T
1 9
3T
— =
a (r
—)
[6-6
3t
r 9r
9r
where a = K/(p c), the thermal diffusivity of the region.
Similar derivations hold for the other 2 dimensions, resulting in
the following form for 3-dimensional heat transfer in cylindrical
coordinates (26)
3T
1 3
3T
2
1 3 T
2
3 T
— =
a “ —
(r -)
+ ~2 ~ +
9t
r 9r
3r
r 30
dz¿
Thus, the rate of temperature change of any region between the trunk
center and wrap surface is dependent on the thermal diffusivity and
temperature gradients in the radial, circumferencial and vertical
dimensions about the region.

71
Equation [6-7] was not solved analytically due to its complexity,
and the fact that the parameters K, p, and c change discretely with r at
the trunk/wrap interface. Instead, a finite difference version of [6-7]
was employed to calculate rates of change in temperature, where second
derivatives were approximated by second forward differences (26)
dTr,e,z = ^ (Tr+l,0,z~2Tr,0,z+Tr-l,0, z ^ + [ ^Tr+1,0,z~Tr-l,9,z^
dt Ar2 r 2Ar
1 (T -2T +T )
v r,0+l,z r,0,z r ,0-1,zJ
2 ,. 2
r A0
(Tr,0,z+l 2Tr,0,z+Tr,0,z-l)
Az2
[6-8]
Hence, if a and the temperatures of the 6 surrounding regions are
known or set to assumed initial conditions, the rate of temperature
change of any region within the trunk/wrap cylinder can be calculated.
In order to use [6-8] , the distributed tree wrap system was divided
into concentric layers in the radial direction, pie-shaped regions in
the angular direction, and disc-shaped regions in the vertical direction
yielding a discrete model system (Fig. 6-2). Therefore, the model
system had a finite number of regions of heat storage each with a single
temperature at any time t, whereas the real system contains an infinite
number of different points and temperatures. Values of A0 and Az were
set at 0.63 radians (36°) and 1.0 cm, respectively, and Ar was either
0.2 or 0.5 cm, which were the maximum achievable without affecting
simulation output, allowing the programs to run in the least amount of
time possible. Using these values there were 5200 (Ar=0.5) or 13000
(Ar=0.2) finite regions of heat storage for a typical trunk/wrap
composite cylinder 13 cm in diameter and 40 cm in height.

72
Fig. 6-2. Three-dimensional representation of the model system showing a
representative finite region of heat storage. For a typical
tree wrap 13 cm in diameter and 40 cm in height there were
5200 regions when Ar=0.5 cm, A0=O.63 radians, and Az=1.0 cm.

73
The temperatures of most interest are those corresponding to the
cambial region of the trunk, because adventitious buds arise from this
area to produce a new canopy. The cambium of a fully acclimated citrus
tree is killed at temperatures of about -6.7° C (157), and it is
important to know conditions under which the wrap/microsprinkler system
allows the temperature of the cambium to reach critical values.
After rates of change were calculated, state variables were updated
by Euler or rectangular numerical integration with respect to time
State = State , + dt(Rate^ ) [6-9]
t t-dt t-dt
where subscripts t and t-dt denote current and previous times.
Temperature was the only state variable of interest in simulations
except for ice layer thickness, which appeared in only those runs of the
irrigation simulation which had rather severe simulated environmental
conditions.
The Euler method assumes that the rate of change of a state
variable is constant over the time period dt, hence dt must be small
enough to justify this assumption. The maximum useful time step in heat
transfer simulations is a function of thermal diffusivity and distance
increment (dx), and generally is described as (26)
(dx)2
dt < [6-10]
2 a
where the calculation is for the component in the system with the
highest a and lowest dx. Time steps of 0.3 or 0.8 seconds were used
when simulating freeze protection with wraps and irrigation or wraps
alone respectively, due to the different assumptions made in each case
(see section on simulation). Greater time steps caused unstable
oscillations of temperatures with time that were fatal to program
execution, while lower time steps did not affect output.

74
Heat Exchange at Che System Boundaries
Internal boundary
The internal boundary of the model system is the center of the
trunk, and its rate of temperature change cannot be calculated using
[6-8] because r=0 at the internal boundary, and [6-8] requires the
temperature at r—1 for calculating radial heat transfer. Therefore, the
temperature of the internal boundary was assummed to equal the average
temperature of the adjacent regions, (i.e., where r=l). This assumption
is often made with cylindrical thermal systems (26).
External boundary
Energy is exchanged between the system and the environment across
the external system boundary, or outermost layer of the system, by the
following processes: irrigation (IR), radiation (R), evaporation (E),
and convection (CV) (Fig. 6-1). Conduction (Q) allows heat transfer to
and from the external boundary, and therefore provides the linkage
between heat transfer at the surface and that within the system. The
external boundary differs in composition in both space and time, being
either wrap material, water or ice, and it is necessary to determine its
state before calculating the energy balance. However, a general form of
the energy balance of the external boundary is
dT
Ar(P c) —- = (Q+IR-R-CV-E) [6-11]
S dt
where the subscript s denotes the external system boundary, and Ar its
thickness. If the irrigation is on, the external boundary is a thin
water layer where water is striking the wrap surface. Field
observations indicated that the thickness of the water layer was about
0.1 cm, and this value was used in all simulations. If the irrigation

75
is off buC an ice layer is present, then IR=0 and E represents
sublimation instead of evaporation. Volume changes upon freezing of
water are assumed negligible, and Ar remains equal to 0.1 cm when the
system boundary is an ice layer. If the system boundary is wrap
material (no irrigation or ice), then IR and E equal 0 and Ar becomes
the thickness of the wrap surface layer, which was either 0.2 or 0.5 cm,
similar to other wrap layers. Use of Ar in [6-11] implicitly assumes
that temperature changes of the system boundary occur uniformly
throughout its volume, which may only be true for small values of Ar.
Process descriptions
The heat transfer processes in the right hand side of [6-11]
(Q, IR, E, CV, R) require specific mathematical descriptions, and all
-2 -1
must be in the same units (cal cm s ) to be summed as shown yielding
the rate of temperature change of the external system boundary.
The irrigation process is given by
IR- [RATE c (T , - T )]/AREA [6-12]
H20 H20 s
where RATE is the amount of water intercepted by the wrap in liters per
second, AREA is the surface area over which the water is uniformly
distributed, T and c are temperature and specific heat of water
rlZO HZO
respectively, and T^ is the temperature of the external boundary. In
[6-12] it is evident that as T aPProaches T , IR approaches 0
regardless of RATE.
Conduction (Q) of heat to the external boundary from within is
given by (128)
Q= K(T. -T )/ [r ln(r /r. )] [6-13]
ins s s in
where T^ and r^ are the temperature and radius of a specified region
internal to the external boundary. For example, if the outer system

76
boundary is wrap material, then T and r^n are the temperature and
radius of the wrap layer beneath the wrap surface layer. Alternatively,
if the external boundary is water, then T. and r. would correspond to
in in v
the temperature and radius of the ice layer or the wrap surface layer,
depending on presence or absence of ice.
Radiative heat transfer is given by
R= 4aT 3 (T -T ) [6-14]
3 S3.
3
where 4GT is the radiative heat transfer coefficient (46, 111). The
3
emmissivity of the surface is assumed to equal 1, and is therefore
omitted in [6-14], Some of the consequences of this assumption are
discussed in chapter VII.
Evaporative heat flux is calculated by multiplying the mass flux of
water vapor from the external boundary by the latent heat of
vaporization (or sublimation)
E= L [D Sh(W -W )] [6-15]
v wv s a
where D is the water vapor diffusivity of air, L is the latent heat
wv v
of vaporization (or sublimation), W and W are water vapor
S 3
concentrations of the external boundary and air, respectively, and Sh is
the Sherwood number which embodies windspeed and wrap dimensions (93).
Water vapor concentration of the air (W^) is calculated from air
temperature and relative humidity using the psychrometric equation. The
air adjacent to the external boundary is assumed to be saturated with
water vapor at the surface temperature (Wg) if the external boundary is
water or ice. Evaporative heat flux equals 0 if the external boundary
is wrap material.
Convective heat transfer was calculated using Monteith's (93)
equation for cylinders

77
Cv = (K Nu)/d (T -T ) [6-16]
3 S 3
where (K Nu)/d is Che convecCive heat transfer coefficient (93, 109),
a
and Nu is the Nusselt number embodying windspeed, wrap dimensions, and
kinematic viscosity of air.
Freezing of water on the external boundary invokes a boundary
condition where the temperature at the ice-water interface is 0° C. The
radius of the ice-water interface (r. ) is therefore important, and it
l-w
is determined by calculating the rate of ice accretion, dr^_w/dt. The
rate of heat conduction away from an ice-water interface (Q. ) is (61)
l-w
dr.
Qi-„ ' h l-w.
[6-17]
dt
where is the latent heat of fusion, and is the density of ice.
Latent heat produced at the interface can move in 2 directions, either
out (Q ) into the water layer or in (Q. ) towards the wrap surface,
out in
hence
and,
o.
+
Q
w
yin
out
[6-18]
Q. = K. (T.-273)/(r. ln(r. /r.)) [6-1'
m i i l-w l-w i
Q (273-T )/r ln(r ,/r. ) (r ,/r. ) [6—2i
out H20 wl wl wl l-w wl l-w
where T., r. and T , , r „ are the temperatures, radii of the ice layer
i i wl wl
and water layer adjacent to the interface, respectively. Substituting
[6-19] and [6-20] into [6-17] and rearranging
dr.
l-w
dt
(Q - Q. )/(L, P.)
out m f i
[6-21]

78
The radius of Che ice-water interface is obtained by numerical
integration of [6-21] yielding ice thickness, and adding to it the
radius of the wrap.
Forcing Functions
The forcing functions or inputs required by the model are soil and
air temperatures, windspeed, and relative humidity as functions of time.
Forcing functions are independent variables that "force" the system to
change state, and their magnitudes are not affected by the state of the
system. With the exception of soil temperature, environmental variables
are readily available in the form of weather forecasts or can be
measured with hygrothermographs and anemometers. Soil temperatures must
be measured with thermocouples or similar devices near the trunk and
just below the soil surface. However, excluding the terms for vertical
heat transfer in [6-8] allows for independence of the model from soil
temperature data, which is desirable provided model behavior is not
greatly altered.
Simulated air and soil temperatures decreased with time from
initial values to desired minima by linear or negative exponential
functions. Relative humidity was either held constant, or allowed to
increase or decrease linearly with time as is often observed during a
freeze. Wind velocity oscillated around a mean value as a sinusoidal
function of time with a given amplitude and a period of about 30 min to
approximate the stochastic nature of wind velocity observed on freeze
nights.
Parameters
Most of the parameters used in the model were obtained from
handbooks (128, 134), and parameters that could not be obtained from the

79
existing literature were estimated through laboratory or field
experimentation. The latter included the thermal properties of tree
wraps and some of the characteristics of the irrigation process. The
determination of K, p, c and a of various tree wraps was rather
involved, and is left for discussion in Chapter VII. Parameters used in
the simulation programs are listed in appendices A and B.
Four characteristics of the irrigation process were required prior
to simulation: water temperature, fraction intercepted by the wrap,
amount of the wrap surface covered with water and distribution of the
water on the wrap surface.
Temperature of the water striking the wrap surface was estimated
with thermocouples on the surface of fiberglass wraps directly in the
path of the water spray. Wraps were placed around trunks of 6,
2-year-old 'Hamlin' orange trees and temperatures were recorded hourly
as trees were irrigated with 38 liter hr ^ emitters during 4 mild freeze
nights in Jan.-Feb. 1987. Similar data were collected during Dec.-Jan.
1985-86 on wrapped 'Hamlin' orange trees irrigated with 38 and 57 liter
hr ^ microsprinklers. Water temperature striking the surface ranged
from 10° to 15° C and was relatively constant over time and freeze
conditions.
To estimate the fraction of water intercepted, a fiberglass wrap
placed around 2.5 cm polyvinyl chloride pipe was hung over a bucket, and
irrigation water applied to the wrap for 20 to 30 min using 38, 57, and
87 liter hr * microsprinklers. Water that dripped from the wrap was
collected and its volume measured in a graduated cylinder. The volume
intercepted was divided by the total volume of water leaving the
microsprinkler during the same time period to give the fraction

80
INTERCEPTION
Fig. 6-3. Schematic diagram of interception of irrigation water by the
tree wrap when raicrosprinklers were positioned so that water
sprayed above the top of the wrap (left side), or only on the
wrap surface (right side). Hatching indicates areas not
covered by water.

81
0.05
0.095
MICROSPRINKLER
Fig. 6-4. Cross-secCion of the model system showing 70% coverage of the
wrap surface with water (sections 1-4,8-10). The numbers
associated with each section indicate the relative amount of
intercepted water distributed uniformly over the surface area
of the section.

82
intercepted. Values ranged from 0.05-0.11 depending on orientation of
the microsprinkler, being lowest when some water sprayed above 40 cm
(top of the wrap) and highest when water sprayed no higher than 40 cm
(Fig. 6-3). Interception values were adjusted accordingly in
simulations as ice accreted on the wrap and produced a larger surface
for interception.
The percentage of wrap surface covered by water and/or ice and the
distribution of water around the wrap surface are closely related.
These parameters vary with freeze conditions and canopy morphology, and
are difficult to measure in the field. The surface layer of the wrap
was equally divided into 10 sections, and each section was treated
separately in order to vary the coverage and distribution of water
around the wrap surface (Fig. 6-4). On the surface towards the
microsprinkler, all sections were assumed to be covered with water, with
distribution was highest for the section 1, intermediate for sections 10
& 2, and lowest for peripheral sections 9 & 3. Values of distribution
on the surface towards the microsprinkler are proportional to the area
of a plane normal to the streamlines of the irrigation water in each
section. Water can reach the surface opposite the microsprinkler
(sections 4-8) after being deflected or dripped from the canopy,
allowing some or all of these sections to be covered with water and/or
ice. Field observations suggested that only sections 8 and 4 received
any water except during severe freezes when all sections could be
covered with ice and water. Therefore, the total amount of wrap surface
covered by water/ice was estimated to be 70% for most simulations, but
provisions were made in simulation programs for varying this value
between 50-100% in increments of 10%. The volume of water distributed

83
on che wrap surface away from Che microsprinkler was uncercain as well,
buc like percenc coverage, ic could be varied in simulación programs.
Wacer deflecced or dripped from Che canopy onco Che wrap surface
creaCes variabiliCy in characCerisCics of che irrigación waCer by
increasing inCercepCion, changing discribuCion, and lowering waCer
CemperaCure due Co concacc wich lower cemperaCure objeecs and longer
disCances Craveled. While Chis may noC be a facCor on Che wrap surface
Cowards Che microsprinkler where direcC inCercepCion prevails, ic is an
imporcanc consideración for Che wrap surface opposiCe Che microsprinkler
because Che only waCer reaching Chis area is Chac deflecced or dripped
from Che canopy. AddiCionally, wacer scriking Che canopy has been
observed Co flow down Che Crunk underneaCh wraps in Che field and reduce
crunk cemperaCure by as much as 6o C ac che 20-cm heighc on mild freeze
nighcs. The same process probably increases Crunk CemperaCures on severe
freeze nighcs when Crunk CemperaCure normally would drop below 0° C in
che absence of liquid wacer inside Che wrap. There is no provision in
Che model Co accounC for wacer flowing down Che Crunk and changing ics
CemperaCure. This faccor, along wich Che degree of uncerCainCy wich
which Che above characCerisCics of irrigación wacer are known, decreases
Che likelihood of accurace Crunk CemperaCure prediccions in irrigación
simulaCions.
Simulación
Simulación programs for Che model syscem were wriCCen in FORTRAN
and run on a Digical Vax-11 compuCer. SeparaCe programs were developed
for cree wraps alone and for irrigación and wraps cogecher, because
differenc simplifying assumpcions were made in each case.

