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I
This is to certify that the
thesis entitled
A Portable Chamber to Measure Plant Water Use: Design
Considerations and Analysis.
presented by
Eric William Harmsen
has been accepted towards fulfillment
of the requirements for
Master of Sciencedegree in Agricultural Engineering
I (f
Major professor
Date January 16, 1981+

 

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OCT 3 0 201

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7.227 13

 

 

A PORTABLE CHAMBER TO MEASURE PLANT WATER
USE: DESIGN CONSIDERATIONS AND ANALYSIS

By

Eric William Harmsen

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

i983

.s/ 7 :7 wry

ABSTRACT

A PORTABLE CHAMBER TECHNIQUE TO MEASURE PLANT
HATER USE: DESIGN CONSIDERATIONS AND ANALYSIS

BY

Eric William Harmsen

Pertinent literature and design considerations are discussed for a
portable chamber to measure plant water use.

A simulation model was developed which performed a nonsteady state
energy balance on a single leaf with boundary conditions similar to
those produced by the portable measurement chamber. The simulation
revealed that leaf transpiration strongly depends on the initial field
wind speed over the leaf and the wind speed within the chamber.

A portable chamber was designed, constructed and tested which
utilized a closable top for the purpose of minimizing alterations of the
canopy microclimate during chamber placement. Comparison of the chamber
values with those of a weighing lysimeter showed the chamber to
overestimate evapotranspiration (ET) by 162.

A laboratory experiment was conducted to compare the chamber design
with a permanently closed top chamber. The opening top chamber
consistently gave higher ET rates. The trapping of water vapor during
top closure was hypothesized as the cause of the higher rates observed.
Large overestimations of ET were observed with both the open top and
closed top chambers when laboratory wind speed was near zero and the
wind speed within the chamber was approximately I m/s. The possible
onset of stomatal closure .from repeated plant enclosure within the
chamber was found not to occur, a fact which has implications for

measurement technique in the field.

DEDICATION

To Rhea: my extraordinary example

ACKNOWLEDGEMENTS

I would like to express my deep graditude to my major professor,
Dr. Ted Loudon, whose guidance and support were indispensible
throughout the duration of this study. The benifits which one derives
from having worked with his major professor are difficult to assess, as
the relationship which develops is quite unique. Unquestionably the
fruits of that relationship do not end when the degree is conferred but
continue long after the student is involved in a career and until the
end of his life. One of the greatest gifts which a teacher can give his
student is the gift of independence. Not an independence which is
accompanied by neglect, but one which exists within a carefully
structured environment and which pushes the student to new limits from
which subsequent growth proceeds. This is simply one example of the
benifits I have enjoyed while working with Ted. I regret, due to the
lack of space, that this acknowledgement, at best, conveys only a small
part of the graditude | feel for him.

Dr. George Merva, though on sabbatical for an extended period
during this study, was of great assistance to me. Over the last several
years, I have grown to admire his deep commitment to the field of
science which is reflected in both his love and attainment of high
quality teaching and research.

I owe a great debt of thanks to my teacher, colleague and friend,
Vincent Bralts, who freely gave me a tremendous amount of technical and
personal support prior to and throughout this study. A special thanks

also to Dr. Maurice Vitosh whose technical and material support are

much appreciated. Much of the work associated with instrumentation was
facilitated through the assistance of Gary Peterson. His ever-readiness
to help, during the entire project, was a valuable lesson and his
friendship will always be special to me.

I would also like to thank Dr. Jim Flore, Dr. Ken Poff and Dr.
Charles Cress for their technical advice.

There are of course many people who assisted, but unfortunately,
they can not all be mentioned by name. Of these people, I would liketo
extend my thanks to each of the members of the MSU Agricultural
Engineering Soil and Water Group. One of the members of this group who
was of special help to me, and who I must thank, is my dear friend and
coworker Arthur Gold.

Finally I would like to acknowledge my family and Baha'i friends
whose continual support and assurance was priceless. Of these, a
special thanks to my beloved wife, Rhea, whose commitment to improving
conditions for all people has been an extraordinary example for me to

follow.

ITABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . . . xi
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . l

CHAPTER I: LITERATURE REVIEW. . . . . . . . . . . . . . . . . . . . 3

CHAPTER 2: CHAMBER DESIGN CONSIDERATIONS. . . . . . . . . . . . . . I2
Physical Considerations l3
Radiation 20
Sensible, Latent and Soil Heat Transfer 26
Chamber Soil Contact 33
CrOp Damage 3“
Measurement Location 3“
Chamber Mobility 35

CHAPTER 3: ENERGY BALANCE OF A LEAF IN MEASUREMENT CHAMBER. . . . . 36
Energy Balance Simulation Model Inputs A9
Energy Balance Simulation Run 50

CHAPTER h: DESIGN, CONSTRUCTION AND TESTING OF A PORTABLE 0
MEASUREMENT CHAMBER. . . . . . . . . . . . . . . . . . . 72

Materials and Methods 7h
Chamber Top Unit 77
Chamber Bottom Unit 80
SUSpension Structure 80
Chamber Measurement Equipment 82

 

Chamber Mixing
Measurement Technique
Data Intrepretation
Chamber Performance Verification
CHAPTER 5: LABORATORY EXPERIMENT .
Materials and Methods
EvapotranSpiration EXperiment
Equipment and Instrumentation
Results and Discussion
CHAPTER 6: SUMMARY AND CONCLUSIONS .

CHAPTER 7: RECOMMENDATIONS .

APPENDIX A: SIMULATION MODEL COMPUTER PROGRAM.

APPENDIX B: CHAMBER CALIBRATION CURVE.

REFERENCES.

vi

83
83
8h
85
90
9I
92
9h
96
l18
l20
l2l
133
13A

5.]
5.2
5.3

5.h

LIST OF TABLES

Mean ET values obtained in Experiment 1, given in grams.
Mean ET values obtained in Experiment 2, given in grams.

Before, during and overall leaf canOpy temperature changes
for the CHZOT and CHZCT treatments in EXperiment l

Before, during and overall leaf canopy temperature changes
for the CHZOT and CHZCT treatments in Experiment 2 .

vii

IOO

IOl

ll3

llh

LIST OF FIGURES

Figure

2.l

2.2

2.3

2.h

3.]
3.2
3.3

3.1.

3-5

3.6

3.7

3.8

Horizontal and vertical energy of a crop canopy (A).
Vertical energy balance of a crop canopy (B). (after
Tanner. I960L . . . . . . . . . . . . .
Idealized net radiation (Rn)’ wind velocity (u),
temperature (T), vapor pressure (e) and CO (C)
profiles for a typical crop canopy. Paramgters are
shown to vary with z where h is the height of the crop.
(After Monteith, I973). . . . . . . . . . .

Infrared radiation transmission with wavelength for
two possible chamber cover materials. . . . . . .

Solar radiation transmission with angle of incidence
for five possible chamber cover materials.

Leaf energy exchange in field.
Energy exchange of leaf enclosed in chamber.

Example of air temperatures during chamber measurement
taken on August 3l, I982 over turfgrass at East Lansing,
Michigan. ,
Change in components of equation 3.] over a simulated
chamber measurement where the initial air temperature,
relative humidity and chamber wind speed were 25 C,
202 and 1.5 m/s, respectively. ,
Change in components of equation 3.l over simulated
chamber measurement where the initial air temperature,
relative humidity and chamber wind speed were 25 C,
202 and 0.5 m/s, respectively.

Leaf temperature changes over simulated chamber
measurements for two levels of humidity and three
chamber wind speeds where the initial air temperature
was 25 C. . . . . . . . . . . . . . . .

Leaf temperature changes over simulated chamber
measurement for two humidity levels, three chamber wind
speeds and initial air temperature 35 C. . . . .

Vapor pressure deficit changes over simulated chamber
measurement for two humidity levels, three chamber wind
speeds and initial air temperature 25 C. .

viii

Page

15

I7

22

25
In
1:2

AB

52

53

56

57

58

3.9

3-13

h.2

h.3

h.h

I..5
the

u.7

h.8

5.1
5.2
5-3

Temperature deficit changes over simulated chamber
measurement for two humidity levels, three chamber wind
speeds and initial air temperature 25 C. .

Latent heat transfer changes over simulated chamber
measurement for three chamber wind speeds, initial
relative-humidity of 202 and initial air temperature
25 C. . . . . . . . . . . . . . . . . .
Latent heat transfer changes over simulated chamber
measurement for three chamber wind speeds, initial
relative humidity 80% and initial air temperature 25 C.

Latent heat transfer changes over simulated chamber
measurement fbr three chamber wind speeds, initial
relative humidity 20% and initial air temperature 35 C.

Latent heat transfer changes over simulated chamber
measuremtent for three chamber wind speeds, initial
relative humidity 80% and initial air temperature 35 C.

Cumulative latent heat produced over simulated

chamber measurements for three wind speeds,

relative humidity 80% and initial air temperature 25 C.
Chamber and suspension structure in field. ,

Basic chamber unit.

Infrared radiation transmission vs. wavelength for
Propafilm CllO, Plexiglass and Lexan.

Percent transmission of visible radiation vs. angle of
incidence for Propafilm CllO.

Chamber top unit.
Chamber bottom unit..

Comparison of ET measured with chamber (open top design)
with weighing Iysimeter over day for August 29, l982 at
Coshocton, Ohio. . . . . . . . . . . .

Comparison of ET measured with chamber with closable
tap, chamber with permanently closed top and weighing
Iysimeter, for three hours on August 29, I982 at

Coshocton, Ohio. .

Experimental setup for Experiment I and 2. .
Comparison of treatments WP] and WPZ.

Comparison of CHZOT and CHZCT treatments with treatment
WPl for Experiment l.

59

6I

62

63

6h

69
73
75

76

78

79
BI

87

88
98

. 103

. IDA

Comparison of CHZOT and CH2CT treatments with treatment
WPl for Experiment 2. .A. . . . . . . . . . . . . . . . . . . 105

Comparison of CHZOT and CH2CT treatments for Experiment
I and 2. . . . . . . . . . . . . . . . . . . . . .‘. . . . . l06

Latent heat transfer changes over simulated laboratory
chamber measurement. Data is shown for a leaf inside
and a leaf outside the chamber. . . . . . . . . . . . . . . . '08

Cumulative latent heat production over simulated
laboratory chamber measurement. Data is shown for a
leaf inside and a leaf outside the chamber. . . . . . . . . . ‘10

Example of variation of leaf canopy temperature during
two consecutive chamber measurements for replication l
of Experiment I. . . . . . . . . . . . . . . . . . . . . . . 115

LIST OF SYMBOLS
Sensible heat transfer (W/mz)
Latent heat transfer (W/m?)
Chamber estimated ET (cm/hr)
Net radiation (W/m?)
Soil heat transfer (W/mz)
Incoming solar radiaition (W/mz)
Solar radiation absorbed by leaf (W/mz)
Infrared radiation (W/mz)
Emitted infrared radiation from leaf (W/mz)
Emitted infrared radiation from atmosphere (W/mz)
Emitted infrared radiation from surroundings (W/mz)
Emitted infrared radiation from chamber cover (W/mz)
Temperature (C)
Air dry bulb temperature (C)
Air wet bulb temperature (C)
Average crop temperature (C)
Leaf temperature (C or K)
Effective sky temperature (K)
Temperature of surroundings (K)
Temperature of chamber cover (K)
Time (s)
Time increment (5)
Height above zero point displacement (m)
a/ax + a/ay ("I")
Height of crop canopy (m)

Average leaf thickness (m)

xi

Length of leaf in direction of air movement (m)
Length of stomatal cavity (cm)

Effective length of stomatal cavity (cm)
Diameter of stomatal cavity (cm)

Thickness of unstirred boundary layer (m)

Cross sectional area of stomatal cavity (cmz)
Horizontal wind velocity in crop canopy (m/s)
Wind velocity over leaf surface (m/s)

Density of leaf (Kg/m3)

Density of air (Kg/m3)

Specific heat of leaf (KJ/Kg-C)

Specific heat of air (KJ/Kg-C)

Sensible heat transfer coefficient (mz/s)
Latent heat transfer coefficient (mz/s)
thermal conductivity (W/m-C)

Oiffusivity of water vapor in air (mZ/s)

Diffusion resistance (s/m)

= Resistance of single stomate to water transport (g/cm3)

Stomatal resistance (s/m)

Boundary layer resistance (s/m)

Sensible heat transfer resistance (C-mZ/W)

Vapor pressure of the air (Pa)

Saturated vapor pressure at the wet bulb temperature (Pa)
Saturated vapor pressure within leaf stomatal cavity (Pa)
Atmospheric pressure (Pa)

Molecular weight of water (Kg/mole)

Molecular weight of air (Kg/mole)

xii

WPZ =

CHZOT

CH2CT

Ratio of mole weights of water to air
Latent heat of vaporization (KJ/Kg)
Gas constant (KJ/K-mole)

8 W/mZ-K)

Stephan-Boltzmann constant (5.67xl5
Leaf albedo

Chamber cover albedo

Leaf absorptivity

Chamber cover solar transmissivity
Chamber cover infrared transmissivity
Leaf infrared reflectivity

Chamber cover infrared reflectivity
Leaf infrared emissivity

Chamber cover emissivity

Emissivity of atmosphere

Emissivity of surroundings

Weighed pots group I

Weighed pots group 2

= Chamber open top group 2

8 Chamber closed top group 2

xiii

INTRODUCTION

In the last 25 years researchers have begun using a chamber
technique to measure evapotranspiration (ET) and canopy apparent
photosynthesis (CAP) in the field. Most of these chambers required the
control of the chamber environment in an attempt to simulate field
conditions. Since the chamber was left in place over plants in the
field for periods exceeding one hour and in some cases for several
weeks, the crop's energy exchange was a steady state process over short
periods of time. The weakness of the technique is the requirement to
simulate actual field conditions which researchers have found difficult
to do.

A distinctly different type of chamber technique places the chamber
over the crop for periods usually less than one minute in duration and
it is this type of chamber which is the focus of this study. The
technique attempts to obtain an instantaneous rate of ET or CAP during
the short measurement interval in the field. This type of chamber uses
no environmental control methods except those that might be considered
passive controls such as a high infrared transmission chamber cover
material. It has been assumed by users of such a type of chamber that
the shortness of the chamber measurement would assure negligible
modification of the crop environment and therefore the ET and CAP rates.
However, only little experimental and no theoretical work has been done
to support this assumption.

The goal of this study was to investigate by analytical and
experimental means the sources, magnitudes and directions of potential

error in ET estimation under specific environmental conditions using a

2
portable field chamber, with special emphasis on disturbances of the
plant environment. Specific objectives were:
I. Review of previous work done using the chamber technique for
estimating gas exchange rates.
2. Identify crop canopy parameters affected by the presence of the
chamber.
3. Develop recommendations for the design and development of a portable
measurement chamber.
The approaches taken to acheive these objectives were:
I. The development of a single leaf energy balance simulation model
with which to observe the trends of nonconstant parameters for a leaf
enclosed in a portable measurement chamber for a short period time.
2. Design, construct and test a portable measurement chamber from which
to evalulate the chamber technique.
3. Perform laboratory experiments to obtain statistically valid

information regarding chamber design and plant microclimate effects.

This analysis will attempt to serve as a base for much needed
further research and as an aid to those who wish to apply the technique

in their research.

CHAPTER I

LITERATURE REVIEW

Most work done with chambers for measuring plant water use (ET)
and/or canopy apparent photosynthesis (CAP) has been with chambers that
are placed in the field over several hours, days or weeks (Musgrave and
~Moss, l96l; Decker et al,l962: Baker, l965: Sakamoto and Shaw, l967;
Jeffers and Shibles, I969; Puckridge,l969; Connor and Cartledge, I970;
Egli, Pendleton and Peters, l970; Leafe, l972: Puckridge l978). It can
be assumed that in this type of chamber the energy balance due to
incoming and outgoing radiation, and sensible and latent heat transfer
is steady state for short periods of time. The energy exchange in this-
type of chamber is similar to that of a greenhouse and has been
described by Businger (l963). Lee(l966) reviewed literature on tent
enclosures and discussed effects of such a chamber on the microclimate
and crop ET.

Another type of chamber used for determining ET and/or CAP in the
field is the so called instantaneous measurement chamber which is the
subject of this thesis. It is called "instantaneous” because the
measurement is made usually in a period of time less than one minute.
The data obtained from a measurement of this length is presumably a
reasonable estimate of the parameter flux for a given point in time.

Reicosky and Peters(l977) and Reicosky(l98l) did not distinguish
between the two types of chambers in their literature reviews. It

should, however, be noted that the non-instantaneous and instantaneous

1,

type chambers are fundamentally different in the theory of their
measurement approach.

In the case of the non-instantaneous chamber the crop environment
is affected by the presence of the chamber and is altered from the
surrounding environment. Some researchers employing this type of
chamber have attempted to artificially simulate the natural outside
conditions by contolling the temperature, humidity and C02 concentration
of the chamber air but without exception have been forced to accept
conditions different from those in the field. Musgrave and Moss(l96l),
for example, replenished their chamber with CO2 at a rate equal to the
assimilation rate of the enclosed plants. An attempt to control air
temperature was made but the thermostat used resulted in fluctuating air
temperatures. The measured reduction in solar radiation was 20% and the
humidity was not controlled. Sakamoto and Shaw(l967) reported similar
problems but in addition found the maintainence of a constant CO level
was difficult to acheive resulting in C02 concentration fluctuations.
Jeffers and Shibles(l969) who measured CAP rates for soybeans stated
that the chamber produced "somewhat artificial conditions”.

The point here is that when a chamber of this type is used,
although an attempt be made to control the chamber environment, complete
simulation of the outside conditions cannot be expected. The result is
a group of plants which may have very different rates of ET and CAP than
the surrounding plants in the field. Despite the inherent weakness in
the technique to measure absolute rates of ET in the field (Lee, l966),
this approach has been found reliable in comparing treatment effects on

ET (Puckridge,l978).

The goal of the instantaneous measurement chamber is to obtain an
accurate, absolute point measurement of ET and/or CAP in the field. To
acheivement this goal, the chamber is lowered over or is placed around a
group of plants and a rapid measurement is taken, typically by means of
an aspirated thermistor psychrometer. It is hoped that the shortness
of the measurement duration will minimize a plant response to the
presence of the chamber. If the plant response is negligible, then the
measured ET and/or CAP will be essentially the same as that of the
plants prior to chamber placement. It would seem that this approach
would give values much closer to the actual field values than the
non-instantaneous chamber and this may be true. However, the speed with
which mechanisms controlling ET and CAP can be changed by the plant must
be considered, both analytically and experimentally, before a judgement
can be made.

This study will address some the physical aspects of the
instantaneous type measurement chamber used for ET estimation which may
affect its operation and performance. In the pages that follow it can
be assumed that any reference made to the “chamber” refers to the
instantaneous type chamber unless otherwise specified or that the

distinction is not important.

