ENERGY BALANCE CONSIDERATIONS IN THE DESIGN OF by

ENERGY BALANCE CONSIDERATIONS IN THE DESIGN OF by
ENERGY BALANCE CONSIDERATIONS IN THE DESIGN OF
FLOATTh1G COVERS FOR EVAPORATION SUPPRESSION
by
Keith Roy Coo ley
A Dissertation Submitted to the Faculty of the
CC4MITTEE ON HYDROLOGY AND WATER RESOURCES
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
WITH A MAJOR IN HYDROLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1969
THE TJJNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by
entitled
Keith Roy Cooley
Energy Balance ConsideratiolE in the Design of Floating
Covers for Evaporation Suppression
be accepted as fulfilling the dissertation requirement of the
degree of
Doctor of Philosophy
,
Dissertation Director
Date
After inspection of the dissertation, the following members
of the Final Examination Committee concur in its approval and
recommend its acceptance:*
*This approval and acceptance is contingent on the candidate's
adequate performance and defense of this dissertation at the
final oral examination. The inclusion of this sheet bound into
the library copy of the dissertation is evidence of satisfactory
performance at the final examination.
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of
requirements for an advanced degree at The University of Arizona
and is deposited in the University Library to be made available to
borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or
reproduction of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College
when in his judgment the proposed use of the material is in the interests of scholarship.
In all other instances, however, permission
must be obtained from the author.
SIGNED:
ACKNOWLEDGEMENT S
The author is grateful to the Graduate College, University of
Arizona, and to his doctoral committee for allowing dissertation
research to be conducted in absentia at the United States Water Conservation Laboratory, Phoenix, Arizona.
The cooperation, encouragement
and assistance of the committee in completing his graduate program are
also appreciated.
Special thanks are due to his dissertation director, Dr. William
D. Sellers of the University of Arizona, and to Mr. Lloyd E. Myers, Dr.
Sherwood B. Idso, Dr. Ray D. Jackson, and Dr. John A. Replogle of the
United States Water Conservation Laboratory for their suggestions and
encouragement throughout the study and during the review of the
manuscript.
The author is especially grateful for the friendly and competent
assistance of Mr. Kenneth C. Mullins, Mr. Leland P. Girdley, Mrs. Frances
Witcher, Mrs. Aleta Morse, Mrs. Lorna Orneside, and Mrs. Beverly Fisher,
in compiling tables, drafting, typing, and reproduction of this dissertation.
111
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS
V
LIST OF TABLES
vii
ABSTRACT
viii
INTRODUCTION
1
REVIEW OF LITERATURE
3
THEORETICAL CONSIDERATIONS
13
EXPERIMENTAL FACILITIES AND SYSTEM EVALUATION
Experimental Site
Evaporation Tanks and Covers
Evaluation of Measurements and
Measuring Devices
Calibration of Insulated Tanks
Evaluation of Insulation
EXPERIMENTAL ANALYSIS AND PROCEDURE
Evaluation of Evaporation Equations
Derivation of Modified Combination Equation
Use of Insulated Tanks
RESULTS AND DISCUSSION
21
21
21
2/i
29
29
33
33
43
53
61
Energy Balance of Tanks
Relationship of Cover Properties to
Evaporation Reduction
Efficiencies of Covers Tested
61
78
84
CONCLUSIONS
86
APPENDIX; METEOROLOGICAL DATA
88
LIST OF REFERENCES
105
iv
LIST OF ILLUSTRATIONS
Page
Figure
Plan view of evaporation tanks and surroundings
22
Layout of evaporation tanks and equipment
28
Temperature at selected locations on tank #4 Feb. 21, 1967
32
Hourly variation of evaporation as calculated by
two Dalton-type expressions (E, Ed), the Bowen
Ratio method (EBR), and the combination method
(E).
.
..
.
39
Hourly variation of evaporation as calculated by
combination method for open tank, and modified
combination method for covered tanks
.
.
.
50
Hourly distribution of the energy balance components
over an insulated evaporation pan with 78 percent
cover of foamed wax blocks
66
Hourly distribution of the energy balance components
over an insulated evaporation pan with 86 percent
cover of white butyl rubber
67
Hourly distribution of the energy balance components
over an insulated evaporation pan without surface
cover
68
Hourly distribution of the energy balance components
over an insulated evaporation pan with 78 percent
cover of lightweight concrete blocks
69
Hourly distribution of the energy balance components
over an insulated evaporation pan with 86 percent
cover of white butyl rubber
70
Hourly distribution of the energy balance components
over an insulated evaporation pan without surface
cover
71
V
vi
LIST OF ILLUSTRATIONS--Continued
Figure
Page
Hourly distribution of the energy balance components
over an insulated evaporation pan with 80 percent
cover of styrofoam
72
Hourly distribution of the energy balance components
over an insulated evaporation pan without surface
cover
73
Hourly distribution of the energy balance components
over an insulated evaporation pan with 26 percent
cover of styrofoam
74
Hourly distribution of the energy balance components over
an insulated evaporation pan with 51 percent cover
of styrofoam
75
Hourly distribution of the energy balance components over
an insulated evaporation pan with 87 percent cover
of styrofoam
76
Relationship between evaporation reduction and reduction
in net radiation
81
Relationship between evaporation reduction and percent
of surface covered
83
.
LIST OF TABLES
Table
1.
Page
Ratio of absorptivity and emissivity of various
materials
20
Comparison of capacitance probe data and pointgage
readings
27
Calibration of evaporation tanks
30
Comparison of calculated and measured evaporation on
open tank
37
Comparison of calculated and measured evaporation on
all tanks 1967
47
Comparison of measured and calculated evaporation on
all tanks 1968
52
Comparison of measured and calculated net radiation
over covered tanks
56
Average albedo of cover materials
58
Longwave radiation calculations
59
Energy balance results on a 24 hour basis 1967
62
Energy balance results on a 24 hour basis 1968
65
Reduction in net radiation compared to evaporation
reduction
79
Efficiency of floating materials in reducing
evaporation
85
Meteorological data
88
vii
ABSTRACT
This study consists of a theoretical analysis of the
energy balance equation for a partially covered body of water, and
experimental analyses of the energy balances of partially covered
insulated evaporation tanks.
The theoretical analysis indicates that surface reflectance
for solar radiation and infrared emittance are the most important
cover properties.
White colored materials were found to satisfy the
requirement that both these parameters be as large as possible.
Experiments were conducted using covers of foamed wax, lightweight concrete, white butyl rubber, and styrofoam.
shapes and sizes were tested.
A variety of
Cover radiative properties were
lg;1iI1
noted to be most important, and thin covers proved to be slightly
more efficient than thick insulated covers of the same size.
Evaporation reduction was found to be proportional to the
percent of surface area covered, the constant of proportionality
depending upon the color and type of material used.
For the white,
impermeable materials tested, the constant of proportionality was
near unity.
It was also noted that reduction in evaporation and
reduction in net radiation, as compared to an open tank, were highly
correlated.
Evaluation of two Dalton-type expressions, the Bowen ratio
method and the combination method, for predicting evaporation from
viii
ix
an open water surface, showed the combination method to be better
under conditions of this experiment.
Based on this finding, a
modified combination method was derived.
This modified equation
proved valid for predicting evaporation from a partially covered
body of water.
The use of insulated evaporation tanks also provided an
easy and accurate method of predicting net radiation over other
surfaces, and long-wave atmospheric radiation.
INTRODUCTION
Hydrologists and engineers have long been aware of the tremendous quantity of pure water lost each year through the process of
evaporation.
Meyers (1962) has estimated this loss to be over 17,000,000
acre feet per year from lakes, reservoirs, and ponds in the 17 western
states alone.
This amounts to considerably more than the average annual
flow of the Colorado River as measured at Lee's Ferry, which is less
than 13,000,000 acre feet per year (U.S.G.S., 1964).
Because of the potential savings ($170,000,000 per year at an
average cost of $10 per acre foot), many studies have been conducted on
methods to reduce evaporation.
By far the greater number of these have
been concerned with the application and utility of various combinations
of mono-molecular layers or films of long-chain alcohols.
In attesta-
tion of this fact are two recent bibliographies on evaporation reduction
(Reidhead, 1960; Magin and Randall, 1960), each containing over 300
references devoted almost exclusively to either the use of monolayers
or the general process of evaporation.
In fact, only one reference
specifically mentions the use of other means to reduce evaporation in
its title.
Another example is the proceedings of a recent conference
on evaporation reduction (Larson, 1963), in which only one short paragraph mentions the use of floating materials other than monolayers.
Since most of the above-mentioned studies have been somewhat
discouraging, with savings of only 10-35 percent realized on field
1
2
tests (Cruse and Harbeck, 1960; Cluff, 1966), it was decided that another
approach to the problem should be investigated.
In particular, the
present study was initiated to determine the physical properties that
should be considered in the design of floating covers used to reduce
evaporation from water surfaces, and to obtain a better understanding
of the evaporation process from a partially covered body of water.
It
consists, first, of a theoretical analysis of the energy relations of
a partially covered body of water, and, second, of controlled experiments on partially covered insulated evaporation tanks.
Only floating
materials covering less than 100% of the surface area are considered;
and a combination aerodynamic-energy balance equation is derived to
predict evaporation from these partially covered surfaces.
REVIEW OF LITERATURE
An investigation of the literature related to evaporation reduction indicates that nearly all of the studies conducted to date
have been of an experimental nature; that is, a material was placed on
or above the water surface, and observations of its effectiveness recorded.
The material most commonly used has been a monomolecular layer
of some long-chain or fatty alcohol which would float on the water surface.
In some cases very detailed studies were conducted; and complete
research teams investigated the effects of various parameters (monolayer
and meteorological) on evaporation.
During these investigations it
was determined that the monolayers had little or no effect on the
reflectance or emittance of the water surface (Harbeck and Koberg,
1959).
Therefore, since one of the purposes of this study is to de-
termine the effects of cover properties (the reflectance and emittance
of which are considered to be very important) on the energy balance and
evaporation, studies relating exclusively to the use of monomolecular
layers will not be discussed in this review.
Rather, this space will
be devoted to those papers that investigate or mention the use of re-
flective materials or application of other methods to change the reflective properties of the water surface.
Although It was noted by Young (1947) that the rate of water
loss from an evaporation pan was affected by the panes color, the first
reference to indicate that the color of the water affected evaporation
3
4
was that of Bloch and Weiss (1959).
They noted an apparent reduction
in evaporation and water temperature when the Dead Sea turned milky
white due to carbonate of lime being dispersed through the surface.
This prompted them to study the effect on evaporation of white polyethylene balls placed on the water surface of small pots.
These balls,
which were about 90 percent submerged, reduced evaporation approximately
40 percent, whereas black balls of the same type and number had no
significant effect on the amount of evaporation as compared to an open
pot.
They attributed the reduction, in both the case of the Dead Sea
brine and the white balls, to the reflective properties of the white
material.
Another example indicating that the color of the water has an
important effect on evaporation was presented by Keys and Gunaji (1967),
in which they showed an increase of evaporation us
in; a blue dye, but
no significant difference when a red dye was used.
Genet and Rohmer (1961) performed studies using beakers of 1
liter capacity on which they placed layers of various thickness of white
polystyrol beads.
One series of studies was conducted in an oven where
only the temperature affected the results.
A later study consisted
of placing the beakers outdoors; and for the same temperature as
that in the oven, the efficiency increased because the white beads
reflected a portion of the incoming radiation.
An increase in
thickness of the layer of beads only slightly improved the efficiency.
This experiment lasted approximately 1 month, and data indicated an
average evaporation reduction of 56 to 64 percent.
The authors
noted that since this study was conducted using small beakers, the
results may not have been representative of what would happen on
larger bodies of water.
Crow and Manges (1965) also reported on the use of white floating
spheres as well as wind baffles, plastic mesh, and two other materials,
to reduce evaporation.
The wind baffles were simply to reduce the
turbulent air motions over the ponds.
The plastic mesh materials were
said to have reduced incoming radiation to the water by shading, as
well as reducing wind speed, since they were suspended above the surface.
The white floating spheres were noted to be more efficient than
any of the other methods, but no mention was made of the process by
which they were able to reduce evaporation so efficiently.
The data
reported were insufficient to allow the reader to make any meaningful
conclusions since the length of the study, dates of observation, and
meteorological conditions were not reported.
These tests were conducted
under field conditions on plastic lined ponds of
30,5 x 36.6 x 1.8
meters (100 x 120 x 6 feet) in size.
Another study conducted under field conditions on 500 m2
ponds was reported by Rojitsky and Kraus (1966).
of floating materials.
They tested a variety
However, most failed due to sinking and deter-
ioration; and no results were reported other than some visual observations,
In another study they placed several different floating
materials, including a variety of aquatic vegetation called Lemna
(duckweed), on Class A pans and observed evaporation, temperature of
6
the top centimeter of water, and wind speed.
period of eight months for some materials.
This study lasted for a
Evaporation reduction of up
to 82 percent was noted with a white polyethylene powder which covered
essentially 100 percent of the water surface, and with the vegetation
ULemnal! which also covered the entire surface.
The vegetative cover also
maintained the water temperature at the lowest average for the study
period.
Hexadecanol reduced evaporation 66 percent during this period,
and the surface temperature was the highest of any recorded.
Cluff (1967) reported on the use of several different types of
floating rafts to reduce evaporation.
of 4-mu
These rafts were constructed
polyethylene plastic sheets, aluminum foil bonded to styro-
foam, butyl rubber, lightweight concrete, and styrofoam sheets painted
white.
He indicated the most promising appeared to be the styrofoam
painted white and the aluminum foil bonded to styrofoam
because
they
are stronger and reflect more energy than some of the oUmer mater i als
No data were included to substantiate these conclusions, however.
An experiment by Yu and Brutsaert (1967) using very shallow evaporation pans of various sizes showed the effect of reflective properties.
Eight pans about 2.5 cm deep and built in three sizes of .3 meters (l'-foot)
square, 1.2 meters (4-foot) square and 2.4 meters (8-foot) square were used,
There were white and black pans of each size, and also a green and grey pan
in the 1.2 meter (4-foot) size.
The albedo of each color of pan with about
16 millimeters (5/8-inch) of water was determined in the laboratory under
simulated clear sky and zenith sun conditions.
These values were reported
7
as an average for weighted wave lengths of the visible spectrum.
values obtained were:
grey - 0.108.
The
white - 0.675, black - 0.054, green - 0.09, and
Meteorological data as well as water temperature and
evaporation were recorded during the series of runs which lasted about
3 hours each.
Results of the experiment showed that the highest rate of evaporation generally occurred on the 2.4 meter (8-foot) black pan while the
lowest was on the 2.4 meter (8-foot) white pan.
For the three black pans,
evaporation generally increased with size while the opposite was true
for the white pans.
A plot, of E/(e
- ea) vs U for the pans indicated that the
coefficients a and b, from the equation
E=a+bU(es -e)
a
[lj
were the same for the same size pan regardless of the color.
equation, E is the evaporation, e
In this
and ea the vapor pressure at the
surface and in the air above, respectively, and U the windspeed at
the place ea is measured.
Since the color of the pan did not alter
the coefficients, the turbulence of the air above the pans must not
have been changed significantly either.
A correlation was also noted between the difference in evaporation between the white and black pans, and the incoming radiation.
Another study on evaporation from shallow water was reported
by Fritschen and Van Bavel (1962 and l963c).
They presented a complete
8
heat balance on an hourly basis from a shallow pond of water.
Their
interest was in determining the effect of the surrounding medium on
evaporation.
Thus, they did not report values of the albedo of
shallow water over a black plastic which they used.
Only one paper was found in which an attempt was made to
determine what effect various covers could have on evaporation
due to their reflective properties (Bromley, 1963).
In this paper
the author noted that much of the heat absorbed by a water surface
come"from incident solar radiation.
The surface water temperature,
and thus evaporation, could therefore be reduced by preventing part
of the solar radiation from entering the water.
Some of the methods
he proposed to accomplish this are:
1 - Produce a smoke or cloud layer above the lake surface,
or otherwise produce a shadow.
(This Is similar to the method
explained by Crow and Manges in which they suspended a plastic mesh
above the surface.)
2 - Float a thin layer of suitable solid on the surface, e.g.
flakes, bubbles, powders, beads, etc.
3 - Float a thin layer of suitable foam on the surface.
4 - Float a solid sheet on the surface to act both as a
diffusion barrier and a radiation reflector.
Although all of these methods should be effective, attention
is confined to the surface coatings.
In order to evaluate the
9
effectiveness of these coatings, he used the energy equation for
an open body of water.
This equation, considering no change in
energy stored within the water, can be written in present notation
as:
(l-r)S + (l_r)Ra - EcT
+ KA(TT)
- LKE(e
ea) = 0
where
=
reflectance of water surface to solar radiation
r
=
reflectance of water surface to atmospheric radiation
S
=
solar radiation
Ra
=
atmospheric radiation
=
emittance of water surface
r
w
w
S tefan-Bol tzniann coim taut
()
=
temperature of water surface
=
temperature of air
KA
=
heat transfer coefficient
KE
=
mass transfer coefficient
L
=
latent heat of vaporization
e
=
saturated vapor pressure at surface water temperature
T
T
w
a
ea
actual vapor pressure of air.
By assuming a set of values for meteorological variables
typical of those observed during summer weather in the southwestern
[2]
10
United States, and using values of
and IKE based on previous studies,
the surface temperature was calculated.
Once the surface temperature
was known, evaporation was calculated using the last term in the
energy equation.
Bromley used the same equation when surface coatings were
considered, except additional assumptions were necessary.
First it
was assumed that the heat transfer coefficient did not change, and
second, that the mass transfer coefficient could be defined as:
i/ic.
1/K
=
w
+ 1/K
[3]
C
where 1/K and 1/K refer to the resistance to evaporation of
c
w
The surface temperature and
the air and cover, respectively.
evaporation were again calculated, and the effectivcnu-s
of th
coating determined by comparing the two values of evaporation
calculated.
These comparisons were made assuming that the follow-
ing surface treatment materials were available to be applied
singly or in combination:
1 - monolayer (1 sec/cm resistance)
2 - monolayer (4 sec/cm resistance)
3 - white material r
= 0.8, r
C
4 - metallic material r
c
5 - impervious coatings.
C
= 0,8
= 0.9, c
= 0.1
c
11
Results of the calculations of evaporation, comparing treated
and untreated surfaces, were presented for three possible situations.
The first considered effectiveness of the coatings after steady state
conditions were reached (in this case a 30-day period).
The second
considered the amount of water lost to evaporation (in the first
three days) if the coating was suddenly removed after steady state
had been reached.
The third situation considered the effectiveness
of the coatings for both a short time coverage, and total savings
for a longer period where the coating was only in place for a short
time.
The general trend of all his calculations indicated that the best
coatings in descending order were:
100 percent impervious white layer,
monolayer (4 sec/cm) plus white surface, 100 percent white or metallic
surface, 100 percent monolayer (4 sec/cm), 50 percent white or rneLaiflc
surface, and 100 percent monolayer (1 sec/cm).
The percent of water
saved ranged from 100 to 17 percent for the above coatings.
Bromley (1963) also conducted two experimental studies using
small plastic or rubber trays approximately 25 mm x 30 mm x 5 mm
(10-inch x 12-inch x 2-inch) deep.
Coatings used during the first
experiment consisted of white diatomaceous earth treated with water reppellent, and a monolayer of 90 percent cetyl alcohol.
Both covers
reduced evaporation by essentially the same amount, averaging 23 percent3
and both showed signs of deterioration after only two days.
During the
12
second experiment coatings of expanded polystyrene beads of various
densities and sizes were placed on the water surface.
The savings
varied from 41 to 59 percent with the lightest beads producing the
best results.
This experiment also lasted for only a couple of days.
Comparison of experimental results with calculated values is
difficult since the calculated values were determined considering
different surface treatments.
Although experiments were conducted
on very small pans and for short time intervals, and calculations
are not verified, both indicate considerable savings can be achieved
using reflective coatings.