84
Simulación of Freeze Protection with Tree Wraps
Heat transfer in the angular direction was disregarded when
simulating tree wraps alone, which assumes that temperature does not
vary with position around the system at any given radius r and height z.
This is a reasonable assumption because temperatures at various
positions around the trunk and wrap surfaces at a given height are
observed to be nearly equivalent in the field. Additionally, it was
found that trunk surface temperatures predicted when considering only
radial heat transfer were within +_ 0.3° C of those predicted for the
20-cm height when considering both radial and vertical heat transfer
(See Fig. 7-3). Trunk temperatures at the 20-cm height were roughly
averages of those for the 1 and 40-cm heights, and disregarding vertical
heat transfer resulted in prediction of a single average trunk
temperature. Disregarding the vertical dimension allowed independence
from soil temperature data if trunk temperatures corresponding to the
20-cm height only were desired, and the simplified program for
1-dimensional (radial) heat transfer ran in 95% less computer time than
the 2-dimensional (radial and vertical) program.
In both the 1- and 2-dimensional simulations, the rate of
temperature change at the wrap surface was calculated using equation
[6-11] (disregarding terms for irrigation and evaporation) after
obtaining values of Q, CV, and R. The terras for angular heat transfer
(and vertical heat transfer for 1-dimensional simulation) were deleted
from [6-8] to calculate rates of temperature change throughout the wrap
and trunk. Distance increments in the radial (Ar) and vertical (Az)
directions were set as high as possible without sacrificing accuracy,

85
which after many simulation trials, were determined to be 0.2 cm and 1.0
cm, respectively.
Simulation of Freeze Protection with Microsprinkler Irrigation and Tree
Wraps
Heat transfer in the vertical direction was disregarded when
simulating wraps and irrigation together, which assumes that vertical
heat transfer has no effect on temperature in the model system. This is
a reasonable assumption because omitting vertical heat transfer in the
wrap simulation resulted in prediction of an average trunk temperature,
or that for the 20-cm height (see Chapter VII). Furthermore, the
3-dimensional heat transfer simulation used 8 hr of computer time for
each hr of time simulated, hence heat transfer in one dimension had to
be disregarded to allow the simulation to run in a managable time
period. The vertical dimension was the obvious choice for omission
because temperature gradients were lower and distances greater than the
other dimensions, and simulations ran about 50 times as fast without
vertical heat transfer calculations.
The outer system boundary was either water, ice or wrap material,
depending on water distribution and the point on the wrap surface being
considered. The rate of temperature change of the system boundary was
calculated using [6-11], omitting terms E and IR for areas of the wrap
surface not covered by water. Heat transfer in Che ice and water layers
was assumed to occur in only the radial direction which simplified
calculations of energy transfer for the outer system boundary. A
subroutine for ice accretion using equations [6—17]—[6—21] was accessed
if the temperature of the water layer was < 0° C or if an ice layer was
already present.
i

36
Equation [6-8] without terms for vertical heat transfer was used to
calculate rates of temperature change throughout the wrap and trunk.
The radial (Ar) and angular (A9) distance increments were set at 0.5 cm
and 0.63 radians (36°) respectively, which were the maximum achievable
without affecting model output. As for the tree wrap simulations, Ar
and A9 were determined after many simulation trials to increase speed of
program execution.

87
Table 6-1. Definition of symbols used in model development,
Symbol
Definition
AREA
c
Cv
d
D
E
h
IR
j
K
L
Nu
Q
R
RATE
r
Sh
T
t
W
z
a
P
a
0
A
*K l)
surface area of wrap_^cm )
specific heat (cal g °K ) 0
convective heat flux (cal cm s ;
characteristic dimension £cm)^
diffusion coefficient (cm s
evaporative heat flux^(cal cm s )
heat content (cal cm )
sensible heat flux^froip irrigation water (cal cm
heat flux (cal cm s ;
thermal conductivity (cal cm s
latent heat (cal g )
Nusselt number (dimensiones^)
heat conduction (cal cm s_?)
radiative heat flux (cal_ym s
irrigation rate (liter s )
radius (cm)
Sherwood number (dimensionless)
temperature (°K or °C)
time (s)
water vapor concentration (g cm
vertical distance (cm)
~2 "In
s )
-1.
-3,
2 -1
thermal diffus^vity (cm s )
density (g cm ) _2
Stephan-Boltzmann constant (cal cm s
angular distance (radians)
"change in"
k"4)
Subscripts
a
f
h2o
i
in
i-w
out
r
s
t
v
wl
wv
z
air
fusion
water
ice
interior region
ice-water interface
outer or exterior region
radial coordinate
system boundary
time
vaporization
water layer
water vapor
vertical coordinate
0
angular coordinate

CHAPTER VII
THERMAL PROPERTIES AND SIMULATION OF FREEZE PROTECTION
PERFORMANCE OF TREE WRAPS FOR YOUNG CITRUS TREES
Introduction
Traditionally, young citrus trees have been protected from freezing
injury by banking soil around trunks during periods of cold weather
(59). Following severe freezes, the tree canopy above the soil bank is
killed, but after removal of the bank trees sprout from the surviving
wood and produce new canopies. Although an effective means of freeze
protection, construction and maintenance of soil banks often causes
mechanical or disease damage to trunks, and are labor intensive. For
these reasons, tree wraps made of inert insulating materials were
introduced in Texas in the mid-1950's (80) and are now used in other
citrus growing areas. It was thought that wraps could provide freeze
protection similar to soil banks, but unlike soil banks could be left in
place for 3-4 years, until the tree was better able to survive freezes
by itself. However, trunk temperatures under soil banks typically
typically 8° C higher than air temperature, but only 0° to 4° C higher
than air temperature under tree wraps (67, 68, 121, 170).
Despite lower potential for freeze protection, wraps are widely
used because they provide sprout inhibition and protection from
herbicide, fertilizer and mechanical injury. Wraps composed of dried
plant materials have been used in California to protect trunks from
wind, rodent and radiation damage (129). Furthermore, wraps augment the
88

89
effect of microsprinkler irrigation during freezes, providing greater
freeze protection than microsprinkler irrigation or wraps alone (30).
Reasons for unpredictable levels of freeze protection provided by
wraps are unclear, although trunk and wrap diameter (170), rate of air
temperature decrease (121), and freeze duration probably are important
factors. Fucik and Hensz (39) tested various wraps in a freeze chamber
and suggested that wraps which caused the bark temperature to decrease
at about 50% (or less) of the rate of air temperature decrease would
provide trunk protection during most freeze conditions. However, Davies
et al. (31) observed similar rates of trunk and air temperature decrease
with soil banks; thus a nearly constant difference between trunk and air
temperature was maintained during freeze events due to initially higher
trunk temperatures and/or a delay in the commencement of trunk
temperature decrease. Because soil banks provide greater protection
than wraps, the suggestion of Fucik and Hensz that relative rates of
bark and air temperature decrease are indicative of freeze protection
capability is true only under certain circumstances.
Turrell (129) compiled a list of thermal properties of some
materials used in wraps and suggested that thermal diffusivity is the
single most important factor determining the freeze protection potential
of a wrap. While this may be true, it provides only a qualitative
understanding of wrap performance, and quantitative estimates of margins
of protection among materials differing in thermal diffusivity remain
unclear. It is difficult to assess in field studies the relative
importance of thermal diffusivity and ocher factors on wrap performance,
and radiation and windspeed regimes cannot be simulated accurately in a
freeze chamber.

90
Modeling and simulation provide a means by which tree wraps can be
studied quantitatively. The objectives of this research were to measure
the thermal properties of tree wraps in-situ and use the simulation
model of the tree wrap system in Chapter VI to analyze wrap performance
under various conditions.
Materials and Methods
Thermal Properties of Tree Wraps
Laboratory studies
Several tree wraps were chosen for analysis of thermal properties.
Five replicates of each type were tested to obtain mean values of
thermal conductivity (K), density (p), specific heat (c), and thermal
diffusivity (a). Wraps ranged from 34-40 cm in height and 8-13 cm in
diameter when properly installed. A thick-walled (2.5 cm) styrofoam
wrap was analyzed with and without its 2 plastic containers of water
inside (ca. 420 ml water). Yelenosky (156) provides a more detailed
description of this wrap. Thin-walled (0.2 cm) polystyrene and
thick-walled (1.8 cm) polyethylene foam wraps had the smallest diameters
(ca. 8 cm) and like the styrofoam wrap, contained free airspaces between
the inner wrap and trunk surfaces. Because the size of the airspace
varies with trunk diameter, 2.4 cm was used for trunk diameter in
volume-weighted calculations of P and c and in wrap simulations, unless
otherwise indicated. The fiberglass wrap consisted of R-ll (9-cm thick)
aluminum foil-faced fiberglass building insulation held in place around
the trunk with wire mesh, and when newly installed there was no airspace
between the trunk and inner wrap surface. Old fiberglass wraps which had
been used for one season in the field and were somewhat weathered, and
new fiberglass wraps wetted to a volumetric water content of about

91
0.125, were also studied. Except fiberglass, other wrap materials did
not absorb water when submerged, nor did they become significantly
weathered after one season's use.
The thermal conductivity of various wraps was measured using an
apparatus which consisted of a heating element inside a 4-cm diameter
tube filled with water (Fig. 7-1). The heating element drew power from
a 28 volt DC power source. Voltage (E) and resistance (R) across the
heating element were measured with a Keithley multimeter, and energy
2
flow (watts) into the heating element (Q) was calculated as E /R.
Temperatures of the tube (T^) and wrap surface (T?) were allowed to
reach a steady-state after placing the wrap around the tube (about 24
hr) at which time the electrical energy flow into the heating element
equaled the heat flow radially outward through the wrap. The top and
bottom of the wrap were insulated with 15-20 cm fiberglass to minimize
vertical heat loss, which would have caused K to be overestimated. The
steady-state equation for heat flow in cylindrical coordinates was
solved for K (128)
Q ln(r /r.)
K = L L. [7-1]
(T -T ) 2 n L
where r and r^ are the radii (cm) of the outer wrap surface and water
tube, respectively, and L is the wrap length (cm). Density was measured
directly on pieces of wrap material, and c values were obtained from
tables of thermal properties of insulation (128). Thermal diffusivity,
ot , was calculated as
K
a = [7-2]
P c
where p and c are volume-weighted averages of the wrap components.

92
k - Q • I n (Vr,)
(T,“Tj) *2 • n • L
Fig. 7-1. Schematic represeatatioa of the device used to measure the
thermal conductivity (K) of tree wraps in-situ. See text for
descriptions of components.

93
The relative freezing behavior of wet and dry fiberglass wraps was
observed in freeze chambers to verify values of thermal properties
obtained for these wraps. Two young citrus trunks ca. 2.4 cm in
diameter were cut into 40-cm segments and each placed inside a dry and a
wet fiberglass wrap. Thermocouples were attached at the 20-cm height on
each trunk and on the surface of each wrap. Air temperature was
decreased asymptotically to minima of -6° and -15° C over periods of 8
hr during 2 separate freezing cycles.
Field studies
The effects of water and ventilation in wraps were studied in the
field. Fiberglass wraps with the water containers from styrofoam wraps
inside were compared with normal fiberglass and styrofoam wraps on 4
mild freeze nights in 1987 for freeze protection capability. Three
wraps of each type were placed around trunks of 2-year-old 'Hamlin'
orange (Citrus sinensis (L.) Osb.) trees having similar diameters, and
thermocouples were attached to each trunk at the 20-cm height in Dec.
1986. Minimum trunk and air temperatures were measured at sunrise on
12, 24, 28 Jan. and 10 Feb. 1987, and analyzed for significant
differences using analysis of variance and Duncan's multiple range test.
Simulation of Freeze Protection Performance of Tree Wraps
A deterministic heat transfer simulation of the tree wrap system
was developed using the discrete model system described in Chapter VI.
Trunk temperature predicted by the model and measured in the field
corresponded to the 20-cm height unless otherwise indicated. Details of
field experiments used for validation with young 'Hamlin' orange trees
have been described in Chapter III. Predicted trunk temperatures within
one standard error of the mean observed value were considered accurate
or valid

94
One-dimeasional (1—D) and 2-dimensional (2-D) models were used to
simulate 5 freezes in 1985-86 for model validation because trunk
temperature data were available and meterological conditions were highly
variable among these dates. The 1-D model was used for all other
simulations because it predicted trunk temperatures at the 20-cm height
within + 0.3° C of those predicted by the 2-D model, and used 95% less
computer time. Environmental inputs were air temperature and windspeed,
which were approximated as functions of time or held constant. The
thermal properties of fiberglass wraps in Table 7-1 and ot for citrus
wood (131) were used in all simulations. Vertical temperature gradients
in the 2-D model were initialized by assuming the trunk temperature 1 cm
above the soil surface was equal to the soil temperature, and the trunk
temperature at 40 cm was equal to the air temperature throughout the
simulation. For validation, radial temperature gradients in both 1-D
and 2-D models were initialized by setting trunk surface temperatures
equal to observed initial values, and wrap surface temperatures equal to
the initial air temperature. In other simulations, radial temperature
gradients were assumed to be 2° C between the trunk to the wrap
surfaces, as often observed in the field. Parameters used in
simulations are given in appendix A.
Several simulation experiments were performed to address various
aspects of interest, which involved little more than changing initial
conditions, parameters, or forcing functions of the simulation prior to
each run of the program. First, predicted trunk temperatures from
simulation of past freezes were compared against observed trunk
temperatures on those dates for model validation. Second, performance
of 4 commercially available wraps was compared under typical freeze

95
conditions, along with a hypothetical wrap with the thermal properties
of soil. Third, possible reasons for variation in the amount of freeze
protection afforded by fiberglass tree wraps under different freeze
conditions were investigated by varying the rate and pattern of air
temperature decrease, and trunk and wrap diameter. Finally, the effects
of windspeed and soil temperature on minimum trunk temperature of
wrapped trees were investigated. A short explanation of each simulation
experiment precedes a discussion of the results.
Results and Discussion
Thermal Properties of Tree Wraps
Laboratory studies
Measured K values for new fiberglass wraps were about 8% higher
-4 -1 -1 -1
than the manufacturer's value of 1.07x10 cal cm s °C (personal
communication, Certainteed Corp.), indicating that the device diagrammed
in Fig. 7-1 measured K values with reasonable accuracy. Compression of
the fiberglass around the water tube or vertical heat loss may have
accounted for slightly higher measured values.
The styrofoam wrap had the lowest a(best insulator) followed by
fiberglass, polyethylene and polystyrene (Table 7-1). This ranking
generally agrees with the level of freeze protection observed in the
field with these wraps. Davies et al. (30) found that polystyrene wraps
caused higher daytime and lower nightime trunk temperatures than
fiberglass wraps, and in turn, styrofoam wraps dampened diurnal
variation in trunk temperatures better than fiberglass. Jackson et al.
(67) found styrofoam was the best insulator in their tests, followed by
fiberglass and then styrofoam without its water containers, which also
agrees with these data (Table 7-1). Data from Chapter V (see Fig. 5-1)

96
Table 7-1. Thermal conductivity (K), density (P), specific heat (c) and
thermal diffusivity (a) of tree wraps used for young citrus
freeze protection.
Thermal property2
K
P
c
a
Wrap (cal
-1 -1
cm s
k-1) (g cm 3)
(cal g 1 k L)
(cm2 s 3)
(xlO-4)
(xlO-2)
(xlO-1)
(xlO-2)
Styrofoam
2.56
13.3
3.5
0.55
Fiberglass (wet)
3.56
14.4
3.4
0.73
Fiberglass (new)
1.15
2.22
2.4
2.16
Fiberglass (old)
1.20
2.22
2.4
2.25
Styrofoam (no water)
2.49
1.88
2.6
5.09
Polyethylene
1.31
0.27
3.6
13.3
Polystyrene
2.27
0.62
2.4
15.3
For K values n=5, for p values n=10, c values are single calculations
and a =k/(p c).