Peters, et al.(l97h) developed a chamber for the measurement of
both plant water use and photosynthesis in the field. The chamber moved
on tracks from one plot to the next where the number of plots was
limited by the length of track, electrical cable and the infared gas
analyzer tubing. The track used for chamber movement required the

elimination of two plant rows adjacent to the plot. The measurement

6

procedure consisted of moving the chamber with front and back open over
the desired plot. When the chamber was properly positioned the front
and back ”doors” closed and the chamber became sealed preventing any gas
exchange with the outside. Wet and dry bulb temperatures as well as gas
samples were obtained over the measurement interval. Upon completion of
the measurement, the front and back of the chamber opened and the
chamber was moved to the next experimental plot.

The chamber was covered with O.l mm Mylar film. 0n the front and
back sides of the chamber the film was wound around horizontal cylinders
the width of the chamber. The cylinders were kept near the top of the
chamber until the chamber was positioned over the crop, at which time
they were rolled down, covering the front and back sides of the chamber
with the film. Rubber seals were used between the rolls and the ground
for sealing the chamber from the outside. The rolls took approximately
l8 seconds to lower.

The researchers stated "The time of measurement depends on the rate
of gaseous flux and the precision of the measurement instruments". Some
measurements were as short as 20 seconds. Determination of the rates of
photosynthesis and evapotranspiration were determined from the slope
changes of CO2 concentration and the wet and dry bulb temperatures,
respectively. Data presented showed the wet and dry bulb temperature
changes to be quite linear over the measurement period. Although a
careful calibration was carried out for the CO2 concentration a
calibration on the psychrometer was not done.

In the introduction of the article Peters, et al. states that in
measuring ET and CAP in the field it is essential that ”the measurement

technique disturb as little as possible the spatial and aerodynamic

7

characteristics of the plot”, and they go on to say that the described
chamber "meets the above mentioned criteria". Whether or not this is
true can not be determined from the information given in the article.
The chamber C02 calibration was done by injecting a known amount of CO2
into the chamber. That the chamber measured the control flux may be of
only secondary importance if the chamber altered the plants microclimate
and rate of C02 assimilation. Schulze(l978) suggested that the two open
rows along side the plot) for the chamber tracks allowed light to
penetrate into the lower canopy, a fact which may have increased
photosynthetic rates. From the article one must conclude that the
extent of the psychrometer calibration was the calibration of the
thermistors (although this information was not given). Again, even if
the psychrometer worked well, if the transpiraton rate of the plants was
changed by the presence of the chamber then the measured ET rate must be
considered in error.

Reicosky and Peters(l977) developed a chamber for measuring plant
water use in the field. The chamber was made of aluminum conduit
covered with 0.127 mm Mylar film and was entirely closed except for its
bottom side. The chamber was appropriately sized for use with soybeans
and the height could be altered for use with corn.

The measurement procedure consisted of lowering the chamber over a
crop by means of a fork lift vehicle. A psychrometer was used for
measuring the rate of vapor density in the chamber over the measurement
interval. While the chamber was suspended above the crop, the
instrument readings were observed until wet and dry bulb temperatures in

the chamber stabilized, at which time the temperatures were recorded.

The chamber was then lowered to the ground for a period of one minute

8

and the final temperatures were read and recorded. After the
measurement was completed the chamber was lifted above the crop, the
internal air purged and the chamber was ready for the next measurement.
The initial and final values of wet and dry bulb temperatures were used
to obtain the change in vapor pressure. Using the change of vapor
pressure in the ideal gas equation along with the chamber dimensions and
measurement time yielded the ET rate in an equivalent depth per unit
time.

The chamber could be lowered to the ground in 5 seconds and raised
in 8 seconds. Fans were used to continuously mix the air and recycled
the air 9 times per minute. The wet and dry bulb thermistors were held
inside a psychrometer shielded from direct radiation.

The chamber was tested by placing it over soybean plants grown in a
hydroponic solution where the solution uptake could be measured. The
plants in solution were placed in the field and exposed to natural sun
light. An entire test run lasted 5 hours. .

The data obtained from the test for August 28, l975 showed very
good agreement. Data obtained on cloudy days, however, showed
significant disagreement between the solution uptake and the measured
transpiration rate where the transpiration rate measured by the chamber
was higher than the solution uptake rate. This disagreement was
attributed to water stored earlier by the plants which was subsequently
released during the test, being measured by the chamber but not by the
control. Reicosky(l98l) later suggested that the disagreement may be
partly due to an insufficient number of data points collected over the
time of interest since the chamber measures instantaneous values of ET

which may vary considerably with minute to minute changes in radiation.

A sensitivity analysis described by Doeblin(l966) was used to
calculate the total error of the system. With wet and dry bulb air
temperatures assumed to be read to +/- O.l C the overall error was found
to be ISX while the probable error was not larger than 11:.
Reicosky(l98l) compared measurements made by the chamber with a weighing
Iysimeter covered with alfalfa at the Minnesota Agricultural Experiment'
Station. For a clear day on July 2, l980 the Iysimeter measured 8.0
mm/day and the chamber measured 7.8 mm/day. Reicosky, Deaton and
Parsons(l980) subsequently used the chamber for measuring ET, attempting
to relate canopy temperatures to plant water status in irrigated and
nonirrigated soybeans. Mason et al.(l980) used this same chamber to
determine ET from irrigated and nonirrigated soybeans on selected days
in Iowa. The data obtained was quite scattered due to the variations in
radiation resulting from intermittent cloudiness, but clearly showed
that the irrigated beans consumed more water than did the nonirrigated
beans. The reseachers, however, attributed this not to water stress in
the nonirrigated treatment since the soil water status was found not to
be different for the two treatments, but to leaf area index which was
greater for the irrigated treatment.

Reicosky(198l) modified his approach by reducing the l minute
measurement to 30 seconds as a result of observing the wet bulb air
temperature in the chamber become asymptotic as saturation was
approached. In addition he covered the chamber with 3.l8 mm plexiglass
instead of Mylar.

In l97h Schulze(l978) developed a chamber for measuring CAP from
soybeans. The chamber design consisted of a l m body with a removable

lid which increased the height of the chamber by 0.3 m and was covered

ID

with O.l mm thick mylar film. To prevent gas exchange with the outside,
one side of an aluminum angle was attached to the bottom of the chamber
frame so that the other side of the angle could be projected into the
soil. The chamber was small enough so that it could be manually placed
over the plants without the use of lift equipment. The lower edges of
the lid frame were lined with l.3 x 2.5 cm foam rubber weather stripping
to provide a seal. Two fans of capacity 9062 l/min were used to mix the
air in the chamber. The fans cycled the air in the chamber about 7
times per minute. Chamber air temperatures were measurued during the
CAP measurements with shaded thermocouples.

In I975 the height of the lid was increased to 0.6 m to accommodate
taller plants. With the greater height the air exchange rate within the
chamber became 5.5 chamber volumes per minute. Schulze stated that this
rate of air mixing was adequate to produce a representative air sample
at the inlet to the C02 gas analyzer hose which was placed at the upper
fan outlet. The new design also included setting the chamber in a
wooden frame which was placed on the ground before the measurement to
further insure a minimum of gas exchange with the outside.

The measurement consisted of placing the chamber over the plants
prior to the CAP measurement. The measurement commenced when the lid
was placed on the chamber and clamped shut. Most runs lasted less than
1.5 minutes. At the end of the run the chamber lid was opened and the
chamber equipment was moved to a second chamber for the next
measurement. The use of two chambers allowed CAP measurements to be
taken once every 5 minutes.

C02 concentrations inside the chamber were observed to decrease

linearly with time. The mean rise in chamber air temperatures over the

ll

first minute observed during the l97h, I975 and I976 tests were l.h,
l.l3 and l.09 C, respectively. The mean temperature rise for the
second minute for the l97h, I975 and I976 tests were l.2l, l.09 and 0.8h
C, respectively. He also observed how the temperature rise was
affected by different levels of solar radiation. The data demonstrated
a tendency for chamber air temperatures to increase with increasing
solar radiation yet the data were quite scattered.

Schulze commented that notwithstanding the techniques obvious
ability to obtain rapid measurements of CAP in the field it necessatated
a high labor requirement of 3 to h people.

Harrison, Boerma and Ashley(l980) used a chamber similar to the
design used by Schulze(l978) for measuring CAP rates in a genetic study
on soybeans. Measurement rises during the chamber measurement were
reported as being under 2 C. Wells, et al.(l982) used the same design
for measuring cultivar differences in CAP and their relation to seed
yield in soybeans. Reported temperature rises within the chamber

averaged l C.

CHAPTER 2

CHAMBER DESIGN CONSIDERATIONS

The presence of the portable chamber over a group of plants causes
an immediate change in the stored internal energy of the crop canopy.
It is desirable, as in any measurement, to minimize the effect of the
measurement system. One way to minimize the effect of the chamber's
presence is to make the measurement before the crop canopy is
significantly effected by the measurement chamber.

Equally important is the design of the chamber itself including the
size of the chamber, the placement of instruments within it, and the
choice of materials with which the chamber is constructed. Ideally the
chamber should cause no change in the radiant, sensible and latent
energy exchange ongoing in the crop canopy. By choosing chamber
materials carefully, the influence of the chamber on the energy exchange
can be minimized.

The instantaneous measurement chamber technique is a relatively new
approach for measuring canopy gas exchange. The energy processes which
take place within the chamber and which determine the rates of gaseous

exchange have not yet been fully addressed in the literature and

therefore will be discussed in the sections that follow.

12

 

l3

Physical Considerations

From basic thermodynamics it is known that if a system is in
equilibrium with respect to the transfer of energy across its boundaries
and the boundary conditions are changed so as to change the net energy
flux across the boundaries, a state of nonequilibrium will prevail until
such time as the first derivative of the stored internal energy of the
system with respect to time is again zero(Van Wylen and Sonntag, I973).
Since latent heat which is produced at the plant and soil surfaces (and
is proportional to ET) is closely linked to the other forms of energy
transfer it will no doubt change when the chamber is introduced.
Whether or not the changing internal energy within the measurement
chamber will cause significant error in ET estimation depends partially
on the length of the chamber measurement and on the degree to which the
chamber‘s original environment has been changed. The complete energy

balance for a crop canopy was given by Tanner(l960) as:

2 z
+ A + + V
Rn E s + of ca ”(pauTa)62 + or (Le/R)vH(ue/Ta)5z
z z
= of CCpC(8TC/8t)62 + of Capa(3Ta/3t)62
2
+0! (Lc/RT)(3e/3t)52 (2.1)

where

R = net radiation (W/mz)

n

A = sensible heat transfer (W/mz)

S = soil heat transfer (W/mz)

E = latent heat transfer (W/mz)

T = average crop temperature (C)

 

Il-I

Ta = air dry bulb temperature (C)

L = latent heat of vaporization (J/Kg)

C 8 heat capacity of air (J/Kg-C)

C = heat capacity of crop (J/Kg-C)

R a gas constant (Pa-m /Kg-C)

v = a/ax 4- a/ay (m'])

e 8 ratio of mole weights of water to air
9 - density of air (Kg/m3)

- mean density of crop (Kg/m3)

= density of water (Kg/m3)

e a vapor pressure (Pa)

t - time (s)

u - horizontal wind velocity (m/s)

2 = height above zero point displacement (m)

The energy balance of the crop canopy is illustrated in Figure 2.l.

The left side of equation 2.l accounts for the net radiation,
horizontal divergence of sensible and latent heat and the vertical
fluxes of sensible , latent and soil heat. The right side of equation
2.l accounts for the change in internal energy with time within the crop
and crop-air volume. The left side of the expression is positive for
energy moving into the canopy and the right side is positive for an
increase in the canopy's stored internal energy. Equation 2.l neglects
energy used by photosysthesis.

For short periods of time in the field the storage terms are
approximately zero. The divergence terms may be significant for an
irrigated crop surrounded by nonvegatated land in arid regions. In

humid regions, however, these terms are usually small, especially well

15

 

 

 

 

 

 

 

 

 

 

et sensible water (ZR)
ation heat vapor
radi [l WCTRP
water . water
vapor E;>' : Storage terms in volume: C::{3r: vapor
sensible 1. Temp. change of crop ,_ sensible
heat E::::::> ' 2. Temp. change of air Ci;> heat
I 3. Abs. humidity changel

 

 

 

 

/_7 “““ ‘1‘ ““““ " —7

 

 

 

soil
heat
net
radiation
evaporation

 

sensible
heat (air)

A

<\\\\\\\\\\\

 

 

\
‘

 

 

 

 

 

 

soil
heat

 

Figure 2.1 Horizontal and verticle energy balance
of a crop canopy (A). Vertical energy balance of a
crop canopy (B). (After Tanner, I960)

 

l6
inside the borders of a cropped field (Tanner, l960). Assuming both the
storage and divergence terms to be zero and letting 672 go to zero
causing the control volume to become a control plane (Figure 2.28)

simplifies equation 2.l considerably giving -

Rn+A+E+S=0 (2.2)

Equation 2.2 is a viable expression for describing the energy
tranfer of a crop over short periods in the field. . Wright and

Brown(l967) gave expressions for the sensible and latent heat transfer

as
= - C dT d 2.
A pa aKA( / z) ( 3)
and
E = “(paeL/PIKE(de /d2) (2J4)
where

KA = sensible heat transfer coefficient (mg/s)

KE - latent heat transfer coefficient (mz/s)

 

T =
e a
z .
pa
.C a
a
e a
L a
P 8
Equations

l7
temperature (C)
vapor pressure (Pa)
heat transfer path (m)
density of air (Kg/m3)
heat capacity of air (J/Kg-C)
ratio of molecular weights of water to air
latent heat of vaporization (J/Kg)
atmospheric pressure (Pa)

2.3 and 2.h are given here to show how each of these modes of

energy transfer are dependent on the temperature difference between two

points in

space. The vapor pressure which is a function of the wet and

dry bulb temperatures was given by List(l958) as

0
e = e
w

where

(‘0
I

..|
I

_'
I

- 66OOOP(TW - Td) (l + O.OOll5TW) (2.5)

vapor pressure (Pa)
saturated vapor pressure (Pa)
dry bulb temperature (C)

wet bulb temperature (C)

The saturated vapor pressure must be calculated at the wet bulb

temperature (Nantou, I979) and is given here in a simplified form of the

Clausius-Clapeyron equation (Merva, I975).

0
ew = I33 ln(21.07'(5336/(Tw + 273-l5))) ‘ (2.6)

l8

The transfer coefficients depend on wind velocity and therefore
depend on height above a datum since the wind velocity varies
approximately logarithmically with height in the field. Figure 2.2
shows the relationship of several of the variables in equations 2.2, 2.3
and 2.h with height above the ground in a typical crop canopy. Figure
2.2, though idealized, conveys a general picture of the sensitive,
interrelated energy complex within a crop canopy. One can imagine that
with a slight modification in one of these parameters the entire system
might be significantly altered from its original state. Such a
modification might be affected by the placement of an enclosure or
chamber over the crop canopy. If the chamber is left over the crop for
a long period of time, for example one or two hours, then equation 2.2
would apply since a psuedo-equilibrium condition would exist. If,
however, the chamber were over the crop for a period less than one
minute (as in the case of an instantaneous measurement chamber),
equation 2.2 would not apply during this time since the energy
components would be changing in time and thus, equation 2.l must be
used. The divergence terms can still be neglected but now the storage
terms may be considerable. Integrating over the height h of the chamber

equation 2.l becomes

+ + + s + + .
Rn A E s CahpaBTd/at ChpCBTC/at th/RTdae /at (2 7)

C

The instant the chamber is put in place a dynamic process begins

since the chamber's presence causes changes in transfer coefficients as

19

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20
well as gradients. A discussion of the terms on the left side of

equation 2.7 is in order.

Radiation

The net radiation, the sum of the various components of radiant
energy transfer in the crop canopy, plays a major role in the energy
process and in some cases may be virtually the sole energy input in the
field, (i.e. Rn is positive while other terms in equation 2.6 are
negative). The net radiation is one of the components of the energy
budget which the designer has some control over. By using a cover
material on the chamber which transmits infrared and visible radiation
well (and by using minimal structural members) it is possible to
minimize a change in the net radiation flux.

As the chamber is lowered into place the crop canopy which it
encloses receives an altered quantity of radiation. The radiation
received at the chamber cover surface is mostly transmitted, but some is
reflected and some is absorbed. "The ideal case would exist if the
reflected and absorbed components of the flux were zero. If this were
the case and all the radiation was transmitted through the cover, this
situation would be equivalent to the condition when the chamber was not
present so far as the radiant exchange is concerned. The transmission
of radiation through a transparent medium is a function of the
wavelength of the radiation (Duffie and Beckman, l97h: Duffie and

Beckman, I980). Many transparent materials (film or rigid sheet)

2l

transmit about 90% of the normally incident visible radiation
(wavelengths between 0.3-0.7 microns) but may transmit radiation poorly
that is composed of wavelengths greater than 0.7 microns(Trickett and
Goulden, I958). For instance, plexiglass though capable of transmitting
about 90% of the normally visible radiation only transmits about IOX of
radiation composed of longer wavelengths. Radiation of wavelengths
greater than 0.7 microns is referred to as infrared radiation(Rosenburg,
l97h). Figure 2.3 shows the infrared radiation transmission spectra for
plexiglass and polycarbonate (Lexan), two commonly used plastic
materials. Curves similar to those shown in Figure 2.3 are given by
Walker and Slack(l970) and Trickett and Goulden(l958) for other commonly
used films. Measurement equipment for the determination of
transmissivities of materials' for radiation between the wavelengths of
0.7 and 2.5 microns is not commonly' available and therefore rarely
reported. However, this does not imply that this incoming or outgoing
radiation is negligible or unimportant and therefore transmission
information for this range should be obtained if possible.

Since all bodies above absolute zero emit radiant energy, the flux
of solar radiation is balanced partly by radiation emitted by the crop
canopy(Davies and Idso,l979). The radiation emitted from the crop is
infrared and, based on the data for the two cover materials' given
above, a large amount of the radiation will either be reflected back
into the chamber or be absorbed by the chamber cover. This radiation,
which is essentially trapped inside the chamber, will be absorbed by the
air and at the chamber surfaces. The molecules, whether in the air or
at a surface will either absorb or reflect a particular wavelength

photon depending upon the type of molecule involved. Water vapor, for

22

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23

instance, absorbs long wave radiation quite well (an unfortunate
coincidence since the goal of the chamber is to trap water vapor and not
radiant energy). The absorption of energy by a molecule will raise the
energy level of the molecule. The increase in energy is manifested as
an excitation which is conveyed to other molecules via molecular
collisions. This process which is less than l002 efficient results in
some sensible heating. Simultaneously, the molecule is emitting radiant
energy to other molecules. If radiation originally received was from a
source of higher temperature than the molecule then the reradiation will
be a lower grade, i.e. of a longer wavelength. This process will
continue until the temperature of the molecules in both the air and
surfaces are elevated sufficiently to counteract the inflow of radiant
energy. This phenomenon has been called the ”greenhouse” effect and has
been described by Businger(l963). This effect should be minimized if
possible and can be at least partially overcome by choosing a chamber
cover material which transmits a maximum in the infrared.