THEORETICAl CONS IDERAT IONS
An equation basic to most of the engineering, hydrological,
and meteorological disciplines is the energy balance or conservation
of energy equation.
In evaporation studies, this equation, relating
the balance between the inf low and outflow of energy in a unit volume
of water, is usually written as:
Rn
LE+G+A
[4]
(Sellers, 1964), where
LE
=
rate of energy used in the evaporation process
(latent heat transfer)
Rn
=
rate of net radiation reception by the water surface
A
=
rate of sensible heat transfer from the surface to the
air
G
=
rate of sensible heat transfer from the surface to
deeper layers of water or change in energy stored in
the water
and all terms are expressed in units of cal
cm2 mm'.
If the energy balance equation is considered for a tline period
such that the change in storage is equal to zero (which may be a
24-hour period, a season, or any other time interval at the extremities
13
14
of which the amount of energy stored in the water is the same), the
storage term can be ignored and the equation [4] written as
LE
=
Rn - A
[5]
Since the objective of evaporation reduction is to minimize
LE, it is obvious that to do this the combination of Rn - A must
also be minimized; and in order to do this, it is necessary to know
the individual constituents of each of these terms and the relationships existing among them.
In the case of a partially covered body
of water, the net radiation may be written as follows:
Rn
=
Ra + S - [(l_p)r
- [(l-p)r
+ pr]S - o[(l-p)c T
ww
+
E
T
cc
4
+ pr]Ra
where
=
percent of surface area covered expressed as a decimal
=
albedo of cover
=
emittance of cover
T
=
temperature of cover surface
r
=
albedo of cover to long-wave radiation
p
r
c
and the other terms are as previously defined.
[6]
15
The term (1-p)r
Ra is generally an order of magnitude or
more smaller than the other terms and is therefore neglected, being
usually less than the errors associated with measurements of the
other parameters.
The equation for sensible heat transfer is commonly written
(Conaway and Van Bavel, 1966) as:
U (T-T)
p c
A
=
[&n
[7]
(z/z)]2
in which
p
=
density of air
C
specific heat of air at constant pressure
k
Von Karman constant
U
=
wind speed at elevation z
T
=
temperature of surface [T
z
=
height above surface at which Ti and T
+ pT]
= (l-p) T
a
=
are measured
roughness parameter of surface
Sensible heat transfer from the air to the surface is defined as
positive for this equation.
Combining equations [6] and [7] yields a working equation
with which to investigate possible ways of minimizing the total
evaporation:
16
Rn - A
Ra + S - [(l-p)r
p c
k2
[(l-p)T4 + pcT4] - pr
+ pr]S
Ra
(T-T)
[8]
2
[ n(z/z)
Floating covers placed on a water surface will not affect
c,
Hucti item8 w Ra, S, r,
k2
and z.
Also, UUCC the
size of cover has been selected the percent of area covered will be
constant.
U and Ta should not be changed by the cover either, since
they represent the general conditions within the air mass.
items such as T
w
T
,
c
and T , will be affected by the cover, however,
S
they cannot be determined prior to application.
items, r
,
,
c
c
r
,
c
Dependent
and z
o
The remaining
are the independent variables that can be
manipulated by the design of the cover and the material used.
r, r, and
Since
appear in negative terms, the larger they are made the
smaller the sum of all terms will be.
The roughness parameter, z, is
also a part of a negative term, and it would appear desirable to make
this factor as large as possible by creating a very rough surface.
However, if Ta is larger than T
on the average, the sensible heat term
will be positive and increase energy available for evaporation.
fore, in this case, a small value of z
0
would be desirable.
There-
One other
observation concerning the sensible heat term can be made; if a very
thin material is used for the cover, the temperature of the cover will
17
be essentially the same as the temperature of the water.
Since the
temperature of the air cools faster than the temperature of the
water after sunset, energy will be transferred from the water to
the air, through the cover, during the early evening hours, thus
reducing the energy available for evaporation.
morning hours the opposite would be true.
During the early
The time of day of maximum
wind activity may therefore determine if rough but relatively thin
covers would be desirable.
Another way to approach the problem of minimizing the net
radiation term, and to get a better feel for the values of r, r,
and c
to design for, is to consider a surface capable of exchanging
heat only by radiation.
This surface would receive long-wave radiation
from the sky (Ra), of which it would absorb a fraction
E
(emittance =
absorptance = 1 - reflectance, for an opaque material and long-wave
radiation).
It would also receive short-wave radiation from the
sun and sky (S) of which it would absorb a fraction a.
Emittance of
radiation by the surface would be determined by its temperature and
emissivity, and the energy balance equation for such a surface
would then be:
cc
T4
=
aS + cRa
[9]
18
Since the lowest evaporation would be associated with the
lowest temperature at the surface, the above relationship is expressed in terms of the temperature as
T
l/4
a
S
=
[10]
a
a
Knowing S is zero at night, it can be seen that at night the
surface temperature is independent of a and c, and depends only
on Ra and
,
neither of which will be altered by a cover.
During
the daytime, since again Ra, c, and S will not be altered by
the cover, the lowest ratio of a/c will produce the lowest surface
temperature.
Moving one step closed to reality, we know that in fact
the surface tnperature is not independent of energy cmi tLed :j
ii ighL,
due to the fact that it is thermally coupled to the water or hiczit
reservoir.
The water reservoir maintains a fairly stable temperature
because of its heat capacity properties
Since the true surface
temperature of the water is always greater than the radiative
temperature of the atmosphere, the argument for a high emittance being
desirable is strengthened, even for nightthne periods.
This is true
since, although a greater percent of energy will be absorbed due to
the higher emittance, the same percentage of a larger term will be
emitted.
19
Using the published values for the absorptivity and emLssivity
of several materials (Brown and Marco, 1958), the ratio of cL/E is
presented in Table 1 below.
As shown there, the lowest ratio of
absorptivity to emittance (which is another way of saying high
reflectivity and high emittance) is obtained from white materials.
Thus, other factors such as roughness, permeability, and thickness
being equal, white materials will be more efficient in reducing
evaporation than the others listed.
Although results of this study cannot be compared directly
with those obtained by Bromley, his calculations also indicate that
white colored materials are the most efficient in reducing evaporation.
20
Table 1
Ratio of absorptivity and emissivity for various materials
Material
White paint
a=
r
0.12 - 0.26
Avg.
White paper
0.80 - 0.95
0.19
0.88
0.27
0.92 - 0.95
0.13 - 0.33
0,22
0.28 - 0.29
Avg.
0.27
0.93
0.29
Roofing paper
0.88
0.91
0.97
Black paint
0.97
0.99
0.96 - 0.98
0.99 - 1.03
0.98
0.97
1.01
Polished aluminum
0.26
0.04
6.5
Polished copper
0.26
Avg.
Avg
0.26
0.02 - 0.03
0.025
8.7
- 13.0
11.0
EXPERIMENTAL FACILITIES & SYSTEM EVALUATION
Experimental Site.
The experimental studies were conducted
during the summers of 1967 and 1968 on four evaporation tanks
located at the U. S. Water Conservation Laboratory near Phoenix,
Arizona, in the Salt River Valley.
The Salt River Valley slopes
gently to the west and is ringed by mountains rising 300 to 900
meters above the valley floor.
In the vicinity of the Laboratory,
the nearest obstruction to wind is a 360 meter high mountain located
about 4 kilometers south of the site,
The Laboratory grounds are
surrounded by the University of Arizona Cotton Research Center.
Farm lands immediately adjacent to the evaporation tank site are
planted to a variety of crops.
The western exposure is dominated
by Laboratory buildings, the nearest of which is located 18.3 meters
(60 feet) west of the western-most tank,
A plan view of the evapora-
tion tanks and Laboratory buildings is shown in Figure 1.
Evaporation Tanks and Covers,
The evaporation tanks consisted
of an outer tank 2.7 meters in diameter and 0.9 meters deep, and an
inner tank 2.1 meters in diameter and 0.6 meters deep,
The smaller tank
was placed inside the larger with the top rims in the same plane.
Perlite ore was placed on the bottom and sides between the two tanks.
The tanks were buried with the rims protruding slightly above ground
level.
The use of insulated tanks more nearly simulates pond or lake
conditions (Riley, 1966), and also simplifies the energy balance
21
22
//
/
N
/
U.S.W.C,L.
7
PAR K I N G
SCALE: ':50
-k-- X-X-X- X X- X
//
/
//
//
//
//
//
/
V
/
//
//
/
/
/
//
/I/
//
/
/I
//
/
7,
/7/ 7;,7/ ,1
//
7
/
//
LL/////// //7//;:
:1 /
)<
(1)
a.
(
t1A it
A r1 t
0
0
I
TANKS
E'EJ
[
x-x.- x- x- x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x-x
CROPS
FIELD
Figure 1..--Plan view of evaporation tanks and surroundings.
23
equation.
Covers were placed on three of the tanks and the fourth
was used as a standard throughout the experiment.
Four covers of two different types, individual floating blocks
and single membranes or sheets, were studied.
used were:
The block materials
white foamed wax formed into blocks about 12 cm in diameter
by 4 cm thick; and lightweight concrete formed into blocks about
18 cm x 28 cm x 4 cm of light grey color.
materials were:
butyl rubber of 15 mu
The membrane or sheet
thickness painted white on top;
and 5 cm thick styrofoam also painted white to establish a similar
reflective surface as the butyl rubber.
The rubber membrane was floated
by means of a sealed plastic pipe attached around its perimeter.
During the summer of 1967 all four of the materials were used.
The percentage of surface area covered by the four materials was
essentially the same.
Both the wax, and concrete,
blocks covercd 78
percent, the styrofoam covered 80 percent, and the butyl rubber covered
86 percent, of the surface area of a tank.
During 1968 only styrofoam and butyl rubber materials were
used.
Six covers were constructed to give different surface area
coverages on the tanks.
All six of the covers were round.
had a large hole (95 cm in diameter) in the center.
One cover
Another cover
had 12 small holes (27 cm in diameter) spaced symmetrically about
the center.
Each of these, referred to as 1-hole and 12-hole,
covered 76 percent of the surface area.
The percentage of area
covered by the other four varied from 26 to 87 percent.
24
Evaluation of Measurements and Measuring Devices.
The
meteorological, heat flow, and evaporation data necessary to determine a complete heat budget on each of the four insulated evaporation
tanks were measured.
for each tank:
This consisted of the following measurements
water surface temperature, water temperature 10 cm
below the surface, water temperature at the bottom, net radiation,
reflected solar radiation, and cover surface temperature.
Also
recorded near the tanks and 0.9 meters above the ground surface were:
solar radiation, dew point temperature, air temperature and wind
speed and direction.
thermocouples.
All of the temperatures were obtained using
The surface temperature of the water was determined
by floating a shaded thermocouple on the water surface (Jarvis and
Kagarise, 1961).
Heat stored in the water was computed from the hourly average
tank temperature which was derived from the temperature profile data.
Net radiation was measured using Fritschen miniature net radiometers
(Fritschen, 1963, 1965a), placed 23 cm above the tanks and 76 cm
from the rim.
The sensible heat transfer to or from the tank was determined as a
residual in the energy balance equation.
However, the necessary data to
calculate sensible heat transfer by means of a Dalton-type expression
which relates sensible heat transfer with meteorological parameters were
available.
The energy used in evaporation was determined from water
25
level measurements, and the heat stored in the cover was determined
from temperature measurements on top and bottom of the cover.
During 1967 all of the above measurements, except evaporation
or water level, were recorded every 30 minutes during the study
periods by means of a data handling system capable of recording, on
punched tape, the output of 49 channels of data.
(For more detail
see Fritschen and Van Bavel, 1963a..)
The water level during 1967 was continuously recorded by means
of Stevens Type F water stage recorders with a magnification of two
times.
Although the original plan was to calculate the heat balance
on an hourly basis, it was impossible to obtain sufficiently accurate hourly
evaporation measurements from the water stage charts,
The minimum
time period that could be used to obtain the desired precision of
measurement was 12 hours on the open tank and 2L hours on the covered
tanks.
It was therefore necessary to use evaporation equations to
compute hourly evaporation values from meteorological data.
These
computed hourly evaporation values were then summed for either 12 or
24 hours, depending on the tank under consideration, and the total
compared to the measured value as read from the water stage chart.
If the two totals were essentially the same, the computed hourly values
were considered representative of actual evaporation and used in the
heat balance calculations.
26
In 1968 the water stage recorders were replaced by capacitance
proximity sensing probes, manufactured by Drexeibrook Engineering
Company.
These probes compare the capacitance between the sensing
plate and the water surface with a reference capacitor in the control
unit.
Variations in the water level changes the variable capacitance
and produces a corresponding change in the output current.
Precision
of these units is better than 1/2 percent of full scale, which in these
studies was less than 16 millimeters.
Since the output from these
units was an electrical signal, they were connected to the data handling system and all data were recorded every 30 minutes on punched tape.
Comparison of evaporation measurements made by a standard point
gage, and the capacitance probes, are presented in Table 2.
show that the two methods give essentially the same results.
These data
The
difference is generally within the possible error of + 0.01 cm which
applies to both methods of measurement.
The worst conditions were
obtained on Tank #4 for the period of 13 to 16 August where a difference
of 0.13 cm is noted.
This may have been due to a bad point gage reading
or an erroneous output from the probe caused by dirt or grass on the
capacitance plate.
It is felt that these measurements are sufficiently
close to allow use of the capacitance probe for all evaporation
measurements.
The evaporation tanks are shown in Figure 2.
This figure shows
the location of the tanks with respect to the nearest buildings, the
.09
.04
.08
.36
2 AUG 0800
2 AUG 1530
3 AUG 1630
Total
.19
.12
.41
15 AUG 0800
16 AUG 0800
Total
.18
.15
.11
.44
22 AUG 0800
23 AUG 0800
24 AUG 1000
Total
20 AUG 1600
.10
14 AUG 0800
13 AUG 0930
.15
.45
.13
.14
.18
.39
.12
.16
.11
.39
.09
.03
.11
.16
.01
.02
.01
.02
.03
.01
.03
.01
.01
.02
.01
Tank #1
Pointgage Probe Diff
1 AUG 1000
31 JUL 0830
Date
2.32
.63
.79
.90
2.32
.65
.89
.78
2.39
.74
.25
.81
.59
2,31
.65
.81
.85
2.31
.64
.88
.79
2.46
.78
.25
.83
.60
.01
.02
.02
.05
.01
.01
.01
.01
.07
.04
-
.02
.01
Tank 2
Pointgage Probe Diff
.63
.15
.23
.25
1.26
.37
.47
.42
.57
.13
.04
.15
.25
.60
.17
.21
.22
1.31
.34
.51
.46
.57
.17
.08
.17
.15
.03
.02
.02
.03
.05
.03
.04
.04
.04
.04
.02
.10
Tank 3
Pointgage Probe Diff
.78
.20
.27
.31
1.82
.58
.62
.62
.76
.21
.27
.28
1.95
.54
.73
.68
.02
.01
-
.03
.13
.04
.11
.06
Tank 4
Pointgage Probe Diff
Comparison of Capacitance Probe Data and Pointgage Readings (cm)
Table 2
28
Figure 2.
Layout of evaporation tanks and instruments.
29
covers and instruments on the tanks, and the general appearance of
a
typical experimental run.
The trailer in the upper left-hand portion
of the figure is a mobile meteorological laboratory
and contains the
recording system and power supply used.
Calibration of Insulated Tanks.
Calibration of the insulated
evaporation tanks consisted of determining how well evaporation compared on the four tanks without covers,
Previous investigators had
noted no difference on the 2.7 meter diameter tanks as long
as the water
level was within 13 cm of the rim (Frasier and Myers, 1968).
In June
and July of 1968 the tanks were again calibrated to determine if
the
modification had affected the evaporation.
measurements are presented in Table 3.
Results of point gage
Values of net radiation for
portions of the calibration period are also presented.
These measure-
ments show that evaporation between the individual tanks varied by
less than 2 percent for the entire period, and less than 2 percent for
individual days.
Net radiation varied by almost 6 percent for individual
days, but only slightly over 3 percent for the total period.
These
values compare favorably with those obtained earlier, and indicate that
evaporation can be considered the same for all tanks.
Evaluation of Insulation.
Evaluation of the insulation was
accomplished by comparing temperature measurements at several points
inside and outside the tanks for 24-hour periods.
Thermocouples were
placed on the center of the bottom and halfway down the sides (at the
30
Table 3
Calibration of Evaporation Tanks
Evaporation in cm, Net radiation in ly
Tank #1
E
Rn
Period
26 JUN 0800-
27 JUN 0800
27 JUN
0800-
28 JUN 0800
28 JUN 0800-
1 JUL 0800
*1 JUL 1600-
Tank #3
E
Rn
Rn
E
Tank #4
E
Rn
.88
466
.88
483
.87
475
.90
469
.93
431
.94
455
.92
458
.95
442
2.61
-
2.58
-
2.59
-
2.65
-
.80
-
.81
-
.81
-
.82
-
2
JUL 1600
2
JUL 1600JUL 1600
.90
517
.91
511
.93
524
.92
528
3 JUL 16004 JUL 1600
.89
513
.88
514
.89
538
.89
530
7.01
1927
7.00
1963
7.01
1995
7.13
1969
3
Total
*
Tank #2
Tanks were refilled on 1 JUL 0800.
31
four compass points) of the outer tank.
Temperatures at the center of
the inner tank were recorded at the surface, at 10 cm below the surface,
at 38 cm below the surface, and at the bottom.
The temperatures were observed for several days.
It was noted
that although the temperature on the bottom of the inner tank followed
a diurnal cycle of about 4°C, the temperature on the bottom of the outer
tank remained constant.
The temperatures at the halfway point of the
outer tank also followed a diurnal cycle, of about 2°C.
This was
probably due to transfer of heat by the metal from the exposed rim to
the buried thermocouple, which was taped to the side of the tank.
Figure 3 shows the 24-hour variation of some of the observed temperatures.
Only one of the side temperatures on the outer tank is shown
since they were all essentially the same.
The effectiveness of the
insulation in minimizing heat flow is clearly illustrated by the
constant temperature at the bottom of the outer tank,
This indicates
that heat transfer through the side and bottom was small and can be
neglected.
32
16
15
14
I3
0
2
0'
o-o-t
Lr-Ao
-
'I
i-&'1/
A%.%
I0
9
8
BOTTOM OF OUTER TANK
sSOUTH SIDE OF OUTER TANK
7
0_41*
BELOW WATER SURFACE
OBOTTOM OF INNER TANK
2
4
6
8
10
12
14
16
18
20 22 24
TIME (hours)
Figure 3.--Ternperature at selected locations on tank #4 Feb. 21, 1967.
EXPERIMENTAL ANALYSIS AND PROCEDURE
Evaluation of Evaporation Equations.
In order to determine
a complete heat balance on an hourly basis, it was necessary to
compute hourly evaporation for the 1967 studies, since water stage
recorders were not sufficiently sensitive.
This necessitated the
selection of an evaporation equation, a number of which are available
in the literature, for use in this study.
Several researchers have compared some of the various evaporation equations (Conaway and Van Bavel, 1967; Fritschen and Van Bavel,
1963b; Pruitt, 1963 and 1966).
It was found that one equation would
be more accurate in some cases, while another would yield better
results under different conditiouH,
It was tiierelorc
ieue-ziry
t
evaluate several of the evaporation equations under the particular
conditions of this study to determine the equation that would produce
the most representative values.
Four equations were evaluated (two Dalton-type, Bowen ratio,
and combination) using measured evaporation on the open tank as a
standard.
The first equation evaluated was a Dalton-type expression
of the form
E
(Pp)
P
(e-e)
f(U)
s
a
33
34
in which
6
P
=
water vapor/air molecular weight ratio (0.622)
=
ambient pressure (970 mb)
wind or transfer function
f
and other terms are as previously defined.