97
further reflects the positive correlation between diurnal fluctuation of
trunk temperature and wrap thermal diffusivity for styrofoam,
fiberglass, and polystyrene wraps.
Wetting the fiberglass wrap caused a 3-fold increase in K, but
increased p and c such that ot was lower for wet than dry fiberglass
(Table 7-1). Trunk temperature under a wet fiberglass wrap generally
was Io to 3° C higher than that of a dry wrap during a controlled freeze
at -15° C, although both trunks eventually reached the same minimum
temperature. However, when frozen at -6° C, trunk temperature under the
wet wrap never went below 0° C, while that under the dry wrap was nearly
-6° C, suggesting that latent heat produced by freezing of water within
the wet wrap was sufficient to prevent trunk temperature from dropping
below 0° C. Rose and Yelenosky (121) found trunk temperatures under wet
fiberglass wraps to be 0.5° to 2° C higher than those for dry fiberglass
during a controlled freeze at -8° C. They also found that temperatures
under wet wraps decreased to 0° C and remained at this temperature for 4
hr, while temperatures under the dry wraps decreased steadily,
consistent with the results obtained in the present study at -6° C.
Field observations indicated that new fiberglass wraps rarely
retain water even after heavy rainfall or long periods of irrigation.
Other investigators have reported that fiberglass wraps retain less than
10% of the initial volume of water 24 hr after saturation with 1.8
liters of water (121). In this research, it was difficult to wet
fiberglass wraps to a volumetric water content of 0.125 by submergence
due to their extreme hydrophobicity. Moreover, fiberglass insulation
collapsed when thoroughly wetted, reducing wrap diameter and creating
gaps and free airspaces. It is unlikely that wet fiberglass wraps would

93
provide greater freeze protection than dry fiberglass wraps under field
conditions although data suggest otherwise (Table 7-1), because
quantities of water retained are small (30 to 60 ml) (121) and gaps
created upon collapse may allow heat to escape from the wrap.
The a of old fiberglass wraps was only 4% higher than that of the
new fiberglass, indicating that after one season's use, fiberglass wraps
retain most of their insulative capacity.
The styrofoam wraps with the water containers removed had a a
nearly an order of magnitude higher than normal styrofoam wraps (Table
7-1). Thus, a relatively small volume of water within the styrofoam
wrap greatly increases its insulative capacity. Furthermore, when water
in the wrap freezes, latent heat production can maintain trunk
temperatures at about 0° C for long periods of time under controlled
freeze conditions (156). Field observations consistently show that
styrofoam wraps provide more freeze protection than other types, but
unlike performance in freeze chambers, they frequently allow trunk
temperatures to drop below 0° C.
The thermal conductivity of the free airspace inside polystyrene
and styrofoam wraps without water containers was calculated by measuring
the temperature and radius of the inner wrap surface and substituting
these values for T? and r? in equation [7-1]. Measured thermal
conductivity values averaged 6.3 times higher than the standard
conductivity of still air (5.78x10 ^ cal cm * s * K ^). Convection
currents due to temperature gradients across the airspace probably were
responsible for increased K. It follows that wraps which have free
airspaces are potentially poorer insulators because convection currents
'.an transfer heat rapidly from the trunk to the inner wrap surface and

99
subsequently out through the wrap. Although the styrofoam wrap has a
free airspace, the water containers inside provide enough heat to offset
the negative effect of the free airspace on wrap performance. Materials
such as fiberglass are desirable in this respect because they normally
lack free airspaces but allow for gas exchange and trunk expansion as
the tree grows.
Field studies
Trunk temperatures under styrofoam wraps were significantly lower
than those under fiberglass wraps with water containers inside on 3 out
of 4 mild freeze nights in 1987 (Table 7-2). This occurred despite the
fact that the a of styrofoam is 19% lower than that of fiberglass (data
not shown), and the insulation thickness was similar for each wrap.
However, styrofoam wraps differed from fiberglass wraps with water
containers inside because the former had ventilation holes in the sides
and top, whereas the latter did not. Ventilation holes in styrofoam
wraps may have allowed air heated by sensible and latent heat from the
water to escape, particularly under windy conditions, thereby reducing
trunk temperatures. Styrofoam and fiberglass wraps with water
containers inside had similar trunk temperatures on 24 Jan. possibly
because convective heat loss from the styrofoam wrap airspace was
minimized under the calm conditions which prevailed on this particular
night. Styrofoam wraps with Blocked ventilation holes had higher
nighttime and lower daytime trunk temperatures than those of ventilated
styrofoam wraps (see Fig. 5-1), providing further support that
ventilation increases heat exchange in styrofoam wraps. Fucik and Hensz
(39) found that clamping the top of a corrugated cardboard wrap around
a tree trunk increased its insulative capacity.

100
Table 7-2. Minimum trunk and air temperatures of young 'Hamlin'
orange trees wrapped with fiberglass (FG), fiberglass with
water containers (FGW), or styrofoam (SF) wraps on 4 mild
freeze nights in 1987.
Tree wrap
Date
12 Jan.
24 Jan.
28 Jan.
10 Feb.
Temperature
(°C)
FGW
2.2aZ
-0.8a
1.5a
1.5a
SF
0.0b
-0.7a
-0.1b
-0.5b
FG
-0.4b
-2.0b
-0.5b
-1.2bc
AIR
-1.5c
-3.0c
-1.4c
-1.8c
Means followed by the same letter within columns are not
significantly different, Duncan's multiple range test, 5% level.
For all temperatures, n=3. Trunk temperatures were measured at
the 20-cm height underneath tree wraps.

101
Data for fiberglass wraps with water containers inside demonstrates
the potential for improved freeze protection by a wrap which has
desirable characteristics such as sprout inhibition (Chapter V) and
durability, and is inexpensive and easy to install. Furthermore,
commercially available wraps which use water containers (styrofoam) are
more expensive and allow more trunk sprouting than fiberglass wraps (67,
Chapter V). However, fiberglass wraps with water containers inside
require field testing under more severe freeze conditions before they
can be recommended for use on young citrus trees.
Simulation of Freeze Protection Performance of Tree Wraps
Validation
Trunk temperatures predicted by the model were generally 1 to 2° C
higher early in the time interval of the freeze event, but within one
standard error of observed mean values later (Fig. 7-2). Predicted
minimum trunk temperature for the 20-cm height were regressed on
observed trunk temperature using the 1-D model on the 5 nights shown in
Fig. 7-2 a-e (square symbols in Fig. 7-3). Also, the minimum trunk
temperature predicted for 3 different heights by the 2-D model were
regressed against corresponding observed minima on the 3 nights in Fig.
7-2 c-e (circular symbols in Fig. 7-3). Data points in Fig. 7-3 lie
reasonably close to the 1:1 correlation line and regression lines have
slopes of 0.8 and 1.1 for 1-D and 2-D programs, respectively. The slope
of the regression line for minimum temperatures on the 5 nights in Fig.
7-2 was <1.0 because trunk temperature on the coldest night was
overpredicted and trunk temperature on one of the warmest nights was
underpredicted. The 2-D simulation tended to slightly over-predict
trunk temperature 3 cm from the top and under-predict temperature 3 cm

102
O
'—✓
LÜ
20 22 00 02 04 06 08
TIME (hr)
Fig. 7-2. Observed trunk (obs.) and air temperatures on 20-21 Jan.
1985 (a), 26-27 Jan. 1985 (b), 25-26 Dec. 1985 (c), 26-27
Dec. 1985 (d), and 27-28 Jan. 1986 (e), and predicted
trunk temperatures (pred.) from simulation of the freezes.
Observed trunk and air temperatures are means of 6
observations, while predicted trunk temperatures are single
determinations. Bars attached to observed trunk temperature
symbols are +_ SE of the mean obtained from regression of
observed trunk temperatures vs. time.

-continued
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104
-7 -5 -3-1 1 3
OBSERVED TEMPERATURE (C)
Fig. 7-3. Regression of predicted vs. observed minimum trunk
temperature using 1-dimensional (1-D) and 2-diraensional
(2-D) models. The square symbols are minimum trunk
temperatures at 20-cm height for the 5 freezes in Fig. 7-2
a-e using the 1-D model, the circular symbols are for
minimum trunk temperatures at the 3-, 20-, and 37-cm heights
for 3 freezes in Fig. 7-2 c-e using the 2-D model. For the
1-D model, n=5, y=0.8x - 0.8, r“=0.98; for the 2-D model,
n=9, y=l.lx + 0.5, r =0.98. The solid line is a 1:1
correlation line.

105
from Che base of the wrap (circles in upper right and lower left hand
corner of Fig. 7-3, respectively), which caused the slope of the 2-D
regression line to be slightly greater than one. Lower top and higher
base temperatures on wrapped trunks have been observed in field studies
with soil banks and fiberglass wraps (31, 80, 121), and lower
temperatures at the top of the trunk may account for dieback into wraps
as observed after severe freezes.
Two explanations can be made for over-prediction of trunk
temperatures early in simulations. First, slight overestimation of
trunk diameter and temperature gradients through the wrap and trunk
caused temperatures to be a few tenths of a degree C higher overall, as
verified by repeating the simulations with lower values of these
parameters. Second, and most important, differences in heat transfer
properties of the real and model systems, particularly within the wrap
and trunk, may be responsible for inaccuracies in model behavior.
Initially, temperature in the model system changes slowly in response to
forcing functions. Later in the simulation, slightly faster rates of
temperature decrease occur in the model than those in the real system .
Further analysis showed that the aberrant model behavior could not be
attributed to inaccuracies in thermal properties of tree wraps, time
step, or distance increment. However, the data show that the model is
able to simulate system behavior and can predict trunk temperature
reasonably well, particularly at the 20-cm height and later in the
simulation when critical temperatures are reached.
Simulation of tree wrap performance
Freeze protection provided by 4 commercial wraps was assessed using
thermal properties in Table 7-1 during a simulated freeze where air

106
Fig.
â–  i I I L
0 2 4 6 8
TIME (hr)
7-4. Predicted truck temperatures for 4 commercially available
wraps, SF=styrofoara, FG=fiberglass, PS=polystyrene,
PE=polyethylene, during a simulated freeze where temperature
drops curviliaearly from 0C
is 0.5 + 0.1 ra s 1.
to -5° C in 8 hr, and wiadspeed

107
temperature decreased in a curvilinear fashion from 0° to -5° C in 8 hr
with light and variable windspeed (0.5 + 0.1 ra s *) (Fig. 7-4). In the
case of the styrofoam wrap, the program had to be modified to account
for freezing of water within the wrap, where it was assumed that the
water would start to freeze at 0° C (no supercooling) and remain at that
temperature until all the water was frozen. Results of the simulations
generally agree with the ot values in Table 7-1 in that predicted trunk
temperatures are highest for styrofoam, intermediate for fiberglass, and
lowest for polyethylene and polystyrene wraps.
Trunk temperature for the styrofoam wrap dropped to 1° C and
remained constant, because during the simulation water inside the wrap
began to freeze after 2 to 3 hr and a Io C gradient was maintained
across the airspace. However, trunk temperature under styrofoam wraps
probably would drop to about 0° C instead of Io C and remain constant
(156), due to the rapid transfer of heat across the free airspace. It
was not practical to account for convection currents in the airspace due
to the excessively low time step (0.01 seconds) dictated by the high ct
of the airspace.
Trunk temperature for the polystyrene wrap was 1 to 2° C higher
than air temperature throughout the simulation (Fig 7-4). This level of
protection with polystyrene wraps is rarely observed in the field;
normally these wraps provide no freeze protection whatsoever (68).
Overestimation of trunk temperature with the polystyrene wrap may be due
to underestimation of radiant heat loss from the wrap surface. There is
no provision in the model for wrap surface temperature lower than air,
because air temperature is used in the radiant heat transfer calculation
(Equation 6-14) and consequently represents the lowest temperature that

103
can be achieved at the outer wrap surface. Additionally, the equation
does not account for differences in emissivity among wraps. Polystyrene
wraps are black, and have higher emissivities than the foil-faced
fiberglass or light green styrofoam wraps (128).
The use of mean radiant temperature (MRT) instead of T in radiant
a
heat transfer calculations and consideration of non-unit emissivity
values may give more realistic prediction of trunk temperature with
polystyrene wraps. The MRT is calculated from the Belding formula (10)
after obtaining the globe thermometer temperature. A globe thermometer
is an ordinary mercury in glass thermometer inserted into a 10 to 15-cm
diameter blackened copper sphere. On a freeze night the globe
thermometer temperature (and the MRT) would be below the air temperature
due to radiant heat losses to its cooler surroundings (i.e., the sky and
surface vegetation). For purposes of illustration, it was assumed that
the globe thermometer temperature was 2° C below air temperature
throughout the simulated freeze in Fig. 7-4. Simulations of fiberglass
and polystyrene wraps were repeated using MRT in the radiant heat
transfer equation, and emissivities of 0.09 and 1.0 for fiberglass and
polystyrene, respectively (128). Predicted minimum trunk temperatures
were unchanged from previous values for fiberglass wraps due to low
emissivity, but were 0.9 °C lower for polystyrene wraps because the wrap
surface was about 0.5° C lower than air temperature throughout the
simulation (Table 7-3). Jackson et al. (68) measured trunk temperatures
under polystyrene wraps in the field slightly lower than temperatures of
unwrapped trunks, which may be explained by assuming that surface
temperature of the polystyrene wraps was at the MRT and cooled the air
inside the nearly airtight wrap below air temperature.