In view of the goal to minimize alteration of the radiant flux
(i.e. maximize transmission) Sestak et al.(l97l) recommended a
polyvinylidene chloride (PVDC) coated polypropolene film (Propafilm) or
polyethylene film. The latter should not be used in photosynthesis work
as the film is rather permeable to C02.

A film which has been used by many of the chamber reseachers with
apparent success is Mylar. Mylar is a thin film material with a high
transmission for infrared radiation but it lacks the ability to give
structural strength to the chamber as would plexiglass or lexan.

Polyethylene, along with being relatively permeable to C02, also becomes

2h
cloudy when left in the sun for only a few days(Decker et al.,l962).
Propafilm C, a thin PVDC coated polypropolene film, has been found to
stand up well in sunlight and is strong and easy to work with based on
this author's experience.

The shape of the chamber can also affect the transmission of
radiation by either reducing or exaggerating the radiation reflected
(Duffie and Beckman, I980 ; Monteith, I973). As the (angle of the
incident radiation increases with respect to a line normal to a
transparent medium the reflected radiation also increases. Figure 2.h
shows the relationship between beam angle and radiant transmission for
some commonly used transparent materials. Most of the chambers used
have been rectangular in shape. One exception to this was a cylindrical
noninstantaneous measurement chamber used by Decker et al. (I962) for
measuring ET from Tamarisk shrub.

The framework of the chamber and the instruments inside can cause a
reduction in the visible radiation while increasing the the infrared
radiation load on the crop due to emittance from the chamber
materials. A change in the quality of the radiation will cause a
repartitioning of the energy within the chamber since the boundaries of
the system (e.g. plant surfaces) absorb, transmit and reflect different
kinds of energy in different ways(Nobel, I970). For this reason the
framework and instruments should block as little of the sun light as
possible and should be painted white or silver to minimize visible

radiation absorption.

25

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26

Sensible, Latent and Soil Heat Transfer

In addition to the radiant effects, another contributing factor to
changes in the chamber air temperature is the sensible heat transfer
from the plant, soil and chamber surfaces. Chamber surfaces here
includes "active" modes of sensible heating such as fan motors. Of
these modes 3 very important point of heat transfer is the plant leaf
since it is the point of the most latent heat production. From equation
2.3 it is seen that the sensible heat transfer is directly proportional
to the temperature difference between two points. In this case the
temperatures include that of the leaf and of the air around it. If the
air temperature is initially above that of the leaf and the air
temperature increased due to the presence of the chamber then the rate
of heat transfer to the leaf would increase. If, however, the leaf
temperature was above the air temperature an increase in air temperature
would reduce the rate of heat transfer from the leaf. The latter case
would be desirable if for example the radiant heat load on the leaf
decreased.

The latent heat exchange is also related to leaf temperature since
the transpiration from the leaf is proportional to a vapor pressure
difference. Assuming the evaporating surface on the leaf to be in a
saturated state (Slavick,l97h) then the relationship of leaf temperature
to saturated vapor pressure can be seen by using the leaf temperature in
equation 2.6. This shows that any change caused in leaf temperature
will affect the rate of transpiration. One way in which the temperature

of the leaf might be changed is by a reduction in the visible radiation

27

intensity by either direct shading from chamber equipment and framework
or a reduction in the quantity of solar radiation received by the leaves
as a result of the chamber cover. Numerous workers have shown the
dramatic and immediate effect on leaf temperature by shading (Arsari and
Loomis, l959; Meidner and Mansfield, I968; Platt and Wolf, I950; Avery,
I967). The expected change in incident solar radiation for a canopy
covered by a measurement chamber is around IOZ. Peters et al.(l97h)
measured a 72 decrease in solar radiation after the placement of their
chamber covered with mylar, while Decker et al. (I962) found an 11:
reduction for a polyethylene covered chamber. This same chamber reduced
incident solar radiaition by 303 after becoming dirty. Reicosky(l98l)
measured an 82 reduction in solar radiation in a chamber covered with
3.l8 mm thick plexiglass.

Equally important if not more important than the gradients in
equations 2.3 and 2.A are the transfer coefficients for sensible and
latent heat, KA and KB. With specific changes in the environment these
coefficients may change by many times their original values. These
coefficients are highly dependent on wind speed (Wright and Brown, I967)
and are considered equivalent under slightly neutral conditions
(Rosenberg, l97h). ”Slightly neutral conditions" refers to atmosheric
stability which is determined by the vertical direction of sensible heat
movement in the environment. A neutral condition exists when the
vertical temperature gradient is zero. Since the chamber air is mixed
during the measurement, and therefore of approximately equal temperature
throughout, the atmospheric conditions would be approximately neutral

making KA approximately equal to KE.

28

Therefore, the mixing rate of the fans inside the chamber is an
important design consideration. The transfer coefficients change
instantaneously with changes in wind speed by either reducing or
increasing the thickness of the unstirred boundary layer over the plant
surfaces (Raschke, I960). By adjusting the mixing rate of the fans
appropriately an attempt can be made to maintain the original transfer
coefficients when the chamber is lowered into place and the mixing fans
are on. An inherent flaw in this strategy occurs when the ambient wind
speed is low. By adjusting the fan speed to a low level, the mixing
rate may be below the lower limit allowable for accurate sensing by the
psychrometer.

In a situation where a canopy is covered by a chamber, K may

E
change differently than KA if the leaf stomatal conductance is made to
change. The diffusion resistance (effective diffusion path length
divided by the diffusivity of water vapor in air) is related to the bulk
transfer coefficient and therefore should be considered in this

analysis. The diffusion resistance from a plant leaf (neglecting

cuticle resistance) can be described as

r = r + r (2.8)

where

rD a diffusion resistance to water vapor (é/m)

rS - stomatal resistance (s/m)

r - boundary layer resistance (s/m)

bl

29

From equation 2.8 the diffusion resistance is directly proportional
to the sum of- the stomatal and boundary layer resistances. The

expression shows that if either rs or rblare large relative to the other

then the larger of the two resistances will control rD. Raschke(l960)
gave the typical range of rS as 30 s/m to I8000 s/m and the' typical

range of rb] as 6 s/m to I80 s/m. Using his example to illustrate the

usual control of rD by rS suppose rS is 3000 s/m, then the total

possible range of rD is 3006 s/m to 3l80 s/m. The example shows that

unless rS is quite small r should have a relatively small effect on a).

bl

The boundary layer resistance was given by Nobel(l970) as 6/0 where
6 is the thickness of the unstirred boundary layer and D is either the
thermal diffusivity or the diffusivity of water vapor in air. Nobel
gave the boundary layer thickness to be proportional to the square root

of the ratio of the length of the leaf in the direction of air movement

L in meters to the wind velocity over the leaf v in meters per second.

1/2
5 = 0.h(L/v) /I00 (2.9)

Other expressions fora (and r can be found in the literature (Raschke,
s

I960;Drake, et al. I970: Gates, I968; Slavik, l97h).
The stomatal resistance is a function of stomatal aperture and its

theoretical form for a single stomate was given by Meidner and Mansfield

(I968) as

r = (l'+'nd/A)DA" I.
s e

ff/DA (2.10)

30

where
r; = stomatal resistance for single stomate (s/cm 3
A' = area of stomatal opening (cmz)
II = length of stomatal passage (cm)
l;ff = effective length of stomatal passage (cm)
d 8 diameter of stomatal opening (cm)
0' = diffusivity of water vapor in air (cmZ/s)

The stomatal resistance is seen to increase with decreasing diameter.
If d is small compared to l'then r; varies approximately inversely with
the square of diameter. If d is not small compared with l'then r; will
not increase so greatly with a decrease in d.

Experimental values for rS as well as functional relationships have
been determined for a wide variety of plant leaves. Gates(l968) has
summarized experimental values obtained by many researchers. Some of
these data were given as high and low values and thus give a range for
the particular plant type. Other researchers have shown the dependence
of rS on ‘light intensity, ambient CO2 concentration and leaf
temperature. Experimental data showing these relationships can be found
in Whiteman and Koller(l96h), Whiteman and Koller(l967), Meidner and

Mansfield(l968) and Pallas(l965). To summarize these effects: a

decrease in light intensity caused an increase in r : an increase in the

s

ambient CO2 concentration increased r ; the relationship between leaf
5

temperature and r has not been fully resolved but seems to be plant and

5
environment specific. Drake et al.(l970) related stomatal resistance to

leaf temperature for Xanthium strumarium L. The control of stomatal
resistance by leaf temperature (or vice versa) was hypothesized as a

result of findings which showed that for air temperatures above 35 C

3l
leaf temperatures were below air temperatures while for air temperatures
below 35 C leaf temperatures were higher than air temperatures. Using a
purely physical energy analysis (which neglected the relationship of rS

to leaf temperature) these trends could not be simulated. Drake

developed regression equations for Xanthium relating r to leaf

5
temperature for high and low humidity levels. The 35 C crossover point
is not significant as this value would change under a different energy
environment. For a comprehensive review of leaf temperature studies the
reader is referred to Jackson (l982). Whiteman and Koller(l967) found
the water vapor conductance for Pinus Halennis to increase with
increasing leaf temperature up to 25 C. Baker(l965) observed a decrease
in stomatal diffusion resistance with increasing cotton leaf
temperatures.

The design implications are relatively straight forward. The
chamber should not cause a decrease in light intensity as might be
caused by a dirty chamber cover or the casting of shadows by the chamber
instruments and framework. Additional CO2 which is produced by a
running tractor in the vicinity of the chamber measurent should be
deverted away from the area , perhaps by means of an exhaust stack with
its outlet at a remote position. Pallas(l965) reported decreased
transpiration rates in soybeans from 3A to 53% when CO2 levels were
increased from 250 to 500 ppm. His microscopic inspection of stomates
indicated that closure had occured. Baker(l965) found cotton stomatal

apertures became affected at C0 concentrations exceeding 600 ppm. Egli

2

et al.(l970) observed a 20% decrease in transpiration rates for one of

their soybean varieties when CO concentrations were increased from 300

2
to A50 ppm while transpiration rates at 600 ppm were only slightly less.

32

The possibility of increased concentrations of CO2 in the crop
environment must be viewed in light of the fact that a decrease in'CO:2

concentration within the chamber occurs during the chamber measurement
since the crop is using CO2 for photosynthesis. Schulze(l978) observed

a decreasing C05 concentration within a measurement chamber of IS

ppm/min. The effect of decreasing CO2 concentration in the plant
environment causes a decrease in stomatal resistance and may tend to
increase transpiration rates slightly.

Leaf temperature changes though harder to control are probably not
as critical since the temperature changes are on the Order of 0.5 to I.5
C and a change of this magnitude will not alter rs seriously (based on
regression equation given by Drake for Xanthium, l970).

Heat transfer to or from the soil may also contribute to a
modification of the environment inside the measurement chamber. During
the daytime the sensible energy transfer is usually into the soil
(Tanner, l960). This means that the air temperature is higher than the
soil temperature at the surface or that the radiant load on the soil
surface is large. If the former is true and the chamber causes an
elevated air temperature then the soil will tend to moderate the effects
of the chamber by taking heat from the air. This moderating capacity of
the soil is probably small, however, since the heat capacity of the soil
is relatively large.

Under all conditions the soil is emitting infrared radiation. This
source of energy will be especially significant during periods of little
ground cover by the crop when soil surface temperatures are high.

Therefore, any moderating effect due to the sensible soil heat transfer

would probably be small compared to the radiation heat transfer from the

33
soil.

Before moving on to some of the mechanical considerations of the
chamber design a last look at equation 2.7 is in order. If both sides
of the equation are divided by the height of the chamber h the energy
balance can be expressed in units of energy per unit time per unit
volume. From the new form of the equation it is clear that a smaller
chamber height will cause a greater change in internal energy with time.
This means that for a similar time rate of change of the chamber
internal energy, a small chamber must make a measurement over a shorter
period of time. For example, if a l m chamber was use over potatoes and
a 3 m chamber over irrigated corn, the time rate of change of the
chamber internal energy for the l m chamber would be approximately 3
times as great as for the 3 m chamber and for this reason it may be
prudent to use an over sized chamber if practical. Schulze(l978) found
this to be true when he observed greater mean temperature rises in his

smaller chamber than in one which was 232 taller.

Chamber Soil Contact

A critical area where water vapor (or CO!) may 'escape from the
chamber is the interface between the soil surface and the chamber frame.
Several methods can be employed to minimize leaks from this interface.
A ID to l5cm deep piece of foam can be glued to the bottom of the frame.
It is not necessary that the material be highly resistant to water vapor
transport since the foam will deform from the weight of the chamber,
thereby greatly decreasing its conductivity to water vapor. Leveling

the ground where the chamber makes contact was suggested by

34
Reicosky(l98l).
Schulze(l978) used a wooden frame which was carefully placed on the
ground prior to the chamber placement. As the chamber was lowered to

the ground it was set into the frame for proper sealment.

Crop Damage

Some crop damage will occur as the chamber is lowered over the
plants even though the chamber size is chosen to fit between rows.
Potatoes, for instance, cover the ground almost completely and some
damage from the chamber is unavoidable. Moving the chamber over a new
group of plants for each successive measurement may minimize influences
of crop damage. In the case of a freely suspended chamber researchers
must walk into the crop canopy to control the position of the chamber
while lowering. Damage caused by trampling can be reduced by using long

gaff poles to control the position of the chamber from a distance.

Measurement Location

To reduce the influence of border effects, the measurements should
be taken as far into the crop canopy as possible where the environment
more closely represents field conditions. The collection of data
successively for several measurement periods from the same plants may
result in inaccuracies in ET estimation introduced by the possible onset
of stomatal closure and/or crop damage. The influence of the Chamber on

the crop physiology is not yet fully understood and will be addressed

35

more closely in Chapter 5.

Chamber Mobility

The portable measurement chamber along with the associated chamber
equipment for chamber movement need to be designed with mobility and
ease of operator use in mind. The designer must consider the following
with respect to chamber design:

I. size

2. weight

3. ease of chamber assembly and disassembly

A. manual and automated control

5. within and between field movement

6. ease of equipment repair in the field

7. total system height

8. intended system operators

9. electric and mechanical power requirements

l0. ruggedness of equipment

Specific examples of designs can be found in Peters et al.,l97h,
Reicosky and Peters, l977 and Schulze, l978 as well as in chapter A of

this thesis.

CHAPTER 3

ENERGY BALANCE OF A LEAF

IN MEASUREMENT CHAMBER

To better understand the complicated interrelations of the
tran5port of energy to and from a leaf (and therefore transpiration
which is usually the major fraction of ET) in a crOp can0py covered by
a measurement chamber a computer model was developed.- The modeling
of an entire cr0p canopy is difficult since there are a great number
of factors involved. Modeling the complete crop canopy was discussed
by Norman (I979). His analysis included simple statistical models
as well as ones more physically based.

It is our objective here to investigate the various energy trends
which occur within the chamber with special attention paid to
evapotranspiration. Since the major fraction of evapotranspiration is
leaf transpiration we have chosen to limit our analysis to the nonsteady
state analysis of a single leaf enclosed by a measurement chamber.
Valuable information can be gleaned from a single leaf model. For
instance, given that the wind velocity over a leaf in the chamber
increases and/or the radiation load decreases and/or the wet and dry
bulb air temperatures increase over the period of the measurement, what
is the effect on leaf temperature and transpiration rate? Perhaps more
importantly,to what degree IStranspiration changed and how does this
change or error (relative to the initial or field condition) vary with

time.

36

 

37

The energy balance on a horizontally oriented leaf can be described

by the following equation:
+ + = .
Rn A E pLCLhL(8TL/at) (3 I)

where
Rn=net radiation on the leaf (W/mz)
A =sensible heat transfer to or from leaf (W/mz)
E =latent heat transfer to or from leaf (W/mz)
CL=leaf specific heat capacity (KJ/Kg-C)
0L=leaf density (Kg/m3)
hL=average leaf thickness (m)
TL=leaf temperature (C)

t =time (5)

Equation 3.l when expressed in a more fundamental form and adapted
to a condition which simulates the presence of the chamber is a function
of time, dry bulb and wet bulb air temperatures, leaf temperature,
effective sky temperature, wind velocity, leaf length in the direction
of air movement, solar radiation, emissivities of the leaf, chamber
cover and sky, solar absorptivity and reflectivity of the leaf, the
infrared transmissivity of the chamber cover, and the leaf density,
thickness and heat capacity.

The placement of an instantaneous measurement chamber over a crop
generally occurs in the following manner. The chamber is prepared by

positioning it over the canopy but spacially above it so that the crop

 

38
is in a state of relative equilibrium and in a state similar to the rest
of the plants in the area. Next, the chamber is lowered to the ground
and the measurement taken for the next 30-60 seconds. At the end of the
measurement the chamber is raised from the canopy and it gradually
returns to it's initial state.

Before and/or during the chamber measurement a given leaf in the
chamber is exposed to solar radiation as well as infrared radiation from
the sky, surroundings and the chamber itself. The leaf cools itself by'
emitting infrared radiation and by latent (and possibly sensible) heat
transfer. When the chamber is lowered over the canopy the leaf is
exposed to both a different radiant and ambient environment. A portion
of the visible and infrared radiation is reflected or absorbed by the
chamber cover and frame and therefore does not reach the leaf. However,
with the chamber in place infrared radiation emitted from the chamber
cover and framework becomes incident on the leaf. The radiation emitted
by the leaf which normally is released from the canopy may be partially
-trapped in the chamber because the chamber cover does not transmit
infrared radiation perfectly. This trapping may result in elevated
surface and air temperatures over the period of the chamber measurement.
If heat was originally leaving the leaf the increased air temperature
will cause a reduction in the leaf/air temperature deficit and a rise in
leaf temperature. With time, the production of vapor in the chamber
will cause the leaf/air vapor pressure deficit to decrease and also the
.leaf temperature to rise. Decreasing these gradients tends to decrease
the rate at which sensible and latent energy leave the leaf. A
compensating effect, however, is at work via the resulting rise in leaf

temperature which produces larger deficits. The wind velocity over the

 

39
leaf works to either increase or decrease the unstirred boundary layer
thickness at. the leaf surface. If the chamber causes reduced air
movement over the leaf then the boundary layer will increase in
thickness reducing the sensible and latent heat transfer to or from the
leaf. An increased chamber air speed would result in an opposite
effect.