According to Sverdrup (1946) and others, f(U) can be
evaluated by the relationship:
k2
=
f(U)
[12]
{n (z/z)]2
The second equation evaluated was also a Dalton-type expression except that the value of f(U) was obtained as suggested by
Sheppard (1958) by writing
*
kU
f(U)
*
-1
[SLn(kU z/D]
[13]
in which
*
-1
U
=
friction velocity (cm sec
D
=
diffusivity of water vapor in air (0.24 cm2 sec1).
)
The friction velocity is defined as
*
U
kU
Zn ( z / z)
[14]
35
The third equation evaluated is a combination of the energy
balance equation and the ratio of sensible heat to latent heat, or
the Bowen ratio (Bowen, 1926).
This equation, which assumes hori-
zontal divergences of sensible and latent heat between the levels
of measurement to be zero, can be used to estimate evaporative flux
from a water surface.
LE
Expressed in present notation it is:
=
1 + y
Rn - G
(T -T )/(e -e )
w
a
s
[151
a
where
psychrometer constant (0.642 mb deg1).
The final equation, proposed by Van Bavel (1966), is referred
to as the combination method of determining evaporative flux.
it Ls
related to both the Dalton-type expression and the Bowen ratio model
and is written as:
LE
=
/y H + LBvda
L/y + 1
in which
/Y
=
a temperature dependent dimensionless number
H
= RnG
By
=
transfer coefficient for water vapor
da
=
vapor pressure deficit of the air at elevation z.
[16]
36
The definition of By is given as:
By
-
pk2
U
[171
P
[gn(z/z)J2
Hourly evaporation values were calculated by using equations
[11], [15] and [16] for two different periods, and compared to
measured evaporation values obtained from the water stage charts
for the open tank.
The comparison periods were selected on the
basis of two criteria, cloud cover and steady state conditions.
Cloud cover affects the radiation readings, and representative values
may not be recorded on cloudy days.
Steady state conditions in this
case refers to the atmospheric conditions being about the same on
each day, in other words, no frontal activity or other rapid
chdnges.
Results of the calculations are presented in Table 4, arid
the percent error shown is calculated with respect to the measured
values.
Of the four equations evaluated, the combination method as
suggested by Van Bavel (1966) gave the best results under the conditions of this study.
Even this method, however, produced errors
for the 12-hour periods as high as 26 percent.
The combination method
was selected to be used for further calculations because the errors based
on the totals for the two comparison periods were small.
Evaporation as calculated by the Bowen ratio method was generally
low, and errors as high as 32 percent were noted for the 12-hour
37
Table 4
Comparison of calculated and measured evaporation on open tank (cm)
Date
Time
Emeas
E
Ed
Error
20 Sep
21 Sep
22 Sep
23 Sep
00-12
28 Sep
29 Sec
30 Sep
Total
-16
14
Error
Error
-42
.27
C
Error
14
.25
5
-26
12-24
.31
.23
-26
18
-40
.22
-27
.23
00-12
.22
17
-22
12
-45
.27
20
.23
4
12-24
.49
.51
4
'33
-33
.33
-32
.38
-23
00-12
.28
50
78
31
9
.29
4
.35
24
12-24
.66
.97
48
.59
-10
.53
-19
.63
- 4
00-12
.27
.28
3
18
-32
.25
-8
.27
0
12-24
.61
1.01
66
.61
0
.45
-27
.59
-
3
3,08
3.87
27
2,46
-20
2.61
-15
2.93
-
5
00-12
.33
38
17
.24
-26
.31
-5
.30
1.2-24
.62
.98
59
.58
-6
.48
-22
00-12
.31
33
6
.21
-31
32
3
.2
12-24
.45
.75
67
.46
2
38
-16
4()
00-12
.28
.29
4
.19
-31
.24
-15
.26
12-24
.30
.40
36
.27
-10
.26
-14
.30
0
00-12
.25
.25
0
.17
-31
24
-4
.25
0
12-24
.34
.58
69
.37
8
.28
-17
.41
20
2.88
3.96
38
2.49
-13
2.51
-13
2.98
3
Total
27 Sep
.20
.24
E
EBR
7.
S
r)
Ed
- Dalton-type expression with f(U) evaluated by Sverdrup method.
E
- Dalton-type expression with f(U) evaluated by Sheppard method.
EBR = Bowen Ratio Method
= Combination Met hod
E
C
-8
3
-
I
38
periods.
A previous study in the same area showed that this method
compared well with evaporative flux from a cropped surface (Fritschen,
l965b).
The two remaining methods were considerably in error as shown
in the table.
The reason for the rather large differences in calculated
evaporation, as determined by the methods evaluated, is not immediately
apparent.
The fact that the Dalton-type expression, using the transfer
function suggested by Sverdrup (1946), produced the poorest results is
particularly puzzling since this same expression is contained in the
combination equation, which produced the best results.
A re-examination
of the equations revealed that small errors in measurement of the surface temperature could cause large errors in calculated evaporation
(Conaway and Van Bavel, 1966).
For example, small errors in surface
water temperature measurements will produce considerably larger errors
in the calculated saturation vapor pressure because of the exponctitial
relationship between them.
Writing the Dalton-type expression, using
the transfer function suggested by Sverdrup (1946),
LE
=
LBv (es_ea)
we note that errors in temperature measurement will be magnified since
calculated evaporation is directly proportional to the vapor pressure
difference.
[18]
39
If we substitute the above relationship into the Bowen ratio
equation and rearrange terms, we obtain:
LE
=
(Rn - G) - LBv y(T -T )
w a
[19]
.
[n this case, errors in the surface water temperature inenmremont
will be reflected in the calculated evaporation.
However, these errors
are smaller than the saturated vapor pressure errors.
These errors
will be dampened somewhat due to the inclusion of the net radiation
and heat storage terms, the combination of which is generally greater
than the sensible heat transfer term.
The factor y being less than
unity also dampens temperature errors.
Again substituting equation [18], as well as the ClausiusClapeyron equation (Sellers, 1965), into the Bowen ratio equation, we
obtain the combination equation written as:
LE(l + y/A)
(Rn - G) - LBv y/(da)
.
[20]
Use of the Clausius-Clapeyron equation eliminates the surface water temperature and errors associated with it.
Errors associated
with the assumptions involved in this substitution will also be dampened since y/
is less than unity in all cases considered here.
40
Since the transfer parameter (By) appears in the same term as
the vapor pressure (or temperature) difference in all three equations,
errors in this parameter would have the same relative effect on
calculated evaporation as errors involved in surface temperature
measurements.
From the above discussion, we note that the Dalton-type expression is more sensitive to errors in either the surface temperature
measurements or the transfer parameters.
Furthermore, the combination
equation is less sensitive then the Bowen ratio method.
Differences
noted between the Bowen ratio, Dalton, and combination equations can
probably he explained on the basis of sensitivity to errors in surface
temperature measurements.
A representative example of the variation in calcuated evapora-
tion by the four methods evaluated is presented in Figure 4 for
September 23, 1967.
The data used to evaluate these equations, and the data used
in subsequent calculations, are presented in the Appendix.
Each table
contains general meteorological data as well as data pertaining to
individual tanks for each hour of the days investigated.
In most
cases these data are smoothed values obtained from lines fitted by eye
through half-hourly measured values.
The value of the roughness parameter used was obtained from
wind profile measurements observed over each of the tanks.
The va1ues
obtained varied from about 1.0 to 0.6 cm, and an average value of 0.8 cm
0
.02
.04
2
Es
4
OEc
S
DE D
L
6
TIME
8
10
12
14
(hours)
SEPTEMBER 231967
16
\
18
20
22
24
Figure 4.--Hourly variation of evaporation as calculated by two Da1tontye expressions
(E,E), the Bowen Ratio nethod (ERR), and tte combination method (E).
0
cr
10
.08
0
E12
E
.16
.18
42
was used for all tanks and covers.
This value agrees well with those
listed by other investigators for short grass (Tanner and Pelton, 1960;
Van Wijk, 1963).
The wind speed, air temperature, and dew point were measured
at the 1 meter level.
Using the air temperature, values of L/y were
obtained from a table given by Van Bavel (1966, p. 467).
The value
of other parameters were listed following their definition.
43
Derivation of Modified Combination Equation.
The combination
method, as presented, is designed to estimate evaporation from an open
water surface.
It was therefore necessary to modify the equation when
considering evaporation from a partially covered tank.
The modifica-
tion is necessary since the reduction in evaporation on the partially
covered tanks may not be proportional to the percentage of the area
covered, or to any other known cover property.
Following a similar procedure and reasoning as that used by
Van Bavel (1966), with the exception that each step is adjusted to
pertain to the substance concerned and percentage of total area involved, the derivation of the modified equation is as follows.
The latent heat transport from the water surface to elevation
z can be defined as
=
LE
LBv (e -e ) cal cm
s
a
-2
.
mm
-1
[211
Because sensible heat transfer may occur from both the water
surface and the cover surface, but at different rates, each will be
discussed separately.
Assuming similarity between vapor and sensible heat transport,
we have
A
=
y LBv (T-T) cal cm2
mm1
[22]
44
where A
C
is the sensible heat transport in the units shown.
This
equation describes sensible heat transfer from the
surface of the
cover.
For the open water portion, using primes
to indicate saturated
values, we can write
(T-T)
W
a
=
(e-e)/
S
a
[23]
Substituting this relationship into equation [221 above,
we obtain
an expression for sensible heat transfer from the water
surface
A
=
y/A LBv (es_ea)
[24]
Combining the above terms, and taking into account the
percentage of area covered, we obtain the expression for sensibie
heat transport from the entire surface area,
V
A
=
y/
I
(l-p) LBv (e -e ) + yp LBv (Tc_Ta)
s
a
where p refers to the percentage (expressed as a decimal) of water
surface covered.
[25]
45
If we now add and subtract e , we obtain
a
A
=
(l-p) LBv (es_ea) - i/A (l-p) LBv (e a -e a )
yIL
+ yp LBv (T-T)
Since ea - ea is equal
to
elevation z, and by considering e
[261
the vapor pressure deficit (da) at
e
as the defining condition her
potential evaporation or evaporation from an open water surface, we have
A
=
y/A LE - y/
LBv (l-p) da + yp 1Ev (TTa)
[27]
in which E = By (e'-e ).
a
s
Substituting this expression into the energy balance equation
(ii + A -
II
nd rear ranging terms we obtain
0)
time equaL Lon br
eHL
I -
mating evaporation from a partially covered body of water, by the
modified combination method, written as
(A/y) tilL - By (l-p) da +
E
=
pB
V
(T -T )
a
C
+ 1
where H = Rn - G - Q and Q is the energy stored within the cover.
This equation is general in nature and should apply to any type of
cover material of which the impervious area is known.
[28]
46
Using the above equation, hourly evaporation values were
calculated for the tanks partially covered by the four different
materials previously described.
As a means of checking the calcula-
tions for the 1967 study, the hourly values were summed for 24-hour
periods and compared to the daily evaporation as recorded on the
water stage charts.
The results of these comparisons are presented
in Table 5.
The evaporation data for September 23 and 27-30, 1967, which
were in Table 4 for the open tank, are presented again in Table 5,
except on a 24-hour basis.
These values, as well as those for
October 18-20, 1967, are presented for comparison purposes, and indicate that the results obtained by the combination method on the open
tank remained essentially the same for the entire period.
Since conditions and results on each tank are different,
the
results presented in Table 5 will be discussed separately and with
respect to the type of cover rather than the number of the tank.
It
should also be noted that the possible magnitude of measurement error
is the same for all tanks and may be as high as ± 0.5 mm.
This value
applies to either individual days or groups of days because of the
techniques used in reading the charts.
of the water stage recorders.
It is due to the nonsensitivity
These recorders would sometimes record
a steplike trace, when in fact, evaporation had been taking place
during the entire period, but the pen arm would only drop after a
certain minimum friction or elevation change had been exceeded.
(Oct)
(807)
Styrofoam
(787)
Tank #4
Lightweight
Concrete
Blocks (Sep)
Tank #3
Open Water
(86
Tank #2
Butyl Rubber
(787)
B locks
Diff.
70 Diff.
Evap Meas
Evap Cal
Diff.
7o Diff.
Evap Meas
Evap Cal
Diff,
Evap Meas
Evap Cal
7 Diff.
Diff.
Diff,
70
.03
.21
.17
-19
.04
.88
.86
-2
.02
.46
.42
-9
.04
-13
0
.38
.44
16
.06
0
-15
.03
.95
.95
.17
.20
.05
24
.36
13
.04
.05
.32
7
-5
.01
.11
.15
36
.04
.76
.81
.02
.14
.14
0
0
.58
.56
-3
.02
.21
.27
29
.06
15
11
.02
.13
.18
38
.05
.60
.66
10
.06
.33
.31
-6
.02
.14
11
1.24
1.38
.09
3
2.89
2.98
11
.08
.58
.64
10
.06
.12
.15
25
.03
21
.03
.05
.11
120
.06
.50
.59
18
.09
.09
.16
78
.07
.01
.49
.48
-2
.01
-11
.08
36
.04
.09
31
11
.01
7
.36
.47
.12
8
1.50
1.62
.07
30
22
.09
.23
.30
15
16
.04
8
13
.02
.09
.11
22
.02
.51
.55
Table 5
Comparison of measured and calculated evaporation values on all tanks 1967 (cm)
Tank & Cover
Sep 1967
Total
Oct 1967
Total
Material
Parameter
23
27
28
29
30
27-30
18
19
20
18-20
Tank #1
Evap Meas
.23
.21
.21
.13
.19
.14
.74
.11
.16
.41
Foamed Wax
Evap Cal
.20
.26
.15
.21
.20
.82
.17
.15
.18
.50
48
The covers on Tank #1 for the entire period, and Tank #4
for the period September 23 and 27-30, consisted of many individual
pieces of the materials noted in the table.
The results show that
during September the maximum error on Tank #1 was 24 percent, or 0.05 cm,
with an average for the period September 27-30 of 11 percent, or .08 cm,
total difference.
On Tank #4 for this same period, the maximum error
was 29 percent, or 0.06 cm, with the average for September 27-30 being
11 percent, or 0.14 cm, total difference.
For the period October 18-20
on Tank #1, the maximum error was 36 percent, or 0.04 cm, for a single
day, and the average for the period was 22 percent,
difference,
or 0.09 cm, total
In other words, the calculated value for any of these days
is well within the limits of measurement capabilities; however, the
total for the periods mentioned is slightly more than can be accounted
for by measurement error alone.
These results would indicate that the
modified equation has a tendency to slightly over-estimate evaporation
from the covered tanks.
However, even the worst results could be well
within the usually sought for 10 percent range if only a portion of the
possible measurement error was subtracted from the total difference
(or added to the measured evaporation).
The fact that evaporation was
quite low during the latter part of the study also tends to make results
look worse when they are expressed in percent.
The covers on Tank #2, for the entire period, and Tank #4, for
the October 18-20 period, consisted of single pieces or membranes of the
49
materials noted in the table.
The maximum error on Tank #2 during
September is 38 percent, or 0.05 cm, and the average for the period
September 27-30 is 10 percent, or 0.06 cm total difference.
period October 18-20, the maximum error is 120 percent,
For the
or 0.06 cm,
and the average for the period is 30 percent, or 0.07 cm, total
difference.
On Tank #4 during the period October 18-29, the maximum
error is 78 percent, or 0.07 cm, with an average for the period of
31 percent, or 0.11 cm, total difference.
In this case, two of the eleven daily values cannot be accounted
for by water level measurement error alone.
However, all of the values
for the three or four day periods except that on Tank #4 for 18-20 October
could be within the desired 10 percent range if possible water level
measurement errors were taken into account.
to over-estimate evaporation.
Again, the equation tends
Although water level measurement error
may be of sufficient magnitude to explain the errors noted, the differences
may be due to errors in the radiation and temperature profile measurements.
For example, in both cases where membrane type covers were used,
the net radiation measured was biased toward the reflective properties of
the cover rather than the water.
Since the cover represented about 80
percent of the surface area and the radiometer is more sensitive to objects directly below it (95 percent of its reading is based on objects
within a 1200 envelope from the sensing element due to cosine response),
even if some of the water was visible to the radiometer due to its placement, the effect of the water on the reading would be much less than
0.I
0.2
0.3
0.4
o
0R.
OPEN TANK
/
0
/OQO
20
22
24
0
vaoraion as calculated by combination method for
open. tank, nnd:.ciffed combination method for covered tanks
TIME (hours)
lB
I
/
/
\\/°
/
i
\o D--D
i,'/
\
0
(86%)
WAX BLOCKS (78%)
WHITE BUTYL RUBBER- /
24:8
o
0\
0
El
CONCRETE BLOCKS (78%)
Figure 5.Houriy vartaio:: c
>
2
ZO.5
E0.6
E
0.7
08:
SEPTEMBER 23, 1967
51
20 percent.
The temperature profiles were obtained by placing thermo-
couples on a stand at different levels within the tank.
This stand was
placed at the edge of the cover, or near the edge of the tank, and may
not represent average conditions within the tank.
It would be affected
by sunlight entering the water and may be more representative of
open water conditions than average conditions.
A representative example of the hourly variation of evaporation
as calculated for the four study tanks is presented in Figure 5 for
September 23, 1967.
As further verification of the modified combination equation,
evaporation was also calculated for the 1968 studies.
The results of
these calculations, as compared to water level measurements obtained
by the capacitance probe, are presented in Table 6.
As noted, about half
of the calculations are within the desired 10 percent range of measured
values, and most of the others are only slightly higher.
Since in this
case water level measurements are much more accurate than those
obtained by water stage recorders, the observed differences are probably due to other factors.
Again the representativeness of the water
profile measurements may be questioned; however, net radiation is more
likely in error in this case.
Net radiation measurements for this
study were quite variable and for the above calculations, computed
net radiation values were used.
These computed values were based on
measurements of net radiation on the open tank, and average albedo
values obtained during both 1967 and 1968 (the method of computing
.
Diff
7. Diff
Evap Meas
Evap Cal
Cover (7.)
Cover (%)
Evap Meas
Evap Cal
% Diff
Diff
.79
.88
11
.09
.15
.19
.12
.14
-7 - .37
.07
.01
.08
-24
(80%)
.34
.26
8
.13
5
.04
Styrofoam
1.54
1.67
.75
.79
Open
42
44
.04
40
.04
.08
.19
.27
.09
.13
Cover (%)
Evap Meas
Evap Cal
% Diff
Diff
1 & 2
Total
.10
.14
2
White Butyl (86%)
1
Evap Meas
Evap Cal
% Diff
Diff
Day
Cover (7.)
Tank
Date
15
.01
.02
3
.64
.66
6
.16
.17
.44
.50
14
.06
(87%)
14-16
Total
.06
7
.12
5
.89 2.42
.95 2.54
Open
.12
.15
25
.03
16
24
.12
22
.31
.01
-1
.04
7
14
.10
.13
6
Styrofoam
(267.)
.54
.73 2.04
.76
.83 2.17
.58
.77
.12
34
Styrofoam (51%)
.35
.50 1.39
.47
.62 1.70
.54
.61
13
.07
.89
.93
4
.04
.16
.18
13
.02
Styrofoam
14
Aug 1968
.60
.58
-3
.02
Open
.01
9
.11
.12
.20
.22
10
.02
.25
.29
16
.04
0
0
.23
.23
Styrofoam
.02
9
.23
.25
22-24
Total
.17
.22
29
.05
(767.)
.13
.14
8
.01
.56
.61
9
.05
1 Hole
.74
14
.09
.65
- 12 Hol
-
.14
7
2.02
2.16
(87%)
.09
.34
.36
.08
-11
6
.01
.02
24
.62
.69
11
.07
Styrofoam
23
Styrofoam (76%)
.80
.89
11
.09
-02
.14
.16
14
22
Comparison of measured and calculated evaporation on all tanks 1968 (cm)
Table 6
53
net radiation will be discussed in more detail in the next section).
It should also be noted that evaporation was very low on the tanks
with large covers, and actual differences between calculated and
measured evaporation were less than those on the open tank for the same
period.
The greatest differences (.07, .12,
.12) between calculated and
measured evaporation were obtained for the 51 percent styrofoam cover
on August 14-16.