109
Table 7-3. Predicted minimum trunk temperatures for the 20-cm height
for simulated freezes when air temperature decrease^ from 0°
C to -5° C in 8 hr with windspeed of 0.5 +_ 0.1 ms using
either air temperature (T ) or mean radiant temperature
(MRT) in calculation of radiant heat transfer.
Wrap type2
Variable in radiant
heat transfer equation
Minimum trunk
temperature (°C)^
Fiberglass
T
a
-2.2
MRT
-2.2
Polystyrene
T
a
-3.6
MRT
-4.5
Emissivities were 0.09 and 1.00 for fiberglass and polystyrene,
respectively.
^ Each temperature is a single determination.

110
Use of MRT instead of T in radiant heat transfer calculations is
a
advisable to avoid overestimation of surface temperature on freeze
nights, especially for objects with high emissivity such as plant leaves
or dark-colored objects. However, this calculation requires the globe
thermometer temperature which is not readily available. Perhaps the
temperature measured by a blackened thermocouple bead exposed to the sky
could be used instead of the globe thermometer temperature.
That soil banks provide better freeze protection than wraps at the
20-cm height is undisputed. This is due in part to the lower thermal
diffusivity of soil compared to wrap materials, and to the larger volume
of a soil bank compared to the volume of a tree wrap. A comparison was
made between soil and fiberglass wraps as insulative materials using the
thermal properties of dry sand as the soil (57), the dimensions of a
fiberglass wrap, and the same freeze conditions as in Fig. 7-4. The
soil provided about 2° C more protection than a fiberglass wrap, but
about 2° to 3° C less protection than a conventional soil bank provides
at the 20-cm height (30) (Fig. 7-5). This suggests that superior freeze
protection performance of soil banks is partially due to greater volume
relative to a tree wrap.
Factors affecting the margin of protection provided by fiberglass tree
wraps
Pactern and rate of air temperature decrease and freeze duration.
Fiberglass wraps sometimes provide 4° C protection, yet on other
occasions afford no protection at all. The pattern and rate of air
temperature decrease and freeze duration can affect the margin of
protection (difference between trunk and air temperature) observed with
fiberglass or any tree wrap. Two patterns of air temperature decrease,

Ill
Fig. 7-5. Predicted trunk temperatures for air, a wrap with thermal
properties of dry sand (SOIL), and a fiberglass wrap (FG).
Freeze conditions are as in Fig. 7-4.

112
linear and exponential, were chosen for comparison at 3 minimum
temperatures (Fig. 7-6). The average rates of air temperature decrease
for both patterns are the same at a given minimum temperature because
initial and final temperatures, and simulated time periods are the same
for both patterns. However, when air temperature decreased
exponentially toward a minimum, trunk temperature was lower than when
air temperature decreased linearly toward the same minimum. Also, the
margin of protection for the exponential pattern at 8 hr at all 3
minimum temperatures is greater than that at 12 hr. The opposite effect
is seen for the linear pattern, where the margin of protection increases
slightly with time due to lower rates of trunk temperature decrease than
air. This indicated that freeze duration can affect margin of
protection positively or negatively depending on pattern of air
temperature decrease.
Longer durations below a given temperature occur with an
exponential pattern than a linear pattern. Integrating over time, there
is more area between 0° C and air temperature for the exponential than
the linear pattern at the same minimum temperature. It seems that the
minimum trunk temperature corresponds to the magnitude of the unit of
integration ("freeze degree hr" ?) and not the minimum air temperature.
It is better to express the intensity of a freeze using the integrated
area below 0° C (or some other threshold temperature) along with minimum
temperature rather than just minimum temperature alone.
The margin of protection increases at greater rates of air
temperature decrease for both patterns of air temperature decrease, as
seen by comparing margins of protection among average rates of air
temperature decrease of -0.25°, -0.5° and -0.75° C hr * (Figs. 7-6a, b

113
TIME (hr)
Fig. 7-6. Predicted truck and air temperatures for young citrus trees
with fiberglass wraps during 6 different simulated freezes.
Minimum air temperatures and average rates of a|.r
temperature decrease are -3° C and -0.25° C hr .(a), -6° C
and -0.5° C hr (b), and -9°^C and -0.75° C hr (c) and
windspeeds are 0.5 + 0.1 m s . Open symbols are for trunk
(circles) and air (squares) temperatures during simulated
freezes with exponential (EXP) patterns of air temperature
decrease, and closed symbols are for trunk (circles) and air
(squares) temperatures during simulated freezes with linear
(LIN) patterns of air temperature decrease.

114
and c, respectively). Rose and Yelenosky (121) obtained similar results
with fiberglass wraps that provided better protection at more rapid
rates of air temperature decrease, particularly at lower heights on the
trunk.
In field studies, margin of protection with fiberglass wraps was
larger and increased throughout the night during the 20-21 Jan. 1985
freeze which had a rapid, linear pattern of temperature decrease, but
margins of protection were small and decreased throughout the night on
21-22 Jan. 1985 when air temperature decreased in an exponential pattern
(see Fig. 3-1). Thus, simulation output agreed qualitatively with field
observations, and suggested that differences in margin of protection
occurring under different freeze conditions may be due to the pattern
and rate of air temperature decrease and freeze duration.
Trunk and wrap diameter. Increasing trunk and wrap diameter
increased the simulated margin of protection provided by a fiberglass
wrap (Fig. 7-7). Wrap diameter seems to have more of an influence on
minimum trunk temperature than trunk diameter, suggesting that it is
more important to increase the path length (wrap diameter) for thermal
diffusion than to increase the amount of stored heat (trunk diameter)
given these 2 alternatives, although an increase in both would have an
additive effect. Young et al. (170) observed a nearly linear increase
in minimum trunk temperature with increasing thickness of fiberglass
wraps on 2 separate freeze nights. Differences in trunk and wrap
diameter may be partially responsible for variations in the margin of
protection observed with tree wraps in the field.
There is an upper limit of trunk diameter above which a decrease in
trunk temperature could be expected due to decreased thickness of

115
0 2 4 6 8
TIME (hr)
Fig. 7-7. Predicted trunk temperatures as affected by variations in
trunk diameter with 13-cra diameter fiberglass wraps (a), and
variations in wrap diameter with 2.4-cm diameter trunks (b).
The values indicated in the lower left hand corner of (a)
are trunk diameters, and those in (b) are wrap diameters.
Freeze conditions are as in Fig. 7-4.

116
insulation as trunk diameter increases and wrap diameter remains
constant. Therefore, it is important to avoid compression of fiberglass
wraps during installation to achieve maximum wrap diameter, especially
with older trees with relatively large diameters.
Effects of windspeed and soil temperature
Windspeed had a relatively minor influence on minimum trunk
temperature, causing a decrease of only 0.4° C when windspeed increased
from 0 to 5 m s-1 (Fig. 7-8). This was because wrap surface temperature
was nearly equal to air temperature regardless of windspeed, and the
trunk temperature of a wrapped tree is a function of wrap surface
temperature and not windspeed or air temperature per se. A temperature
difference of 0.4° C is below the sensitivity of thermocouples and the
confidence limits of this simulation model. Furthermore, variations in
windspeed are less likely to affect the margin of protection of tree
wraps than variations in wrap and trunk diameter, rate and pattern of
air temperature decrease, and freeze duration.
The influence of soil temperature on trunk temperature was
investigated by running simulations using 3 different soil temperature
regimes as follows: I) decreasing from 2° to -6° C in 11 hr; 2) constant
5° C; 3) constant 10° C. Minimum trunk temperature at the 3-cm height
increased substantially with soil temperature, although trunk
temperatures at the 20- and 37-cm heights were unaffected by soil
temperature regime (Table 7-4). This suggests that heat moving upward
from the soil moves radially outward through the wrap before it can
influence the temperature at the 20-cm or greater heights. Thus, heat
added to the soil via irrigation water probably does nor affect trunk
temperature on freeze nights when irrigation is used for freeze
protection.

TEMPERATURE (C)
117
0 1 2 3 4 5
WINDSPEED (ms-1)
Fig. 7-8. Predicted minimum trunk temperatures of young citrus tree
trunks under fiberglass wraps as influenced by windspeed
when air temperature drops from 0° to -5° C in 8 hr.

118
Table 7-4. Simulated minimum trunk temperatures underneath fiberglass
wraps at various heights from simulations using different
soil temperature regimes and freeze conditions from 21 Jan.
1985.
Soil temperature
regime
Minimum trunk
z
temperature
(°C)
Height on trunk
2° to -6° C
in 11 hr
Constant 5° C
Constant 10° C
3 cm
-5.4
2.1
6.1
20 cm
-6.7
-6.8
-6.4
37 cm
-10.4
-10.7
-10.7
Each temperature is a single determination.

119
Conclusions
The level of freeze protección provided by a tree wrap was
inversely related to the thermal diffusivity; i.e., a wrap with a lower a
will provide more protection chan one with higher a under similar freeze
conditions. The heat transfer model of the tree wrap system predicted
minimum trunk temperatures within 1 standard error of observed minimum
trunk temperatures under a range of freeze conditions. However,
predicted trunk temperature early in simulations usually was 1 to 2° C
higher than observed trunk temperature. Less freeze protection can be
expected with a given tree wrap when: air temperature decreases rapidly
at first then remains nearly constant for the remainder of the night;
rate of air temperature decrease is relatively low and freeze durations
are relatively long; caliper of the tree is excessively low or high i.e,
trees less than 1-year or greater than 3-years old; wraps are installed
at diameters less than maximum. The ideal tree wrap would have low
thermal diffusivity, the largest diameter economically feasible, lack
free airspaces or ventilation holes, allow for gas exchange and trunk
expansion, and last for 3 years without significant reduction in
insulative capacity. Windspeed and soil temperature do not
significantly affect temperature above the bud union of wrapped trees.

CHAPTER VIII
SIMULATION OF PROCESSES INVOLVED IN MICROSPRINKLER
IRRIGATION FOR FREEZE PROTECTION OF YOUNG CITRUS TREES
Introduction
Microsprinkler irrigation is widely used in the Florida citrus
industry for freeze protection of young trees (29). This system protects
the lower 0.5 to 0.7 m of a young citrus tree even during severe
advective freeze conditions (11, 30, 104). Tree wraps are often used in
conjunction with microsprinkler irrigation for freeze protection because
wrapped trunks intercept more irrigation water than bare trunks, and
wraps provide additional trunk protection if the irrigation system fails
during a freeze (30).
Guidelines for microsprinkler irrigation use on young trees have
emerged from field studies (30, 104, Chapter III) and observations (103,
106). Current recommendations dictate that microsprinklers should be
placed 0.3 to 0.8 m northwest of the tree because winds are normally
from this direction during advective freezes (103). Trees irrigated
from the downwind side or from distances > 1 m often sustain more damage
than trees irrigated according to recommendations (104). Data from
Chapter III demonstrate that a 90° spray pattern is superior to a 360°
pattern, and irrigation rates as low as 22 liters hr ^ provide adequate
trunk protection under advective freeze conditions. Use of relatively
high irrigation rates (87 liters hr ^) results in marginally better
canopy protection than lower rates (38 liters hr ^), but decreases the
number of trees that can be irrigated during a freeze event due to
120

121
limitations on pumping capacity of irrigation systems. Low irrigation
rates (<38 liters hr *) or intermittent sprinkling (32) may permit
growers to irrigate larger acreages than currently possible on a given
freeze night.
Investigators have speculated on the mechanisms of freeze
protection with irrigation, often attributing trunk temperature
elevation to latent heat of fusion of water (103, 104). Sensible heat
transfer is assumed to be a negligible part of the microsprinkler
irrigation process, a concept which has been carried over from models of
overhead irrigation (104). However, trunk temperatures several degrees
above 0° C frequently are observed during freeze events which cannot be
explained by latent heat production alone. The effects of temperature,
and interception and distribution of water on trunk temperature are
unknown for microsprinkler irrigation, but these and other factors may
have a substantial influence on freeze protection performance. More
detailed information on the microsprinkler irrigation process is needed
to assess the potential of higher risk techniques such as intermittent
sprinkling and low (< 38 liters hr 1) irrigation rates.
Modeling and simulation provide a means of analyzing the
raicrosprinkler irrigation process in detail. Specific mechanisms can be
addressed individually and their relative importance to the system as a
whole evaluated. Simulation models of irrigation for freeze protection
(46, 111) have been used to predict irrigation rates for canopy
protection, but are not appropriate for studying trunk protection with
the wrap/microsprinkler system. The simulation model described in
Chapter VI was used in this chapter to analyze the raicrosprinkler
irrigation process in the overall wrap/microsprinkler system. The

122
objective was to identify parameters of the irrigation process that
influence trunk temperatures, and possibly suggest modifications in the
system to maximize freeze protection performance.
Materials and Methods
The microsprinkler irrigation process was analyzed for wrapped
trees only, because the wrap/microsprinkler combination provides
advantages over either wraps or microsprinkler irrigation used alone
(30) and wraps are often used in conjunction with microsprinkler
irrigation by growers.
Due to the large number of parameters in the simulation model,
values of several parameters were held at nominal values while others
were changed in behavior analyses. Thermal properties of fiberglass
tree wraps as determined in Chapter VII were used in all simulations.
Trunk diameter was set at 2 cm for all simulations except validations
for Jan. 1985 and Jan. 1987 where values from field measurements of 3
and 1 cm, respectively, were used. The following set of parameters
describing the irrigation process were used as "standard" values in all
simulations except where indicated otherwise: irrigation rate, 38 liters
hr fraction of water intercepted by the wrap, 5%; water temperature,
12° C; percent coverage of the wrap surface with water (or ice), 70 %;
the distribution of water around the wrap surface, as given in Fig. 6-4.
Averages of field measurements, assumptions and calculations were used
to arrive at "standard" values (see Chapter VI, section on parameters ).
Validation
Trunk temperature data from field studies using young 'Hamlin'
orange trees wrapped with fiberglass tree wraps during Jan. 1985 and
Dec-Jan. 1985-86 were used for validation of the simulation model.

123
Conditions on these dates are described in detail in Chapter III. In
addition, data from 2 freezes on 11-12 Jan. and 23-24 Jan. 1987 were
used for validation; both freezes had minimum air temperatures of about
-2.0° C, but the latter was a calm night while the former had windspeeds
of about 2.5 m s Observed and predicted trunk temperatures
correspond to the 20-cm height underneath fiberglass tree wraps in all
cases. Freeze conditions (air temperature, windspeed, humidity) were
approximated as closely as possible in simulations as linear,
curvilinear or sinusoidal functions of time. Temperatures predicted
within 1 standard error of observed means were considered valid.
During the 2 freezes of Jan. 1987, microsprinklers were carefully
positioned to eliminate water from spraying into the canopy of trees.
Trunk temperature changes as high as 6° C were observed on mild freeze
nights due to water striking the canopy and then flowing down the trunk
inside wraps. Repositioning microsprinklers eliminated this effect, and
reduced variability in interception and percent coverage of the wrap
surface by water. Values of fraction intercepted and percent coverage
of the wrap surface were changed from "standard" conditions to 11% and
50%, respectively due to changes caused by repositioning the
microsprinklers. Although the freezes in Jan. 1987 were mild and freeze
protection was unnecessary for tree survival, validation on these dates
was particularly important because values of percent coverage of the
wrap surface and interception were known with much more confidence than
on other dates used for validation. Furthermore, by eliminating water
flowing down inside the wrap and resulting trunk temperature changes,
deviations between predicted and observed trunk temperatures would be
attributable solely to inaccuracies in the model.