In order to better understand the effect of the chamber on a leaf
inside it is necessary to analyze equation 3.I and observe the action of
each of the components of equation 3.I over the period of the chamber
measurement.

The solution of equation 3.I requires its simplification so that
only one dependent variable exists for one or more independent
variables. Parameters which change over time and upon which the terms
in equation 3.I depend are leaf temperature and the chamber air wet and

dry bulb temperatures. To support this statement the terms in equation

3.I will now be replaced with expressions involving the temperatures
mentioned above. The expressions given below will transform equation
3.I into a functional form that can be solved on a digital computer. A

simplifying assumption which will be made is that the leaf is oriented

horizontally so that all energy transfer is in the vertical direction.
The net radiation term in equation 3.I is the sum of the solar

radiation, both direct and diffuse, and the infrared radiation from the

sky, surroundings, and leaf. The net radiation can be expressed as

R = R + IR + IR - IR .2
n L a s L (3 )

AD

R = solar radiation absorbed by leaf (W/mz)

IR = infrared radiation from atmosphere absorbed

by leaf (W/mz)

IR = infrared radiation from surroundings absorbed

by leaf (W/m2)

IRL= infrared radiation from leaf emitted to
the surroundings (W/mz)
The components of energy transfer to or from the leaf are depicted under
field conditions in figure 3.I and under chamber conditions in figure
3.2.

Solar radiation absorbed by a leaf was given by Nobel(l970) as
R R(i+')' (33)
s pLO‘L ‘

where

RS= incoming solar radiation (W/mz)

l

pL= leaf albedo
I

aL= leaf absorptivity

I I
The product aLpLRs accounts for the solar radiation reflected to the

leaf from the leaves below it. Radiation heat transfer can more

fundamentally be described by the Stephan-Boltzman equation

L,

R ‘enoT (3.1+)

41

 

RS IR RS
’OLRs A E
UPPER LEAF
.4
A E
2.
_, PLRS
1RL ,
L IRL PLRS

 

 

3.1 Leaf energy exchange in field.

42

 

 

 

 

 

 

IRa RS TZIRL
logglRa Pgas
RS
, , A 1RC
V TCPLRS E PIIIR
" C L
TCIRa
I
PcRs I UPPER LEAF
E
, i
v TCPLRS A IRL
l'éRS CPLRS IRL ,
\I
LOWER LEAF
_V___.
II II I] II II II II II // // 7

3.2 Energy exchange of leaf enclosed in measurement
chamber.

A3
where
R = infrared radiation heat transfer (W/mZ)
e”= emissivity

8 W/mZ-K I

0 = Stephan-Boltzman constant (5.67xl0
T = absolute temperature of emitting body (K)
The terms in equation 3.2 which involve the transfer of long wave

radiant energy are given by

ll L.
IR = 5 0T (3.5)
e e e
ll
IR = E or“ (3.6)
s s 5
ll [4
IR = T (3.7)
L ELC’L
where
ll
ee- effective sky emissivity
5:” emissivity of surroundings
l
€C= emissivity of leaf
Te= effective sky temperature (K)

T = average temperature of the surroundings (K)

TL= average leaf temperature (K)
It can be assumed that any infrared radiation emitted from the leaves
below to the leaf in question is approximately equal to that emitted by

the leaf to the lower leaves and that their sum is nearly zero since

Jl

 

AA
their temperatures are approximately equal. It follows then that the
quantity of long wave energy from the surroundings is entirely due to
the chamber cover and frame. Since, however, we have restricted our
analysis to the vertical direction we will further assume that a typical
leaf is not aligned with the chamber frame or instruments so that the
infrared radiation from the chamber is recieved only from the chamber

cover. With this qualification equation 3.6 becomes
IR " Th 8)
c 8c0 c (3'

where
IR = infrared radiation emitted from the chamber
cover (W/mz)
e 8 Chamber cover emissivity
T = chamber cover temperature (K)
Equation 3.8 would of course not be applicable for periods when the
chamber is not enclosing the leaf.

Sensible heat transfer to or from the leaf can be expressed as

A = -k(dT/dz) (3.9)

where
k = thermal conductivity of the air (W/m -C)
T = temperature (C)

2 = heat transfer path direction (m)

A5

The functional form of equation 3.9 is

A = -(TL - Td)/rA

where
TL = leaf temperature (C)
18 = air temperature (C)
3‘ = sensible heat transfer resistance (mz-K/W)

The sensible heat transfer resistance is a function of the

boundary layer resistance or

r = k
A 6/
where
5 = unstirred boundary layer thickness (m)

The functional form of the latent heat transfer is given by
0
E = -LMw(ew - e )/RTdrD

where
L = latent heat of vaporization (2.A7xl03 KJ/Kg)
R = gas constant (KJ/K-mole)

T = air temperature (K)

e = saturated vapor pressure in leaf stomatal cavity (Pa)

(3.10)

unstirred

(3.11)

(3.12)

A6
e = vapor pressure of the air (Pa)
rD = diffusion resistance (s/m) (see chapter 2)

M = molecular weight of water (0.0l8 Kg/mole)

The derivative in equation 3.I can be approximated by using a
finite difference form involving the leaf temperature at the real time
and one time step earlier. This form has been called the backwards

difference approach (Von Rosenberg, I969) and is given as

aTL/at = (TL,i - TL’i_1)/At (3.13)

where

TL , = temperature of leaf at time i
, I

T =
L,i-l

At = time step (5)

temperature of leaf at time i-l

By replacing the terms in equation 3.I with equations 3.3, 3.5,
3.6, 3.8, 3.l0, 3.l2 and 3.l3 the functional form of the nonsteady state
energy balance for a leaf enclosed within a measurement chamber is

obtained.

. A A _ A _ _ T
TcRs (] + pL)aL + TC 6e oTe + 6c oTc EL oTL (TL d)/rA

LMw(ew - el/(RTer) = oLCLhL (TL . - TL 1-1)/At (3.IA)

The transmissivities (T) shown in the first two terms on the left side

of equation 3.IA account for the reduction in radiation received by the

A7
leaf due to the chamber cover.

Parameters which vary in equation 3.IA are the wet and dry bulb air
temperatures, the leaf temperature and time. Time is the independent
variable which leaves three unknowns but only one equation. Therefore,
we must 'either hold two of the temperatures constant or supply data at
known points in time during a simulation run so that ‘only one
temperature is unknown. The way in which we will handle this
requirement is to assume initial and final wet and dry bulb air
temperatures for any given run. We will further assume that these air
temperatures vary linearly with time. The assumption of linear changes
in air temperatures appears justified based on data in the field.
Example data collected in the field over turfgrass on August 3l, I982 at
East Lansing, Michigan are shown in figure 3.3. With air temperatures
known the only unknown variable is leaf temperature and the boundary
condition required to solve equation 3.IA is the initial leaf
temperature.

The energy balance model(equation 3.lA) was put into the form of a
computer program coded in the Fortran V computing language (see Appendix
A for program listing). The computer program first computes the steady
state leaf temperature in the field (STL/3t=0). With the initial leaf
temperature determined the leaf temperature at discrete points in time
can be determined. With leaf temperatures known the terms in equation

3.I can also be determined.

TEMPERHTUREI C l

 

48

 

F.’
u)—
o1
III
III
El
°3 m
‘3‘ in
El
, L'J
NJ:
‘7
R‘ A
a
A
A
“3
o- A
N A
g In dry bulb temperature
A
m A wet bulb temperature
3’. - 1 ' r ' 1 ' 1 ' 1
0.0 7.0 14.0 21.0 28.0 35.0
Figure 3.3 Example of air temperatures during
chamber measurement taken on August 31, 1982 over

turf grass at East Lansing, Michigan.

49

Energy Balance Simulation Model Inputs

Equation 3.lh is a general expression describing the transport of
energy to and from as well as heat stored in a leaf. With the
appropriate coefficients a simulation can be run for any type of leaf
enclosed in a chamber covered by any type of material. In the
simulation data that follows, an attempt has been made to use parameters
which might be similar to those possessed by a field bean leaf. The
parameters pertaining to the chamber are those found for a film such as
mylar or Propafilm C. A list of the parameters used and their sources

are list below.

l. Solar radiation, RS=872 W/m2 (Shaw and Decker,1979).

2. Effective sky temperature, Ta= 2 C (observed).

3. Wind velocity in the field, v =l.0 m/s (Monteith, 1973).

h. Wind velocity in the chamber V =0.5, 1.0, l.5 m/s.

5. Length of leaf in direction of wind velocity, l=0.08 m
(observed).

6. Average leaf thickness,hL=l.7xl0-3 m (observed).

7. Specific heat capacity of the leaf,cL=h KJ/Kg-C (for asparagus,
Heldman. l98l).

8. Density of the leaf,pL=l.O3 kg/m (for asparagus,
Heldman. l98l).

9. Leaf stomatal resistance, r =220 s/m (for beans.
Kruiper, l961)

I

l0. Solar absorptivity of the leaf, aL=0.78 (Rosenberg, l97h).

 

50

ll. Solar reflectivity of the leaf, pL=0.22 (Rosenberg, 197A).

12. Infrared emissivity of the leaf,e: =.97 (Davies and ldso, 1979)

13. Solar transmissivity of the chamber cover, T;=0.89
(observed, Propafilm CllO).

lh. Infared transmissivity of the chamber cover, r:-0.75
(observed, Propafilm CllO).

l5. Infrared emissivity of chamber cover, =0.25 (observed,
Propafilm CllO).

l6. Initial chamber air dry bulb temperatures, Td=25 C and 35 C
(low and high values).

l6. Final chamber air dry bulb temperatures, Td=26 C and 36 C
(l C rise observed in field).

17. Initial relative humidities, rh=202 and 80%. (low and
high values).

l8. Time increment, At=0.25 5

l9. Total duration of run, t=36 5 (measurement time used
in field, see chapter h)

20. Chamber cover temperature, Tc=Td=25 and 35 C (assumed

equal to initial air temperatures)

Energy Balance Simulation Run

Running the model using the parameters listed in the previous
section yielded the results graphed in Figures 3.h-3.l3. Figure 3.h
shows the simulated total energy balance of a leaf enclosed in the

measurement chamber for 36 seconds. The initial air temperature and

51

relative humidity were 25 C and 202, respectively. For convenience each
of the initial values of the components of equation 3.l were subtracted
from values obtained during the run, hence showing the change in energy
transfers. The wind velocity over the leaf prior to the chamber
placement was 1 m/s as with all the runs and the chamber wind speed was
l.5 m/s.

Net radiation (see Figure 3.h) is seen to decrease by 58 W/m2
remaining approximateley constant throughout the rest of the run.
Sensible heat transfer from the leaf decreased by #5 W/m2 then increased
above its initial rate at t > 9 seconds. The latent heat transfer from
the leaf also decreased being reduced by ll W/m2 but then increased
throughout the measurement until at t = l6 seconds it became constant
until the end_of the run. The storage term shows a marked drop at the
beginning attaining a maximum negative value of -ll0 W/m2 (recall that
prior to the placement of the chamber the storage term is zero since
steady state conditions exist). The storage term is composed of the
time rate of change of the leaf temperature, the specific heat, density
and thickness of the leaf. Since the last three cited components of the
storage term are constants the storage term can be viewed as a relative
measure of the rate and direction of leaf temperature changes. The
immediate drop in the storage term at the beginning of the run means
that at that point in time the leaf was dropping in temperature at the
greatest rate. Between 0.25 s and 20 s the leaf temperature was
dropping but at a lower rate until at 20 s the leaf began to experience
a temperature rise. The leaf temperature change can be seen in figure
3.6 along with leaf temperature changes for three wind speeds and a high

and low humidity level.

ENERGY CHANGE(WAlTS/SQ M)*102

52

0-9
I

 

 

3

net radiation
sensible heat

3
G

 

 

 

o-
l
A latent heat
assa-
e“—
?_ 4- storage
_ zero line
‘7
T ' I ' I ' I ' I ' I
0.0 8.0 16.0 24.0 32.0 40.0

TIMEESEC]

Figure 3.4 Change in components of equation 3.1
over a simulated chamber measurement where the
initial air temperature, relative humidity and
chamber wind speed were 25 C, 20% and l.5m/s,
respectively.

 

ENERGY CHANGE(WAlTS/SQ M)*102

53

 

 

 

m net radiation

 

 

 

N
cli- 0 sensible heat
latent heat
+ storage
“2
D_ ..
l
- zero line
C!
T l I r I I r i f I
0.0 8.0 16.0 24.0 32.0 40.0

TIMEiSEC]

Figure 3.5 .Change in components of equation 3.1
over a simulated chamber measurement where the
initial air temperature, relative humidity and
chamber wind speed were 25 C, 20% and 0.5m/s,
respectively.

 

51+

Figure 3.5 shows the simulated change in energy with the placement
of the measurement chamber for a chamber wind velocity, initial air
temperature and relative humidity equal to 0.5m/s, 25 C and 202,‘
respectively. From this plot it can be seen that near the end of the
run the latent heat transfer became approximately equal to the storage
term. This means that the net radiation and sensible heat transfer were
equal but opposite in sign.

At the highest chamber wind speed the leaf temperatures are seen to
decrease throughout the first half of the run and increase during the
second half (see Figures 3.6 and 3.7). The initial decrease was due to
the sudden increase in sensible and latent heat transfer from the leaf.
The increase in heat transfer tended to decrease the leaf/air vapor
pressure and temperature deficits thereby causing the leaf temperature
to increase during the last half of the run. At the lowest wind speed
the latent and sensible heat transfer suddenly decreased so the leaf
experienced a rise in temperature throughout the run. The rate of
increase was, however, most extreme at the beginning and became
approximately constant during the last half of the run due to the
increasing rates of heat transfer. When the chamber wind speed was
equal to the field wind speed the leaf temperature is seen to remain
closest to the original leaf temperature. The slight drop in leaf
temperature at the beginning of the run was due to the reduced radiation
load on the leaf.

Figures 3.6 and 3.7 also clearly show the effects of relative

humidity and initial air temperature on leaf temperature. The high

 

 

55

relative humidity produces a low vapor pressure deficit and resulted in
an elevated initial leaf temperature relative to the low humidity
condition. The air temperature also plays a part in determining the
initial leaf temperature and from the figures it can be seen that the
higher initial air temperature causes higher initial leaf temperatures.
At the higher initial air temperature at 20% relative humidity the
initial leaf temperature is very close to the air temperature. From
this it is reasonable to assume that the cross over for the leaf and air
temperatures (i.e. when they are equal) is probably near 36 C at 202
relative humidity and a wind velocity of 1 m/s (Drake et al.,1970).

As mentioned above the leaf/air vapor pressure and temperature
deficits change as a result of the changing leaf and chamber air
temperatures and are shown in figures 3.8 and 3.9 for the 25 C initial
air temperature runs. Wind can be seen as a controlling factor for the
0.5 m/s run where. notwithstanding the fact that the leaf/air vapor
pressure deficit increased, a leaf temperature rise still occured over
the run. This can be explained by the large initial reduction in latent
heat transfer due to the decreased wind speed. which could not be offset
by the increasing rate of transpiration over the run (see Figure 3.10).
The chamber wind speed alters the thickness of the unstirred boundary
layer at the leaf surface which controls the rate of heat transfer.

From a practical stand point the latent heat transfer is highly
important since the latent heat transfer divided by the latent heat of
vaporization yields the leaf transpiration rate. Figures 3.10 and 3.11
show the latent heat transfer during a run for 20 and 803 relative
humidity for the three wind velocities and an initial air temperature of

25 C while Figures 3.12 and 3.13 show the same but for an initial air

56

 

 

 

 

 

LERF TEMPERRTURElC]

 

 

‘7 T I T I

l l
0.0 8.0 16.0 24.0 32.0 40.0

TIMElSEC]

Figure 3.6 Leaf temperature changes over simulated chamber
measurements for two levels of humidity and three chamber
wind speeds where initial air temperature was 25 C.

LERF TEMPERRTUREEC]

57

 

ID
é
rh=80%

c3

8‘ m 0.5m/s
0 1.0m/s

"3 A 1.5m/s

$—

 

 

 

 

l I I I
0.0 8.0 16.0 24.0 32.0 40.0

TIMElSEC)

Figure 3.7 Leaf temperature changes over simulated
chamber measurements for two initial humidity
levels, three chamber wind speeds and initial air
temperature of 35 C.

VAPOR PRESSURE DEFICIT (P0)

2.0

58

 

  
  

 

 

 

 

 

 

 

1
rh=20% __
m QSm/s
0 LOm/s
A LSm/s .
__ l
— rh=80%
I r j 1 I I I ' I l
0.0 8.0 16.0 24.0 32.0 40.0

TIMElSEC]

Figure 3.8 Vapor pressure deficit changes over
simulated chamber measurements for two initial
humidity levels, three chamber wind speeds and
initial air temperature of 25 C.

TEMPERATURE DEF I C I T l C l

59

 

 

‘1‘
O)
rh=80%
e;:.
0 ‘E‘c.
PM El 0.5m s
(D
0 1.0m/s
‘ LSm/s
‘9-
ID
02‘ ‘;;:;“3;;.._.
* 5“--
rh=20%
‘3’
m r r I l r
000 800 1690

1
24-0

TIMElSECl

Figure 3.9 Temperature deficit changes over
simulated chamber measurements for two initial
humidity levels, three chamber wind speeds and
intial air temperature of 25 C.

60
temperature of 35 C. The negative latent heat transfer values shown in
figures 3.10-3.13 imply energy leaving the leaf. For the rh=202,
T =25 C run the change in wind speed due to the chamber had a large
effect on altering the rate of latent heat transfer but almost as soon
as the change occurred other parameters began to control until at around
20 seconds the rates for each wind speed became similar. This might
lead one to assume that the rates of transpiration were approaching some
similar value with time but from figure 3.11 we see this is not true,

but that there is a strong dependence on the humidity level of the air.

In an actual measurement chamber the typical way of obtaining the
rate of evapotranspiration is by observing the change in humidity over
the period of the chamber measurement within the chamber. If the rate
of leaf transpiation decreases as shown (fig. 3.10, 0.5 m/s wind speed)
then the actual rate of humidity increase in the chamber will also be
decreased and the measurement will be an underestimate of actual field
ET. In fact the calculations indicate that the 1.5 m/s chamber wind
velocity in figure 3.10 would yield an integrated quantity of energy (or
water) closest to that of the actual rate or field rate over the same
time interval.