Since the modified combination method produced good
results in all other cases tested, this discrepancy could have been
caused by a non-representative temperature measurement, or a combina-
tion of errors, neither of which was obvious during the experiment or
calculations.
From the above calculations, using four different cover
materials and several different sizes, it is concluded that the
equation as modified is valid for computing evaporation from partially
covered tanks.
The results of such calculations should be within 10
percent of the measured values if measurements are representative of
average conditions.
Use of Insulated Tanks.
The use of insulated evaporation tanks
in these studies provides several advantages over other types.
The
evaporation from an insulated tank more nearly represents evaporation
from ponds or small lakes since heat exchange through the sides and
bottom is negligible.
Energy balance investigations are also simp1i
fied when heat exchange from the sides and bottom can be neglected.
54
Being able to neglect this one heat exchange term also provides
an
easy and accurate method of determining long-wave radiation from the
atmosphere, and net radiation over other surfaces where albedos
are
known (Harbeck, 1954; Anderson and Baker, 1967; Kohler and Parmele,
1967).
Net radiation over the open tank and measured albedos were
used in the 1968 studies to compute net radiation over the covered
tanks.
Neglecting the reflected long-wave radiation term, which is
very small for water surfaces and most cover surfaces, the net radiation
for an open tank is expressed as
Rn
=
Ra+S-EGT4-rS
[29]
For the partially covered tank the expression is:
Rn
c
=
Ra + S - [l_p)rw + pr]S - G[c
(l-p)T4 + EpT4]
.
[30]
C
Since atmospheric radiation is the same for both tanks, the two
equations can be combined by eliminating this term.
Solving for the
net radiation over the covered tank we obtain:
Rn
=
Rn + C[EwTw
- s(l_p)T4
- CcPTc
I + pS[r-r]
[31]
55
All of the parameters in this equation were either known
or measured,
thus allowing computation of net radiation over the partially
covered tank (Rn).
The calculated values for 1968 are presented
with the other hourly data in the Appendix.
The agreement of
measured and calculated evaporation shown in Table 6 is an indication
of the validity of these computed values of net radiation.
As an
example of the need for these calculations, the net radiation as
measured and calculated for two tanks on two different days is
presented in Table 7.
The net radiation over the open tank is also
shown for comparison purposes.
The reason the measured values are
not always representative is that the radiometer does not always
view the correct proportion of cover and water.
This occurs be-
cause wind action moves the cover away from the net radiometer
position part of the time.
At other times the radiometer views only
the cover surface and readings are again nonrepresentative.
Obser-
vation of Table 7 will show some readings over the covered tanks
to be essentially the same as those over the water surface of the
open tank.
This is particularly true on Tank #4 on August 15, 1968.
In other cases the readings are much smaller - notice Tank #3 on
August 15, 1968.
If the readings are representative, they should
be an essentially constant percentage less than those on the open tank
during the daylight hours.
This percentage, of course, depends on the
area covered and the reflective properties of the cover.
Covers
- .05
-.06
-.05
-.01
-. 10
-.09
-.09
.01
.13
.28
.41
.50
.52
.54
.51
.42
.30
.16
.04
3
4
5
7
-.05
-.07
-.07
-.07
-.07
-.07
172
18
19
20
21
22
23
24
602
17
10
11
12
13
14
15
16
8
9
6
17
-.01
-.06
-.04
-.04
-.04
-.05
-.05
.02
.09
.11
.13
.15
.14
.13
.08
.01
.02
-.04
-.04
-.06
-.09
-.09
-.09
1
381
-.10
-.09
-.10
-.09
-.09
290
403
.81
.60
.33
1.04
1.13
1.11
1.04
.38
.67
.93
-.14
-.13
-.04
-. 14
-.15
-.15
-.14
Rn meas
-.09
-.08
-.12
-.12
-.13
-.13
-.13
.65
.48
.28
.08
-.07
.77
.05
.24
.46
.64
.76
.81
.82
-.11
-.11
-. 12
-.11
-.11
-.11
Rn cal
Tank #4
Styrofoam (26%)
-.09
-.12
-.13
-.13
-.13
-.13
.88
.65
.38
.11
1.03
1.10
1.11
1.04
.87
.09
.36
.64
-.15
-.14
-.14
-.14
-.13
-.12
Rn meas
Rn meas
Rn cal
Time
2
Tank #2
Open
Tank #3
Styrofoam (517.)
15 Aug 1968
Tank #3
409
259
82
-.10
-.11
-.11
-.12
-.12
-.12
-.06
-.07
-.07
-.07
-.08
-.08
-.06
-.05
-.05
-.06
-.05
-.05
.94
.69
.36
.19
1.02
1.13
1.18
1.10
.32
.66
.85
- .05
-.15
-.14
-. 15
-.15
-.16
-.15
Rn meas
.60
.41
.21
.11
.77
.74
.21
.42
.52
.68
.74
-.11
-.11
-.02
-. 11
-.10
-.10
-.11
Rn meas
Tank #2
Open
.02
.12
.19
.26
.31
.36
.33
.26
.17
.07
.01
- .03
-.06
-.06
- .06
-.07
-.06
-.07
Rn cal
Styrofoam (767.)
1-hole
23 Aug 1968
82
-.06
-.05
-.05
-.06
-.05
-.05
.02
.12
.19
.26
.31
.36
.33
.26
.17
.07
.01.
-.06
-.06
-.03
- .06
-.06
-.07
-.07
Rn cal
95
-.04
-.04
-.05
-.04
-.06
-.06
.06
.20
.22
.25
.35
.41
.32
.22
.16
.04
.04
- .00
-.07
-.07
- .07
-.07
-.05
-.07
Rn meas
Tank #4
Styrofoam (76%)
12-hole
Comparison of measured and calculated net radiation over covered tanks (ly/min)
Table 7
57
such as the styrofoam cover with 12 holes,
or the wax blocks, are
not usually a problem since the radiometer views a representative
sample all the t:Ime.
This is shown in Table 7 where measured and
calculated values are seen to be essentially the same for the 12-hole
cover.
The 1-hole styrofoam cover should receive about the same net
radiation since the area covered and albedo are the same.
However,
in this case the readings are biased towards the open water portion
in the center due to the placement of the radiometer.
The hourly albedos of the cover materials investigated are
presented in Table 8 for the period of daylight.
This table was
derived from plots of half-hourly measured values recorded at various
times throughout both the 1967 and 1968 studies.
If equation [29] is rearranged, the long-wave atmospheric
radiation can be determined since all of the other parameters are
either known or measured.
Ra
= Rn-S+E woT w +rS
w
[32]
Long-wave radiation on September 29, 1967, as calculated by this method,
is presented in Table 9 for both the open and partially covered tanks.
Although the values obtained from open tank data are undoubtedly more
accurate, the other values are in good agreement with them.
The values
obtained from the partially covered tanks are subject to more error
58
Table 8
Average Albedo of cover materials
Open
Water
Wax
Blocks
White
Butyl
6
.99
.99
.98
.99
.43
7
.82
.88
.90
.55
.21
8
.72
.80
.84
.46
.13
9
.66
.75
.81
.43
.10
10
.64
.73
.79
.41
.09
11
.62
.72
.78
.40
.08
12
.62
.71
.77
.40
.077
13
.63
.71
.77
.40
.077
14
.65
.72
.78
.40
.08
15
.67
.73
.80
.41
.09
16
.70
.75
.82
.46
.11
17
.74
.80
.86
.55
.15
18
.83
.88
.91
.69
.25
19
.99
.99
.98
.99
.52
10.28
11.16
11.79
7.54
2.40
.73
.80
.84
.54
.17
Time
Avg.
Styrofoam
Cement
Blocks
59
Table 9
Longwave Radiation Calculations
September 29, 1967
(ly/min)
Open
Cement
Blocks
.52
.53
.53
.50
.51
.52
.53
3
.51
.51
.52
.53
4
.50
.50
.49
.52
5
.49
.50
.51
.52
6
.49
.50
.51
.52
7
.49
.50
.51
.52
8
.56
.59
.54
.51
9
.60
.64
.55
.59
10
.63
.65
.59
.62
11
.65
.66
.62
.61
12
.67
.66
.63
.61
13
.68
.65
.63
.61
14
.66
.65
.67
.57
15
.68
.57
.62
.58
16
.65
.56
.62
.55
17
.64
.59
.61
.58
18
.61
.58
.62
.60
19
.55
.56
.56
.57
20
.55
.55
.55
.56
21
.53
.53
.51
.54
22
.54
.55
.55
.57
23
.54
.55
.55
.57
24
.53
.53
.54
.54
60E
825
817
813
806
Time
Wax Blocks
1
.50
2
White Butyl
60
since more measurements are required and net radiation is subject to the
same Limitations as mentioned above.
The 813 langleys per day obtained
by this method is within reason when compared to values obtained by
Koberg (1964) by another method.
His values for both Lake Mead and
Roosevelt reservoir range between 650 and 820 langleys per day for the
same season during the l950's.
RESULTS AND DISCUSSION
The objectives of this study were to determine the physical
properties that should be considered in the design of floating covers
used to reduce evaporation from water surfaces, and to obtain a better
understanding of the evaporation process from a partially covered body
of water.
Results of the study that pertain to these objectives are
presented and discussed in this section.
Where possible, the results
are compared with those of previous investigators.
However, due to a
lack of studies of this type, this is possible in only a few cases.
The significant findings of each aspect of the study are also pointed
out.
Energy Balance of Tanks.
Daily totals of the parameters in
the energy balance equation are presented for the 1967 study in Table
10.
These values were obtained by measuring the net radiation and
evaporation, and calculating the energy in storage in the water and
cover.
The sensible heat term was then determined as the residual
in the energy balance equation.
This method of determining the sen-
sible heat transfer has some disadvantages since all errors in the
other terms of the energy balance equation are accumulated in the
residual term.
However, other methods to determine the sensible heat
transfer (A) have also been shown to be considerably in error at times
(Conaway and Van Bavel, 1966).
Therefore, the above method is probably
as good or better than any other available.
61
62
Table 10
Energy balance results on a 24-hour basis, 1967 (ly/day)
Date
Tank and Cover
Term
Sep 1967
Oct 1967
23
27
28
29
30
18
19
20
122
-13
114
107
56
52
56
27
3
0
-125
-16
0
-121
4
-2
8
0
19
0
2
Q
73
4
0
-76
-1
72
C
0
-4
-111
20
-80
22
-62
8
-93
33
103
25
0
94
11
90
86
59
55
59
4
6
9
0
-116
-12
-62
-43
0
-80
-14
0
-75
-17
-23
0
-31
340
328
-62
-338
141
349
48
-551
154
316
-14
-347
45
Material
Tank #1
Foamed
Wax Blocks
(787)
Tank #2
Butyl Rubber
(807)
Rn
LE
A
-134
Rn
C
137
-31
0
-120
Q
LE
A
Tank #3
Open Water
Tank #4
Lightweight
Concrete
Blocks
Sep (787)
Styrofoam
Oct (8O°h)
Rn
C
LE
A
Rn
25
14
366
4
-511
11
12
-444
92
72
189
182
G
2
15
169
-6
164
-21
Q
1
-1
-1
-3
-1
-222
26
-187
-124
-16
-191
LE
A
Rn
G
Q
LE
A
-271
79
25
0
-53
-5
0
-54
-10
256
202
259
-37
1
-4
-293
-285
74
82
-298
/H
-7
145
--2
49
20
17
5
28
0
-54
0
-89
9
54
0
-71
46
18
U
63
The sign convention used in this section of the study is as
follows:
Rn is positive when energy is being added to the water.
G is positive when the average water temperature is decreasing,
since the energy is then available for use in the evaporation
process.
Q is positive when the average cover temperature is decreasing.
LE is negative when evaporation is occurring.
A is positive when heat is flowing from the air to the water.
It is obvious from the results presented in Table 10, that the
net radiation and evaporation terms are by far the largest, except for
the styrofoam cover, in which case the evaporation and sensible heat
transfer terms are the largest.
From these results, it would appear
that generally the way to influence the evaporation term (LE) the most,
would be to change the net radiation term (Rn).
Small changes in the
reflective properties would have a much greater effect on the evaporation
term than would small changes in the sensible heat transfer characteristics, since for all covers except the styrofoam, it is of rather
minor importance.
The heat stored in the cover is noted to be less than 4 percent
of the evaporation term in all cases, and in fact, it is zero in most
cases.
Because of the small magnitude of this term, it was neglected in
all of the 1968 studies.
If other cover materials are used, however, this
term should be investigated.
64
Daily totals of the parameters in the energy balance equation
are presented in Table 11 for the 1968 studies.
In this table the
net radiation values were computed as noted in the previous section.
These data again indicate that, except for the large styrofoam cover,
the net radiation and evaporation are of greatest magnitude.
It is interesting to note that in most cases, for both the
1967 and 1968 studies, the sensible heat transfer is positive.
This
means that energy is being transferred from the atmosphere to the water,
and is therefore available for use in the evaporation process.
In the
case of the open water and the white butyl cover, this term is negative
about 1/4 to 1/3 of the time, indicating energy is being transferred to
the atmosphere, thus decreasing the energy available for evaporation.
This could indicate that if the albedo of the styrofoam and butyl were
the same, and if they both covered the same surface area,
would be more efficient in reducing evaporation.
the butyl
Data to verify this
assumption, however, are not available.
The results of the energy balance calculations are also presented
in graphical form in Figures 6 through 16.
The hourly values of evapora-
tion used in the 1967 graphs are calculated using the modified combination
method.
Totals will therefore differ slightly from those presented in
Table 10, which are based on evaporation measurements as recorded by
the water stage recorders.
These graphs show the hourly variations and
magnitudes of the energy balance parameters, revealing considerably
more than the daily totals presented in the tables.
Tank #4
Tank #3
Tank #2
Tank #1
Tank
Variable Date
Cover & 7 Area
Area
Open
-18
-86
19
85
-462
-24
St rofoam
27
459
125
-37
-56
-32
White Butyl
1
G
LE
A
Ua (cm/sec) 108
A
Cover &
Rn
G
LE
Rn
C
LE
A
Cover & 7 Area
Rn
Cover & io Area
A
Rn
C
LE
Table 11
124
-112
43
77
-8
-2
80
480
-44
-434
(867)
141
-29
-55
-57
2
-
15
1968
20
Open
402
-71
10
41
7
-317
18
-448
83
11
9
67
-53
-371
27
22
St rofoam
184
173
62
36
-312
-204
66
-5
St rofoam
298
290
412
78
-517
31
32
-93
30
Styrofoam
14
AUGUST
3
16
16
-64
29
19
22
-118
15
81
35
80
-132
41
10
St rofoam
81
81
28
-132
23
0 en
414
416
69
-116
-352
-467
52
-16
St rofoam
34
23
-79
22
81
30
-146
1
23
Styrofoam
22
267
325
18
-423
57
-291
37
(517)
197
435
14
-519
70
26
-95
36
(87
Energy ba1nce results ona 24 hour basis, 1968 (ly/day)
84
-8
-96
20
88
76%-12 hole
-76
3
84
-11
767.-1 hole
-5
-55
-362
422
-52
14
9
24
(877)
29
66
1.6
I
I
FLUX (LY MIN')
1.4
I
I
I
SEPT. 27, 1967
TANK Ui
1.2
O Rn
114iy
A LE -149
1.0
0.8
27
DA
8
0.6
0.4
-
,
0.2
+
0.0
0
0.
-
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1ST
1.6
0
2
I
I
I
4
6
8
I
10
I
12
I
I
14
$6
IS
I
20 22 24
Figure 6.--Hourly distribution of the energy balance components
over an insulated evaporation pan with 78 percent
cover of foaned wax blocks.
67
1.6
I
T
I
FLUX (LV MIN1)
I
J
SEPT. 27, 1967
TANK #2
1.2
o Rn IO3Iy
' LE -127
'.0-
0.80.60.40.2-
25
-I
DA
0
,0
0l
'0
+
DOD..D
0.0
-
0.20.40.60.8
1.01.2 1.4
TST
I.6
0
I
I
I
I
I
I
2
4
6
8
10
2
I
$4
I
$6
I
$8
I
20 22 24
Figure 7.--Hourly distribution of the energy balance components
over an insulated evaporation pan with 86 percent
cover of white butyl rubber.
68
1.6
'.4
I
1
1
I
FLUX (LV MIN')
SEPT.27,1967
TANK
.2
3
oRn 3491y ALE -553 -
1.0
/
0.8
0.6
0.4
.G
+
.O. 0
D\
0.0
-.
/
0.2
t
D.0t
8Loo&oC
I
0,4
156
o
/
0.2
48
\DA
O
1-
A
0.6
A'
0.8
1.0
1.2
1.4
1.6
1ST
I
0
2
4
6
8
l0
12
'4
I
6
I
I
IS
20
.1
22 24
Figure 8.--Rourly distribution of the energy balance components
over an insulated evaporation pan without surface
cover.
69
1.6
I
I
FLUX (LY MIN
I
SEPT. 27, 1967
)
TANK 4*4
1.2
o Rn
182Iy
oA
15
LLE-254
I.0
0.8
58
0.6
0.4
0
/
0.2
0
ci
0
0.0 DO.DO-D-D..
/if
U-
0.2
-
h
0.4
0.6
0.8
1.0
1.2
1.4
1ST
1.6
0
I
I
L
I
I
I
I
I
I
2
4
6
8
tO
12
14
16
18
I
i
20 22 24
Figure 9.--Hourly distribution of the energy balance corponent:s
over an insulated evaporation pan with 78 percent
cover of lightweight concrete blocks.
70
1.6
I
I
I
I
I
I
FLUX (LY MIN1 )
1.4
I
I
AUG. 2,1968
TANK
2
o Rn
1
141 ly
LE -55
1.0
G
oA
0.8
-29
-57
0.6
0.4
0.2
+
0.0
0.2
0.4
0.6
0.8
1.0
12
1.4
1.6
0
2
4
6
8
tO
12
14
(6
(8
20 22 24
Figure 1O.--Hourly distribution of the energy balance component:s'
over an insulated evaporation pan with 86 percent
cover of white butyl rubber.
7]-
1.6
FLUX (LV MIN't
4
TANK2
I/
oO\
1.2
i.0
0.8
o Rn 48OIy
LLE-434
o G -44
\oA -2
000
/
0.6
0.4
AUG. 2, 1968
)
- e.IIs
0
0.2
0-0,
-0'
+
0.0
0-0'
0-0 0
0
/
0.2
0.4
0.6
1'
0.8-
5-
1.01.2
1.41.6
02 4
TST
6
8
I0
12
14
16
18
20 22 24
Figure 11. --Hourly distribution of the energy balance components
over an insulated evaporation pan without surface
cover.
72
1.6
I
1.4 -
I
I
I
I
I
FLUX(LYMII(')
T
I
AUG. 2, 1968
TANK *13
1.2
77Iy
o Rn
i0
'
LE -112
-8
G
DA
0.8
43
0.6
0.4
OOO
n'tJ-D'
0.2
+
0.0
gRja
Lr
,-,ri
-;
A'
0.2
0.4
0.6
0.8
1.0
1.2
1.4
TST
1.6
0
2
4
6
8
10
12
14
16
18
20 22 24
Figure l2 --Hourly distribution of the energy balance componeits
over an insulated evaporation pan with 80 percent
cover of styrofoam.
73
1.6
I
1
t
AUG.16,1968
1.4
TANK 4*2
o Rn 4351y-
1.2
LE -519
14
oG
1.0
-
0.8
0.6
0.4
0.2
+
0.0
0.2
0-- OO..O..Q..O..0
-
\
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0
-
TST
-
2
I
I
4
6
_J__J
8
10
I
12
I
14
_...,_J
16
I
18
I
I
20 22 24
Figure 13. --Hourly distribution of the energy halnce components
over an insulated evpora.tion pTL without surface
cover.