124
Parameters Describing the Irrigation Process
Due to the stochastic nature of the 4 parameters describing the
irrigation process, analyses were performed to assess potential changes
in trunk temperature resulting from various levels of each parameter.
Analysis was accomplished by varying one or more of the parameters at a
time, and maintaining the others at "standard" levels. Two sets of
freeze conditions were selected for these analyses: a severe advective
freeze and a calm radiative freeze, which occurred on 20-21 Jan. 1985
and 26-27 Jan. 1985, respectively. Conditions from these dates
represent the extremes of damaging freezes that occur in Florida, and
are described in Chapter III.
The fraction of water intercepted was varied between 5 and 11% in
increments of 2% in simulation analyses in order to span the range of
measured values in the field. Water temperature was varied by +_ 5° C of
the mean value measured in the field, i.e., 7°, 12° and 17° C. The
effect of percent coverage of the wrap surface was determined by
simulation using values of 50, 70 and 90%, which also spanned the range
of observed values in the field. The volume of water reaching the wrap
surface opposite the microsprinkler was set at 10% of the fraction
intercepted for both the 70% and 90% coverage simulations. Distribution
of water on the wrap surface towards the microsprinkler was maintained
as shown in Fig. 6-4, amounting to 100% of the fraction intercepted.
The volume of water reaching the wrap surface away from the
microsprinkler was specified at 5, 10, or 20% of the fraction
intercepted. Thus, total amount of water on the wrap surface was either
105, 110 or 120% of the fraction intercepted, because the water reaching

125
Che surface away from Che microspriakler was in addiCion Co, and noc
Cakeu from, che fracción inCercepced.
Windspeed and Relacive Humidicy
The effeecs of windspeed and relacive humidicy on Crunk CemperaCure
were simulaced wich Che same 2 seCs of freeze condiCions used for
analyzing Che parameCers describing che irrigación process. SimulaCions
were run ac windspeeds of 0, 1, 4.5, and 10 m s \ and relacive
humidicies of 80 and 20%. During windspeed analyses, observed values of
relacive humidicy were used, and during analyses of relacive humidicy,
observed values of windspeed were used. The observed values of windspeed
and relacive humidicy were, respeccively: 4 + 2 m s ^ and 50% decreasing
co 25% on 20-21 Jan. 1985; 0 m s * and 50% increasing Co 90% on 26-27
Jan. 1985.
Resulcs and Discussion
Validación
Simulación of freezes of Jan, 1985
PredicCed crunk cemperacure under che severe adveccive freeze
condiCions of 20-21 Jan. 1985 was similar Co Chac observed early in
simulacions, buc generally 2 Co 3° C lower Chan observed means coward
che end of Che simulaced cime incerval, regardless of irrigación race
(Figs. 8-la, 8-2a, 8-3a). Discrepancies coward Che end of Che
simulación may be explained by Che freezing of waCer inside Che wraps in
Che real syscem, which would maincain Crunk cemperacures around 0° C,
and lack of accounC for chis effecC in Che model syscem. Closer
agreemenc occurred for all irrigación races for Che 26-27 Jan. 1985
freeze which was mild by comparison (Figs. 8-lb, 8-2b, 8-3b). The
predicced values show Che same rapid inicial increase and subsequenC

126
Fig.
4
O
-4
-8
-12
8
4
O
-4
-8|-
- i tM ‘ i í! 11 ( t
â–  OBS
a PRED
★ AIR
-I L
g â–¡
<> ii
. ★ ★
o Q Q
a â–¡ â–¡ D
★ ★
★ ★
* ★ ★
★ ★ ★
I I
20 22 00 02 04 06 08
TIME (hr)
8-1. Predicted (PRED) aad observed (OBS) trunk temperatures at the
20-cra height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappeejl with fiberglass tree wraps and
irrigated with 38 liters hr microsprinklers during an
advective freeze on 20-21 Jan. 1985 (a) and a radiative
freeze on 26-27 Jan. 1985 (b). Observed values are means +_
SE, n=6.

127
4
O
(° i
i I * f ( K |
-4
★
-8
â–  OBS
a PRED
-12
-
★ air
J L
UJ
o.
8
4
0
4
8
ii ii
n i: (! '5
3 i] i j
. ★ ★
★ ★
★ ★
* ★ ★
★ ★ ★
20 22
00 02 04 06 08
TIME (hr)
Fig. 8-2. Predicted (PRED) and observed (OBS) trunk temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappetjl with fiberglass tree wraps and
irrigated with 57 liters hr microsprinklers during an
advective freeze on 20-21 Jan. 1985 (a) and a radiative
freeze on 26-27 Jan. 1985 (b). Observed values are means +
SE, n=6.

123
4
O
-4
S -8
-12
8
iD \
H i h h m
Ui
oc
Q-
SE
ui
â–  OBS
O PRED
★ AIR
J I L
4
0
-4
-8-
o ic
!¡ !! ni
na
a 'ti ¡b
â–¡ ib
★ ★
★ ★
★ ★
* ★ ★
★ ★ ★
J L
20 22 00 02 04 06 08
TIME (hr)
Fig. 8-3. Predicted (PRED) aad observed (OBS) trunk temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappe^ with fiberglass tree wraps and
irrigated with 87 liters hr microsprinklers during
an advective freeze on 20-20 Jan. 1985 (a) and a radiative
freeze on 26-27 Jan. 1985 (b). Observed values are means +
SE, n=6.

129
slow decrease as che observed values for Che 26-27 Jan. 1985 freeze,
indicaCing chac Che model behavior is qualicacively similar Co real
sysCem behavior under mild, "radiaCive" freeze condicions.
Simulación of freezes of Dec, and Jan. 1985-86
PredicCed Crunk CemperaCures generally were 1 Co 3° C lower chan
Chose observed for all irrigación races for Che Dec.-Jan. 1985-86
simulacions (Figs. 8-4, 8-5, 8-6), wich che excepción of Che 22 liCers
hr * race for che 26-27 Dec. 1985 freeze (Fig. 8-2b) where crunk
CemperaCures were overpredicCed by 1 Co 2° C. However, Che model
behavior closely approximaces ChaC of Che real sysCem because boch
predicCed and observed Crunk CemperaCures remain relacively conscanc
over cime for all irrigación races on all daces.
Simulación of freezes of Jan. 1987
The freezes of 11-12 and 23-24 Jan. 1987 provided Che mosc rigorous
Cese of che predicción capabilicies of Che simulación model, even Chough
Che freezes were excremely mild. As previously scared, paramecers were
known wich more cercaincy and waCer was prohibiced from enCering che
wrap on Chese daces due Co posicioning of Che microsprinklers. However,
predicCed crunk CemperaCures sCill were 2 co 3° C below chose observed
on boch daces (Fig. 8-7). Because no ice formed on Che wrap surfaces on
eicher of chese daces, che simulación model underescimaced Che amounc of
sensible heac cransfered from che irrigación wacer co che Crunk, ac
lease under mild freeze condicions. This is supporced by validación on
ocher daces where predicCed crunk CemperaCures were generally 1 co 3° C
lower Chan Chose observed.
The behavior of Che model syscem approximaCed chac of Che real
syscem on 23-24 Jan., buC deviaced subsCancially on 11-12 Jan. (Fig.

TEMPERATURE (C)
130
4
-
-
0
.
★ s
1
c
1
â–¡
â– 
â– 
â–  [
â–  â–¡
â–  â–¡
â–¡
â– 
★
u a â–  .â–¡
* * *
-4
-
â–  OBS
★ ★
â–¡ PRED
* * *
-8
★ AIR
1 1
★
4
-
0
-4
â– 8
4
0
4
8
★ ★
a a a o a
â–¡ a â–¡ â–¡ â–¡ â–¡ a
★ ★
* ^ * ★ ★ ★ *
|[
â–¡ â–¡
★ ★
a â–¡ S â–  B B
★ ★
★ ★ ★
j I
20 22 00 02 04 06 08
TIME (hr)
Fig. 8-4. Predicted (PRED) aad observed (OBS) trunk temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappe irrigated with 22 liters hr raicrosprinklers during
advective freezes on 25-26 Dec. 1985 (a) and 27-28 Jan. 1986
(c), and a radiative freeze on 26-27 Dec. 1985 (b).
Observed values are means +_ SE, n=2. SE were smaller than
the symbols, i.e., < 0.4° C.

131
OC
4
O
-4
-8
4
O
-4|-
Ud ^
h- “8 “
4-
0-
4
â– 8
I !â–¡
â–¡ â–¡ a
a â–¡
★ ★
★ ★
★ ★
n n :
3 ® i] o b b
★ ★
★ ★
**★*★★★★
J I I I I L.
II H
â–¡ D â–¡
â–¡ â–¡
â–¡ a
★ ★
^ ★
★ ★ ★
J L
J L
20 22 00 02 04 06 08
TIME (hr)
Fig. 8-5. Predicted (PRED) aad observed (OBS) truck temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappetjl with fiberglass tree wraps and
irrigated with 38 liters hr raicrosprinklers during
advective freezes on 25-26 Dec. 1985 (a) and 27-28 Jan.
1986 (c), and a radiative freeze on 26-27 Dec. 1985 (b).
Observed values are means + SE, n=2.

132
O
Ul
4
O
-4
-8
4
O
-4
-8
4
O
-4
-8
3 13
★ ★
¡1 13
★ ★
★ ★
D 'b
★ ★
i¡ il iP 11°
na id
D 1C ID
★ ★
****★★★*
J L
J L.
3 (1 13 I) 3
3 13 13
3 3
★ ★
★ ★
★ ★ ★
J !
J L
20 22 00 02 04 06 08
TIME (hr)
Fig. 8-6. Predicted (PRED) aad observed (OBS) trunk temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrappe^ with fiberglass tree wraps and
irrigated with 57 liters hr raicrosprinklers during
advective freezes on 25-26 Dec. 1985 (a) and 27-28 Jan. 1986
(c), and a radiative freeze on 26-27 Dec. 1985 (b).
Observed values are means + SE, n=2.

133
Fig. 8-
UJ
QC
8
6
4
2
O
-2
8
fin
* I I H -
â–¡ â–¡
â–  OBS
a PRED
★ AIR
★
★ ★
★ ★
J L
£ 6
ui 4 -
►—
2 -
0
-2
-4 -
ia
â–¡ n
â–¡ â–¡
â–¡ o â–¡
* * ★
* * * ★
J L
21 23 01 03 05 07
TIME (hr)
7. PredicCed (PRED) aad observed (OBS) crunk temperatures at the
20-cm height and air temperatures (AIR) for 2-year-old
'Hamlin' orange trees wrapg^d with fiberglass tree wraps and
irrigated with 38 liter hr microsprinklers during mild
freezes on 11-12 Jan. 1987 (a) and 23-24 Jan. 1987 (b).
Observed values are means + SE, n=6.

134
8-7). Predicted trunk temperatures follow the same general pattern as
air temperature on 11-12 Jan., while the correlation between observed
trunk and air temperatures is rather poor.
Ice accretion
The only other state variable in the simulation model aside from
temperature was ice thickness. Ice accretion in the model system was
qualitatively similar to that in the real system under severe advective
freeze conditions because more ice accreted on the sides of the wrap
than on the front or back, as observed in the field (Fig. 8-9).
Non-uniform ice coverage results from uneven distribution of irrigation
water around the wrap surface. Distribution is lowest on the sides,
allowing ice to accrete rapidly there, and high enough on the wrap
surface towards the microsprinkler to maintain temperatures above 0° C,
prohibiting ice formation.
The quantity of ice predicted by the model was much lower than that
observed in the field. This may be due to ice forming on the ground and
accreting towards the wrap in the real system producing large ice
masses, whereas the model system does not account for ice accretion
other than that which occurs directly on the wrap surface. Differences
in quantities of ice produced by the model and real systems is not
thought to have an effect on trunk temperatures during constant
irrigation because the temperature of a water-coated ice mass should be
nearly 0° C regardless of its size.
Summary of model validation
Minimum predicted trunk temperatures were plotted against observed
minima for all dates and irrigation rates from validation simulations in
Figs. 8-1 to 8-7 (Fig. 8-8). Most of the data points lie below the 1:1

135
-4 -2 0 2 4 6 8
OBSERVED TEMPERATURE (C)
Fig. 8-8. Predicted minimum trunk temperatures plotted against those
observed at the 20-cm height for all irrigation rates and
dates used for validation. The solid line is a 1:1
correlation line with slope=1.0 and intercept=0.^. The
linear regression equation is y=-1.38 + 0.94x, r =0.65.

136
ICE ACCRETION
EMITTER
Fig. 8-9. Cross-section of a wrap showing the thickness of simulated
ice on different regions of the wrap surface. Numbers
indicate the ice thickness in cm for the adjacent region
after 11 hr of irrigation with 38 liter hr microsprinklers
under simulated severe advective freeze conditions.

137
correlation line, reemphasizing that the model tends to underestimate
the amount of heat added to the system by the irrigation process.
Therefore, trunk temperature predictions by the model are conservative,
and on average, about 1 to 3° C lower than those observed. Possible
reasons for underprediction are discussed in the following sections
where parameters describing the irrigation process, windspeed and
relative humidity are analyzed.
Parameters Describing the Irrigation Process
Fraction of water intercepted
Increasing the fraction of water intercepted by the wrap resulted
in increases in trunk temperature of about 0.25° C per each additional
percent intercepted under both advective (Fig. 8-10a) and radiative
freeze conditions (Fig. 8-10b). Higher fractions intercepted are
obtained by positioning microsprinklers such that no water sprays over
the top of the wrap, or by moving the raicrosprinklers closer to the
tree. However, positioning microsprinklers in this manner to maximize
interception results in a concomitant decrease in the percent of wrap
surface covered with water, since water must be deflected from the
canopy to reach the surface opposite the microsprinkler. The
interaction between fraction intercepted and percent coverage will be
addressed after discussion of the effects of the latter in another
section.
Higher irrigation rates with lower fractions intercepted would
result in the same volume of water per unit time reaching the wrap
surface as lower irrigation rates with higher fractions intercepted.
Therefore, use of more limited spray patterns with lower irrigation
rates should result in the same level of protection as a wider spray

138
Fig. 8-10. Simulated temperatures at the 20-cm height for 2-cm-diameter
citrus tree trucks with fiberglass tree wraps under severe
advective (a) and radiative (b) freeze conditions.
Simulations were run using different values of fraction of
water intercepted by the wrap, indicated in the lower left
corner of (a).