At the higher humidity (see Figure 3.11), the latent heat transfer
under the 1.5 m/s chamber wind speed, although increasing slightly at
first, decreases throughout the measurement. Since the diffusion
resistance becomes constant after its initial change all further change
in the latent heat transfer can only be due to the vapor pressure

gradient between the leaf and the air. The leaf temperature, which is

LATENT HEAT(WATTS/SQ M)*102

61

 

 

 

 

 

“J
V s
I l u c
9 ii“:
w.—
I
n ’4 .d/‘
e “
t-l "
l ‘1
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*-d
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E! 0.5m/s
“3
d 0 O
T 1 Om/s
i ‘ 1.5m/s
°.’
T ' I ' I F T ' l a I
0-0 8-0 16-0 24-0 32-0 40-0

TIMElSECl

Figure 3.10 Latent heat transfer changes over
simulated chamber measurement for three chamber
wind speeds, inial initial relative humidity of 20%
and initial air temperature of 25 C.

LATENT HEAT(WATTS/SQ M)*102

 

62

,..-I-_;_;_..__---
.__,-—
.,-

 

~ m 0.5m/s
«'3- ‘-_.. 0 1.0m/s
I ‘~-_ A .5m/s
of ‘22.”:3'4:
‘1’ . I ' I ' I ' I j I
0.0 8.0 16.0 24.0 32.0 40.0

TIMElSEC]

Figure 3.11 Latent heat transfer changes over
simulated chamber measurement for three wind
speeds, initial relative humidity of 80% and
initial air temperature of 25 C.

63

 

    

0 1.0m/s
e 1.5m/s

LATENT HEAT(WATTS/SQ M)*102

 

T

“603
_l__

I I I ' I ' I
0-0 8-0 13-0 24-0 32-0 40-0

TIMElSECl

Figure 3.12 Latent heat transfer changes over
simulated chamber measurements for three wind
speeds, initial relative humidity of 20% and
initial air temperature of 35 C.

 

LATENT HEAT(WATTS/SQ M)*102

 

 

“309

6A

a
'- " v u— - - - - V ‘9 ‘— u— —
a ‘ _, d ‘1 "
d u-
4

_
- -
-_—' ......
u._._

 

0-0

T l T

l T
8-0 16-0 24-0 32-0 40-0

TIMElSECl

I

Figure 3.13 Latent heat transfer changes over
simulated chamber measurements for three wind
speeds, initial relative humidity of 80% and
initial air temperature of 35 C.

65

higher than the air temperature, drops rapidly at t=0.25 seconds (see
Figure 3.6, rh=80%, v=1.5m/s) and so the saturated vapor pressure
(calculated at the leaf temperature) at the leaf's surface decreases.
The air temperature increases linearly throughout the run yet so does
the wet bulb air temperature and increases by the same amount so the
vapor pressure of the air changes as the saturated vapor pressure of the
air calculated at the wet bulb temperature. This is because the wet and
dry bulb air temperature deficit ramains constant (see equation 2.5).
Therefore if the leaf saturated vapor pressure decreases as a result of
a decreased leaf temperature and the air vapor pressure increases with
the saturated vapor pressure of the air at the wet bulb temperature then
the vapor pressure deficit also decreases. At the low chamber wind
speed the opposite is true . The leaf saturated vapor pressure
increases and the response of the vapor pressure of the air remains as
before, thus giving a leaf/air vapor pressure deficit which is
increasing at a slower absolute rate. The result is that the absolute
value of the rate of change of the leaf/air vapor pressure deficit is
greater for the higher chamber wind velocity than for the low chamber
wind velocity.

In Figures 3.10-3.13 the alteration of the latent heat transfer at
the beginning of the run is less for the 1.5 m/s than for the 0.5 m/s
chamber wind speed. This is due to the relationship of wind velocity to
the thickness of the unstirred boundary layer. In Chapter 2 the
thickness of the boundary layer was shown to be inversely proportional
to the square root of the wind velocity over the surface of the leaf.

The result is that, for increasing chamber wind speeds, the boundary

 

66
layer resistance approaches zero while the diffusion resistance
approaches the stomatal resistance. ‘With increases in wind speed a
reduced overall effect in latent heat production will be observed.

Figures 3.12 and 3.13 show the simulated latent heat production
rate over the measurement interval at the 2 humidities and 3 chamber
wind speeds for a 35 C initial air temperature. These figures clearly
show how the wind has a greater effect at the lower humidity level and
this is simply a result of the larger vapor pressure deficits at 202
relative humidity. Since the change in the chamber wind speed results
in the same boundary layer resistance and therefore the same diffusion
resistance for both humidity levels and since for the 20% relative
humidity a larger vapor pressure deficit exists, then a larger initial
change in latent heat transfer must result. At the higher humidity
level the subsequent changes in the latent heat transfer are seen to be
more severe. This is due to the larger changes in the vapor pressure
deficits (see Figure 3.8).

In using an actual measurement chamber the fans used for mixing the
air may either be running when the chamber is put into place (similar to
Reicosky, 1977) or they may be left off until the chamber is in place
and the measurement started (similar to Peters, et al. 197A and
Schulze, 1978). In the first case the leaf experiences the change in
wind speed before the measurement begins while in the latter case the
leaf experiences an increase or decrease in wind speed from t=0. Since
the fans take a few seconds to reach their operating speed or mixing
rate the effect is more gradual. In addition, and pertinent to both
cases, the speed at which the air moves over the leaf may vary with

time. In order to obtain a working model we have assumed that the fans

 

 

67
produce a constant wind speed over the leaf, that they are started at
t=0 and require one time increment to reach their operating speed.

The components of equation 3.1 for a leaf in an actual measurement
chamber probably begin to change before t=0. If the chamber is
suspended over the crop, the incident radiation may be reduced. As the
chamber is being placed the wind velocity profile in the canopy changes
which may alter the the ongoing processes at the plant leaf surface. In
the development of the model this had to be ignored by assuming the
placement of the chamber to be instantaneous. And finally, the leaf
stomatal resistance, though known to change with leaf temperature, was
held constant. Holding stomatal resistance constant was done based on
resistance changes determined by a regression given by Drake, et
al.(l970) when leaf temperature was increased by l C. The resulting
changes in stomatal resistance were about 5%. Since stomatal resistance
is primarily determined by stomatal aperture, and it is not known how
quickly or hif the stomatal aperture changes with the placement of a
measurement chamber. the decision to hold stomatal resistance constant
appears justified. A

A question might be raised as to the nonlinear rates of latent heat
transfer during the simulation runs shown in Figures 3.10-3.13, in light
of the fact that researchers have observed linear increases in vapor
density within the chamber during the chamber measurement. Peters et
al.(l97h) and Reicosky and Peters(l977) inferred that the linear
increase in vapor density within the chamber meant that the chamber
environment was not adversely changing the ET rate. The latent heat
transfer rates shown in Figures 3.10-3.13 are shown at descrete points

in time, whereas the production of vapor within the chamber is measured'

68
on a cumulative basis.

Figure 3.lh shows the instantaneous latent heat transfer values
which were given in Figure 3.11 on a cumulative basis. Shown in this
way, the latent heat production appears approximately linear. Comparing
the curves calulated for the three chamber conditions to the curve for a
leaf outside the chamber, each is seen to have a different slope.
Therefore, a linear vapor density slope (which is used to determine the
ET rate) does not imply that the ET rate measured is the same rate of ET
which existed prior to chamber placement.

Despite the numerous assumptions required for the model's
development, the model seems to illustrate logical trends which would
occur for a leaf enclosed within a measurement chamber with regard to
its energy budget.

To summerize and comment on the information discussed in this
section:

1. A leaf enclosed in a measurement chamber was shown to experience a
lower net radiant energy input because the portion of visible and
infrared radiation from the sky, that was not transmitted through the
chamber cover, was greater than the infared radiation emitted from the
chamber cover towards the leaf, thus a drop in net radiation. The
change in the leaf temperatures, which were typically < l C, caused the
net radiation (an energy input) to decrease slightly over the simulated
chamber measurement period with increasing leaf temperatures, and caused
an increase with decreasing leaf temperatures.

2. Leaf temperatures decreased for a wind speed greater than that
existing over the leaf before the chamber placement, whereas a lower

chamber wind speed caused an increase in leaf temperatures. In addition

 

 

69

asM/s
LCM/s

LSM/S
WHHOUT CHAMBER

G

D

LRTENT HERTIJ/SG I‘llx101

 

 

0.0

I T I I

I I I
0-0 8-0 16-0 24-0 32-0 40-0

TIMEISECJ

Figure 3.14 Cumulative latent heat produced over simulated
chamber measurements for three wind speeds, relative
humidity 80% and initial air temperature 25 C.

70
to the leaf temperature changes due to the initial radiation changes,
the initial change in wind speed caused either an increase or decrease
in the unstirred boundary layer at the leaf surface which changed the
rate of sensible and latent heat transfer.
3. Leaf temperature changes as well as the leaf/air vapor pressure and
temperature deficits changed nonlinearly during the first half of the
simulation runs but became linear during the second half. This was due
in part to the relatively small leaf thickness which allowed for high
temperature changes with respect to time.
A. The lowest chamber wind Speed reduced and the highest chamber wind
speed increased initial values of latent heat transfer from the leaf.
These changes occurred virtually instantaneouSly since the change in the
boundary layer thickness can occur rapidly (0.25 s which was one time
step).
5. The lower chamber wind speed changed the latent heat transfer more
than the higher chamber wind speed even though each was 0.5 m/s
different than the initial wind speed over the leaf. The reason for
this is that as wind speed increases the boundary layer resistance
approaches zero leaving only the stomatal resistance (assumed constant)
to control latent heat transfer.
6. After the initial resetting of the boundary layer resistance and
incoming radiation, further changes in sensible and latent heat transfer
resulted mainly from changes in the leaf/air vapor pressure and
temperature deficits.
7. The average change in the latent heat transfer for the three wind

speeds, two humidity levels and two initial air temperatures was between

 

7l

5 and 15 2 below initial latent heat transfer values. The decreases
observed were due to the particular conditions used and we shall see in
chapter 5 that large overestimations relative to initial values may also
occur.

8. When the latent heat production was shown on a cumulative basis the
curves appeared to be linear. Researchers have incorrectly assumed that
the linear increase of vapor density within the chamber meant that the
ET rate measured was the same as the ET rate that existed prior to the
placement of the chamber.

From these results it appears that a leaf enclosed within a
portable measurement chamber has the capacity to respond rather quickly
(mainly due to its small thickness) to changes made in its microclimate
and the placement of a measurement chamber over a group of plant leaves,

therefore, has the potential to cause error in ET estimation.

wtvu

CHAPTER A

DESIGN, CONSTRUCTION AND TESTING OF A

PORTABLE MEASUREMENT CHAMBER

In May of 1982 construction was begun on the MSU portable
evapotranspiration measurement chamber and a boom structure for chamber
suspension and positioning. The equipment was ready for use in mid-July
of that same year. The goal of the project during that first summer was
to get the system operational, to identify problems with the measurement
and transport equipment, and to minimize or correct these problems.

The design used here is similar to the design used by Peters, et
al.(l97h) and Schulze(1978) in some respects. Both of these designs
positioned the chamber over or around the crop with part of the chamber
open. The chamber was then sealed shut immediately prior to the chamber
measurement. In the case of Schulze(l978) little mention was made as to
the reason for the removable lid. The rationale may have in part been
due to the fact that the chamber was put in place manually by two
people, thus breaking the chamber into two sections made it more
managable. Peters, et al.(l97h) required the open front and back sides
of their chamber since the chamber ran on tracks through the field. In
the case of the design to be discussed here, the reason for the closable
top is solely for the purpose of minimizing alteration of the crop
microclimate. Figure h.l shows the various components of the Michigan
State University portable measurement chamber system positioned in the

field about to obtain a measurement.

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Materials and Methods

A lightweight 2.5h cm diameter tubular aluminum frame was
constructed to support a film plastic material. The film formed a
transparent chamber which could be set over a group of plants to trap
water vapor being given off. A frame measuring l.22xl.22xl.52 m
provided the basic unit in which instruments were mounted and was used
for measurements over low growing crops including potatoes, soybeans and
turfgrass. Another frame measuring l.22xl.22xl.83 m was attached to the
smaller chamber to make a taller unit for use with corn. The combined
chamber measured 1.22x1.22x3.35 m. Figure h.2 shows the single smaller
chamber with dimensions. By welding gusset plates to the chamber
corners through which diagonal tension wire was strung, the chamber
frame was kept square and rigid.

The chamber was covered with Propafilm C110 donated by ICI Americas
Inc. The film plastic was attached to the chamber using double stick
transparent cellophane tape.

The selection of the film was based on tests run with a Beckman
BD-GT grating spectrophotometer which revealed the film's capacity to
transmit long wave radiation well. Figure h.3 shows the transmissivity
of the film for wavelengths between 2.5 and 16 microns. The integrated
average infrared transmissivity of the film was determined to be 753
compared to Plexiglass and Lexan which transmitted about 10%. In the
range from 0.7-2.5 microns the transmission characteristics of the these
materials could not be obtained as the necessary equipment could not be

found to run the test.

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77

A test was also run to determine the solar transmissivity of the
film with changing beam angle (see Figure A.A). The test was run with a
Licor pironometer positioned 25 cm from a LOO-watt high pressure sodium
lamp. With the film plastic positioned between the sensor and the lamp,
its angle was varied with respect to the light beam through 70 degrees.
From 70 to 90 degrees the measurement could not physically be obtained
so the curve was extrapolated to 0% transmission at 90 degrees and is

represented with a dashed line.

Chamber Top Unit

The chamber top could be opened and closed. A separate unit
consisting of a roller for rolling back the film and a magnetic seat for
closure as the film unrolled across the top was constructed and attached

to the top of the chamber frame. Figure h.5 shows the chamber top unit.

A spring loaded aluminum roller mounted in a small chassis with a
sliding door track on each end held a roll of the film plastic. A strip
of 1.9 cm wide spring steel was taped onto the edges of the film. The
spring steel contacted a magnetic strip mounted around the top of the
frame sealing the plastic down as the roller moved across the frame and
unrolled the film. The two ends of a light twisted wire cable were
attached to the two sides of the roller chassis. The wire cable was
double wound around a small pulley on a reversible DC motor to open and

close the top. The motor rested on a bar fixed to the top frame which

allllllilil‘ ‘

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I'I'I'I'I'I'I'I'i
10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

RNGLE 0F INCIDENCE

I

Figure 4.4 Percent transmission of visible .
radiation vs.- angle of incidence for Propafilm
CllO.

spring steel

roller track

roller chassis

plastic film

 

 

Spring loaded l

roller

magnetic strip

80
also served as the mount for the cable from which the chamber was
suspended for raising and lowering. Limit switches were placed at the
ends of the roller chassis track to stop the travel of the roller frame.
The entire top unit was bolted to the top of the chamber frame. A
switch to reverse the direction of travel and activate the roller motor
was placed at the bottom of the chamber and was actuated when the

chamber was lowered to or raised from the ground.

Chamber Bottom Unit

A separate bottom unit was constructed which held a 10 cm layer of
foam rubber which served as a ground seal around the bottom of the
chamber during the measurement. The unit was easily attached to the
bottom of the chamber frame using small lag bolts and thumbnuts. Eye
bolts were welded to the four corners of the unit which served as gaff
pole catches to control the movement of the chamber in the field while
keeping people several meters away from the point of measurement.

Figure A.6 shows the chamber bottom unit separate from the chamber.

Suspension Structure

A tractor mounted suspension structure was built to suspend the
chamber above the crop and lower it into place for measurement. The
suspension structure is shown in Figure A.l, along with the chamber and

farm tractor used for support and mobility. Rigid television antenna

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82

tower sections were used for the suspension tower. The tower sections
could be increased in height to accommodate the tall chamber by adding
additional sections. The original cross bracing was reinforced at
points of critical stress. A 37.3 watt (1/20 HP) permanent magnet
reversible motor was used to move the chamber laterally on a trolley set
inside a heavy-duty rolling door track on the horizontal boom section.
The chamber was raised from or lowered to the ground using a braided
wire cable connected to a hh50 newton (lOOOlb.) capacity 12 volt DC
winch. The winch was rigidly attached to a plate on the trolley in the
door track.

The vertical portion of the tower structure rested in a steel three
point hitch connected frame which prevented the tower from tipping and
provided for rotation (see Figure h.l). The bottom of the tower was
positioned on a steel plate which rested on a rotation bearing. The
structure was made to rotate about its vertical axis by use of a
manually operated chain and sprocket attached to the lower portion of
the suspension structure support frame. After the boom was rotated to

the desired position, a brake could be set to avoid further rotation.

Chamber Measurement Equipment

The determination of the vapor density within the chamber was
accomplished using an aspirated thermistor psychrometer. The
psychrometer consisted of a 2 cm inside diameter aspiration tube with a
small attached water reservoir. At the rear end of the tube the intake

3
of a 2500 cm /s DC fan was attached. The resulting wind velocity over

83
the two thermistors positioned in the tube was 8 m/s. The thermistors
were rigidly placed within the tube along its central axis separated by
5 cm. The thermistor closest to the aspiration fan was enclosed in a
cotton jacket shoelace which was connected to the water reservoir. The
entire psychrometer was placed within a short section of Hancor Archflow
white drain tile to eliminate radiation heating. A data logger was used
to collect thermistor data which was subsequently written to a magnetic

tape for storage.

Chamber Mixing

Two .065 mé/s fans were used for mixing the air inside the chamber
over the measurement interval. Each fan was attached to a rod located
at opposite corners of the chamber by means of laboratory clamps. The
clamps allowed the fans to blow in any direction and were also
vertically movable along the length of the rod. The theoretical mixing

rate of the l.5h and 3.35 m chambers were 3.5 and 1 cycles per minute,

respectively.

Measurement Technique

The chamber was positioned over the crop with the tractor mounted
boom structure. The chamber was lowered with the top open and the fans
off to prevent expelling air from the crop canopy. Upon contact with
the ground the top closed automatically and the fans started when the
top had completely closed. Data collection was begun upon top sealing
and continued for 36 seconds while 95 paired values of wet bulb and dry

bulb temperatures were logged. The data collected were transferred to a

84
magnetic tape from computer memory after completion of data collection.
The chamber was then raised above the crop, the top opened and the fans
turned off after purging the chamber. Two or three runs were completed
on the same plants and averaged to achieve measurement of the ET rate at
that time of day. A new group of plants was usually selected for the

next measurement one time Increment later.