74
1.6
FLUX (LV MIN)
1.4
AUG. 16,1968
-
TANK it 4
o Rn 3251y -
2
L-423
l.0
0.8
DA
\0
0
/
0.6
0
0
0.2
+
0._a
--
/.' '.,'D
0.0
80
\
0
04
8
0
0.2
0.4
0.6
0.8
1.0
1.2
'.4
16
0
2
4
6
8
tO
12
'4
$6
18
20 22 24
Figure 14. --Hourly distribution of the energy balance components
over an insulated evaporation pan with 26 percent
cover of styrofoam.
75
(.6
'.4
- FLUX (LV MIN1)
AUG. (6, (968
TANK *3
o Rn 1971y
LE -291
(.2
I.0
37
57
oA
0.8
0.6
o_
0.4
0.2
±
0/0/
/
-
0/0%
0-0
0.0
0.2
"0-0
\ti'
\
1hA
>t\ /\l
,
0.4
Si .)w._a
P.
0-0
a
A
I
0.6
0.8
1.0
(.2
'.4
TST
8
(0
(2
4
(6
(8
20 22 24
Figure 15. --Hourly distribution of the energy balance components over
an insulated evaporation pan with 51 percent cover of
styrofoam.
76
1.6
AUG. 16,1968
.4
TANK *1
o Rn 33Iy
1.2
LLE -95
10
26
36
oA
0.8
0.6
0.4
0.2
+
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
4
6
8
10
12
14
16
18
20 22 24
Figure 16. --Hourly distribution of the energy balance components
over an insulated evaporation pan with 87 percent cover
of styrofoam.
77
In Figures 6 and 7 the daily totals for all the parameters are
of corresponding magnitude.
However, the variation in the energy stored
in the water is considerably different.
They butyl cover, being very
thin, allows heat to pass through during the day, thus increasing
energy stored in the water.
the
At night, heat is transferred back through
the cover, decreasing the energy stored in the water.
The cover of
wax blocks, on the other hand, allows very little heat transfer; thus,
variation of energy stored in the water is small.
In Figures 8 and 9 the variations are shown for the open tank
and concrete block cover, respectively.
The variations as shown in
Figure 9 for the lightweight concrete blocks are seen to be about
midway between those observed on the open tank and the tank with wax
blocks as a cover.
The heat storage in the open tank varies considerably
since radiation penetrates into the water and warms a deeper layer.
Also, back radiation at night is not restricted by a cover.
Comparison of variations for styrofoam and butyl, shown in
Figures 10 and 12, respectively, indicate that the styrofoam cover
dampens the variation of all parameters considerably, although there
is still a slight peak near midday.
In this particular case, evapora-
tion from the tank with the butyl cover is minimum during midday,
indicating that the radiative energy is being stored in the water.
The
other two tanks show maximum evaporation at midday under the same
atmospheric conditions.
Variations on the open tank are presented in
Figure 11 for comparative purposes.
78
Figures 13 through 16 present the variations as determined for
August 16, 1968.
In this case the effects of three styrofoam covers of
different sizes are compared to the open tank.
The areas covered in
Figure 14, 15, and 16 were 26, 51, and 87 percent, respectively.
These
graphs present a vivid display of the dampening effect of this type of
cover.
The magnitude of variations are seen to be inversely proportional
to the area covered.
The effect of these covers on average water temperatures may
be an important design consideration.
The amplitude of the variation of
energy stored in the water, as shown in Figure 16, indicates a nearly
constant average temperature (with a range of less than 1°C in this case),
whereas the average temperature within the open tank, as indicated by
variation of stored energy, may vary by several degrees (5°C in this
ca.e)
.
ThIs change In temperature ro1ine may L;Imi t the spec lc's o
plants and animals that could adapt to these conditions.
Relationship of Cover Properties to Evaporation Reduction.
In
an attempt to relate the amount of evaporation reduction to some physical
property of the covers, it was noted that the percent of evaporation
reduction was almost the same as the percent of net radiation reduction.
Table 12 shows the percent of reduction in net radiation and evaporation as
compared to that measured over the open tank.
For evaporation, both cal-
culated and measured values compared to values of net radiation reduction,
are presented.
These comparisons also give an indication of the validity of
the calculations of evaporation by the modified combination method.
79
Table 12
Reduction in Net Radiation Compared to Evaporation Reduction
Period, Material,
and percent
coverage
Percent Reduction
in Net Radiation
As Compared to
Open Tank
Percent Reduction in
Evaporation as Compared
to Open Tank
Calculated
Measured
23-30 Sep 1967
Wax (78%)
72
74
73
White Butyl (86%)
70
79
79
Concrete (78%)
50
55
53
Wax (78%)
77
73
69
White Butyl (86%)
76
84
82
Styrofoam (80%)
92
76
69
White Butyl (86%)
72
88
84
Styrofoam (80%)
83
78
83
Styrofoam (87%)
93
82
82
Styrofoam (51%)
56
43
30
Styrofoam (26%)
27
16
10
Styrofoam (87%)
93
83
83
Styrofoam (76%-i Hole)
80
72
70
Styrofoam (76%-12 Hole)
80
68
64
18-20 Oct 1967
1-2 Aug 1968
14-16 Aug 1968
22-24 Aug 1968
80
A comparison of measured evaporation reduction and measured net
radiation reduction is presented in Figure 17 in order to emphasize
this relationship.
Regression analysis of the data pertaining to the
styrofoam covers produces a correlation coefficient of 0.99.
In other
words, there is a very close correlation between the reduction in net
radiation and evaporation reduction as compared to an open tank.
Regression analysis was not undertaken for the other cover
because of lack of data.
materinlH
However, the available data are shown in
Figure 17 for comparative purposes.
These data show that for the same
percentage of reduction in net radiation, the other materials reduced
evaporation more than styrofoam.
The thin white butyl cover would
appear to be the most efficient of any material tested.
The plots
of
hourly distribution of the energy balance equation components indicated
that: the butyl may be more efficient, but were not sufficient them-
selves to warrant this conclusion.
The close correlation between evaporation reduction and reduction
in net radiation also points out that in designing covers to reduce
evaporation, emphasis should be aimed at increasing the reflectance
and emittance of the cover material.
For example, changing the rough-
ness would be of minor importance compared to reflective characteristics.
The percent of surface area covered was also found to correlate
with evaporation reduction.
This relationship is presented in Figure 18.
81
2
0
I-I00
4
c
4
o STYROFOAM
CONCRETE BLOCKS
WAX BLOCKS
O
8O
WHITE BUTYL
RUBBER
w
2
87
D
0
I0
w
4o
Iw
0
cr
w
a-
0
20
40
60
80
100
PERCENT EVAPORATION REDUCTION
Figure 17.--Relationship between evaporation reduction and reduction
in net radiation.
82
These data are presented in Table 13 of the following section.
Regres-
sion analysis of the data pertaining to styrofoam covers produced a
correlation coefficient of 0.99.
This close correlation would probably
be found for eachcover material tested, however, the slope of the
best fit line may be considerably different as suggested by the data
point for concrete blocks.
Accord lug to Figure 18, the rnrit erial s are aht)t.t equal ly
efficient, except for the concrete blocks, which reduce evaporation
less than the others for the same area covered.
Since Figure 17 in-
dicated the concrete blocks would be more efficient than the styrofoam,
if the reduction in net radiation were the same, this difference must
be due to lower albedo of the concrete blocks.
While studying various types of hexadecanols for use in reducing
evaporatior, luritzen (1967) experimented with a black foamed poi.yethylene.
Although his tests were
onducted on small laboratory dishes
and may not represent field conditions as far as absolute values are
concerned, he did note a correlation between area covered and evaporation
reduction.
The four values he reported are presented in Figure 18.
correlation coefficient was again 0.99.
The
These data are presented for
comparison purposes only and undoubtedly would be different under field
conditions where radiative effects were present.
83
/0
100
Ui80
0
Ui
>
0
0
60
Ui
I-
40
0 STYROFOAM
2
WAX BLOCKS
CONCRETE BLOCKS
WHITE BUTYL RUBBER
Ui
0
o
0 BLACK FOAMED
w 20
a-
POLYETHYLENE
(LAURITZEN, 1967)
0
20
40
60
80
100
PERCENT EVAPORATION REDUCTION
Figure 18. --Relationship between evaporation reduction and perceilL
of surface covered.
84
Efficiencies of Covers Tested.
Evaporation measurements recorded
during this study are presented in Table 13.
Also shown are the percent
of surface area covered and the percent of evaporation reduction as
compared to the open tank.
The measurements cover a longer period than
the energy balance results presented in Tables 10 and 11, since only
data on selected days were used in those calculations.
Figure 18,
which was derived from the same data, shows that for these covers, all
of which were white or light colored, evaporation reduction was essen-
tially equal to the precent of surface area covered.
It should also
be noted that all of these covers were impermeable except for the
lightweight concrete blocks, which allowed some transfer of moisture.
An interesting point noted was that the styrofoam cover with
1 hole was more efficient than the one with 12 holes, although both
were the same color and covered the same area.
In order to eliminate
any effect of exposure, the covers were alternated on August 29, and
evaporation was again recorded.
Exchanging the covers had no effect
on the results obtained for the 12-hole cover, and only slightly
affected results for the 1-hole cover.
still the more efficient.
The cover with 1 hole was
From the measurements available, it was
not possible to determine the cause of this difference.
It could have
been due to a difference in roughness or to reduced air transfer and
turbulence within the smaller holes.
2 Oct 67
Cover
19 Aug - 29 Aug 68
29 Aug - 10 Sep 68
10 Aug - 19 Aug 68
4 Oct - 7 Nov 67
22 Jul - 3 Aug 68
17 Sep - 1 Oct 68
11 Oct - 18 Oct 68
11 Sep
Period
-6.97
- .92
1.l6
83
84
Styfofoam
84
Open
- 5,58
Styrofoam
-1.05
Open
- 637
77
Foamed Wax
75
Foamed Wax
7,
Red
-3.56
-2,84
(cm)
Evap
-15.45
- 4.98
- 6.84
- 2.69
Open
-11.36
Open
(cm)
Evap
87
86
87
78
78
7,
Area
7,
Red
7,
Area
51
80
80
80
80
-1.35
-1.87
73
76
76
76
Styrofoam - 1 hole
-3.31
Styrofoam
48
79
.56
-
76
74
-3.45
-1,17
-1.75
Styrofoam
78
Concrete blocks
60
-4.50
78
(cm)
Evap
Efficiency of floating materials in reducing evaporation
Table 13
.74
.66
22
Styrofoam
75
82
85
76
Butyl rubber
81
26
86
86
80
80
86
7,
Area
Butyl rubber
7,
Red
-1.67
-2.12
70
70
76
76
Styrofoam - 12 hole
-4.96
-
-1.66
-
-2.74
-2.21
(cm)
Evap
CONCLUS IONS
The following conclusions are based on:
a theoretical analysis
of the energy balance equation as it applies to a partially covered
body of water; and experimental analysis of the energy balance for
partially-covered insulated evaporation tanks.
The conclusions are:
The most important properties to consider in the design
of floating materials for reducing evaporation are reflectance and
emit tance.
Covers should be colored white.
The combination method of determining evaporation from
an open water surface proved best for use under the conditions of
this study.
The modified combination method of determining evaporation
from a partially covered water surface is valid as derived in this
study.
The use of insulated evaporation tanks provides an easy
and accurate method of determining long-wave radiation from the atmosphere, and net radiation over other surfaces where reflectance is known.
For the covers tested in this study, the reduction in net
radiation, occurring due to covering part of the surface, is highly
correlated with the reduction in evaporation from that surface as
compared to an open water surface.
86
87
For styrofoam covers of the type used in this study, the
percent of evaporation reduction occurring due to placing a cover on
the surface is highly correlated to the percent of area covered.
For all of the covers tested, the percent of evaporation
reduction was almost the same as the area covered.
The styrofoam cover with 1 hole was more efficient than
the one with 12 holes, although both were the same color and covcrcd
the same area.
It is believed that this study has provided important information
to consider in the design of floating covers to reduce evaporation, as
well as providing considerable insight into a relatively untouched
subject of evaporation from partially covered bodies of water.
27
22
5
6
46
21
41
67
89
78
Units:
Avg
21
22
23
24
20
10
11
12
13
14
15
16
17
18
19
9
8
7
4
3
51
130
152
112
129
121
119
136
113
113
73
54
49
43
47
38
81
2
1
Time
15
13
13
14
13
15
13
16
13
13
13
13
13
13
11
12
12
12
13
11
11
11
12
10
10
-
-.04
-.08
-.08
-.09
-.08
-.08
.87
.75
.50
.20
1.00
1.01
.07
.28
.56
.73
.89
-.10
-.10
-.10
-.09
-.10
-.10
-.07
20.3
20.1
20.8
20.3
19.3
19.1
19.8
19.8
19.3
19.3
20.8
22.6
22.8
24.0
24.5
25.3
25.0
24.8
25.0
24.3
24.0
23.8
23.8
22.6
22.1
25.6
25.2
23.9
260
23.1
22.8
22.5
22.2
21.9
21.7
21.4
21.2
21.1
21.4
22.1
22.9
23.7
24.5
25.4
26.1
26.5
26.7
26.6
26.5
26.3
91
31
29
30
67
60
125
147
107
100
95
166
147
152
226
162
47
56
113
79
93
70
41
40
47
36.6
34.2
31.8
30.9
30.28.7
27.3
28.8
16
17
17
374
.94
17
16
.77
18
17
16
17
17
17
17
16
17
17
17
18
-
-.01
-.04
-.04
-.02
-.07
-.07
.88
.72
.50
.20
1.01
1.00
.10
.31
.58
17
16
16
16
15
15
-.08
-.09
-.09
-.08
-.08
-.09
-.09
14
14
24.8
24.0
23.3
23.3
22.3
20.8
19.8
22.1
24.5
27.7
29.7
31.1
32.6
34.2
36.2
37.4
25.0
25,1
27.5
26.7
25.3
25.8
25.8
29.4
22.3
23.8
24.0
25.0
25.8
26.5
27.5
29.4
29.7
23.1
23.3
22.8
23.1
22.1
22.1
22.1
23.8
23.7
23.5
23.4
23.5
23.8
24.3
25.0
26.0
26.9
27.7
28.5
28.9
28.9
28.3
27.8
27.4
27.1
26.8
26.6
25.9
25.0
24.8
24.6
24.3
24.0
21 September 1967
Open Tank
R
T
e
T
Tavg
U
w
a
n
339
401
329
336
233
237
188
228
221
118
141
84
84
103
161
55
88
136
207
51
78
43
48
51
55
29.7
28.2
25,8
30.2
17
24.0
25.0
24.0
23.5
22.3
23.1
28.2
30.6
33.3
34.5
35.7
36.6
37.1
38.3
36.6
36.0
34.2
32.3
31.8
16
15
15
15
17
16
16
17
16
15
15
18
16
16
14
17
17
17
17
16
16
16
17
16
27.7
25.3
-
-.00
-.04
-.04
-.03
-.03
-.07
.25
.64
.99
.86
.83
1.01
.05
.28
.56
.78
.93
-.07
-.08
-.07
-.04
-.03
-.06
-.08
25.3
24.0
23.1
22.8
24.3
23.1
23.8
23.8
25.5
26.0
27.7
28.2
29.2
29.7
30.2
30.9
29.9
29.4
28.2
27.2
26.7
26.2
25.8
25.0
26.5
22 September 1967
Open Tank
R
T
T
U
e
w
n
a
a
Wind speed cm/sec, temperature °C, radiation ly/min, vapor pressure mb
26.0
24.8
24.0
25.9
27.7
21.1
20.1
17.8
17.8
17.8
17.6
18.3
18.6
21.6
24.8
27.7
31.1
31.8
33.1
33.5
34.0
35.5
34.2
32.1
29.9
20 September 1967
Open Tank
T
U
e
R
T
Tavg
a
a
n
w
Meteorological Data
APPENDIX Table 14
. 6
. 4
26.5
26
26.8
27. 2
27
28.0
28.2
28.3
28.2
28.0
27 . 7
27 . 2
25.7
26.2
26.7
25 . 2
26.4
26.1
25.7
25.4
25.1
24.9
24.8
24.8
24.9
Tavg
79
64
64
124
96
75
Units:
Avg 137
24
23
20
21
22
17
18
19
10
11
12
13
14
15
16
9
8
7
6
5
4
13
16
13
14
12
13
16
14
15
18
19
19
19
18
18
19
18
16
15
14
14
0
0
0
0
0
.88
.63
.09
.04
1.14
1.06
0
0
0
0
0
0
0
.14
.42
.68
.90
1.05
1.12
S
-.05
.-.02
-.04
-.04
-.02
-.05
-.03
.41
.39
.35
.26
.16
.35
.02
.11
.20
.30
-.01
-.04
-.03
-.02
-.04
-.05
-.05
20.5
20.6
20.5
20.0
20.1
19.8
19.5
19.0
20.4
22.0
23.1
23.7
23.7
23.2
22.7
21.9
20.9
20.1
19.7
19.4
19.3
19.3
19.4
19.7
20.8
39,7
33.8
29.6
27.4
25.7
24.2
23.0
21.8
28,5
20.1
25.8
31.8
37.0
40.8
43.1
44.2
44.3
43.0
16.7
16.3
20.8
19.9
19.0
18.2
17.4
24.5
24.4
24.3
24.3
24.2
24.1
24.0
23.9
23.9
24.0
24.2
24.4
24.6
24.7
24.8
24.9
24.9
24.9
24.9
24.9
24.9
24.8
24.8
24.7
24.5
-.08
- .04
-.07
-.08
-.04
-.07
-.06
.45
.41
.31
.18
.18
.31
.41
.49
.50
-.07
-.05
-.08
-.08
-.09
-.01
-.04
-.08
fl
R
W
23.3
22.8
22.6
22.3
22.1
21.8
22.1
22.1
22.1
23.3
25.8
27.5
27.7
29.4
29.9
30.2
29.2
27.0
25.8
25.3
24.5
24.0
24.0
23.8
24.9
T
C
26.5
26.1
30.3
23.4
26.3
30.5
35.1
39.0
41.4
42.7
42.8
41.5
37.2
32.4
30.1
28.8
27.9
27.2
25.7
25.0
24.4
23.9
23.5
23.2
23.1
T
White Butyl (86%)
25.7
25.9
25.5
25.6
25.8
25.6
25.3
25.3
25.0
24.6
24.3
24.2
24.0
23.8
23.7
23.6
23.6
23.5
23.4
23.5
23.9
24.2
24.5
25.1
25.4
Tavg
-.03
-.04
-.02
-.05
-.04
-.02
-.05
.39
.25
.50
.17
.33
.41
.52
.55
.55
-.02
-.05
-.04
-.03
-.05
-.05
-.05
-.01
23.3
22.3
23.1
22.6
21.1
21.6
21.6
21.8
22.1
23.1
25.0
25.0
24.3
24.5
24.5
24.8
23.5
23.1
22.6
23.8
23.3
23.3
23.3
22.8
23.2
27.5
25.5
24.8
24.0
22.9
23.2
22.1
21.1
20.4
19.9
19.9
20.2
21.3
24.0
29.2
33.8
36.6
38.2
39.1
39.0
37.9
35.0
29.6
26.9
26.1
24.7
24.4
23.7
23.6
23.6
23.7
23.9
24.1
24.5
24.8
24.9
25.0
25.2
25.1
25.1
25.1
25.0
25.0
24.8
24.4
24.3
24.1
24.0
23.9
23.8
Concrete Biks (78%)
T
T
Tavg
R
c
n
w
Wind speed cm/sec, temperature °C, radtation ly/min, vapor pressure mb
29.7
26.5
29.3
34.2
36.2
36.9
37.1
37.1
36.4
34.7
31.8
32.3
32.1
30.2
23.5
23.5
22.1
21.1
19.8
21.3
24.8
28.2
31.1
39
39
36
52
65
69
115
3
160
163
201
318
348
291
284
254
219
16
27.2
24.8
58
76
1
2
15
17
16
a
e
a
T
U
Time
Wax Blocks (787.)