139
pattern used with a higher irrigation rate. This contention is
supported by field studies using 90° vs. 360° spray patterns, where the
90° pattern provided superior freeze protection at all irrigation rates
(Chapter III). More restricted spray patterns than 90° might allow use
of low (< 38 liters hr *) irrigation rates for freeze protection, thus
increasing the acreage that can be irrigated during a freeze event.
However, such restricted spray patterns increase the risk of wind
diverting irrigation water away from the tree, and may not be as
reliable as the wider spray patterns. Furthermore, restricted spray
patterns and low irrigation rates would be undesirable for water
application on a routine basis due to more frequent clogging of emitters
and reductions in wetted soil surface area.
Water temperature
Raising or lowering water temperature by 5° C from the mean value
of 12° C changed trunk temperatures by about + Io C early in simulations
of advective freeze conditions, but had little effect toward the end of
the simulation (Fig. 8-1 la). This was because ice formation occurred at
all 3 water temperatures toward the end of the simulations, which
invoked a boundary condition of 0° C at the' ice-water interface. Hence,
wrap surface temperatures were similar even though water temperature
differed, and in the model system trunk temperatures respond to wrap
surface temperatures, not environmental conditions per se. Under
radiative conditions and in the absence of ice formation, water
temperature is the major determinant of wrap surface temperature, and in
turn, trunk temperature (Fig. 8-1 lb). Despite the substantial effect of
water cemperature on trunk temperature under radiative conditions, it
does not appear that heating irrigation water would improve freeze

140
TIME (hr)
Fig. 8-11. Simulated temperatures at the 20-cm height for 2-cm-diameter
citrus tree trucks with fiberglass tree wraps under
severe advective (a) and radiative (b) freeze conditions.
Simulations were run using different values of water
temperature, indicated in the lower left corner of (a).

141
survival of young trees since even the 7° C water temperature maintained
trunk temperatures above damaging levels under both radiative and
advective freeze conditions.
Water striking the canopy and dripping onto the wrap would
be expected to have a lower temperature than water directly intercepted.
Thus, simulations were run where the water distributed on the wrap
surface opposite the microsprinkler was 7° C, and water on the surface
towards the microsprinkler was maintained at 12° C (data not shown).
Under radiative conditions, lower water temperature on the surface
opposite the microsprinkler reduced trunk temperatures 0.5° to 0.9° C
compared to standard conditions where water was 12° C over the entire
wrap surface. Trunk temperatures under advective conditions were
unaffected by reduced water temperatures on the surface opposite the
microsprinkler, as would be expected from data in Fig. 8-lla.
Unlike models of overhead irrigation for freeze protection (20, 46,
109, 114), sensible heat of the irrigation water is a major component
responsible for the elevation of temperatures of plant parts in the
simulation model of the wrap/microsprinkler system. This is probably
due to shorter distances between sprinklers and trees in microsprinkler
systems (1 m or less) than in overhead systems (several m) resulting in
less cooling of the water as it travels through the air (46). Water
arriving at leaf or stem surfaces from overhead sprinklers has a
temperature of about 0° C regardless of its initial temperature (49);
whereas, water from microsprinklers cools only about 5° C before it
reaches the wrap or tree canopy (data not shown).

142
_J I I I I I 1—
2 0 22 00 02 04 06 08
TIME (hr)
Fig. 8-12. Simulated temperatures at the 20-cm height for 2-cm-diameter
citrus tree trunks with fiberglass tree wraps under severe
advective (a) and radiative (b) freeze conditions.
Simulations were run using different values of percent
coverage of the wrap surface with water, indicated in the
lower left corner of (a).

143
Percent coverage of the wrap surface with water
The percentage of the wrap surface covered by water (ice) greatly
affected trunk temperatures, especially under advective freeze
conditions (Fig. 8-12). Trunk temperature increased 4.5° and 2.5° C
when percent coverage was increased from 50 to 90% under advective and
radiative conditions, respectively. Differences in trunk temperatures
between the 70% and 90% simulations suggest that spreading water over
more area of the wrap surface opposite the microsprinkler is better than
applying the same amount of water (10% of fraction intercepted) over a
smaller area.
The magnitude of trunk temperature differences in Fig. 8-12 as
compared to that in Fig. 8-10 suggests that microsprinklers should be
positioned in order to maximize wrap surface coverage and not fraction
intercepted. This is especially true under advective freeze conditions
where differences in trunk temperature due to percent coverage were much
greater than those due to fraction intercepted.
Distribution of water on the wrap surface
Trunk temperatures were unaffected under advective freeze
conditions when the amount of water reaching the wrap surface opposite
the microsprinkler was varied from 5 to 20% of the fraction intercepted
(data not shown). However, under radiative conditions, trunk
temperatures were 1° to 2° C higher when assuming 10 or 20% of the
fraction intercepted reached the wrap surface opposite the
microsprinkler as opposed to only 5%. Discrepancies between freeze
conditions occurred because wrap surface temperatures opposite the
raicrosprinkler were increased as the volume of water reaching this area
increased under radiative conditions, causing the elevation in trunk

144
temperature. Conversely, ice accretion on the wrap surface opposite the
microsprinkler occurred under advective freeze conditions regardless of
volume applied, causing wrap surface temperatures to remain at about 0°
C throughout the simulations.
Windspeed and Relative Humidity
Increasing windspeed from 0 to 10 m s ^ caused decreases in minimum
trunk temperatures of about 5° C under simulated advective and radiative
freeze conditions (Fig. 8-13). Relative humidity, however, had little
or no affect on trunk temperatures at any time with the simulated air
temperature and windspeed regimes of either set of freeze conditions
(Fig. 8-14). Holding relative humidity constant as air temperature
decreased caused dewpoint temperatures in simulations to decrease with
time. Low dewpoint, or dry air, is often cited as a major factor
limiting the use of irrigation for freeze protection (86, 104, 112).
While this may be true for exposed plant tissues, data in Fig. 8-14
indicate that humidity is not a limiting factor for trunk protection of
wrapped trees using microsprinkler irrigation. Windspeed on the other
hand, is an extremely important consideration when using microsprinkler
irrigation on wrapped trees, as it is with exposed plant tissues (20,
46, 109).
The data suggest that efforts to modify the microclimate of young
citrus plantings should be directed at moderating windspeed rather than
increasing relative humidity for best use of resources and labor.
Conclusions
The simulation model of the tree wrap/microsprinkler irrigation
system consistently underestimated trunk temperature at the 20-cm height
by 1 to 3° C, although the dynamic behavior of the model and real

145
WINDSPEED (ms1)
Fig. 8-13. Simulated minimum temperatures at the 20-cm height for
2-cm-diaraeter citrus tree trunks with fiberglass tree wraps
under severe advective (ADV) and radiative (RAD) freeze
conditions. Simulations were run at windspeeds of 0,1,
4.5, and 10 m s-1

146
20 22 00 02 04 06 08
TIME (hr)
Fig. 8-14. Simulated trunk temperatures at the 20-cm height for
2-cm-diameter citrus tree trunks with fiberglass tree wraps
under severe advective (a) and radiative (b) freeze
conditions. Simulations were run using different values
relative humidity, indicated in the upper right corner of
(a).

147
systems were qualitatively similar. Sensible heat transfer from the
irrigation water, although underestimated, was a major factor in the
simulation model, unlike models of overhead irrigation. Although water
temperature had a substantial influence on trunk temperature under
radiative freeze conditions, increasing water temperature by 5° C did
not alter minimum trunk temperature under advective freeze conditions.
Microsprinklers should be positioned to maximize the percentage of wrap
surface covered by water/ice, even though this would probably decrease
the fraction of water intercepted. Windspeed influenced trunk
temperatures to a much greater extent than relative humidity under
advective and radiative freeze conditions.

CHAPTER IX
CONCLUSIONS
The overall purpose of this research was to study the freeze
protection capabilities of the tree wrap/microsprinkler irrigation
system for young citrus trees. Research can be classified into 2 main
areas: applied field research (Chapters III through V), and more basic
laboratory and computer simulation analyses (Chapters VI through VIII).
Field Research
Microsprinkler irrigation applied in a 90° pattern was superior to
that applied in a 360° pattern with respect to elevation of trunk
temperature, freeze survival and regrowth of young 'Hamlin' orange
trees. A microsprinkler irrigation rate of 38 liters hr 1 applied in a
90° pattern provided the greatest increase in trunk temperature per unit
water applied of all rates tested (0, 12, 22, 38, 57, and 87 liters
hr 1). Rates < 38 liters hr * provided Io to 4° C additional trunk
protection over fiberglass tree wraps alone and may allow larger
acreages to be irrigated on a given night.
Microsprinkler irrigation did not increase air temperature,
dewpoint, or net radiation above the wetted area of irrigated trees.
Soil temperature was increased by irrigation rates > 38 liters hr * and
reduced by rates < 38 liters hr ^ with respect to the unirrigated
condition. However, simulation results suggested that a 5° to 10° C
increase in soil temperature would not increase trunk temperatures at
the 20-cm height. Therefore, most if not all of the increase in trunk
148

149
temperatures for irrigated trees results from release of sensible and
latent heat of irrigation water directly, and not through microclimatic
changes.
Freeze-damaged trees with wraps that excluded light entirely had
lower numbers and dry weights of trunk sprouts than trees with wraps
that allowed some light to reach the trunk. Therefore, opaque or
dark-colored wraps which exclude light are probably best for trunk
sprout inhibition. Alternatively, wraps should be removed from trees
killed to the top of the wrap in order to encourage development of trunk
sprouts and reestabishment of the canopy.
Laboratory and Computer Simulation Studies
Thermal diffusivity of various tree wraps was indicative of their
freeze protection capability. Therefore, materials with low thermal
diffusivity which are durable and inexpensive would make good tree wraps
with respect to freeze protection.
Less freeze protection can be expected with a given tree wrap under
the following conditions: air temperature decreases rapidly at first
then remains constant the remainder of the night; rate of air
temperature decrease is relatively low and freeze duration is relatively
long; wrap diameter is less than optimum due to improper installation or
weathering; trunk caliper is particularly low (< 1 cm) or high (> 5 cm).
Microsprinklers should be positioned to maximize the percentage of
wrap surface covered by water/ice, although this would probably decrease
the fraction of water intercepted. The potential exists to use
irrigation rates of about 4 liters hr ^ for freeze protection because
wrapped trunks intercept only 5 to 11% of the water applied from 38
liter hr ^ emitters, and water that misses the wrapped trunk does not

150
indirectly influence trunk temperature. Water temperatures of 7° and
17° C provided essentially the same level of protection in simulations
of severe advective freezes. However, water temperature had a
substantial influence on trunk temperature under radiative freeze
conditions or in the absence of a simulated ice layer. Windspeed had a
much greater influence on trunk temperature than relative humidity.
Therefore, efforts to modify the microclimate of young citrus trees
should be directed at reducing windspeed rather than increasing relative
humidity for best use of resources and labor.

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APPENDIX A
The following is a listing of the 2-D tree wrap simulation code in
FORTRAN, which begins with a list of variables used throughout the program.
The 1-D program was similar, lacking terms and the loop for vertical heat
transfer.
MARK RIEGER
WRAP2D.F0R VERT. HEAT FLUX TRUNK WRAP SIMULATION
VARIABLES:
AMP=AMPLITUDE OF EXPON. TEMP. DECREASE FN
AREA=SURFACE AREA OF WRAP (CM2)
CPA=SPECIFIC HEAT OF AIR (CAL/KG*K)
CPB= " " BARK
CPW= " " WRAP
CV=RATE OF CONVECTIVE HEAT LOSS(CAL/S)
D=CHARACTERISTIC DIMENSION (CM)
DT=DELTA T
DTDT=TIME RATE OF CHANGE IN TEMP (°C/S)
DTSOIL=TIME RATE OF CHANGE OF SOIL TEMP (°C/S)
DR=RADIAL DISTANCE INCREMENT (CM)
DZ=VERTICAL DISTANCE INCREMENT (CM)
EMIS=EMISSIVITY OF WRAP SURFACE
G=HEAT CONDUCTION THRU OUTERMOST WRAP LAYER (CAL/CM2 S)
GRAD=GRADIENT IN TEMP. THRU WRAP
HC=CONVECTIVE HEAT TRANSFER COEF. (CAL/CM2 S K)
KA=THERMAL CONDUCTIVITY AIR(CAL/S CM K)
KB= " ” BARK
KW= " " WRAP
MID=MIDPOINT BETWEEN SOIL AND TOP OF WRAP
NU=NUSSELT NUMBER
PI=3.141592654
PR=PRANDTL NUMBER
R=RADIATIVE HEAT TRANSFER FROM WATER/ICE(CAL/S)
RDS=RADIUS # (ITERATION)
RE=REYNOLDS NUMBER (V*D/U)
RH=RELATIVE HUMIDITY
RHOA=DENSITY OF AIR (KG/CM3)
RHOW= " WRAP
RHOB= " BARK
RWRAP= ” WRAP
RBARK= ” BARK
SBC=STEFAN-BOLTZMANN CONSTANT(1.355E-12CAL/CM2 S K4)
ST=STOP TIME
T=TEMP. IN °K
TA=TEMPERATURE OF AIR (K)
TAMIN=MINIMUM AIR TEMP
151

152
C TCA=TEMP. IN °C
C TIME=TIME (SEC)
C TO=STARTING TIME
C TOP=HEIGHT OF TOP OF WRAP (CM)
C TSOIL=TEMPERATURE OF THE SOIL SURFACE (°K)
C TSOILI=INITIAL
C TAU= K IN EXPON. TEMP DECREASE
C U=KINEMATIC VISCOSITY AIR (CM2/S)
C V=WIND VELOCITY (CM/S)
C VAMP=AMPLITUDE OF WINDSPEED FLUCTUATION (CM/S)
C VERT=# OF ITERATIONS OF VERTICAL DIMENSION (TOP/DZ)
C VXBAR=MEAN WINDSPEED (CM/S)
C
C
C DECLARATIONS ETC.
C
REAL AMP,CP,CPA,CPB,CPW,CV
REAL D,DR,DTDT(50,40),DZ,EMIS,G,GRAD
REAL HC,K,KA,KB,KBLONG,KW,NU,PI,PR
REAL R,RDS,RE,RHO,RHOA,RHOB,RHOW
REAL RBARK,RWRAP,SBC,TA,T(50,40),TSOIL,TSOILI
REAL TC(50,40),TAMIN,TAU,U,V,VAMP,VXBAR,XMAX
REAL TIME,TO,ST,DT,VERT,MID,TOP,DTSOIL , X
INTEGER INT
OPEN(UNIT=50,FILE='WRAP3D.DAT',STATUS='OLD')
OPEN(UNIT=51,FILE='WRAP3D.OUT’,STATUS='NEW')
READ(50,*) TO,ST,DT,AMP,TAU,TAMIN,V,VAMP,VXBAR
+,RWRAP,RBARK,GRAD,EMIS,KW,RHOW,CPW,
+KB,RHOB,CPB,TSOILI,DTSOIL,D,DR,DZ,TOP
CPA=241.9
KA=0.0000578
KBL0NG=0.00142
PI=3.141592654
RDS=RWRAP
RHOA=0.000001304
SBC=1.355E-12
TIME=0
TA=273.
TCA=0.
TSOIL=TSOILI
U=0.133
C
C INITIALIZE TEMPS TO STARTING VALUES (2 C GRADIENT THRU WRAP)
C
DO 10 J=2,TOP-1
DO 20 1=1,RWRAP
TC(I,J)=GRAD-((GRAD/RWRAP)* I)
TC(I,1)=TSOIL
TC(I,TOP)=TA
T(I,J)=TC(I,J)+273.
20 CONTINUE
10 CONTINUE
C
c
OUTPUT HEADINGS