Data Interpretation

The raw data stored on the tape was transferred to a microcomputer
and converted to temperature in degree centigrade via emperical formulas
derived from thermistor calibration data. Each discrete sample
consisted of a measurement of dry bulb temperature, wet bulb temperature
and the absolute time. The vapor pressure of the air in the chamber was
calculated using a rearranged form of the psychrometric equation and was
given as equation 2.5. The change in the vapor pressure of the chamber
air with time was then used in the ideal gas equation to obtain the
slope of the vapor density increase within the chamber. Dividing the
expression by the density of liquid water and multiplying by the ratio
of chamber volume to the area of the chamber base, the ET rate was
obtained as an equivalent depth of water per unit time. The equation

used to obtain ET estimates from the chamber is given below:

ET = (l8.0V/RpowA)de/dt (h.l)

where

85

ET chamber estimated ET (cm/hr)

e = vapor pressure of chamber air (Pa)
t a time (hr) ‘

r) = density of liquid water (g/cm3)
Td a dry bulb temperature of the chamber air (K)
R = universal gas constant (Pa-cm3/mole-K)

V a chamber volume (cm3)

A = area of chamber base (cmz)

de/dt vapor pressure slope over chamber measurement (Pa/hr)

The computed water depth-time data pairs were curve-fitted using a
linear least squares approximation. The result is a slope of a line
(given by ET in equation h.l) representing the increase in water vapor
in the chamber over the measurement time in centimeters per hour.
Plotting the individual slope values against the time of day and
integrating allowed computation of the total daily ET as an equivalent

water depth.

Chamber Performance Verification

The chamber was used in East Lansing and Montcalm County, Michigan
for estimating daily water use for corn, soybeans and potatoes. The
data collected were, however, not reliable since a complete chamber
calibration had not been performed. It was felt then that the most
important goal that first season, after attaining operational status,
was to test the chamber against a reliable control. On August 29, 1982

the chamber was tested against a corn covered weighing Iysimeter at the

86

ARS Experiment Station at Coshocton, Ohio. The sky was very clear
during the day of the test with a high temperature near 30 C. Figure
A.7 shows the point measured values of ET obtained from the portable
chamber and average hourly ET values from the Iysimeter on August 29
plotted throughout the day. By interpolation a line connecting the
values was drawn and the area under the curve integrated over time. The
test data obtained showed the weighing Iysimeter lost 0.38 cm of water
while the chamber estimated 0.h3 cm of water loss. Thus the chamber
overestimated the ET rate as compared to the weighing Iysimeter. No
attempt was made to smooth the daily ET curve; however, this may
possibly be a means to improve the estimate.

Due to the late stage of growth the corn had attained, coupled with
the near frost conditions ocurring nightly and several electrical and
mechanical problems encountered, only the one day's data was obtained
for comparison. This experience pointed out the need for a controlled
experiment where statistically based information could be obtained.

The overestimation by the open top chamber measurement which
converted to a 16% difference was larger than that reported by
Reicosky(1981) for his closed top chamber when tested in Minnesota next
to a weighing Iysimeter. This indicates that there may possibly be an
inherent flaw in our open top approach.

Data collected during a three hour period at Coshocton with the top
closed similar to Reicosky's approach is shown in Figure A.8 compared to
the opentop chamber and Iysimeter ET values for the same time period.
The figure shows that the closed top approach consistently measured
lower rates of ET than did the open top. From the closed top data there

is reason to believe that before the measurements were taken, the

0.75

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0-45

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ETICll/HRlarlU'1

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AUGUST 29, 1982 o
COSHOCTON, OHIO
CHAMBER
o LYSIMETER

 

 

o rFr—rIrI—r'l—rr—[fiFI—l—r
1.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0

TIMEIHR]

Figure 4.7 Comparison of ET measured with chamber
(opening top design) with weighing lysimeter over
the day for August 29, 1982 at Coshocton, Ohio.

ETICll/HRJXIO"

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10-0 11-0 12.0 13.0

TII‘lEIHRl

Figure 4.8 Comparison of ET measured by chamber
with closable top, chamber with permanently closed
top and weighing lysimeter, for three hours on
August 29, 1982 at Coshocton, Ohio.

89
chamber was not properly purged of the moist air from the preceeding
runs and therefore the lower rate may be due to the lower vapor pressure
deficits during the runs. In order to identify possible problems
associated with the open top approach, a laboratory experiment was

planned and will be discussed in the next chapter.

CHAPTER 5

LABORATORY EXPERIMENT

A laboratory experiment was desirable in which certain
environmental parameters could be controlled and enough replications
made to yield statistically valid information about the chamber effect
on crop ET.

Questions that needed to be answered were: Does the chamber create
an artificial environment which yields chamber data which is not
representative of the crop? Does the succesive lowering of the chamber
over the crop for a 36 second period at 15 minute intervals alter the
crop physiology thereby altering the rate of transpiration? Is there a
significant difference between the open top and closed top approaches as
measured in chamber performance? (The initially open top approach is
similar to the methods used by Peters et al.(197h) and Schulze(l978)
while the top always closed approach is similar to the method used by
Reicosky(l977)). Does the chamber alter ET more with respect to a
control under no-wind or wind conditions? How is leaf canopy
temperature affected by the chamber? If changes in the canopy
temperature occur, is there a significant difference between the mean
temperature changes for the open and closed top approaches? The
information obtained by answering these questions is valuable and will
help to determine appropriate field measurement procedures and under

what conditions the chamber may or may not give reliable ET estimates.

9O

91

To answer these questions two experiments were performed. The
first consisted of lowering the chamber over a treatment group of potted
plants which were weighed at the beginning of the replication. A
control group consisting of the same number of potted plants was also
weighed at the beginning of the replication. The control group was
located next to the treatment group, and was exposed to identical
environmental conditions. During the A hour replication the chamber
measurements were taken every 15 minutes on the treatment group.
Whether an open top or a closed top was used for any one measurement
depended upon a previously randomized schedule. At the end of the
replications the pots were again weighed and the amount of water loss
determined.

The chamber measurement system was calibrated using an independent
measure of vapor introduced into the chamber. The reason for this
calibration was to assure that any instrumentation error could be

separated from any error due to plant and microclimate effects.
MATERIALS AND METHODS

Beginning on January 27, 1983 been plants (Phaseolus vulgaris L.,
Seafarer) were grown in the Michigan State University Horticulture
Greenhouse under natural and supplemental lighting. Eighty pots were
seeded with density ranging from 5-8 seeds per pot and a resulting
emergence of 3-5 plants per pot. The soil used was a loam soil with a
1:1 ratio of vermiculite peat and average bulk density of l.h g/cm3.
Supplemental lighting was used to encourage the natural bush like

architecture of Seafarer found in the field. Lighting was accomplished

92
using a high pressure sodium lamp, in combination with a metal haylide
lamp both rated at AOO watts. Plants were periodically rearranged with
respect to the lamp positions in order to eliminate light stratification
effects.

Plants were irrigated with tap water and recieved a 200:5h:187 ppm
constant liquid feed fertilizer mixed with the water every several
waterings. Approximately 3 weeks after emergence the plants were moved
to the Agricultural Engineering Building on the Michigan State
University campus. The plants were illuminated with 1002 artificial
light from the two aforementioned lamps.

During the experiment the plants appeared to be in good condition
with respect to disease and insects although some of the lower leaves
began to yellow and this became more noticeable throughout the
experiment. Plants which were especially small were removed from the
group of 80 during the experiment which lasted in all about two weeks.

The plants left at the end of the experiment numbered about 65.

Evapotranspiration Experiment

From the total group of plants(65-80) AO were randomly chosen for
any given replication. From the ho pots chosen 20 were randomly
selected to be in a control group and the remaining 20 were put into a
treatment group. One of the two groups was randomly selected for
obtaining initial pot weights. After the group was finished being

weighed the other group was similarly weighed.

93

With the completion of the weighing of the pots the chamber with
top open was lowered over the treatment group. Upon ground contact the
top closed automatically, fans were started and the measurement begun.
Over a 36 second period AZ data points for each of 5 parameters were
logged. The parameters were wet and dry bulb temperatures for a
psychrometer positioned at approximatey 30 cm above the crop canopy, wet
and dry bulb temperatures for a psychrometer positioned approximately 10
cm above the crop canopy and crop canopy temperature from an infrared-
thermometer positioned 15 cm above the crop.

Before raising the chamber the fans were switched off an the
chamber top roller motor disabled so that the top would remain closed
while the chamber was raised. The chamber was then lifted above the
crop canopy and held until the next measuremnt 15 minutes later.

_ After fifteen minutes, the chamber fans were started and the
chamber was purged for 30 seconds. The chamber was then lowered with
the top closed and fans on. The subsequent steps were identical to the
first measurement.

For statistical purposes the replication was broken up into 1/2
hour periods. Each 1/2 hour period consisted of 2 measurements with
one an open top and the other a closed top run. The choice of making
the first run an open top or a closed top was determined by the flip of
a coin. Within any of the designated 1/2 hour periods there was always
an open top and closed top run. However, when all the 1/2 hour periods
were put together, which making up the h hour replication, new 1/2 hour
periods resulted which may have contained two open top or two closed top
runs. This method of randomization was seen as the best alternative to

having two chambers run simultaneously side by side. The use of a

9h
second chamber and therefore a third group of plants was not a practical
consideration.
At the end of the h hour replication, the group of pots first
weighed were again weighed and recorded. Then the other group was
weighed, the information recorded and this completed a single

replication.

After the completion of the first experiment which consisted of 5
replications a second experiment was begun where two 45.7 cm fans were
used to produce a 1.5 m/s wind velocity over the plants for the entire A
hour replication. The second experiment also consisted of 5

replications.

EQUIPMENT AND INSTRUMENTATION

During the first A days of the experiment the two lamps were placed
about 1.2 m from the two groups of plants such that each lamp
illuminated either group approximately by an equal amount. The lights
were held at a 30 degree angle from the horizontal at a position of l.2m
from the floor. Lighting for the plants therefore entered the chamber
through one of its sides. 0n the fifth day of the experiment a 3rd lamp
was employed in order to increase transpiration rates and to increase a
statistical block effect within the experiment. When the chamber was
lowered, radiation incident on the plants was found to decrease by 6% as
measured by a model LI 200$ LICOR pyronometer.

Two fans were used to stir the chamber air during a measurement. A
h5.7 cm AC fan was postioned at the top of the chamber and directed air

down at the crop. A 12 volt DC fan was placed in a corner of the

95

chamber at 35 cm from the floor. The average wind speed in the chamber
was found to be approximately 1 m/s. This average was obtained from
horizontal and vertical wind speed measurements at 15 locations in the
chamber. Wind speeds were obtained using a Weathertronics model 2th
hot wire anomometer.

Two psychrometers were used for the collection of wet and dry bulb
temperatures in the chamber. The psychrometers were a redesign of the
psychrometer used during the previous summer. Two water reservoirs were
added. The wicks consisted of 0.3 cm cotton string which was folded
over two of the four thermistors which were routed to the reservoirs.
In addition to the string wicks, a piece of tissue paper was wrapped
around the thermistor beads to insure complete wetting. A third order
polynomial calibration equation was developed for converting the
thermistor resistances to- temperature. The calibrations were
accomplished by submerging the thermistors in a water bath of known
varied temperature. The water temperature was measured to within
+/-0.05 C.

Plant canopy temperatures were collected using an infrared
thermometer aimed at a selected group of plant leaves which included
both shaded and nonshaded leaves. The infrared gun was held
approximately 15 cm above the top of the plant canopy. A calibration
was performed by aiming the gun at a flat black aluminum container
filled with water of known varied temperature. The water temperature
was measured to within +/-0.05 C. It was assumed that the emissivity of
the container was close to that of the plant material and that the
thermal conductivity of the container wall was sufficiently high so that

the wall temperature was the same as the water temperature within the

9231.41?

96
container.

Upon completion of the experiments the thermistors and infrared
thermometor were recalibrated as a double check on the first calibration
and to determine if the instrumentation experienced drift over the
experimental period. The thermistors had not changed during the
experiment whereas it was discovered that the infrared thermometer had
been calibrated incorrecly the first time. In order to be sure that the
experimental results were those due to chamber effects and not due to
chamber equipment error, a calibration was run on the chamber by
releasing a known amount of water vapor into the chamber air via boiling
water from an insulated container placed within the chamber. The
container was placed on a Mettler digital scale and the change in mass
due to the vaporization of water was measured to within +/- 0.1 g.~ The
chamber was periodically purged when humidity levels became high. It
was felt that water vapor which was produced from the boiling water
represented a forced vapor source which could not be controlled by the
chamber environment as perhaps plants might. The calibration curve for

the chamber is given in Appendix 8.

RESULTS AND DISCUSSION
The laboratory experiments performed provided data which aided in
answering the questions posed at the beginning of the chapter. The
statistical design used for analyzing the evapotranspiration data was a
randomized complete block design along with a Least Significant
Difference (LSD) test for comparisons between treatments. The four

treatments were:

97
l. The group 1 ET obtained by weighing each of the pots at the
beginning and end of the replication.
2. The group 2 ET obtained by weighing each of the pots at the
beginning and end of the replication.
3. The group 2 ET as measured by the chamber using the initially open
top approach.
A. The group 2 ET as measured by the chamber using the tap always
closed approach.
For convenience the legend given below summarizes the abbreviations
which will be used in referring to the treatments, and the reader may

wish to refer to it from time to time while reading this chapter.

Treatment Legend
WPl . . . . . . . . . . Weighed pots group 1
WPZ . . . . . . . . . . Weighed pots group 2
CHZOT . . . . . . . . . Chamber open top group 2
CH2CT . . . . . . . . . Chamber closed top group 2
The physical arrangement used in Experiments 1 and 2 is illustrated in
Figure 5.1.
Experiment 1 consisted of determining the water consumption from
the plant groups 1 and 2. Evapotranspiration was measured from group 1
by observing the change in mass of the potted plants over a h hour
period(treatment WPl). Evapotranspiration from group 2 was determined
by the same method as group 1(treatment WP2) and in addition ET rates
were obtained by use of the chamber(treatments CH20T and CH2CT).
Experiment 1 was run under a no-wind condition (i.e. the movement
of air could not be detected by a hot wire anomometer). A summary of

the test of significance and the analysis of variance (ANOVA) table for

Experiment 1 are shown in Table 5.1. A block design was chosen with

 

98

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99
time as the block since from day to day the conditions in the laboratory
tended to vary. Conditions which could not be controlled completely
were air temperature, relative humidity, and soil moisture which varied
from moist for some replications to dry to the touch for others. The
block effect was found to be highly significant which confirms the
appropriateness of the statistical design chosen. The values shown are
means taken over 5 replications and are in grams of water. The

underscore indicates no significant difference found at the 52 level.

The two psychrometers were compared by using a t-test over the 5
replications in Experiment 1 and the difference was not significant at
the 52 level. The fact that the data from the two psychrometers was
similar indicates that the air was not stratified with respect to vapor
density. The use of two psychrometers also acted as a double check and
would have revealed equipment problems if the measured temperatures had
been grossly different. Since the data gave similar, results only the
data from the upper psychrometer has been used in obtaining the chamber
data shown in Tables 5.1 and 5.2.

In Experiment 2 the plants were exposed to an average wind speed of
1.5 m/s measured at the top of the plant canopies. The block effect was
found to be significant at the 5% level over the 5 replications. A
summary of the test of significance and the analysis of variance (ANOVA)
for Experiment 2 are shown in Table 5.2. The values shown are means
taken over the five replications and are given in grams of water. The

underscore indicates no significant difference at the 52 level.

100

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102

The data given in Tables 5.1 and 5.2 are shown graphically in
Figures 5.2-5.5.

From Tables 5.1 and 5.2 it can be seen that no significant
difference was found between treatments WPl and WPZ. From these results
we may conclude that permanent or long term stomatal closure did not
occur in the leaves of the group 2 plants as a result of the their
successive enclosure within the measurement chamber. The implications
of these findings may be important in the field where, for matters of
convenience, it is desirable to obtain measurements over the same group
of plants for an extended period of time rather than moving to a new
group of plants after each measurement. These results should however be
viewed with caution since during the experiment the plants were exposed
to a very low level of visible radiation, which may have translated into
high stomatal resistances. If this were the case, then the effects of
the chamber to. reduce the visible radiation may not have been a
significant factor in altering stomatal resistance.

From the two tables we see that under the no-wind condition the
chamber measurement resulted in a serious over-estimation of ET (see
Figure 5.3). The results of the wind experiment on the other hand
indicate that the chamber estimated the actual ET much more closely (see
Figure 5.h). The gross over-estimation of ET by the chamber in
Experiment 1 can be at least partly attributed to the sudden reduction
in the unstirred boundary layer over the leaf surfaces caused by the
chamber fans.

A large change in transpiration was confirmed theoretically by

employing the computer model described in Chapter 3. By using the

NPZlG/4HRlak102

103

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8‘ '1' wind
. no—wind E

 

 

 

2-0

' r

T r ' I I ‘
200 ‘02 8“ 806 1008 1300

NPllG/4HRlx102

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Figure 5.2 Comparison of treatments WPl and WP2.

CHRI’IBERI G/4HR larlC]2

101+

 

 

 

 

O
:3
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.A
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2.0 4.2 0.4 8.6 ‘0.8 13.0

NPZIG/4HRi3K102

Figure 5.3 Comparison of CHZOT and CH2CT
treatments with treatment WPl for Experiment 1.

CHRMBERIG/ZIHRlxlU2

105

 

 

 

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Figure 5.4 Comparison of CHZOT and CH2CT
treatments with treatment WPl for for Experiment 2.

 

CH2CTIG/4HJBK102

106

 

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Figure 5.5 Comparison of CHZOT and CH2CT
Treatments for Experiments 1 and 2.

107

appropriate quantity for the solar radiation input, the average
laboratory ceiling temperature for the effective sky temperature, and
the actual average wet and dry bulb temperatures obtained for several of
the no-wind measurements, the over estimation of transpiration for a
single leaf can be determined. The data used in the simulation run
were: 20.0 W/m (observed in the laboratory) for solar radiation, 28 C
for the average ceiling temperature, the average wet and dry bulb air
temperatures obtained during the first seven runs of the first
replication of Experiment 1 (consisting of both CHZOT and CH2CT
measurements), the laboratory wind speed which the leaf was initially
exposed to assumed .05 m/s, a chamber wind speed of 1.0 m/s , a
measurement interval of 36 seconds and a stomatal resistance of 330 s/m
which is considered a upper limit by Kruiper(l96l) for beans. Figure
5.6 shows the graphical comparison of the change in latent heat transfer
during one of the runs from which the average temperatures were
obtained.

By integrating the latent heat transfer over the measurement
interval and dividing by the latent heat of vaporization the total
quantity of water per unit area is found. The average calculated over
estimation of leaf transpiration was 65% relative to the initial
condition transpiration.

Since the model considers a single leaf and not the whole canopy, a
high degree of correlation between the model and laboratory results was
not expected. The use of the model here is only to show that,
theoretically, altering the plant environment, the ET (or transpiration)

rate can be seriously affected over the short measurement interval.

108

 

00 El WITH CHAMBER
“‘ WITHOUT CHAMBER

LRTENT HERTIN/SQ M]
6

 

0.0

 

I I fi I I

I 1
0-0 ' 8-0 18-0 24-0 32-0 40-0

TIMEISEC]

Figure 5.6 Latent heat transfer changes over simulated
laboratory chamber measurement. Data is shown for a leaf
inside and a leaf outside the chamber.