T
T
R
Tavg
w
n
c
September 23, 1967
Neteorological Data
Table 14--Continued
-.02
-.06
-.05
-.03
.94
.75
.50
.01
-.04
-.02
1.02
1.01
.27
.57
.78
.96
-.04
-.08
-.09
-.09
.04
'-.07
25.3
25.0
26.2
30.2
30.7
30.9
30.2
28.2
27.0
27.0
26.2
27.7
28.9
29.9
25.0
24.3
23.5
24.3
24.3
22.3
21.6
22.3
23.1
24.5
26.0
24.6
24.9
25.3
26.1
27.0
27.8
28.2
28.6
28.7
28.5
28.3
28.0
27.7
27.3
26.8
26.3
26.4
24.4
25.7
25.3
25.0
24.7
24.6
24.4
26.0
Open Tank
T
Tavg
n
w
-.03
-.08
R
270
87
22
23
Units:
24
74
vg 178
175
182
326
300
124
30
123
79
58
79
84
73
218
49
117
165
168
337
395
385
368
20
21
19
18
17
16
15
14
13
10
11
12
9
8
7
6
5
4
3
2
1
Time
U
14
14
14
14
14
14
14
14
13
14
15
16
16
16
16
15
15
14
15
14
14
14
14
14
14
0
0
0
0
0
.60
.33
.03
.85
1.04
1.12
1.11
1.02
0
0
0
0
0
0
.13
.42
.68
.89
0
-.06
-.05
- .06
-.05
-.06
-.06
.40
.41
.38
.33
.24
.14
.03
.37
.12
.26
0
-.06
-.06
-.06
-.06
-.06
-.06
-.06
19.8
20.0
19.8
19.6
19.1
19.3
19.1
19.3
20.1
20.3
20.8
21.1
21.3
21.3
21.3
21.1
20.3
20.1
19.1
19.1
19.3
19.3
19.3
19.3
20.0
26.0
16.5
17.0
16.5
15.9
15.7
15.5
15.4
15.3
17.3
26.2
32.7
36.8
38.9
40.3
41.1
41.0
40.0
37.5
32.5
27.8
24.6
22.1
20,0
18.0
C
0./
23.3
23.2
23.2
23.1
23.2
23.4
23.5
23.5
23.4
23.5.
23.6
23.5
23.3
23.2
23.2
23.1
23.0
22.9
22.9
22.9
22.9
23.0
23.1
23.3
23.4
Tavg
-.07
-.08
-.08
-.08
-.08
-.08
.41
.34
.24
.12
.01
.27
.40
.43
.46
.17
0
-_lO
-.09
-.09
-.09
-.09
-.09
-.09
fl
R
w
C
867)
37.9
38.7
38.9
38.4
36.0
31.7
28.3
26.5
25.1
24.2
23.5
22.9
28.1
36.5.
22.5
22.2
21.9
21.7
21.5
21.4
21.4
22.8
26.4
30.4
33.8
T
23.4
23.4
23.7
23.5
23.2
23.2
23.0
22.9
22.8
22.6
22.5
22.4
22.3
22.4
22.6
23.0
23.4
23.8
24.1
24.4
24.5
24.5
24.3
24.1
23.9
Tavg
-.05
-.06
-.06
-.06
-.06
- .05
.32
.41
.52
.57
.59
.51
.39
.25
.10
.17
-.06
-.07
-.07
-.07
-.06
-.06
-.05
-.02
n
R
h
25.5
25.8
26.2
26.2
25.3
23.8
23.1
22.3
22.1
22.1
21.6
21.6
23.0
21.3
21.3
21.3
21.6
21.3
21.1
20.3
21.3
22.3
23.8
24.8
24.8
w
. 1
25 . 0
24.9
23.3
22.0
20.9
20.1
19.5
27
35.9
36.9
34.7
32.8
30.4
35. 1
19.7
19.2
18.8
18.5
18.3
18.3
18.4
20.2
24.4
28.7
32.3
Concrete Biks
y/nin, vapor pressure
21.1
20.8
20.8
20.3
20.1
20.1
20.3
20.8
20.8
21.6
23.5
25.8
26.5
27.0
28.2
28.2
27.5
25.8
23.8
23.1
22.3
21.8
21.6
21.1
23.0
T
White But 1
September 27, 1967
Wind speed cm/sec, temperature °C. radiat::.
21.8
21.0
20.1
19.8
19.8
19.8
20.0
20.9
25.2
27.7
29.8
31.4
32.4
33.1
33.7
34.1
33.5
32.2
30.1
28.1
26.3
24.7
23.3
22,1
26,3
Wax Blocks
R
w
n
14--Continued
Meteorological Data
Table
avg
- .09
23.4
23.2
23.4
- . 09
- . 08
- . 08
- . 07
23.5
- . 05
- . 03
.99
.89
.70
.45
.21
94
1.02
.03
28
.56
.81
- . 09
- .09
- .09
25.8
26.7
27.5
27.7
28.2
28.4
28.2
27.7
25.5
24.8
23.8
22.8
22,3
22.1
24.3
25. 0
23. 9
24.5
24.2
24. 2
avg
. 4
26.5
25.9
25,4
24.9
24.6
24.3
24.8
27. 1
27
27 . 2
23.5
23.2
23.0
22.9
23.0
23.3
23.8
24.5
25.4
26.1
26.7
Tank
20.3
21.5
21.8
21.6
21.3
21.1
20.5
23.3
24.5
I. en
-.10
-.10
-.10
K
23. 7
23.4
23.7
23.9
24.0
24.0
24.0
23,9
23. 2
23.6
23.4
23.4
23.3
23.2
23.0
22.9
22.8
22.8
22,8
22,9
23.1
78%
84
78
53
126
166
143
6
a
- .07
0
0
0
0
0
-.06
-.06
-.01
- .04
-.05
- . 05
- . 07
n
0
S
19.1
19.3
19.6
19.6
19.1
18.8
18.8
19.3
19.8
20.3
20.8
20.8
21.1
21.1
20.8
20.8
20.3
19.3
19.1
18.8
18.6
18.3
19.1
19.3
w
15.6
14.8
14.3
14.2
14.5
14.9
15.5
17.1
25.5
30,8
C
23.1
23.1
23.1
23.1
22.8
22.7
22.6
22.6
22.5
22.5
22.6
22.7
22.8
22.9
23.0
23.1
23.7
23.3
23.3
23.3
23,3
23.2
23.2
23.1
23.0
-.09
-.10
-.10
-.10
-.08
-.09
-.10
R
n
44
28
288
212
110
53
59
55
17
18
19
20
21
22
23
24
304
267
293
207
325
16
15
10
11
12
13
14
8
9
7
13
13
12
13
13
12
12
12
12
12
12
13
13
13
13
13
13
13
0
0
0
0
0
.84
.60
.32
.03
1.12
1.11
1.01
.68
.90
1.05
.15
.47
.01
-.05
- . 05
- . 06
- . 05
-.07
-.06
.12
.01
.39
.36
.31
.22
.37
.38
.14
.25
19.7
16.7
15.4
14.9
14.5
14.3
24.1
35.2
38.3
40.0
40.8
40.8
39,3
36.4
31.2
23.0
-.02
-.10
-.10
-.10
-.10
-.11
-.10
.11
.19
.25
.39
.44
.46
.43
.34
.23
.02
Wind speed cm/sec, temperature °C. radia:ic
a
Units:
12
12
12
12
13
13
12
e
Avg 134
20.2,
21.0
20.3
19.8
19.6
T
w
c
22.5
22.0
21.7
21.8
21.7
21.4
21.2
22.2
25.9
29.2
28.9
34.5
36.7
37.9
37.4
36.4
34.3
31.7
27.4
25.3
24.6
23.1
22.5
22.2
27.2
T
22.0
22.0
22.1
22.2
22.5
22.9
23.4
23.9
24.1
24.2
24.1
24.0
23.9
23.6
23.4
23.1
23.0
23.0
22.7
22.5
22.3
22.2
22.1
23.1
22.9
Tavg
- . 06
- . 06
- . 06
- . 06
- . 06
- . 06
22
07
44
.52
.52
.52
.45
.35
15
.33
.01
- . 06
- .05
- . 05
- . 06
- .06
- . 06
- .06
23. 1
23.0
18. 2
23
22.5
. 8
. 6
23
. 0
23.7
23.7
23.6
23.4
23.2
23
23.1
23.1
23.0
22.9
22.6
22.4
22.3
22,3
22.3
22.4
22.5
22.6
22.8
23.0
23.2
23.5
18.2
22.1
25.6
28.8
31.5
33.5
34.8
34.5
33.5
31.5
28.4
23.9
21.3
19.9
19.2
18.6
17 . 1
19.1
18.6
18.0
18.1
18.2
17.5
20.8
20.3
21.3
21.3
20.3
19.8
20.3
21.1
21.8
22.8
23.1
24.0
24.5
25.8
25.8
25.8
25.0
23.5
23.3
22.3
22.1
21.8
21.6
21.3
Concrete Biks (78%)
Tavg
T
T
R
c
w
n
mm, vapor pressure mb
20.1
20.3
20.3
20.3
20.1
19.8
19.8
20.3
19.8
20.3
21.8
23.8
25.3
26.5
26.2
26.2
26.0
24.5
23.1
23.1
23.1
21.8
21.3
21.1
22.3
T
White Butyl (86%)
20.5
19.8
19.8
24.2
26.9
28.9
30.4
31.5
32.2
32,6
32.8
32.5
31.7
29,5
26.8
24.6
23.0
21.9
21.2
25.5
5
36
67
122
65
42
U
4
3
2
1
Time
Wax Blocks (78%)
T
T
Tavg
R
September 28, 1967
Meteorological Data
Table 14--Continued
-.10
-.10
-.10
- . 10
-.09
17
- .06
.69
.43
.87
.33
.54
.80
96
1.03
98
05
- . 09
- .09
- .07
-.10
-.10
- . 09
w
25. 2
23.9
23. 9
24.8
24.5
24.3
24.0
25
24.0
23.6
23.8
23.1
22.3
22.3
23.3
. 8
26. 2
25. 9
24.8
25.5
24. 2
23.9
23.7
23.3
23.0
22.6
22.4
22.1
22.0
22.1
22.4
22.8
23.4
Tavg
27. 2
27 . 2
26.5
26.7
27.0
25.0
26.0
21.3
21.1
20.8
20.6
18.6
19.8
20.3
21.6
22.6
23.8
24.5
T
Open Tank
- .09
n
R
117
94
Avg
Units:
30
123
65
42
36
75
115
80
60
205
178
70
78
80
146
159
150
180
47
55
a
11
11
12
12
12
12
12
13
14
15
15
14
13
13
12
12
12
14
14
14
14
14
14
14
13
e
0
o
0
.83
.59
.30
.03
0
0
1.05
1.13
1.10
1.01
0
0
0
0
0
0
.01
.13
.41
.67
.89
S
-.05
-.05
-.06
-.06
-.06
-.06
.08
.01
.27
.15
.30
.18
.25
.32
.35
-.07
-.01
.10
- .07
-.06
-.07
- .06
-.06
- .06
19.1
18.6
18.6
18.6
17.8
17.6
18.3
18.3
18.3
20.3
21.3
21.3
21.6
22.6
22.3
22.3
22.3
21.3
20.0
19.3
19.3
19.3
19.3
18.8
19.8
14.3
14.1
13.5
13.0
13.1
13.4
13.9
16.4
24.2
31.8
37.2
40.4
42.6
43.6
43.7
42.6
38.7
31.4
22.7
19.0
17.4
16,7
16.5
16.6
24.9
1967
-.01
-.10
-.10
-.11
-.09
-.0
-.C9
.43
.41
.34
.24
.12
.01
.16
.27
.38
.42
-.10
-.10
-.10
-.10
-.10
-.10
-.10
28.5
26.4
25.0
24.1
23.5
23.1
27.6
35.4
31.9
21.7
21.4
21.2
21.1
21.0
21.0
21.1
21.9
24.4
29.1
32.9
35.6
37.5
37.7
38.3
37.8
22.7
22.6
22.4
22.3
22.1
22.0
21.9
21.8
21.8
21.9
22.0
22.3
22.7
23.3
23.7
24.0
24.2
24.2
24.2
24.1
23.8
23.4
23.2
23.1
22.9
-.06
-.07
-.07
-.05
-.04
-.06
.31
.19
.05
.49
.44
.55
.19
.34
.44
.52
-.06
-.06
-.06
-.06
-.06
-.06
-.06
-.02
27.7
26.7
24.8
23.3
22.6
22.3
22.3
21.3
23.6
21.3
21.1
21.3
21.1
20.8
19.8
20.3
20.1
21.3
23.1
24.8
25.8
28.2
28.2
28.2
29.4
17.9
17.6
17.4
17.2
17.0
16.8
16.7
18.5
23.4
28.4
32.3
35.4
37.9
39.0
38.6
36.8
33.8
29.7
23.7
22.4
21.5
20.9
20.5
20.2
25.2
23.1
22.9
23.7
23.7
23.7
23.6
23.5
23.3
23.2
22.9
22.7
22.6
22.5
22.4
22.2
22.1
22.0
22.0
22.2
22.3
22.6
22.8
23.0
23.3
23.6
Concrete Biks (78.)
Tavg
R.
T
T
w
C
n
1v.'in. vapor pressure mb
27.7
27.7
28.7
27.5
27.0
25.8
23.5
22.6
22.1
21.8
l.3
22.9
20.3
20.3
20.3
20.1
20.1
19.8
19.6
19.6
19.6
21.3
22.6
24.5
25.8
white Butyl (867
R
T
Tavg
T
C
w
n
radiati:
22.9
22.8
22.6
22.5
22.4
22.4
22.3
22.3
22.2
22.3
22.4
22.5
22.6
22.8
23.0
23.1
23,2
23.2
23.2
23.1
23.1
23.1
23.0
23.0
22.8
Wax Blocks (,R7)
T
R
Tavg
Wind speed cm/sec, temperature
26.3
24.4
23.1
22.4
25.9
30.8
31.9
32.8
33.5
33.9
33.9
33.3
31.9
29.4
20.5
20.0
19.6
19.2
18.8
18.5
18.3
19.8
23.6
26.7
29.1
a
68
56
51
18
19
20
21
22
23
24
17
10
11
12
13
14
15
16
9
8
7
4
5
6
3
2
1
Time
T
U
September 29,
Meteorological Data
Table 14--Continued
-.08
-.09
-.10
-.08
-.08
-.09
.86
.67
.43
.16
1.00
1.00
.02
.26
.54
.78
.93
-.09
-.10
-.10
-.10
-.10
-.09
-.10
w
22.3
22.1
20.8
19.6
20.3
19.8
20.3
19.8
21.6
24.0
25.0
25.8
26.5
27.7
27.7
28.4
27.7
27.5
24,8
24.5
23.5
23.5
23.3
23.1
23.7
T
Open Tank
R
n
23.8
23.4
23.1
22.7
22.4
22.1
21.9
21.6
21.6
22.1
22.7
23.5
24.4
25.3
26.1
26.6
26.9
26.9
26.6
26.3
26.0
25.7
25.3
25.0
24.3
Tavg
95
159
83
70
51
74
267
119
134
184
183
Units:
.06
.01
0
0
0
o
0
.89
.26
.38
1.02
1,10
1.01
21.1
20.8
20.5
-.05
- . 05
21.1
20.8
19.6
19.6
20.3
20.8
19.3
19.1
19.3
18.8
18.8
18.8
18.1
18.3
20,1
21,6
22.1
22.3
23.1
22,6
23.1
21.3
- . 05
-.04
- .02
-.03
-.01
.08
.16
.21
.31
.33
.29
.18
.13
.03
-.01
- . 06
- .05
- . 05
-.04
- .02
- .02
0
0
0
0
0
0
.13
.39
.66
.88
- .02
Wax Blocks
R
T
n
w
0
S
C
31.5
27.8
25.5
24.0
23.0
21.9
21.0
20.5
26.5
45.2
44.0
37.2
17.2
17.8
17,9
16.7
14.9
14.1
14.5
17.0
26.0
33.1
38.4
42.2
45.3
T
7 87)
n
-.04
- . 04
-, 96
-. 97
-
23. 1
23.3
23.3
23. 1
23.0
22.9
22.8
-.
- . 06
16
.01
25
34
.41
.37
.01
.15
.28
-.06
-.04
-.05
-.08
-.08
-.10
-.10
R
21.3
21.1
20.8
20.3
20.1
20.1
19.8
19.6
20.1
22.3
23.1
25.8
28.6
28.7
29.4
27.2
26.2
24.8
24.3
23.8
23.3
24.5
22.3
22.3
23.3
T
w
c
23.1
23 . 3
22.8
22.6
22.5
22.4
22.3
22.1
22.0
21.9
21.9
22.1
22.3
22.9
23.6
23.9
24.2
24.3
24.3
24.3
24.2
24.1
23.9
23.7
23.4
Tavg
-.06
-.05
-.05
- .04
-.03
-.02
-.03
.25
.11
.23
.33
.41
.46
.44
.45
.34
-.06
-.06
-.02
- .05
-.05
- .03
n
-.03
-.02
R
19.3
20.8
20.8
21.6
24.0
25.8
26.7
28.2
29.4
29.7
29.9
27.0
27.0
25.0
24.0
23.3
23.5
23.3
22.3
21.6
24.1
T
w
21.3
21.3
21.8
19.8
C
27.5
26.1
25.1
24.4
23.6
22.5
21.7
26.4
20.0
20.2
19.9
19.1
18.3
17.6
17.0
18.0
25.0
30.4
35.3
38.9
41.4
40.6
37.8
33.5
29.9
T
22.5
22.7
23.0
23.3
23.5
23.7
23.8
23.9
23.9
23.9
24.0
23.8
23.6
23.3
23.2
23.1
23.0
22.9
22.7
22.6
22.4
22.3
22.2
22.1
22.3
Tavg
Concrete Biks (78)
vspor pressure nb
25.3
24.6
24.0
28.0
40.0
40.6
39.6
35.9
32.4
29.9
28.2
27.0
26.2
36.7.