153
C
WRITE(51,700)KW,RHOW,CPW,KB,RHOB,CPB,RWRAP,RBARK,VXBAR
700 FORMAT(' ',15X,'WRAP3D SIMULATION OUTPUT6X,
+'KW= ',F10.8,2X,'RHOW= ',F10.8,2X,'CPW= ',F5.1,/,
+6X,'KB= ',F10.8,2X,'RHOB= ',F10.8,2X,'CPB= ',F5.1,/,
+6X,'WRAP RADIUS(5mm)= ',F4.1,2X,’TRUNK RADIUS(5mm)= ',F4.1,/,
+6X,'AVE. WINDSPEED= ',F5.1,//,
+ 1X,'TIME',3X,'AIR TEMP.',2X,'WRAPT20',2X,'BARKT20',2X,
+'BARKT3',2X,'BARKT37'/)
C
C BEGINNING OF TIME LOOP
C
DO 100 TIME=TO,ST,DT
C
C CALL SUBROUTINES TO GET SFC HEAT LOSS
C
DO 150 VERT=1,TOP
CALL CONV(U,V,D,CPA,RHOA, KA, TA,T(RWRAP,VERT),CV,NU,RE,PR,HC)
CALL RAD(EMIS,SBC,TA,T(RWRAP,VERT),R)
G=(KW*(T(RWRAP-1,VERT)-T(RWRAP,VERT)))/((DR*RWRAP)
+*ALOG(RWRAP/(RWRAP-1)))
DTDT(RWRAP,VERT) = (((G-R-CV)/DR)/(RHOW* CPW))
150 CONTINUE
C
C LOOP FOR HEAT CONDUCTION THRU WRAP AND TRUNK
C
DO 999 VERT=2,TOP-1
DO 200 RDS=RWRAP-1,2,-1
IF(RDS.LE.RBARK)THEN
K=KB
KBLONG=KBLONG
RHO=RHOB
CP=CPB
ELSEIF(RDS.GT.RBARK)THEN
K=KW
KBLONG=KW
RHO=RHOW
CP=CPW
ENDIF
TERM1=(K/(RH0*CP))
TERM2=(T(RDS-1,VERT)-2*T(RDS,VERT)+T(RDS+1,VERT))/(DR**2)
TERM3 = (1 / ( DR*RDS ) )* ( (T( RDS-1 ,VERT)-T(RDS+1,VERT))/(2* DR))
TERM4=(T(RDS,VERT+1)-2*T(RDS,VERT)+T(RDS,VERT-1))/(DZ**2)
DTDT(RDS,VERT) = (TERM1*(TERM2+TERM3)) + (KBLONG/(RHO* CP))* TERM4
200 CONTINUE
999 CONTINUE
C
C UPDATE STATE VARIABLES VIA EULER
C
DO 333 VERT=2,TOP-1
DO 500 RDS=2,RWRAP
T(RDS,VERT)=T(RDS,VERT) + DT*DTDT(RDS,VERT)
TC(RDS,VERT)=T(RDS,VERT) — 2 7 3.
T(RDS,1)=TSOIL

154
T(RDS,TOP)=TA
500 CONTINUE
T(1,VERT)=T(2,VERT)
333 CONTINUE
C
C WRITE TO OUTFILE
C
MID=TOP/2
INT=IFIX(TIME*(1/DT))
IF(MOD(INT,900).EQ.0)THEN
WRITE(51,1000)TIME,TCA,TC(RWRAP,MID),TC(RBARK,MID),
+TC(RBARK,3),TC(RBARK,(TOP-2))
1000 FORMATC ',F6.0,5X,F6.2,5X,F6.2,5X,F6.2,5X,F6.2,5X,F6.2)
ENDIF
C
C FORCING FUNCTIONS
C
TCA=AMP+(TAU*TIME)+TAMIN
TA=TCA+273
V=VAMP*(SIN(.167*TIME))+VXBAR
TSOIL=TSOILI-(DTSOIL*TIME)
100 CONTINUE
STOP
END
C
C SUBROUTINES
C
SUBROUTINE RAD(EMIS,SBC,TA,T,R)
REAL EMIS,SBC,TA,T,R
R=4*EMIS*SBC*(TA**3)*(T-TA)
RETURN
END
C
c
SUBROUTINE CONV(U,V,D,CPA,RHOA,KA,TA,T,CV,NU,RE,PR,HC)
REAL U,V,D,CPA,GR,NUFREE,NUFRC,RHOA,KA,TA,T,CV,NU,RE,HC
RE=(V*D)/U
IF(V.LE.10.AND.V.GT.0)THEN
NUFRC=0.62*(RE**.47)
ELSEIF(V.LE.100.AND.V.GT.10)THEN
NUFRC=0.17*(RE**.62)
ELSEIF(V.LE.1000.AND.V.GT.100)THEN
NUFRC=0.024*(RE**.81)
ENDIF
C
C FREE CONVECTION CALCULATION (WHEN V IS LOW)
C
GR=((1/273)*980*(40**3)*(T—TA))/(U**2)
NUFREE=0.58*(GR**.25)
C
C CHOOSE APPROPRIATE NUSSELT NUMBER (FROM MONTEITH)
C
IF((GR/RE** 2).GT.16)THEN
NU=NUFREE

ELSEIF((GR/RE**2).LT.0.1) THEN
NU=NUFRC
ELSEIF(0.1.LT.(GR/RE**2).AND.(GR/RE**2).LT.16)THEN
NU=(NUFRC+NUFREE)/2
ENDIF
HC=(KA*NU)/D
CV=HC*(T-TA)
RETURN
END

o o
APPENDIX B
The following is a listing of the FORTRAN code for the microsprinkler
irrigation simulation, which begins with a list of variables used
throughout the program.
C MARK RIEGER
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
MIS.FOR MICROSPRINKLER IRRIGATION SIMULATION
LIST OF VARIABLES:
A=Y-INTERCEPT OF LINEAR TEMP. INCREASE
AMP=AMPLITUDE OF EXPON. TEMP. DECREASE FN
AMT=AMOUNT OF FRACTION INTERCEPTED ON WRAP SURFACE SECTION
AREA=SURFACE AREA OF WRAP (CM2)
B=SLOPE OF LINEAR TEMP. INCREASE FN
CATCH=FRACTION OF WATER INTERCEPTED BY WRAP
CPA=SPECIFIC HEAT OF AIR (CAL/KG*K)
CPB= ” " BARK
CPH20= " WATER
CPI= " " ICE
CPW= ” " WRAP
CV=RATE OF CONVECTIVE HEAT LOSS(CAL/CM2 S)
DCHARACTERISTIC DIMENSION (CM)
DICEDT=RATE OF ICE ACCRETION ON WRAP SURFACE (CM/S)
DTDT=TIME RATE OF CHANGE OF A VARIABLE
DTDTICE=TIME RATE OF CHANGE OF ICE TEMPERATURE (°C/S)
DTDTWF= WATER "
DT=DELTA T- TIME INCREMENT (S)
DR=RADIAL DISTANCE INCREMENT (CM)
DWV=MOLECULAR DIFFUSIVITY OF WATER VAPOR(CM2/S)
E=RATE OF EVAPORATIVE HEAT LOSS (CAL/CM2 S)
EMIS=EMISSIVITY WRAP SURFACE
FREEZ=RATE OF HEAT CONDUCTION FROM ICE-WATER INTERFACE THRU ICE
G=RATE OF HEAT CONDUCTION INTO OUTERMOST WRAP LAYER (CAL/CM2 S)
GR=GRASHOF NUMBER, USED IN FREE CONVECTION
GRAD=INITIAL GRADIENT OF TEMPERATURE THROUGH THE WRAP (°C/CM)
GBL=BOUNDARY LAYER CONDUCTANCE (MONTEITH,P. 135 "rv")
HC=CONVECTIVE HEAT TRANSFER COEF. (CAL/CM2 S K)
IR=RATE OF HEAT TRANSFER FROM IRRIGATION WATER (CAL/CM2 S)
KA=THERMAL CONDUCTIVITY AIR(CAL/S CM K)
KB= " " BARK
KH20= " WATER
KI= " " ICE
KW= " " WRAP
LEFT=FURTHEST SECTION OF WRAP ON LEFT SIDE COVERED WITH WATER
LHF=LATENT HEAT OF FUSION (CAL/CM3)
156

o o
157
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
LHV=LATENT HEAT OF EVAPORATION (CAL/CM3)
NA=//MOLES WATER VAPOR IN AIR (SUBROUTINE EVAP)
NWF= " " " " BOUNDARY LAYER OF SYSTEM
NUFRC=NUSSELT NUMBER FOR FORCED CONVECTION
NUFREE=NUSSELT NUMBER FOR FREE CONVECTION
PI=3.141592654
PR=PRANDTL NUMBER
PSA=SATURATION VAPOR PRESSURE OF AIR (KPA)
PSWF= " ” WATER FILM (KPA)
R=RADIATIVE HEAT TRANSFER FROM WATER/ICE(CAL/CM2 S)
QH20=RATE OF HEAT CONDUCTION THRU WATER FILM ON WRAP (CAL/CM2 S)
QICEI= " ” INNER ICE LAYER "
QICEO= ” " OUTER ICE LAYER "
QWF= ” " WATER FILM ON ICE
RATE=IRRIGATION RATE (L/HR)
RE=REYNOLDS NUMBER
RH=RELATIVE HUMIDITY
RHOA=DENSITY OF AIR (KG/CM3)
RHOH20= " WATER
RHOI= ” ICE
RHOW= " WRAP
RHOB= " BARK
RIGHT=FURTHEST SECTION OF WRAP ON RIGHT SIDE COVERED WITH WATER
RICE= RADIUS TO OUTSIDE OF ICE (CM)
RWRAP= " WRAP
RBARK= " BARK
RTICE=RADIUS OF THE ICE LAYER (CM)
SBC=STEFAN-BOLTZMANN CONSTANT(1.355E-12CAL/CM2 S K4)
SC=SCHMIDT NUMBER
SH=SHERWOOD NUMBER
ST=STOP TIME (S)
TA=TEMPERATURE OF AIR (K)
TCA=TEMPERATURE OF AIR (C)
TH20= ” IRRIGATION WATER (K)
THAW=RATE OF HEAT CONDUCTION THRU WATER LAYER ON ICE (CAL/CM2 S)
THETA=INTEGER FOR # OF SECTIONS OF WRAP SURFACE IN CIRCUM. DIR.
TAMIN=MINIMUM AIR TEMP (°C)
TTMIN=TIME OF TAMIN (S)
TIME=TIME (S)
TICE=TEMPERATURE OF THE ICE LAYER (°K)
TO=STARTING TIME
TAU= EXTINCTION COEF. IN EXPON. TEMP DECREASE
TWF=TEMPERATURE OF THE WATER FILM (°K)
U=KINEMATIC VISCOSITY AIR (CM2/S)
V=WIND VELOCITY (CM/S)
VAMP=AMPLITUDE OF WINDSPEED VARIATION (CM/S)
VXBAR=MEAN WINDSPEED (CM/S)
WSA=SATURATION VAPOR DENSITY OF WATER/ICE SURFACE (GM/CM3)
WAA= ” ” " " AIR (GM/CM3)
X=DELAY IN TIME FUNCTIONS
Z=DEPTH OF WATER FILM (CM)
DECLARATIONS ETC.

158
REAL AMP,AMT,CATCH,CPA,CPB,CPH20,CPI,CPW,CV,DICEDT
REAL D,DR,DTDT,DTDTWF,DWV,E,EMIS,FREEZ,GRAD
REAL HC,G,GBL,GR,IR,K,KA,KB,KH20,KI,KW,LHV,LHF,NA,NWF,NUFREE
REAL NUFRC,NU,PI,PR,PSA,PSWF,RATE,R,RDS,RE,RH,RHO,RHOA
REAL RH0H20,RHOB,RHOI,RHOW,RICE,RBARK,RWRAP,SBC,SC,SH,TA,T
REAL TC,TAMIN,TAU,TH20,THAW,TWF,U,V,WAA,WSA,WSWF,X,Z
REAL TIME,TO,ST,DT,QICEI,QICEO,QH20,QWF,VAMP,RHB,RHA,VXBAR
REAL TH20I,DTH20,RICEI
INTEGER FLAG,THETA,LEFT,RIGHT,INT
DIMENSION T(0:50,0:11),TC(0:50,0:11),DTDT(0:50,0:11)
DIMENSION RICE(0:11),DICEDT(0:11),DTDTWF(0:11),TWF(0:11)
DIMENSION TICE(0:11),RTICE(0:11),DTDTICE(0:11)
OPEN(UNIT=50,FILE='MIS27.DAT',STATUS='OLD')
OPEN(UNIT=51,FILE='MIS27.OUT',STATUS='NEW')
OPEN(UNIT=52,FILE='SFC27.DAT',STATUS='NEW')
READ(50 ,* ) TO,ST,DT,AMP,TAU,TAMIN,V,VAMP,VXBAR,
+RH,RHA,RHB,TH20I,DTH20,RWRAP,RBARK,GRAD,EMIS,RATE,
+KW,RHOW,CPW,KB,RHOB,CPB,RICEI
CATCH=RWRAP
CPA=241.9
CPH20=1000.
CPI=450.
D=13.
DR=0.5
DWV=.212
KA=0.0000578
KH20=0.0013917
KI=0.005019
LEFT=8
LHF=80.
LHV=598.
PI=3.141592654
RHOA=0.000001304
RHOH20=0.00
RHOI=0.00092
RIGHT=4
SBC=1.355E-12
TIME=0.
TCA=AMP+TAMIN
TA=TCA+273
THETA=11
TH20=TH20I
U=0.133
Z=0.1
C
C INITIALIZE TEMPS TO STARTING VALUES ("GRAD" GRADIENT THRU WRAP)
C
DO 20 J=0,THETA
DO 10 1=1,RWRAP
TC(I,J)=GRAD-(GRAD/RWRAP*I)
T(I,J )=TC(I,J)+273
10 CONTINUE
TWF(J)=T(RWRAP,J)