109

In Chapter 3, a nonlinear change in latent heat transfer, which was
produced by the presence of the chamber, resulted in an approximately
linear curve when plotted on a cumulative basis. Figure 5.7 shows the
instantaneous latent heat transfer values from Figure 5.6 plotted on a
cumulative basis. The slopes of the two curves shown are dramatically
different and clearly illustrate the flaw in assuming that a linear
increase in vapor density within the chamber implies an accurate
estimate of ET.

The estimation error which might be expected in the field would
probably not be as great as that found in the laboratory since the
average field wind speed may, on the average, be 5 to 30 times greater
than the small wind speed attainable in the laboratory. The typical
average wind velocity found in a bean field might be 0.25-l.5 m/s.
Using a wind velocity of 0.75m/s, 872 W/m2 for solar radiation, 2 C for
the effective sky temperature, a 36 5 measurement time, a chamber wind
speed of 1 m/s (observed in the l.5h m chamber), and the initial wet and
dry bulb temperatures 30 and 2h C respectively with subsequent increases
of l C over the run, the model predicts that the transpiration produced
over the chamber measurement is 6% under that of a leaf not enclosed in
the chamber. This slight underestimation indicates that the chamber
technique will probabaly give more accurate results under field
conditions.

The fact that the wind had such a great effect on the ET rate in
the laboratory is surprising in view of the fact that the stomatal

resistances were probably high. As discussed in section on Chamber

LFlTENT HERTI J/SQ M]

110

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I

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0.0 8.0 16.0 24.0 32.0 40.0

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5.7 Cumulative latent heat production over simulated laboratory
chamber measurement. Data is shown for a leaf inside and a
leaf outside the chamber.

111

Design Considerations, in most cases the stomatal resistance may be an
order of magnitude greater than the boundary layer resistance, which
means that with changes in the boundary layer resistance the total
diffusion restistance should not be greatly affected. If the stomatal
resistance in the laboratory was high and the sudden changing of the
initial low wind condition to the high chamber wind condition did have
such a dramatic effect, then we can only surmise that the effect might
even be greater in the field where stomatal resistances are low during
much of the day.

The ET values shown in Tables 5.1 and 5.2 also show the CHZOT
values to be higher than the CH2CT values in both Experiments 1 and 2
(and this was also found in the field, see Chapter A). The CHZOT values
were on the average 100 9 over the CH2CT values or roughly 102. A
reasonable explanation for this is found in the additional time required
for the CHZOT treatment top closure.

The chamber top required 9 seconds to close. During this time the
plants were in a still environment regardless of whether Experiment 1 or
2 is considered. This still environment is similar to the no—wind
experiment which for the WP2 treatment produced an average of A10 9 of
water per replication. This is equivalent to 0.26 9 over the 9 second
closing time. Assuming that the transpiration rate can change
immediately with changes in wind speed (which is supported by the
laboratory and model data), then the transpiration rate of the plants
during the run was controlled by the chamber wind speed. When the
chamber measurement was begun, the fans were turned on and the plants

were exposed to a high wind environment. From Table 5.2 the high wind

112
condition produced an average WP2 ET of 9A3 g per replication or 2.A g
per chamber run. Summing the 2.A g and the 0.26 9 gives 2.66 grams of
water. This value is 10.82 greater than the actual 2.A 9 produced over
the 36 seconds. Hence, the approximate 100 g greater estimate by the
CH20T treatment relative to the CH2CT treatment was due to the
additional time required to close the chamber top.

The chamber used by Peters, et al.(197A) required 18 seconds to
close and therefore may have produced similar errors. However, the
chamber used was equipped with roll open sides which may have allowed a
breeze to pass through the chamber and therefore may have been
advantageous. The open top chamber design used here on the other hand
probably experienced neglible exchange with the outside air during top
closure since an unlikely down draft would be required.

Leaf canopy temperatures were also observed before and during the
chamber measurements. Tables 5.3 and 5.A summarize the average changes
in leaf canopy temperatures over three time periods. The mean changes
in leaf canopy temperature over the 5 replications were compared using a
student t-test where the asterisk indicates significance at the 53
level. The time periods for which temperature changes were observed
were: A0 seconds prior to the start of the chamber measurement to the
beginning of the measurement (t=-AO s to t=0 s); from the start of the
measurement to the end of the measurement (t=0 s to t=36 s); and from A0
seconds proir to the start of the measurement to the end of the
measurement (t=-AO s to t=36 5).

Tables 5.3 and 5.A show that though the CHZOT treatment tended to
decrease before the run (from t=-A05 to t=Os) and the CH2CT treatment

temperatures tended to increase, during the run (t=Os to t=36s) opposite

 

sagas—4...”.

113

Table 4.1

Before, during and overall leaf canopy temperature changes for the CHZOT
and CH2CT treatments in Experiment 1. Values are given in degree centi-
grade.

 

Replication CHZOT CH2CT
t= -40 s to t= O
l 0.00 0.50
2 -0.10 0.65
3 -O.3S 0.10
4 -0.05 0.45
5 —O.10 0.45
mean - .12 .43 *
t= 0 to t= 36 s
1 0.95 0.70
2 0.90 0.35
3 0.35 0.10
4 0.70 0.45
5 0.85 0.20
mean .75 .36 *
t= —40 s to t= 36 s
1 1.10 1.20
2 0.80 1.00
3 0.00 0.15
4 0.75 0.70
5 0.75 0.65
mean .68 .74

CH20T= = chamber open top grOUp 2
CH2CT = chamber closed top group 2

Before, during and overall leaf can0py temperature changes for the CHZOT
Values are given in degree centi-

114

Table 4.2

and CH2CT treatments in Experiment 2.

grade.

Replication

= -40 s to t= O

U'l-hUJNH

mean

t= 0 to t= 36 s

n
ll

CH20T=

CH2CT

waH

mean

-40 to t= 36 s

U'IanNH

mean

= chamber Open top grOUp 2
= chamber closed tOp group 2

CHZOT-

-O.10
-0.25
-O.50
-0.10
-0.20
-O.23

 

0.10
0.10
0.35
0.15
as:

0.05
-0.20
-0.15

0.00

0.10
-0.04

 

CH2CT

0.00
0.05
0.05
0.10
0.05

.05

-0.05
-0.10
-O.10

0.00
-0.05
-0.06

 

0.05
-0.15
-0.05

0.10

0.10

.01

 

LERF TEMPERRTURE [C]

H5

.0

24.8 25

24.8

m CH20T
‘ CH2CT

24 2

1.0

 

f f

1 r r r 1*
0.0 8-0 18.0 24.0 32.0 40.0

TIMEISEC]

 

24

Figure 5.8 Example of variation of leaf canopy
temperature During two consecutive chamber
measurements for replication 1 of Experiment 1.

116

or small changes occurred, thus resulting in similar overall temperature
changes (from t=-hOs to t=365). As expected, the leaves experienced
greater initial temperature changes (from t=~hO to t=0) for the CHZCT
treatment than for the CH20T treatment in the no-wind experiment. This
was since, in the CH2CT treatment the fans within the chamber, which is
suspended above the crop, were turned on at t=-h0 and left running
during chamber lowering. For the wind experiment the temperature
changes for the CH2CT were small since activating the fans in the
chamber did not significantly modify the plant's environment.

Once the chamber measurement was begun for each of the treatments,
the environments became similar and the ultimate temperature equilibrium
values were the same. The fact that the overall temperature changes
were similar shows how quickly the plant leaves can adjust to a change
in their environment. Figure 5.8 shows the leaf canopy temperature
changes for a CHZOT run and the following CH2CT run.

The overall canopy temperature changes were less for the wind
experiment. This is due to the wind speed change from a 1.5 m/s to the
1.0 m/s wind speed in the chamber which is a smaller wind speed change
than the plants experienced in the no-wind experiment. This may also
explain why the no-wind experiment chamber ET estimates exceeded the WP1
and WP2 treatments. As the leaf temperature rises the saturated vapor
pressure in the leaf stomates increases. If this increase is greater
than the increase in the vapor pressure of the air, then the
transpiration will increase.

To summarize the results in the laboratory:

1. No significant treatment difference was found between the WP1 and

117
WP2 treatments. The successive lowering of the chamber over the group 2
plants did not alter their ability to release water vapor to the air and
therefore it can be assumed that stomatal apertures are not effected
over relatively long time periods.
2. The CH2CT treatment compared fairly well to the WP1 and WP2
treatments in Experiment 2 (wind condition) but grossly overestimated
the weighed treatments in Experiment 1. A high level of overestimation
was calculated using the simulation model introduced in Chapter 3 which
determines transpiration from a single leaf, thus supporting the
hypothesis that the sudden increase in wind speed from near zero to 1.0
m/s was significant in causing the dramatic increase in transpiration.
3. The CHZOT treatment was found on the average to exceed the ChZCT
treatment by 102. it was concluded that the greater amount measured was
due to the additional time required in closing the chamber top.
h. Overall leaf canopy temperature changes were increased and were
greater for the no-wind experiment and may have contributed slightly to

the overestimated ET rates observed.

CHAPTER 6

SUMMARY AND CONCLUSIONS

1. A literature review of the use of field chambers revealed that two
distinct chamber techniques exist: instantaneous and noninstantaneous.
2. The physical relationships involved in the canopy energy exchange
for a crop enclosed in a portable measurement chamber and their design
implications were discussed.
3. A model was developed which simulated the nonsteady state energy
balance on a single leaf enclosed in a portable measurement chamber.
Variation in the cumulative latent heat production (or transpiration)
relative to that produced under initial conditions was shown to be as
great as 653. The nonlinearity of the latent heat transfer over the
simulated chamber measurement was shown to be approximately linear when
plotted on a cumulative basis. Researchers have assumed that a linear
production of water vapor within the chamber meant that a negligible
change in ET rate had occurred due to the chamber's presence and
therefore their ET estimates were accurate. Examples were given,
showing significant estimation error which can occur using this
assumption.
4. A portable measurement chamber was designed, constructed and tested
in the field.

a. The design used a thin plastic film called Propafilm C which

was found to be ideally suited for the chamber application.

b. The chamber design included a closable top for the purpose of

minimizing disturbance of the crop canopy during chamber placement.

c.The chamber was tested beside a weighing lysimeter and was found

118

119
to overestimate ET by 16% relative to the weighing lysimeter.
5. Laboratory experiments were conducted in which statistically based
information could be obtained.
a. No significant difference was found between the two mass
balance treatments (WPl and WP2). From these findings it was
concluded that stomatal closure did not occur as a result of
succesive plant enclosure by the portable chamber.
b. The open top treatment gave higher ET values than did the
closed top treatment. The additional build up of water vapor
during top closure was hypothesized as the cause.
c. Both chamber treatments seriously overestimated ET for the
no-wind experiment. The overestimation observed was found to be
due to the large change in wind speed over the plants during the
chamber placement.
d. No significant difference was found between the closed top
chamber treatment and the mass balance treatments. for the wind
experiment. The results can be attributed to the similar wind
speed which existed inside and outside the chamber.
6. Leaf canopy temperature changes were different just before and
during the measurements for the two chamber treatments but overall

temperature changes were similar.

CHAPTER 7

RECOMMENDATIONS

1. Further research is needed to determine ways in which the canopy
wind velocity and profile can be simulated within the chamber. Wind
speed was shown to be a very important factor in controlling the canopy
ET rate and therefore wind speed studies appear to be justified.

2. Further research is needed on the open top chamber design. For
those researchers who wish to apply the technique in their research, it
is my opinion that the open top chamber design should not be used, since
the present design tends to increase ET estimation error and also
complicates the chamber design and operation.

3. Field tests should be carried out with weighing lysimeters under a
variety of environmental conditions with a basic and economical chamber
design. The initiation of this research could begin with a national
conference with all those who have worked with portable field chambers
as participants. A conference of this type might lead to a standard
design with which a great deal of information could be obtained by many
researchers. At present many designs exist and perforance data is often
chamber specific. A standard design would make the chamber technique a

practical alternative to researchers throughout the plant sciences.

120

APPENDIX A

121

COMPUTER PROGRAM

PROGRAM ENERGY(INPUT,0UTPUT,TAPE5=|NPUT,TAPE6=OUTPUT)

 

 

 

 

C ..................................................................
C

C NONSTEADYSTATE ANALYSIS OF A LEAF IN AN ENCLOSED CHAMBER
C

C

C GLOSSARY

C ..................................................................
C

C NAME TYPE UNITS PURPOSE

C TDI VARIABLE C INITIAL DRY BULB

C TEMPERATURE

C

C TWI VARIABLE C INITIAL WET BULB

C TEMPERATURE

C

C TDF VARIABLE C FINAL DRY BULB

C TEMPERATURE

C

C TWF VARIABLE C FINAL WET BULB

C TEMPERATURE

C

C TL VARIABLE C STEADY STATE LEAF

C TEMPERATURE IN FIELD(OR LAB)
C

C TD ARRAY(200) C DRY BULB AIR TEMPERATURE
C IN CHAMBER

C

C TW ARRAY(200) C WET BULB TEMPERATURE

C IN CHAMBER

C

C T ARRAY(200) C TEMPERATURE OF LEAF

C IN CHAMBER

C

C K VARIABLE CAL/CM-MIN-C THERMAL CONDUCTIVITY

C

C YR VARIBL. CU CM-ATM/K-MOLE GAS CONSTANT

C

C L VARIABLE CM LENGTH OF LEAF

C IN DIRECTION OF WIND

C

C P VARIABLE MBARS ATMOSPHERIC PRESSURE

C

C SB VAR. CAL/SQ CM-K**h-MIN STEFAN BOLTZMANN CONSTANT
C

C TCOEF VARIABLE SOLAR TRANSMISSIVITY OF
C

CHAMBER COVER

nnnnnnnnnnnnnnnnnnnnonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

CVRIRT

EA

EIR

EIRS

TSE

RH

ERH

RS

RSADJ

RSRCD

RSRCDF

XIRAF

XIRS

RSABS

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

122

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

LONGWAVE TRANSMISSIVITY
0F CHAMBER COVER

SOLAR REFLECTIVITY
0F LEAF

SOLAR ABSORPTIVITY
OF LEAF

EMISSIVITY OF THE SKY(OR
CEILING)

EMISSIVITY OF THE LEAF

EMISSIVITY OF THE
CHAMBER COVER

EFFECTIVE SKY(OR CEILING)
TEMPERATURE

RELATIVE HUMIDITY
DUMMY VARIABLE
SOLAR RADIATION

SOLAR RADIATION WHICH
TRAVELS THROUGH THE
CHAMBER COVER

SOLAR RAD RECEIVED BY
THE LEAF IN CHAMBER

SOLAR RADIATION RECEIVED
BY LEAF IN FIELD(0R LAB)

IR COMPONENT FROM SKY(0R
CEILING)

RECEIVED BY LEAF IN
CHAMBER

IR COMPONENT FROM SKY(0R
CEILING)

RECEIVED BY LEAF IN

IN FIELD(0R LAB)

IR COMPONENT FROM
CHAMBER COVER RECEIVED
BY LEAF

TOTAL RADIATION RECEIVED
BY LEAF IN CHAMBER

nnnnnnnnnnnnnnnnonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

RSABSF

VCH

VF

DEL

DELF

RINT
RBL
ITIME
TIME

SLOPETD

ROAI

ROA

081

OS

QLl

QL

ROLl

ROL

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE

VARIABLE
VARIABLE
VARIABLE
ARRAY(200)

VARIABLE

VARIABLE

ARRAY(200)

VARIABLE

ARRAY(200)

VARIABLE

ARRAY(200)

VARIABLE

ARRAY(200)

123

CAL/SQ CM-MIN

CM/S

CM/S

CM

CM

S/CM

S/CM

SEC

C/S

G/CU

G/CU

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CAL/SQ

CM

CM

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

CM-MIN

TOTAL RADIATION RECEIVED
BY LEAF IN FIELD(DR LAB)

AVERAGE WIND VELOCITY IN
CHAMBER MOVING OVER LEAF

AVERAGE WIND VELOCITY IN
THE FIELD(OR LAB) MOVING
ovER LEAF

AVERAGE THICKNESS OF
BOUNDARY LAYER ON LEAF
SURFACE

AVERAGE THICKNESS OF
BOUNDARY LAYER ON LEAF
SURFACE IN FIELD(OR LAB)
STOMATAL RESISTANCE
BOUNDARY LAYER RESISTANCE
INDEx FOR TIME ARRAY

TIME

SLOPE 0F WET AND DRY BULB
TEMPERATURE CURVES

VAPOR DENSITY OF THE AIR
AT FIELD(0R LAB) CONDITIONS

VAPOR PRESSURE OF AIR
IN CHAMBER

SENSIBLE HEAT TRANSFER
FROM LEAF UNDER
FIELD(0R LAB) CONDITIONS

SENSIBLE HEAT TRANSFER
FROM LEAF IN CHAMBER

LATENT HEAT TRANSFER
FROM LEAF UNDER
FIELD(OR LAB) CONDITIONS

LATENT HEAT TRANSFER
FROM LEAF IN CHAMBER

VAPOR DENSITY IN LEAF
STOMATAL CAVITY

VAPOR PRESSURE IN LEAF
STOMATAL CAVITY WITHIN

 

nononnnnnonnnnnnnnnnnnnnnnnnnnnnnnnn

:1-

12h
CHAMBER

ETl VARIABLE G/CU CM/SQ CM-MIN TRANSPIRATION RATE
FROM LEAF UNDER
FIELD(OR LAB) CONDITIONS

ET ARRAY(200) G/CU CM/SQ CM-MIN TRANSPIRATION RATE
OF LEAF IN CHAMBER

EOLl VARIABLE ATM SATURATED VAPOR
PRESSURE WITHIN LEAF
UNDER FIELD(OR LAB)

CONDITIONS

EOL ARRAY(200) ATM SATURATED VAPOR PRES-
SURE WITHIN LEAF IN
CHAMBER

El VARIABLE ATM VAPOR PRESSURE OF THE
AIR UNDER FIELD(0R LAB)
CONDITIONS

E ARRAY(200) ATM VAPOR PRESSURE OF THE
AIR IN CHAMBER

AIR VARIABLE I FLAG FOR EITHER MOIST
OR DRY AIR

F ARRAY(200) DUMMY ARRAY

DIFO VARIABLE DUMMY VARIABLE

DIFl VARIABLE DUMMY VARIABLE

DIMENSION E(200),EO(200),RNET(200),EOL(200),T(200).QS(200)
DIMENSION QL(200).ROAIZOO),ROL(200),TD(200),TW(200),XIRU(200)
DIMENSION ET(200),TIME(200),F(200).EOW(200)
DIMENSION RELHIZOO)
REAL XIRAA,XIRAF X,XIRS,K,L

INITIALIZE VARIABLES

K=3.37E-3
L=8.0
YR=82.05
P=1000.0
$B=8.13E-11
TCOEF=0.89
R=0.22
A=0.78
EA=0.97
EIR=O.97
EIRS=O.250

125

 

 

TSE=2.0
CVRIRT=O.75

3?