23.0
22.9
22.6
22.0
21.3
21.0
21.2
21.8
24.8
29.1
33.0
T
White Butyl (86%)
23.2
23.1
23. 2
22.9
22.8
22.7
22.6
22.5
22.4
22.3
22.2
22.2
22.5
22.7
22.8
23.0
23.1
23.2
Tavg
Wind speed cm/sec, temperature °C. rdiat::
14
16
16
14
15
15
15
16
13
14
14
13
22.1
22.0
21.7
21.1
20.4
19.9
19.5
19.7
25.0
28.1
30.3
32.0
33.3
34.1
34.6
34.8
34.4
33.1
31,7
30.3
29.0
27.7
26.5
25,3
26.5
39
55
69
65
70
82
79
74
40
107
111
94
126
14
13
13
12
12
11
11
12
13
13
13
13
13
a
Avg 101
18
19
20
21
22
23
24
17
16
15
10
11
12
13
14
9
8
7
6
5
4
3
2
1
Time
a
e
T
U
September 30, 1967
Meteorological Data
Table 14--Continued
-.05
-.06
-.08
-.07
-.01
-.02
-.03
.27
.01
.25
.54
.76
.92
1.01
.89
.82
.61
w
23.3
22.3
22.1
19.8
19.6
20.3
20.8
21.3
25.0
25.8
25.8
27.2
29.7
28.9
28.7
29.4
28.9
27.0
26.2
25.3
24.8
24.5
22.8
22.1
24.7
26,1
25.7
25.2
25.2
27.7
27.5
27.1
26.8
22.5
26.0
26.9
27.4
27.7
24.7
24.5
24.2
23.8
23.5
23.2
22.9
22.7
22.9
23.2
23.8
24.7
Open Tank
T
Tavg
n
-.06
-.05
-.05
-.09
-.09
-.10
-.09
R
28
39
19
20
21
22
23
24
57
55
108
Jnits
¼vg
112
32
40
155
18
396
281
246
194
61
60
45
74
43
71
76
121
113
86
49
151
17
16
15
10
11
12
13
14
8
9
7
6
5
4
3
2
1
T ime
U
a
.95
.76
.50
.21
6
6
6
6
7
7
7
7
7
6
6
0
O
0
0
0
0
1.04
6
7
7
7
6
6
6
6
6
6
6
6
7
a
S
0
0
0
0
0
0
0
.08
.36
.63
.85
.96
1.07
6
e
n
-.06
--.06
-.06
-.08
-.06
--.05
-.05
.31
.26
.18
.07
.27
.33
.06
.14
.23
-.07
-.06
-.06
-.08
-.06
-.07
-.08
-.02
R
7.3
7.2
7.2
7.3
6.6
6.2
6.8
7.9
19.1
27.5
32.8
35.9
37.9
39.5
38.7
36.3
32.2
24.6
13.1
9.8
8.2
7.1
6.2
5.5
18.0
12.6
14.3
13.3
12.8
14.1
12.8
12.6
13.8
14.3
17.3
19.3
20.8
21.8
22.3
22.3
22.3
22,1
19.6
13.8
14.6
12.8
13.6
13.8
13.1
16.3
16.7
16.6
16.5
16.6
16.6
16.5
16.4
16.3
16.2
16.1
16.0
16.0
16.0
16,1
16.2
16.5
16.8
17.1
17.2
17,3
17,3
17.2
17.0
16.9
16.8
Tavg
-,i
-.11
-.1
-.10
-.12
-.11
-.11
.0
.43
.39
.42
.36
.30
.20
.27
16.6
15.8
15.1
14,3
16,6
13.6
13.3
13.3
13.1
12.8
12.8
12.6
14.1
13,3
14.6
16.3
18.6
19.3
22.1
23.3
23.3
23,1
20.3
19.3
17.1
-.10
-.10
-.10
-.10
-.10
-.11
-.11
-.04
.10
w
T
n
R
White Butyl
16.1
15,9
16,0
15.6
14.8
21.3
16.6
164
15.8
15.7
15.5
15.4
15.2
15.0
14.9
14.8
14.9
15.1
15.3
15.8
16.4
16.9
17.2
17.3
17.4
17.3
17.1
16.9
14.8
14.6
14.4
14.3
14.2
14.3
14.1
14.2
18.0
22.1
26.4
30.4
34.0
36.1
36.5
34.8
30.9
24.8
19.9
18.2
17.5
16.6
C
(86%)
T
Tavg
-.01
-.04
-.03
-.03
-.04
-.03
-.04
-.03
.15
.17
.15
.12
.06
.1].
.02
.07
- .02
- .04
- .04
- .03
- .05
- .03
- .03
- .05
U
17.3
17.3
17.1
17.1
17.1
16.8
16.8
17.1
17.1
17.8
18.3
19.1
18.6
19.6
19.8
19.8
19.8
19.3
18.6
17.8
17.8
17.6
17.3
17,1
18,0
W
8.6
7.3
6.8
6.0
4.8
16.7
iLl
7.8
7.2
7.7
8.7
8.6
7.4
6.4
10.1
18.4
24.8
29.1
32.2
34.5
35.3
34.6
32.8
29.2
22.1
C
Styrofoam (80%)
R
T
T
C, radiation ivin, vapor pressure nib
C
T
(787.)
w
T
Wax Blocks
Wind speed cm/sec, temperature
15.7
21.9
15.4
15.0
14.9
14.8
14.6
14.1
13.4
13.7
20.5
24.4
27.2
29.5
31,2
32.5
33.1
33,2
32.3
30.0
25,5
21.5
18.9
17.6
16,6
T
October 18, 1967
Meteorological Data
Table 14--Continued
-.11
-.12
-.11
-.12
-.12
-.12
.71
.82
.96
.91
.81
.61
.30
.02
17.7
17.7
17.9
18.0
18.1
18.3
18.5
18.6
18.7
18.7
18.5
18.4
18,3
18.2
18.1
177
18
.47
-.11
-.11
-.12
-.11
-.06
-11
-.11
-.11
Rn
23.1
20.8
23.8
24.3
24.3
23.5
21.6
17.6
16.3
18.1
16.6
17.3
14.3
18.1
21.1
18.5
18.0
14.8
15.1
12.1
14.3
14.3
13.1
13.3
14.6
19.8
20.8
18.9
19.6
20.3
20.9
21.1
20.9
20.6
20.3
20.0
19.6
19.3
19.0
18.7
176
182
17,2
16.9
16.6
16.5
16.5
16,8
17.1
176
Tavg
T
Open Tank
17.6
17.7
17.7
17.8
179
18.2
18.1
18.1
18.0
Tavg
64
60
64
89
130
138
134
6
43
36
63
86
303
101
98
51
58
50
Units:
24
Avg
14
15
16
17
18
19
20
21
22
23
13
10
11
12
9
8
7
5
137
136
128
37
36
4
3
2
43
43
31
1
Time
7
7
7
15.9
15.0
20.8
-.07
-.08
-.06
-.05
-.06
-.05
.07
.15
.23
.27
.34
.29
.25
.15
.06
-.05
-.06
-.06
-.05
-.08
-.08
-.08
-.08
-.03
13.6
13.6
13.8
13.1
12.8
13.8
12.6
12.6
15.3
17.3
19.6
21,3
21.8
22.3
23.5
22,3
21.6
19.3
17.3
16,3
14.8
15.3
14.3
14.6
16,8
Wax Blocks
R
T
fl
w
c
0
8.3
7.5
7.0
17.3
24.7
25.8
11.2
9.3
36.4
31.9
7.7
17.1
25,5
31.8
35.9
38.1
39.3
38.9
4.0
5.3
4,5
4,3
3.9
3.5
3,2
T
78%
Wind speed crn/sec, temperature
6
6
6
6
6
6
6
0
0
0
0
0
.94
.75
.49
.20
0
6
6
1.06
1.04
.62
.84
.99
0
.07
.35
0
0
0
0
0
0
6
7
7
7
6
6
6
6
5
6
6
6
6
a
27.4
29.1
30.4
31.5
31,9
31.8
30,6
27.0
22.0
19.4
17,3
14.7
13.6
12.4
11.6
12.3
13.0
13,3
14.1
18.0
21.9
25.0
e
-.10
-.11
-.11
-.11
-.11
-.11
-.10
.07
.40
.43
.42
.37
.28
.17
.10
.25
-.11
-.11
-.11
-.11
-.11
-.11
-.11
-.04
16.7
14.1
15.8
15.1
12.8
12.8
12.8
12.6
12.6
12.8
13.8
15,8
18.3
20.8
22.8
23,3
23.3
22.3
20.3
17.8
17.6
16.6
16.3
15.3
14.6
14.3
13.9
13.6
13.5
13,4
13.3
13.4
13.9
16.3
21.5
30.5
37.0
39.3
40,5
39.9
36.4
31.2
24.4
18.6
15.5
13.6
12.6
11,9
11.4
21.2
14.7
14.6
14.5
14.6
15.0
15.5
15.9
16.2
16.8
17.1
17.3
17.1
16.9
16.7
16.4
16.2
16.0
15.8
15.6
15.8
15.1
14.9
15,7
15.5
15,3
bite But 1 86%
R
T
T
Tavg
n
w
c
-.05
-.03
-.03
-.02
-.03
- .03
.04
.10
.12
.14
.16
.14
.11
-.02
-.03
-.03
-.03
-.03
-.03
-.04
-.03
-.04
-.04
-.03
17.1
17.6
17.3
16.6
16.6
16.6
16.3
16.6
16.8
17.3
18.1
19.1
18.8
19.3
20.1
20.3
19.8
19.1
18.3
17.8
17.6
17.3
17.1
17.1
17.9
St rofoam
R
T
w
n
radiation ly/rnin. vapor pressure mb
16.4
16.3
16.2
16.1
15.9
15.8
15.7
15.7
15,7
15.8
16.0
16.3
16.6
16.8
16.9
16.9
16.9
16.8
16.7
16.7
16.6
16.5
16.4
16.4
16.3
Tavg
October 19, 1967
Meteorological Data
Table 14- -Continued
C
9.7
16.0
23.0
27,7
30.9
33.0
33.9
33,6
32.3
29.0
22.6
12.6
8.6
7.2
6.4
6.0
5.9
15.3
3.5
3.0
3.0
3.5
4.2
5.1
6.7
T
80%
17.7
17.8
18.1
18.0
17.9
17.8
17.7
17.6
17.5
17.4
17.4
17.3
17.4
17.5
17.6
17.8
18.0
18.2
18.3
18.4
18.3
18.2
18,0
17.9
17.8
Tavg
18.4
18.6
O.en Tank
R
T
Tavg
n
w
16.1 18.7
-.13
16,6
18.3
-.13
-.12 17.3 17.9
-.12
15.8
17.6
-.12 12.8
17.2
16.8
-.12 15,1
-.11 13.8 16,4
-.11 14.6
16.3
-.07
17.8
16.3
.15
18.3
16.6
20.1
17.1
.44
21.6 17.9
.69
.84
23,8 18.8
23.3
19.7
.98
24.3
20.5
.88
23.5
21.0
.78
23.1 21.1
.29
.02
21.3 20.9
-.10 19.3
20.5
-.10 18.3 20.2
-.11
15,8
19.8
-.12
16.8
19.5
-.12
15.8
19.1
-.11
15,8
18.8
116
110
67
130
39
22
66
57
73
40
55
107
132
111
50
154
171
234
182
130
138
107
105
42
Units:
Avg 102
15
16
17
18
19
20
21
22
23
24
10
11
12
13
14
8
9
7
6
5
4
3
2
1
Time
Ti
a
a
7
7
7
7
7
7
7
6
O
0
0
0
0
0
.60
.31
6
6
.97
.82
1.05
1.05
0
0
0
0
0
.03
.29
.57
.81
.98
0
0
S
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
e
.14
.22
.29
.29
.28
.26
.20
.10
-.03
-.05
-.05
-.05
-.05
-.05
-.05
.05
-.06
-.07
-.08
-.06
-.06
-.08
-.08
-.08
n
R
c
6.8
6.9
5.8
4.5
4.7
6.7
8.3
7.5
15.0
23.4
29.0
32.8
36,3
38.9
38.7
37.4
33.7
27.5
14.8
9.5
8.7
8.3
8,0
7.6
17.5
13.3
14.3
14.3
13.8
11.8
11.8
13.8
12.8
13.8
17,1
18.6
20.1
21.6
23.3
23,1
23.1
22.6
20.1
17,6
15.6
14.6
14.8
13,3
13.0
16,6
I
787)
w
T
16.4
16.3
16.2
16.1
16.0
16.2
16.7
16,5
16.3
16.2
16.1
16.0
15.9
15.8
15.7
15.5
15.5
15,6
15.7
16.0
16.4
16.6
16.8
16.9
16.9
Tavg
-.1!
- .04
.39
.32
.23
10
)
.41
41
05
23
-. 11
-.11
£4.
11
16.3
16.1
15.6
13.0
16.9
1.i
13.3
12.8
13.1
12,3
13.8
15.3
17.3
20.8
22.6
24.5
25.0
24.5
22,6
19.3
15 . 7
15 .7
19.5
vapor pressure nib
15. 9
16. 1
16, 3
-.03
-.03
-.Q3
-.03
-.02
-.02
-Q3
.02
16.7
16.5
.07
17.0
16.8
.03
.08
.10
.14
.16
.14
.11
-.04
-'.05
-.04
-.04
-.03
-.05
-.05
'-.04
0
5.8
6.3
6.5
5.8
5,3
6.0
7,5
8.8
12.9
21.0
26,4
29.9
32.1
33,3
33,4
32.5
29.9
23,1
10.9
8,4
7.0
6.4
6.1
6.0
15.5
16.8
16.8
16.8
16.6
16,3
16,6
16.3
16.3
16.6
16.8
17.3
17.8
18.6
19.1
19.3
20.1
19.8
19.3
18.3
17.6
17.3
17.1
17.1
17.1
17. 6
C
W
Styrofoam (8O7)
T
T
R
17 . 0
16,6
16 . 2
15 . 6
15. 2
14.6
14.5
14.4
14.6
14.9
15.4
13.9
12.9
12.0
11.4
1.8
14.4
21.3
29.0
34.6
38.6
40.0
39.4
37.4
33,4
26.4
9.6
9.8
9,6
White Butyl (867)
R
I
T
Tavg
W
0
C
15.3
-.10 14.3 11.2
15. 1
-.10 14.3 10.8
- 11
10.2 15.0
13.8
14,8
9.6
13.6
-.11
14.7
13.3
9.4
-.11
Wind speed cm/sec, temperature °C, radiation ly/nin
14.5
13.8
12.9
11.6
10.6
11.1
12.2
11.4
14.3
20.0
23.5
26,0
28.1
29.9
31.3
32,1
31.9
30.8
28.0
23.6
20,6
18.1
16.2
15.9
20.4
T
October 20, 1967
Neteorological Data
Table 14--Continued
17.4
17 . 6
17 . 6
17 . 7
17.9
17.8
17 . 9
18.0
18.0
17 . 9
17.3
17.5
17. 1
17 . 0
16.9
16.9
16.9
17 . 0
17. 1
17.1
17. 2
17.6
17.5
17.4
17.3
Tavg
-.09
-.11
-.11
-.11
-.10
-.11
.67
.41
.15
.14
.39
.66
.82
.88
.90
.82
-.10
-Il
-.J_J_
n
-.11
-.11
-.12
-.12
-.12
-.11
12,3
15.8
17.6
19.3
20.3
22,1
23.5
24.5
24.0
23.5
22.1
19,3
16.3
17.6
16.6
13.8
11.1
17.5
J_J._j
14,8
12.8
12.6
15,.1
14.8
16.3
Open Tank
R
T
C'
16,1
16.1
16.3
16.6
17.2
18.1
19.1
20.0
20.5
20.7
20.7
20.4
20.0
19.6
19.2
18.9
18.6
18.4
18.5
18.2
17.9
17.6
17.2
16.9
Tavg
8
9
10
11
12
13
Units:
Avg
24
23
19
20
21
22
18
17
15
16
14
117
85
7
a
23
24
24
23
24
22
26
24
25
26
24
24
26
24
23
22
20
22
21
20
21
20
19
19
19
e
.33
.04
0
0
0
0
0
.87
.61
1.21
1.29
1.28
1.21
1.07
0
0
0
.03
.32
.59
.82
1.02
0
0
S
a
-
-.02
-.06
-.06
-.06
-.06
-.06
0
.08
.15
.27
.30
.37
.37
.39
.32
.25
.16
.07
-.05
-.05
-.06
-.05
-.05
-.06
w
27.3
28.8
27.5
30.8
32.8
32.8
32.2
32.9
32.6
31.7
31.1
30.2
28.8
28.2
29.5
26.4
26.1
25.9
25.7
25.5
25.8
26.0
26.5
28.0
26.7
C
28.7
28.1
27.4
26.8
31.2
25.1
27.6
30.7
33.9
37.0
39.4
41.1
40.5
40.6
38.7
36.4
33.5
31.0
29.6
25. 0
26.4
25.8
25.5
25.2
25.1
. 9
27
. 2
28.3
28.5
28.6
28.6
28.5
28.3
27.9
27.6
27.3
27
26.7
26.6
26.5
26.4
26.2
26.1
25.9
25.9
26,1
26.3
26.5
26.8
27.4
27.7
- .03
-.03
- .01
- .04
-.03
- .03
.22
22
19
.19
16
.13
.04
.01
02
14
19
.22
- .02
-.03
- .03
- .03
- .02
-.02
w
28.0
28.0
29.1
28. 2
27.0
27.1
27.3
27.6
27.8
28.5
29.9
30.9
31.5
31.7
31.7
31.6
31.4
31.0
30.5
29.9
29.1
28,4
27 . 2
27.5
27.5
C
30.4
23.5
37.3
32.3
26.3
22.8
24.0
24.8
24.3
47.0
44.4
41.5
36.4
41.5
44.5
46.6
47.9
19.8
19.2
19.4
19.0
17.8
17.6
21.4
29.1
28.9
29. 1
28,2
28.1
28.1
28.2
28.5
28.7
29.0
29.2
29.4
29.5
29.5
29.5
29.6
29.6
29.6
29.4
29.3
29.2
28. 2
28.7
28.6
28.4
28.3
Styrofoam (80%)
Rn
T
T
Tavg
Wind speed cni/sec, temperature °C, radiation ly/min,
vapor pressure nib
106
230
170
108
114
127
146
157
155
132
108
62
70
264
89
104
48
6
26.9
26.3
25.3
24.4
23.9
24.4
26.9
29.2
31.0
32.5
33.8
34.9
35.5
36.1
36.6
36.9
36.8
36.2
34.5
32.3
30.5
29.1
27.9
27.2
30.8
a
36
62
42
66
67
35
5
4
3
2
Time
T
U
White Butyl (86%)
R
T
T
Tavg
August 1,1968
Meteorological Data
Table 14--Continued
- .07
- . 06
- .05
- .08
-.09
- .05
.47
.01
.89
.75
1.10
1.13
1.10
1.10
.66
.87
.37
12
-.10
-.07
- .09
-
-
-
30.5
31.0
31.4
30.2
30.2
31.4
31.7
31.1
30.6
32.2
28.2 29.6
28.2 29.3
27.5
29.2
28.4 29.1
27.7 29.3
28.7 29.6
30.5 30.2
31.1 30.9
31.1 31.7
32.3 32.7
32.7 33.4
33.6 33.8
33.8 34. 2
33.3 34. 1
32.8 33.7
32.6 33.2
32.1 32.7
Open Tank
T
Tavg
w
.08
29.0 30.7
.08
28.6 30.4
.09
27.7
30.0
Rn
51
118
78
124
55
37
73
149
156
137
118
123
100
88
108
156
129
150
163
Units:
Avg
19
20
21
22
23
24
16
17
18
15
10
11
12
13
14
9
8
7
6
5
3
4
117
107
a
24
25
24
25
24
24
23
24
25
25
24
24
23
23
22
22
22
23
21
21
22
26
26
24
24
e
0
0
0
0
0
.86
.60
.33
.07
1.03
1.19
1.29
1.29
1,22
1.07
0
0
0
0
0
.04
.32
.60
.83
S
-.02
-.05
-.06
-.05
-.05
-.06
.04
.29
.34
.41
.41
.32
.29
.20
.12
.25
.02
.16
-.01
-.01
-.06
-.07
-.06
-.06
27.7
29.7
26.2
26.7
27.5
28.7
30.2
31.7
32.9
33.8
34.2
33.7
40.0
33.1
31.7
30.8
29.9
29.1
28.3
25.7
25.8
27.1
26,7
26.3
25.9
29.3
28.8
28,2
27,6
27,1
31,.