159
RICE(J)=RICEI
TICE(J)=273.
20 CONTINUE
C
C OUTPUT HEADINGS
C
WRITE(51,700)KW,RHOW,CPW,KB,RHOB,CPB,RWRAP,RBARK,V,RH,TH20
700 FORMAT(' ',10X,'COS-CORRECT IRRIGATION SIMULATION OUTPUT6X,
+'KW= ',F10.8,2X,'RHOW= ',FLO.8,2X,'CPW= ',F5.1,/,
+6X,'KB= ' ,F10.8,2X,'RHOB= ',F10.8,2X,'CPB= ',F5.1,/,
+6X,'WRAP RADIUS(5mm)= ',F4.1,2X,'TRUNK RADIUS(5mm)= ',F4.1,/
+6X,'WIND(CM/S)= ',F4.0,2X,’RH= ',F3.0,2X,'WATER TEMP= ',F4.0,//
+,2X,'TIME',5X,'AIR TEMP.',4X,'TWF1',5X,'WRAPTI',5X,
+'WRAPT6',4X,'BARKT6',4X,'BARKTI',4X,'BARKT 3',/)
WRITE(52,234)
234 FORMATC ','TIME',2X,'AIRT',2X,'RICE7',2X,'RICE8',2X,'RICE9',
+2X,'RICE 10',2X,'WRAPT7',2X,'WRAPT8',2X,'WRAPT9',2X,'WRAPT10',/)
C
C BEGINNING OF TIME LOOP
C
DO 100 TIME=TO,ST,DT
DO 800 THETA=0,11
C
C CALL SUBROUTINES TO GET SFC HEAT BALANCE
C
CALL CONV(U,V,D,CPA,RHOA,KA,TA,T(RWRAP,THETA),TWF(THETA)
+,THETA,LEFT,RIGHT,RWRAP,CV,RICE(THETA))
CALL RAD(EMIS,SBC,TA,T(RWRAP,THETA),TWF(THETA),THETA
+,LEFT,RIGHT,RWRAP,R)
CALL IRIG(KH20,TH20,TWF(THETA),CPH20,RATE,RICE(LEFT),
+THETA,LEFT,RIGHT,IR,DR,RWRAP)
CALL EVAP(U,V,D,DWV,TWF(THETA),TA,LHV,RH,THETA,LEFT,RIGHT,
+E,RICE(THETA))
G=(KW*(T((RWRAP-1),THETA)-T(RWRAP,THETA)))/((DR* RWRAP)
+ * ALOG((DR* RWRAP)/((DR* RWRAP)-DR)))
IF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN
FLAG=0
IF(TWF(THETA).LT.273.0R.RICE(THETA).GT.RICEI)THEN
FLAG=1
RTICE(THETA)=(DR*RWRAP)+(RICE(THETA)/2)
CALL FREEZE(KI,KH20,LHF,RHOI,TWF(THETA),T(RWRAP,THETA)
+ ,RICE(THETA),RWRAP,THETA,DICEDT(THETA),DR,Z,
+ TICE(THETA),RTICE(THETA))
END IF
IF(FLAG.EQ.1)THEN
QICEO=KI*(TICE(THETA)-273)/((RICE(THETA)+(DR*RWRAP))
+ * ALOG(((DR*RWRAP)+RICE(THETA))/RTICE(THETA)))
QICEO=QICEO*((DR*RWRAP)+RICE(THETA))/RTICE(THETA)
QICEI=KI*(T(RWRAP,THETA)-TICE(THETA))/
+ (RTICE(THETA)*ALOG(RTICE(THETA)/(DR*RWRAP)))
DTDTICE(THETA)=(QICEI-QICEO)/(RICE(THETA)/2)/(RHOI*CPI)
DTDT(RWRAP,THETA)=((G-(QICEI*RTICE(THETA)/(DR*RWRAP)))/DR)
+ /(RHOW*CPW)

160
QWF=KH20*(273-TWF(THETA))/(((DR*RWRAP)+RICE(THETA)+Z)*
+ ALOG(((DR* RWRAP)+RICE(THETA)+Z)/((DR* RWRAP )+RICE(THETA))))
DTDTWF(THETA)=((QWF+IR-R-E-CV)/Z)/(RH0H20*CPH20)
ELSEIF(FLAG.EQ.O)THEN
QH20=(KH20*(T(RWRAP,THETA)-TWF(THETA)))/(((DR* RWRAP)+Z)*
+ ALOG(((DR*RWRAP)+Z)/(DR*RWRAP)))
DTDT(RWRAP,THETA) = ((G-(QH20*((DR* RWRAP)+Z)/(DR* RWRAP)))
+ /DR)/(RHOW*CPW)
DTDTWF(THETA) = ((QH20+IR-R-E-CV)/Z)/(RH0H20* CPH20)
END IF
ELSEIF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
DTDTWF(THETA)=0.0
DTDT(RWRAP,THETA) = ((G-R-CV)/DR)/(RHOW* CPW)
ENDIF
800 CONTINUE
C
C LOOPS FOR HEAT CONDUCTION THRU & AROUND WRAP AND TRUNK
C
DO 200 RDS=RWRAP-1,2 , -1
DO 300 THETA=1,10
IF(RDS.LE.RBARK)THEN
K=KB
RHO=RHOB
CP=CPB
ELSEIF(RDS.GT.RBARK)THEN
K=KW
RHO=RHOW
CP=CPW
ENDIF
TERM1=(K/(RH0*CP))
TERM2=(T(RDS+1,THETA)-2*T(RDS,THETA)+T(RDS-1,THETA))/(DR**2)
TERM3=(1/(DR*RDS))*((T(RDS+1,THETA)-T(RDS-1,THETA))/(2*DR))
TERM4=(1/(DR*RDS)**2)*((T(RDS,THETA+1)-2*T(RDS,THETA)+
+T(RDS,THETA-1))/0.62831853**2)
DTDT(RDS,THETA)=TERM1*(TERM2+TERM3+TERM4)
300 CONTINUE
200 CONTINUE
C
C UPDATE STATE VARIABLES VIA EULER
C
DO 300 THETA=1,10
DO 600 RDS=2,RWRAP
T(RDS,THETA)=T(RDS,THETA) + DT*DTDT(RDS,THETA)
TC(RDS,THETA)=T(RDS,THETA)-273.
T(RDS,0)=T(RDS,10)
T( RDS , 11 ) =T( RDS , 1)
600 CONTINUE
T(1,THETA)=(T(2,6)+T(2,1))/2
C THE ABOVE MAKES MIDDLE CYLINDER AN AVE. OF FRONT & BACK TEMPS
TWF(THETA)=TWF(THETA)+DT* DTDTWF(THETA)
IF(TWF(THETA).LT.273.0R.RICE(THETA).GT.RICEI)THEN
RICE(THETA)=RICE(THETA)+DT*DICEDT(THETA)
TICE(THETA)=TICE(THETA)+DT*DTDTICE(THETA)
ENDIF

500 CONTINUE
TWF(0)=TWF(10)
TWF(11)=TWF(1)
RICE(0)=RICE(10)
RICE(11)=RICE(1)
C
C WRITE TO OUTFILE
C
INT=IFIX(TIME*(1/DT))
IF(MOD(INT,2400).EQ.O)THEN
WRITE(51,1000)TIME,TCA,TWF(1),TC(RWRAP,1),TC(RWRAP,6),
+TC(RBARK,6),TC(RBARK,1),TC(RBARK,3)
1000 FORMAT(' ',F6.0,5X,F6.2,5X,F6.2,5X,F6.2,5X,
+F6.2,5X,F6.2,5X,F6.2,3X,F6.2)
WRITE(52,123)TIME,TCA,RICE(7),RICE(8),RICE(9),RICE(10),
+TC(RWRAP,7),TC(RWRAP,8),TC(RWRAP,9),TC(RWRAP,10)
123 FORMAT(' ',F6.0,IX,F5.1,IX,F8.4,IX,F8.4,IX,F8.4,IX,
+F8.4,1X,F8.4,1X,F6.2,1X,F6.2,1X.F6.2)
ENDIF
C
C FORCING FUNCTIONS
C
IF(TIME.LE.10800)THEN
X=0.
ELSEIF(TIME.GT.10800.AND.TIME.LE.36000)THEN
X=10800.
TAU=-.0001389
TAMIN=-4.
VAMP=40.
VXBAR=175.
ELSEIF(TIME.GT.36000)THEN
X=36000.
TAU=0.
TAMIN=-7.2
VAMP=40.
VXBAR=130.
ENDIF
TCA=AMP+(TAU*(TIME-X))+TAMIN
RH=RHA+RHB*(TIME)
TA=TCA+273.
V=VAMP*(SIN(.167*TIME))+VXBAR
TH20=TH20I-(DTH20*TIME)
100 CONTINUE
STOP
END
C
C SUBROUTINES
C
SUBROUTINE RAD(EMIS,SBC,TA,T,TWF,THETA,LEFT,RIGHT,RWRAP,R)
REAL EMIS,SBC,TA,T,TWF,R,RWRAP
INTEGER THETA,LEFT,RIGHT
IF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
R=4*EMIS*SBC*(TA**3)*(T-TA)
ELSEIF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN

n n n non nn
162
R=4*EMIS* SBC*(TA** 3)*(TWF-TA)
ENDIF
RETURN
END
SUBROUTINE CONV( U, V, D, C PA,RHOA,KA,TA,T,TWF,THETA,
+LEFT,RIGHT,RWRAP,CV,RICE)
REAL U,V,D,CPA,GR.NUFREE,NUFRC,RHOA,KA,TA,TWF,T,CV
REAL NU,RE,HC,RWRAP,RICE
INTEGER THETA,LEFT,RIGHT
re=(v*(rice+d))/u
IF(V.LE.10.AND.V.GT.0)THEN
NUFRC=0.62*(RE**.47)
ELSEIF(V.LE.100.AND.V.GT.10)THEN
NUFRC=0.17*(RE**.62)
ELSEIF(V.LE.1000.AND.V.GT.100)THEN
NUFRC=0.024*(RE**.81)
ENDIF
FREE CONVECTION CALCULATION (WHEN V IS LOW)
IF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
GR=((1/273)*980*(40**3)*(T-TA))/(U**2)
ELSEIF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN
GR=((l/273)*980*(40**3)*(TWF-TA))/(U**2)
ENDIF
NUFREE=0.58*(GR**.25)
CHOOSE APPROPRIATE NUSSELT NUMBER (FROM MONTEITH)
IF((GR/RE** 2).GT.16)THEN
NU=NUFREE
ELSEIF((GR/RE**2).LT.O.1) THEN
NU=NUFRC
ELSEIF(0.1.LT.(GR/RE**2).AND.(GR/RE**2).LT.16)THEN
NU=(NUFRC+NUFREE)/2
ENDIF
C X=1.72*((RICE+D)*U/V)**0.5
HC=(KA*NU)/(RICE+D)
IF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
CV=HC*(T-TA)
ELSEIF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN
CV=HC*(TWF-TA)
ENDIF
RETURN
END
C
C
SUBROUTINE IRIG(KH20,TH20,TWF,CPH20.RATE,RICE,
+THETA,LEFT,RIGHT,IR,DR,RWRAP)
REAL KH20,TH20,RATE,IR,TWF,CATCH,RICE,DR,RWRAP,AMT,AREA
INTEGER THETA,LEFT,RIGHT
IF(THETA.EQ.1)THEN

no no no on nnnn
163
AMT=0.31
ELSEIF(THETA.EQ.2.OR.THETA.EQ.10)THEN
AMT=0.25
ELSEIF(THETA.EQ.3.OR.THETA.EQ.9)THEN
AMT=0.095
ELSEIF(THETA.EQ.4.OR.THETA.EQ.8)THEN
AMT=0.05
ENDIF
CATCH=(((DR*RWRAP)+(RICE-0.4))*2)/260
AREA=(((DR*RWRAP)+(RICE-0.4))*2)*3.14*40/10
C "CATCH" IS THE AMOUNT OF WATER INTERCEPTED BY THE WRAP/ICE
WHERE 120 IS AN ASSUMED PATH WIDTH AT 1 METER TO APPROX.
THE MEASURED INITIAL INTERCEPTION VALUE =0.11
"AMT" IS THE COSINE-CORRECTED AMOUNT OF WATER PER THETA INCREMENT
"AREA" IS THE SURFACE AREA OF A THETA INCREMENT
IF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN
IR=((((RATE* 3.78/3600)*CATCH)*CPH20*(TH20-TWF))*AMT)/AREA
ELSEIF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
IR=0.0
ENDIF
RETURN
END
SUBROUTINE EVAP(U,V,D,DWV,TWF,TA,LHV,RH,THETA, LEFT,RIGHT
+,E,RICE)
REAL U, V, D,DWV,RE,NA,NWF,LHV,X,PSA,PSWF,RH,TWF,TA,WSA,WAA,WSWF
REAL E,SH,SC
INTEGER THETA,LEFT,RIGHT
SC=U/DWV
RE=(V*(RICE+D))/U
PHILLIP'S EQN IS SH=2+(0.37*RE**0.6*SC**0.33)
THIS IS MONTEITH'S EQN, PAGE 138
SH=(0,26*(RE**0.6)*(SC**0.33))
PSA=EXP(24.2779-(6238.64/TA)-(0.344438*ALOG(TA)))
PSWF=EXP(24.2779-(6238.64/TWF)-(0.344438*ALOG(TWF)))
NA=(0.01*PSA)/(0.0821*TA)
NWF=(0.01*PSWF)/(0.0821*TWF)
WSA=NA*0.018
WAA=WSA*(RH/100)
WSWF=NWF*0.018
THIS FOR FLAT PLATE FROM MONTEITH
X=1.7 2*((RICE+D)*U/V)**0.5
GBL=(DWV*SH)/(RICE+D)
IF(THETA.GE.LEFT.OR.THETA.LE.RIGHT)THEN
E=LHV*GBL*(WSWF-WAA)
ELSEIF(THETA.LT.LEFT.AND.THETA.GT.RIGHT)THEN
E=0.0
ENDIF
END
SUBROUTINE FREEZE(KI,KH20,LHF,RHOI,TWF,TWRAP,
+RICE,RWRAP,THETA,DICEDT,DR,Z,TICE,RTICE)

164
REAL DICEDT,KI,KH20,LHF,RHOI,TWF,TWRAP,RICE,RWRAP,DR
REAL FREEZ,THAW,Z,TICE,RTICE
INTEGER THETA
THAW=(KH20/(LHF* RHOI*1000) )* ((273-TWF)/((RICE+(DR*RWRAP)+Z)
+*ALOG((RICE+(DR* RWRAP)+Z)/(RICE+(DR* RWRAP)))))
THAW=THAW*(RICE+(DR* RWRAP)+Z)/(RICE+(DR*RWRAP))
FREEZ=-1*((KI/(LHF*RHOI*1000))*((TICE-273)/
+((RICE+(DR*RWRAP))*ALOG((RICE+(DR*RWRAP))/(RTICE)))))
DICEDT=FREEZ + THAW
RETURN
END

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BIOGRAPHICAL SKETCH
Mark Rieger was born in Columbus, Ohio in June of 1960. Shortly
thereafter, he moved to Pittsburgh, Pennsylvania where he graduated from
high school in 1978. Mark became a forestry major at West Virginia
University following high school, but transferred to Penn State his
sophomore year and became a student of horticulture. Mark graduated
with honors from Penn State on 29 May 1982, and began working on a
Master of Science project dealing with water relations of pecan
seedlings at the University of Georgia on 1 June 1982. He began working
on a Ph.D. project on freezing stress and freeze protection of young
citrus trees directly following graduation at Georgia in June 1984.
Mark will return to the University of Georgia as Assistant Professor of
Horticulture in July 1987.
178

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Frederick S. Davies, Chairman
Associate Professor of Horticultural Science
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as ^ dissertation for the degree of
Doctor of Philosophy.
1¿M /tyfrih*'—
K*-' Jackson, Cochainr
Lavfo K* Jactyson, Cochairman
Professor of "Horticultural Science
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation fQ£ the degree of
Doctor of Philosophy. ' 7,
A
Glen H. Smerage
issociate Professor of Agricultural
Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as_a dissertation for the. degree of
Doctor of Philosophy.
Wiltbank
»sor of Horticultural Science
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality/)as a dissertation for the degree of
Doctor of Philosophy.

This dissertation was submitted to the Graduate Faculty of the College
of Agriculture and to the Graduate School and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
August, 1987
x. &
_a¿/k
>llege of Agriculture
Dean,
Dean, Graduate School

UNIVERSITY OF FLORIDA


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