* DATA INPUT SECTION

it
PRINT*,'INTITIAL DRY BULB TEMPERATURE (c)'
READ *.TD|

3':

it
PRINT*,'FINAL DRY BULB TEMPERATURE (c)'
READ *,TDF

it
PRINT*,'ENTER INITIAL WET BULB TEMPERATURE'
READ*,TWI
PRINT*,'ENTER FINAL WET BULB TEMPERATURE(C)'
READ*,TWF
PRINT*,'ENTER EFFECTIVE SKY(0R CEILING) TEMPERATURE'
READ*,TSE

*GENERATE LINEAR EQUATIONS FOR TEMP WITH TIME
it
SLOPETD=(TDF-TDI)/36.0
SLOPETW=(TWF-TW|)/36.0

it
*THE INTERCEPTS FOR THE EQUATIONS ARE THE INITIAL TEMPS
3':

PRINT*,'SOLAR RADIATION'

 

 

READ *,RS

it

* OPTIONAL INPUT SECTION

it
PRINT*,'DO YOU WANT THE TOTAL INPUT OPTION?I
READ(5.*)IN
IF(IN.EQ.1)THEN
PRINT*,'COVER TRANS. COEF FOR SOLAR RAD.‘
READ *,TCOEF

3':

*ENTER CROP REFLECTIVITY AND ABSORPTIVITY FOR
*SOLAR RADIATION
it
PRINT*,'REFLECTIVITY AND ABSORPTIVITY FOR SOLAR RAD'
READ *,R,A
:1:
*ENTER EFFECTIVE SKY(0R CEILING) TEMPERATURE IN DEGREES C
*EMISSIVITY 0F ATMOSPHERE AND IR TRANSMISSION
*COEFFICIENT FOR THE CHAMBER COVER
7:
PRINT*,'EFF SKY(0R CEILING) TEMP, EMIS 0F ATM AND TRANS COEF OF CO
+VER'
READ *,TSE,EA,CVRIRT

126

:‘c

* ENTER EMISSIVITY OF THE PLANT MATERIAL

* .
PRINT*,'PLANT EMISSIVITY '
READ *,EIR

it
*ENTER EMISSIVITY OF THE LOCAL ENVIRONMENT
3':

PRINT*,'EMISSIVITY OF SURROUNDINGS'
READ *,E|RS
it
*THE ABOVE CALCULATION IS BASED ON THE INITIAL
*DRY BULB TEMPERATURE
2':
*ENTER AVE WIND VELOCITY AT A HEIGHT OF 1M
*IN THE FIELD(OR LAB) AND IN THE CHAMBER

 

 

3':
END IF
PRINT*,'VFIELD(0R LAB),VCHAMBER'
READ *,VF,VCH
‘k
D0 6161 IAO=I,A
it
* RADIATION CALCULATIONS
it

*CALCULATION OF THE SOLAR RADIATION WHICH TRAVELS
*THROUGH THE COVER
RSADJ=RS*TCOEF
*CALCULATE SOLAR RAD RECIEVED BY THE LEAF
*IN CHAMBER
RSRCD=RSADJ*A*(1.0+R)
*CALCULATE VALUE OF SOLAR RAD RECIEVED
*BY LEAF NOT UNDER CHAMBER
RSRCDF=RS*A*(I.O+R)
*CALCULATION OF IR COMPONENT FROM SKY(0R CEILING)
*RECEIVED BY LEAF IN CHAMBER
X=EA*SB*CVRIRT*((TSE+273.15)**h.0)
*CALCULATE THE IR COMPONENT FROM SKY(0R CEILING) RECIEVED
*BY A LEAF NOT UNDER THE CHAMBER
XIRAF=X/CVRIRT
*CALCULATION OF IR FROM SURROUNDINGS
*WHERE SURROUNDING SURFACES ARE AT TDI
XIRS=EIRS*SB*((TDI+273.15)**A.O)
*CALCULATION OF RADIATION ABSORBED BY LEAF
*IN CHAMBER
RSABS=RSRCD+X+XIRS
*CALCULATION OF TOTAL RAD ABSORBED BY THE
*LEAF NOT UNDER THE CHAMBER
RSABSF=RSRCDF+XIRAF

...................................................................

*THIS PORTION OF THE PROGRAM PRINTS OUT ALL DATA BEING USED

127

*AND THE RESULTS OF ANY CALCULATIONS
PRINT*,‘ '
PRINT*,' '
PRINT*,' '
PRINT*,'|NITIAL DRY BULB TEMPERATURE=',TDI
PRINT*,'FINAL DRY BULB TEMPERATURE=‘,TDF
PRINT*,'INITIAL WET BULB TEMPERATURE=',TWI
TWF=36.0*SLOPETW+TWI
PRINT*,'F|NAL WET BULB TEMPERATURE=',TWF
PRINT*,' '
PRINT*,'LINEAR TEMPERATURE EQUATIONS:'
WRITE(6,26)TDI,SLOPETD
26 FORMAT(“1","TD=",F6.2,”+(",F8.5,“)*TIME”)
WRITE(6,27)TWI,SLOPETW
27 FORMAT(”0”,”TW=”,F6.2,”+(",F8.5,”)*TIME”)
WRITE(6,28)RS
28 FORMAT(”0",”RS=“,F6.2)
WRITE(6,29)TCOEF
29 FORMAT("o“."CHAMBER SOLAR TRANS COEF=”,F6.2)
WRITE(6,30)RSADJ
3o FORMAT("0",”RS THROUGH COVER =”,F6.2)
NRITE(6,3I)A
31 FORMAT(”0“,”SOLAR ABSORPTIVITY OF LEAF=",F6.2)
WRITE(6.32)R
32 FORMAT("0","REFLECTIVITY OF PLANT MATERIAL=“,F6.2)
WRITE(6,88)RSRCDF
88 FORMAT(”0”,“SOLAR RAD ABSORBED BY LEAF IN FLD".F6.2)
NRITE(6.33)RSRCD
33 FORMATI"O","SOLAR RAD RECIEVED BY LEAF IN CHAMBER=”,F6.2)
NRITEI6,3h)TSE
3h FORMAT(”0",”EFFECTIVE SKY(OR CEILING) TEMP=”,F6.2)
wRITEI6,35)EA
35 FORMAT(“O“,”THE EMISSIVITY OF THE ATMOSPHERE=”,F6.2)
XIRAA=X/CVRIRT
WRITE(6,36)XIRAA
36 FORMAT(”O”,”IR FROM SKY(0R CEILING) ABSORBED BY LEAF IN
+FIELD (OR LAB)=“.F6
+.2)
NRITE(6,37)CVRIRT
37 FORMAT(”0”,”TRANS COEF FOR THE CHAMBER COVER=”,F6.2)
WRITE(6,38)X
38 FORMAT(“0",”IR RAD FROM SKY(0R CEILING) ABSORBED BY LEAF
+IN CHAMBER =“,F6.2)
WRITE(6,39)EIRS
39 FORMAT(”O",”EMISSIVITY OF CHAMBER COVER=”,F6.2)
NRITE(6,ho)XIRS
ho FORMAT(”0“,”IR ABSORBED BY LEAF FROM CHAMBER COVER=”,F6.2)
NRITE(6,AI)RSABS
hl FORMAT(“0“,"TOTAL RAD ABSORBED BY LEAF IN CHAMBER=”,F6.2)
WRITE(6,IOZ)RSABSF
102 FORMAT(”0",”TOT RAD ABSORBED BY LEAF IN FIELD(OR LAB)",F6.2)
WRITE(6,h2)VF
A2 FORMAT(“O”,”AVERGE WIND VELOCITY IN FIELD(OR LAB)=”,F6.2)

128

wRITE(6,A3)VCH
A3 FORMAT(”O”,”AVERAGE WIND VELOCITY IN CHAMBER=“,F6.2)
PRINT*,'LEAF LENGTH IN THE DIRECTION OF AIR MOVEMENT ',L
DEL=0.h*((L/VCH)**0.5) A
DELF=O.A*((L/VF)**O.5)
NRITE(6,AA)DELF
hh FORMAT(”O",”AVE BOUNDARY LAYER IN FIELD(OR LAB)=”,F6.2)
WRITE(6,A5)DEL
A5 FORMAT("0“,”AVE BOUNDARY LAYER IN CHAMBER=“,F6.2)
WRITE(6.h6)
h6 FORMAT(”1”," ")
A DETERMINATION OF STEADYSTATE ENERGY BALANCE
* IN FIELD(0R LAB) PRIOR TO CHAMBER PLACEMENT
CALL STEADY(TL,YR,DELF,K,D.ROAI.SB,EIR,RSABSF, QSl,QLl,
+ROL1,RNETl,ETl,EOLl,El,E01,TDI,TWI,P,AIR)
RH=El/EOI*100.0
ROA(1)=ROA1
Q$(1)=QSI
QL(1)=QL1
ROL(l)=ROLl
RNET(1)=RNET1
ET(l)=ETl
E(I)=EI
E0(l)=E01
TD(l)=TDI
TW(l)=TWI
DO 773 I=I,2oo
RELH(I)=RH
T(I)=TL
F(|)=TL
773 CONTINUE
ITIME=o
TIME(l)=0.0
Do 96 ITER=1,500
DIFO=0.0
Do I ITIME=2,lhA
TIME(ITIME)=TIME(ITIME—I)+o.25
DETERMINATION OF NONSTEADYSTATE ENERGY BALANCE
A OVER PERIOD OF CHAMBER MEASUREMENT
*CALCULATE THE TEMPERATURES AT TIME ITIME
2’:
TD(ITIME)=TDI+SLOPETD*TIME(ITIME)
TW(ITIME)=TWI+SLOPETW*TIME(ITIME)
:‘c
*DETERMINE THE SATERATED VAPOR PRESS OF THE AIR
7!

CALL SATVP (TW(IT|ME) ,EOW(|TIME) , ITIME)
:‘c

EOW(IT|ME)=EOW(ITIME)*(1.3329)
*DETERMINE THE VAPOR PRESSURE OF THE AIR EA

 

129

CALL VAPRES(TD(ITIME).Tw(ITIME),P,Eow(ITIME),E(ITIME))
EOW(IT|ME)=EOW(lTIME)/1013.0

E(ITIME)=E(ITIME)/IOI3.O
ROA(ITIME)=18.0*E(ITIME)/YR/(273.15+TD(ITIME))

CALL SATVP(TD(ITIME),EO(ITIME))
ED(ITIME)=ED(ITIME)/76O.O
RH=E(ITIME)/E0(|TIME)*100.0

RELH(IT|ME)=RH
AIR=1.
|F(RH.GE.50.0)THEN
A|R=2.0
END IF

* CALCULATION OF LATENT HEAT TRANSFER
CALL LATENT(T,YR,DEL,K,D,ROA,SB,EIR,RSABS, QS,QL,

+ROL,RNET,ET,EOL,E,TD,ITIME,A|R)

DIFl=ABS(T(ITIME)-F(ITIME))
F(|TIME)=T(IT|ME)
IF(DIF1.GT.DIFO)DIFO=DIF1

1 CONTINUE
IF(DIFO.LT.0.0I)GOTO 81

96 CONTINUE

81 CONTINUE
PRINT*,'DIFO=',D|FO
PRINT*,'ITER=',ITER

WRITE(6,1919)
1919 FORMAT('O','TIME'.T10,'TL',T18,'TD'.T29,'TW',T39,'RNET',
+Th9.'QS'.T59.'QL'.T69.'RH') I
D0 11 M=1,lhh
WRITE(6,1920)TIME(M).TIM),TD(M),TW(M),RNET(M).QS(M).QL(M),
+RELH(M)
1920 FORMAT('0‘,F3.0,T9,F5.2,T18,F5.2,T28,F5.2,T37,
+F6.3,Th7,F6.3,T57,F6.3,T67,F5.2)
ll CONTINUE
VCH=VCH+50.0
6161 CONTINUE
STOP
END
SUBROUTINE LATENT(T,YR,DEL,K,D,ROA,SB,EIR,RSABS, QS,QL,
+ROL,RNET.ET,EOL,E,TD,ITIME,AIR)

...................................................................

A
* SUBROUTINE LATENT PERFORMS AN ENERGY BALANCE ON THE LEAF
* FOR A GIVEN POINT IN TIME

DIMENSION EOL(2oo),T(2oo),ROA(2oo).QS(2oo),QL(zoo),
+F(200),X|RU(200)

DIMENSION ROLI200).RNET(200),TIME(2OD),
+ET(200),E(200),TD(200)

130

REAL K
EOL(ITIME)=2.7182**((21.07-(5336.0/(273.15+T(ITIME)))))
EOL(ITIME)=EOL(ITIME)*0.0013I
ROL(ITIME)=18.0*EOL(ITIME)/(YR*(T(ITIME)+273.15))
RBL=DEL/Ih.h
CALL INTERNR(T(ITIME),AIR,RINT)
QL(ITIME)=(-2.0)*580.0*(ROA(ITIME)-ROL(ITIME))/(RBL+RINT)
QS(ITIME)=2.0*(-K)*(TD(ITIME)-T(IT|ME))/DEL
XIRU(ITIME)=EIR*SB*((T(ITIME)+273.15)**A.O)
RNET(ITIME)=RSABS—XIRU(ITIME)
T(ITIME)=T(ITIME-l)+(RNET(ITIME)-QS(|TIME)-QL(|TIME)

+)*o.ooA2 ,

+/1.025/0.956*50.0
ET(ITIME)=QL(ITIME)/580.o
QS(ITIME)=-QS(ITIME)

QL(ITIME)=—QL(ITIME)

 

 

 

RETURN
END
SUBROUTINE SATVP(TD,EO)
* SUBROUTINE SATVP CALCULATES SATURATED
* VAPOR PRESSURE
EO-2.7182**((21.07-(5336.0/(273.l5+TD))))
RETURN
END
SUBROUTINE VAPRES(TD,TW,P,EO,E)
* SUBROUTINE VAPRES CALCULATES
* VAPOR PRESSURE

E=EO-(0.00066)*(P)*(TD-TW)
+*(l.0+(0.00115*TW))

 

RETURN

END

SUBROUTINE STEADY(TL,YR,DELF,K,D,ROA,SB.EIR,RSABSF,QS
* SUBROUTINE STEADY PERFORMS A STEADYSTATE
* ENERGY BALANCE ON THE LEAF

....................................................................

+,QL,ROL,RNET,ET,EOL,E,EO,TDI,TWI,P,AIR)
REAL K
CALL SATVP(TWI,EOW)
it
EOW=EOW*(l.3329)
*DETERMINE THE VAPOR PRESSURE OF THE AIR EA

ic
CALL VAPRES(TDI,TwI,P,Eow,E)
EOW=EOW/1013.0
E=E/IOI3.O
ROA=18.0*E/YR/(273.15+TDI)

3':

CALL SATVP(TDI.EO)
Eo=EO/76o.o

I31

AIR=1.0
RH=E/EO*IO0.0
IF(RH.GE.50.0)THEN
AIR=2.0

END IF

TP=5.0

TL=5.0

FUNC=1.0
DO 321 III=1,5oooo
IF(FUNC.LT.O)THEN
TL=TL-5.o
TP=.01
END IF
TL=TL+TP
CALL LATSTED(TL,YR,DELF,K,D,ROA,SB,EIR,RSABSF, QS,QL,FUNC,
+ROL,RNET,ET,EOL,E,TDI,TWI,P,AIR)
IF(ABS(FUNC).LT.O.01)GOT0 3A5
321 CONTINUE
3A5 CONTINUE
RETURN ‘
END
SUBROUTINE LATSTED(T,YR,DELF,K,D,ROA,SB,EIR,RSABSF, QS,QL,FUNC.
+ROL,RNET,ET,EOL,E,TDI,TWI,P,AIR)
REAL K,X|RU
EOL=2.7182**((21.07-(5336.0/(273.15+T))))
EOL=EOL*0.00I316
ROL=18.0*EOL/(YR*(T+273.15))
QS=(-K*2.0)*(TDI-T)/DELF
RBL=DELF/1h.h
CALL INTERNR(T,AIR,RINT)
QL=(-2.0)*580.0*(ROA-ROL)/(RBL+RINT)
XIRU=EIR*SB*((T+273.15)**h.0)
RNET=RSABSF—XIRU
FUNC=RNET-QS-QL
QL=-QL
QS=-QS
ET=QL/580.0
RETURN
END
SUBROUTINE INTERNR(T,AIR,RINT)
SUBROUTINE INTERNR CALCULATTES THE INTERNAL
DIFFUSION RESISTANCE FOR A GIVEN TEMPERATURE

NOTE: THE INTERNAL DIFFUSION RESISTANCE CAN

BE SET EQUAL TO A CONSTANT (AS WAS THE CASE IN
THE RUNS MADE SHOWN IN CHAPTERS 3 AND 5) 0R

AN EXPRESSION CAN BE USED FOR ITS CALCULATION.
WHICH EVER WAY IS USED MUST BE DECIDED BY THE
USER AND APPROPRIATE MODIFICATIONS DONE.

THE SUBROUTINE AS SHOWN SETS THE INTERNAL
DIFFUSION RESISTANCE EQUAL TO .055 MIN/CM.

LX-x-x-x-x-x-wx-x-x-x-

L

 

$631-$3-

it

132

IF(AIR.EQ.2.0)THEN

THE EQUATIONS BELOW WERE GIVEN FOR XANTHIUM BY DRAKE ET AL.(1970)

FOR "WET" AIR USE THIS EQUATION
RINT80.292+O.1397*T-0.003A2*(T**2.0)
ELSE

FOR l”DRY" AIR USE THIS EQUATION
RINT=7.95-O.18*T
END IF
RINT=R|NT/60.0
RINT=.055
RETURN
END

APPENDIX B

CHRMBERIG/SBSECJ

.95

U

 

 

 

U U 1

1 T 1 ' I ' 7
0-9 1.3 2.3 3.0 3.7

CONTROLIG/368EC]

Calibration curve for the chamber for use with
experimental data from Experiments 1 and 2.

REFERENCES

REFERENCES

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ENERGY CHANGE(WATTS/SQ 1.1):«102

52

 

 

 

 

 

 

“3..

O

'93

O

ci‘ . , - ‘
0 net radiation
0 sensible heat
‘ latent heat

‘7 _____

C? + storage

‘ _ zero line

‘2

T I ' I I I r I I 1 . I

0.0 8.0 16.0 24.0 32.0 40.0

TIMEISEC]

Figure 3.4 Change in components of equation 3.1
over a simulated chamber measurement where the
initial air temperature, relative humidity and
chamber wind speed were 25 C, 20% and l.5m/s,
respectively.

II—