40.0
40,4
40.2
39.6
38.5
36.6
34,0
31.1
28.3
30.8
33.8
38.5
27.0
27,4
27.8
28.1
28.4
28.7
28.9
29.0
29.0
29.0
28.8
28,6
28.2
27.6
26.7
27.2
27.0
26.9
26.8
26.7
26.6
26.5
26.4
26,3
26.4
Tavg
rr1r
26.4
26.2
26.2
25.7
25.1
24.8
26.0
White Butyl (867)
R
T
T
n
w
C
Uind s;eed cm/sec. te:peretur
31,5
29,6
28.6
27.9
27.3
30.5
30.4
31.9
33,3
34,4
35,3
35.8
36,1
36,1
35.8
34.7
26,7
26.5
26,2
24.7
23.6
23.6
24.8
27.1
28.9
97
124
187
352
2
a
1
Time
T
U
w
29,
30,0
30.2
30.6
31,1
31.6
31.5
31.3
30.8
30.8
30,0
29.6
29,3
29,1
28.8
28.6
28.7
29.3
27.7
28.1
28.0
27.8
27.6
27.4
27.4
C
30.9
21,7
22.3
22.5
23.1
23.1
24.1
23.1
21.0
19.6
24,5
30.8
36.5
40.1
45.0
47.1
47.2
45.8
43.7
41.1
37.8
33.0
27.0
21.6
20,3
T
807
29,7
29,6
29.7
29.7
29.6
29,4
29 2
29,1
29.0
28.9
28.7
28.6
28.5
28.4
28.3
28.3
28.5
28.8
29.0
29,2
29,3
29.5
29.6
30.0
30.0
Tavg
1y/Ln. vcper pressure mb
-.03
-.02
-.02
-.01
-.03
-.02
.01
.18
.22
.18
.17
.12
.09
.11
.07
.00
.16
.19
-.02
-.02
-.02
-.01
-.01
-.02
n
Styrofoam
R
T
August 2, 1968
Meteorological Data
Table 14--Continued
-
-.09
-.09
-.07
-.07
-.08
.10
.03
.47
.92
.73
1,02
1,16
1,19
1.09
.13
.51
.66
.75
-.06
-.05
-.04
-.04
-.05
-.05
33.1
33.5
33.5
33.5
33.3
33.1
32.6
32,1
31,4
31.1
30.8
32,3
29.9
29.4
29.2
28.7
28.2
27.7
28.2
28.4
28.9
29.5
30.0
30.7
31,6
o en Tank
R
T
n
w
0
31.8
31,3
31,1
0
30,2
29.8
29.4
29.0
28.5
28.0
28,1
28.4
28.9
29.5
30,3
31.2
32.0
32.8
33,5
33,9
34.0
33,7
33.3
33,0
32,7
Tavg
97
93
85
194
217
149
162
199
196
186
163
118
8
10
11
12
13
14
15
16
17
18
19
Units:
Avg 111
21
22
23
24
20
9
54
84
63
36
46
108
7
6
5
87
75
47
53
106
45
4
3
2
1
Time
10
10
ii
ii
11
9
8
8
7
8
9
9
10
11
13
14
14
14
14
13
12
11
10
10
9
0
0
0
0
0
.90
.61
.30
.02
1.09
1.25
1.33
1.33
1.27
1.12
0
0
.03
.29
.58
.86
0
0
0
-
-.06
-.05
-.05
-.03
-.02
-.04
-.04
-0
.17
.13
.07
.19
.03
.11
.16
.18
-.03
-.03
-.03
-.03
-.03
-.04
-.03
-.01
26.5
26.3
26,3
26.3
26.2
26.1
26.2
26.8
27,8
28.6
29,1
29.3
29.3
28,3
28.2
27.5
27.0
26,5
26.5
26.6
26.3
26.3
26.3
26.1
27.1
T
c.
11,5
9.5
8.0
7.5
7.0
22.1
11.0
11.0
10.2
9.5
9.5
10,0
14.5
23.1
30.5
36.1
40.5
43,2
44.1
43.1
40.0
36.5
31.5
25.0
17.5
87
Wind speed cm/sec. temperature
17.5
20.6
23.3
25.6
28,3
31.0
32.0
32.9
33,6
33.5
33.3
32,8
31.6
29.8
27.0
26,1
26,1
20,8
18,5
26,1
23.0
22,0
20.6
19.3
18.0
Styrofoam
R
T
w
n
-
-.07
-.09
-.09
-.08
-.09
-.08
.01
.17
.56
.58
.54
.46
.33
.01
.17
.27
.42
.52
-.08
-.07
-.08
-.08
-.08
-.08
C
8.5
9,0
8.1
7,3
7.2
7.6
11,3
18.7
25.1
29,9
33.6
36.0
36.9
36.3
34.0
30.9
26.8
21.1
13.6
9.4
7.3
6.1
5,4
4.6
18.1
T
5 1°,'.
28.1
27.8
27.7
27.4
27.2
27.0
26.7
26.6
26.9
27.1
27.4
27.7
28.2
28.4
28.6
28,7
28.4
28.4
28,1
27.9
27.6
27.4
27.2
27.0
27,6
Tavg
-
-.09
-.11
-.10
-.10
-.11
-.12
.06
.81
.69
.51
.29
.65
.78
.84
.86
.24
.44
.05
-.10
-.09
-.10
-.10
-.10
-.09
25.9
25.7
25.5
25.0
24.8
24.5
24.4
24.4
24.9
25.3
25.7
26.1
26.7
27.0
26.9
26.7
26.4
26.3
26.1
25.8
25.6
25,3
25.0
24.6
25,6
St rofoam
R
T
in. vapor pressure nib
25.6
25.7
26.3
26.9
27.3
27.5
27.8
28.0
28.1
28.1
27.8
27.4
27.0
26.7
26.4
26,2
26.1
25.9
25.7
27,9
27.0
26.7
26.4
26.1
25.9
St rofoam
R
T
n
w
radiatic:
27.6
27.4
27.3
27.2
27,3
27.1
26.9
26.9
26.9
27.1
27.1
27.2
27.7
27.6
27.6
27.6
27.4
27.3
27.3
27.2
27.0
27,0
26,9
27.1
27.2
Tavg
August 14, 1968
Meteorological Data
Table 14--Continued
17,2
9.7
7.2
5.0
4.2
3.2
2.2
14.1
28.0
25,3
22.0
19.7
23.6
26.6
28.8
29.7
29.5
6.0
7.0
6.0
5.1
4.8
5.2
8.0
14.3
c
267,,
27.6
27.4
27.2
26.8
26.6
26.4
26.0
26.2
26.4
26.7
27.2
27.5
28.1
28.6
28.9
28.9
28.6
28.3
28.1
27.8
27.3
27.1
26.8
26.6
26.2
Tavg
-
-.10
-.14
-.13
-.13
-.14
-.15
.92
.69
.41
.10
1.12
1.14
1.07
L04
.87
.08
.34
.61
253
25.5
25.0
24.5
24.0
23,8
23.6
23.7
24.2
24.7
25.2
25.7
26,1
26.9
27.5
27.7
27.7
27.5
26,9
26,1
25,2
24.5
24.2
23.9
23,7
T
0'en Tank
-.13
-.12
-.13
-.13
-.13
-.11
R
'C
'C
27.3
26.8
26.7
26.1
25.8
25.3
25.1
25.0
25.9
26,3
26.9
27.5
28.4
29.1
29.5
29.7
29.4
28.9
28.3
27,7
27.1
26.6
26.3
25.9
25.9
Tavg
22.3
26.2
28. 2
29.9
31.6
32.6
33.4
33.6
33.5
33.4
32.4
29.9
27. 2
107
153
86
91
99
120
147
133
131
117
129
121
137
164
143
95
36
36
33
38
32
97
2
4
5
18
19
20
21
22
23
24
Avg
Units:
17
10
11
12
13
14
15
16
8
9
7
6
3
a
12
12
12
12
12
13
13
13
13
13
13
12
12
11
11
10
10
10
10
11
11
12
13
14
12
e
0
0
.56
28
.03
0
0
0
1.10
1.26
1.34
1.34
1.26
1.09
.84
- .04
0
0
0
0
.03
.30
.60
.87
- .02
-.02
-.03
-.02
- .04
- .03
0
0
14
14
10
.05
.04
10
13
.12
- .02
- .03
26.6
26.2
25.8
25.7
25.4
25.2
26.7
27. 1
27.7
28.4
26.7
27.0
28.0
28.9
29.2
29.1
28.8
25.0
25.0
25.4
26.3
-.05
- .05
25. 1
25.9
25.7
25.4
w
- .05
- .05
- .04
n
T
C
21.4
16.5
14.0
10,0
9.5
9.0
8.0
8.0
8.0
7.0
11.5
22.0
30.0
36.0
41.0
45.0
45.5
43.1
41.0
37.5
32.0
20.5
6.5
5.5
7.5
T
Styrofoam (87.)
R
0
S
Wind speed cm/sec, temperature
24.4
22.0
20.0
18,8
24.7
17 . 1
17.7
16.9
16.2
15.5
15.7
15.2
a
33
39
102
1
Time
T
U
- .09
26.1
26.1
26.0
25.9
26.1
26.4
26.5
26.8
27.0
26.8
26.8
26.8
26.8
26.7
26.5
26.4
26.3
26.1
26.1
26.5
24.8
24.4
24.0
23.7
23.9
24.3
24.7
25.1
25.6
26.1
26.5
26.8
27.0
26.9
26.7
26.4
26.3
26.1
26.0
25.8
25.6
25,3
25,5
25 . 2
25.4
. 0
26 . 3
26 . 4
-.09
- . 09
-.10
-.09
-.10
26.9
26.6
26,6
- . 07
27. 1
. 3
.05
24
.46
.64
.76
.81
.82
.77
.65
.48
28
.08
-.11
-. 11
27. 2
27
27. 2
27 . 2
27
27. 1
25,9
26.4
26.8
.
25. 2
33.5
36.8
37 9
36.8
34.8
31.5
26.9
18.5
13.4
9.8
7.3
6.7
6.1
5,5
17.0
-. 11
26.1
25.9
25.5
25.2
24.9
24.9
24.9
-.12
-.11
-.11
n
'
. 9
. 3
25.1
24.5
24.4
25
26.1
26.0
25.7
25.8
26.0
25.5
25
25.7
25. 3
24.3
24.0
23.5
23.0
22.3
21.9
22.1
22.6
23.1
23.7
24.3
24.8
w
1.4
1.8
3.0
3.0
2.4
1.8
4.3
9.2
16.5
22.2
25.9
28.5
30.4
30.4
28,5
25,5
21,8
16.4
10.2
5.6
4.6
3.9
3.2
2.9
12.6
c
Styrofoam (267.)
T
T
R
26.7
26,5
29. 1
15.6
23,2
4.0
3.7
5.3
5.5
5.2
4.4
7.9
Tavg
radiation ly/min, vapor pressure mb
-.07
-.07
- . 07
- . 07
04
-.05
-.07
.01
13
28
.41
.50
.52
.54
.51
.42
.30
16
- . 09
- . 09
- . 09
- .09
Styrofoam (517.)
T
T
n
w
C
R
26. 2
26.7
26.8
26.6
26.5
Tavg
August 15, 1968
Meteorological Data
Table 14--Continued
26.2
26.6
27.3
27.7
27.9
27.9
27.7
27.5
27.4
27.0
26.7
26.4
26.1
26.1
25 . 3
24.0
24.2
24.7
24. 1
26.2
25.9
25.4
24.9
24.6
24.3
Tavg
-.12
-.13
-.13
-.13
-.13
- .09
.88
.65
.38
.11
1.03
1.10
1.11
1.04
.09
.36
.64
.87
-.12
25.2
24.8
24.4
25. 2
27.4
27.4
27.0
26.5
26.0
25.5
27. 1
23.4
23.0
22.2
21.5
21.1
21.0
21.3
22.2
23.0
23.7
24.2
24.5
25.5
26.6
. 9
.
1
26.7
26.4
26.0
25.8
27
27.5
27
28.5
28.7
28.7
28.5
27 . 7
26.9
25. 9
25.0
24.5
23.9
23.3
22.9
22.8
22.6
23.2
24.0
24.9
25 . 3
Open Tank
T
Tavg
-.15
-.14
-.14
-.14
-.13
R
155
70
51
255
150
126
93
313
290
142
146
174
187
210
179
253
271
40
70
71
91
52
54
98
Units:
Avg 148
19
20
21
22
23
24
15
16
17
18
10
11
12
13
14
9
8
7
6
4
5
3
2
1
Time
U
14
13
12
12
12
13
18.5
18.2
17.8
16.4
15.5
15.3
17.8
22.0
25.7
28.9
31,6
34.1
35.6
36.0
36.0
36.2
35.9
35,0
31.8
29.2
29.7
26.8
22.1
21.0
26.5
0
0
0
0
0
.88
.60
.30
.02
1.09
1.24
1.33
1.33
1.26
1.10
0
0
0
0
0
.02
.28
.57
.86
-
-.02
-.06
-.05
-.02
-.02
-.03
-.04
.18
.18
.17
.11
.08
.02
.15
.04
.10
-.02
-.04
-.04
-.03
-.03
-.04
-.03
-.01
25.2
25.2
25.2
25.0
24.8
24.8
24.8
25.2
26.3
27.1
27.5
27.8
27.8
27.8
27.7
27.2
26.5
26.6
25.3
24.9
24.9
24.9
25.0
25.0
25.9
St rofoam
R
T
w
n
c
22.5
19.5
15.5
13.5
13.5
14.5
23.7
28.5
7.0
6.0
7.0
10.5
21.5
31.0
37.5
42.0
44.5
46.0
45.5
43.5
39.0
34.0
9.5
7.5
9.0
T
877,,
25.9
25.9
26.1
25.9
25.6
25.7
25.7
25.6
25.8
25. 9
25.4
25.4
25.6
25.6
26.0
25.9
26.1
26.1
25.7
25.4
26.1
26.1
26.1
26.1
26.0
Tavg
-
-.07
-.07
-.06
-.05
-.06
-.07
0
.13
.28
.42
.52
.53
.58
.55
.45
.34
.20
.07
-.07
-.08
-.08
-.08
-.08
-.08
c
33.7
29.8
25.2
20.2
17.1
13.8
11.9
11.2
11.4
19.5
377.
39.4
39.3
37.6
8.7
16.3
23.2
28.8
33.7
5.2
4.4
3.7
5.1
5.7
5.8
T
517.
26.5
26.8
26,8
26.9
26.8
26,6
26.5
26.3
26.0
25.9
25.6
25.8
26.1
25.9
25.5
25.4
25.2
25.0
24.7
24.6
24.8
25.0
25.3
25.9
26.1
Tavg
24.7
24.4
24.2
24.0
23.7
23.4
24.0
-.06
-.07
-.06
-.07
-.08
-.07
-
.03
.24
.46
.65
.78
.86
.87
.82
.70
.54
.34
.13
24.1
23.7
23,4
23.1
22.8
22.5
22.4
22.5
23.4
24.0
24.4
24.6
24.7
25.0
25.3
25.3
25.1
24.9
-.09
-.10
-.10
-.10
-.10
-.10
St rofoam
R
T
n
w
1y/in. vapor pressure mb
24.9
24.7
24.4
24.0
23.8
23.6
23.7
24.0
24.4
24.9
25.5
26.0
26.4
26.6
26.7
26.5
26.3
26.0
25.9
25.7
25.5
25.3
25.0
24.8
25.2
St rofoam
T
R
n
w
Wind speed cm/sec, temperature °C, radiatic
13
12
11
11
11
11
11
11
12
14
13
13
14
14
13
14
15
15
15
_j
e
a
T
S
August 16, 1968
Meteorological Data
Table 14--Continued
c
14.6
12.1
10.2
8.8
8.2
15.3
20.0
25.4
30.8
32.8
33.0
31.7
28.4
25.5
21.8
17.8
2.6
2.4
2.0
1.7
1.4
3.3
6.8
11.0
15.3
T
267.
25.7
25.9
25.5
25.1
24.9
24.7
24,3
24.1
24.0
24.3
24.8
25.4
25.9
26.4
26.8
27.3
27.3
27.1
26.9
26.7
26.4
26.1
25.9
25.6
25.4
Tavg
Oien Tank
T
Tavg
w
-.13 24.2 25.5
-.13 23.6 25.1
-.12 23.1 24.6
22.6 24.3
-.13
22.1 23.9
-.13
-.12 21.7 23.4
21.4 23.1
.07
.35
21.6 23.2
23.0 23.7
.63
23.9
24.4
.87
1.05
24.4 25.0
1.14 25.0 26.0
1.16
25.4 26.9
1.08
26.3 27.8
.93
26.8 28.2
.71
27.0 28.4
27.0 28.3
.45
.17
26.8 27.8
-.08 26.3 26.8
-.10 25.8 26.8
-.10 25.4 26.4
-.10 25.0 26.1
-.10 24.4
25.6
-.10 23.9
25.3
24.4 25.7
R
8
7
6
5
13
6
8
8
7
9
16
14
13
14
14
13
11
10
10
10
17
16
18
16
16
16
15
.59
.27
.02
0
0
0
0
0
.87
1.08
1.24
1.32
1.33
1.25
1.10
.01
.27
.57
.86
0
0
0
-.01
-.07
-.06
-.05
-.04
-.04
-.02
.08
.10
.16
.20
.22
.18
.13
.10
.01
0
-.05
-.05
-.04
-.03
-.04
-.05
-.04
24.3
24.5
24.5
24.3
24.3
23.8
24.3
25.0
25.8
26.5
27.0
27.5
27.2
27.2
26.0
25.5
25.0
25.0
24.8
24.3
24.0
24.3
23.3
23.8
25.1
9.6
8.8
8.0
7.7
8.3
10.9
14.3
18.4
23.8
36.3
40.3
42.0
42.8
43.2
41.0
35.5
31.3
26.0
20.0
16.3
13.3
11.0
9.0
7.1
21.9
24.9
25.0
24.7
24.5
24.5
24.4
24.2
24.4
24.5
24.9
24.9
25.0
25.3
25.2
25.3
25.2
25.4
25.3
25.1
24.9
24.9
24.9
25.0
24.6
24.9
-.01
-.08
-.08
-.06
-.06
-.07
-.04
.29
.33
.36
.31
.25
.18
.07
.03
.14
.23
-.03
24.0
24.0
24.4
25.3
25.5
26.1
25.8
25.6
25.6
25.3
25.0
24.5
24.8
24.9
24.2
24.6
24.3
23.9
24.7
15.2
20.0
25.5
32.5
37.4
40.2
40.8
40.6
38.7
35.0
30.8
26.3
20.8
17.3
14.5
12.0
10.2
8.4
22.1
24.7
24.9
24.9
25.4
25.6
25.8
25.8
26.1
26.2
26.3
26.4
26.3
26.3
26.0
25.9
25.9
25.8
25.5
25.7
-.01
-.08
-.08
-.06
-.06
-.07
-.04
.25
.18
.07
.03
.14
.23
.29
.33
.36
.31
-.08
-.07
-.06
-.06
-.06
-.07
-.03
22.1
21.7
21.6
21.4
22.2
21.3
21.4
22.2
23.5
24.2
24.2
23.8
24.0
23.7
23.3
22.4
23.0
22.8
22.6
22.6
22.4
23.2
22.9
22.1
22.7
25.7
25.6
25.6
25.5
25.5
25.1
25.1
25.1
24.8
24.7
25.0
34.0
32.1
28.8
24.3
20.6
18.3
16.3
15.0
13.9
12.7
21.5
32.3
33.7
34.6
34.7
11.3
12.4
16.2
20.6
25.4
28.7
25.0
25.2
24.8
24.8
24.7
24.5
24.5
24.4
24.5
24.8
24.9
25.1
25.4
25.6
13.0
12.6
12.3
11.8
Styrofoam-12 (76)
T
Tavg
R
T
w
n
C
Wind speed crn/sec, temperature °C, radiation ly/min, vapor pressure nib
Styrofoam-i (757)
T
T
Tavg
R
w
ri
C
-.08 24.8 11.7 25.8
24.5
-.07
10.6 25.8
-.06 24.1
9.7 25.7
-.06
24.3
9.0 25.5
-.06 24.1
9.6 25.2
-.07
23.8
12.4 25.0
Units:
Tavg
116
137
106
9
10
65
11
85
12
109
13
164
14 165
15
233
16
283
17
263
152
18
19
108
20
68
21
71
22
70
23
60
24
108
Avg 115
80
74
58
4
3
2
49
69
74
1
0
0
Styrofoam (877)
R
T
T
n
w
C
a
S
16
16
e
a
T
18.0
17.4
17.0
16.9
17.1
17.9
19.6
22.8
26.2
28.9
31.4
32.4
33.3
33.6
33.5
33.3
32.5
31.3
29.6
27.3
25.1
23.2
21.4
19.5
25.4
TimeU
August 22, 1968
Meteorological Data
Table 14--Continued
Open Tank
T
Tavg
fl
w
-.15 24.2 26.5
-.15
23.4 26.2
-.14 22.8 25.7
-.13
22.6 25.2
22.3 24.8
-.13
24.4
-.11 21.3
21.6
24.0
.07
.33
22.3
24.1
24.5
.62 23.0
24.8 25.5
.86
1.04 24.6 26.3
1.13
25.5
27.3
25,6 27.9
1.16
1.07
26.9 28.8
.93
25.6
29.0
.70 26.7
29.2
.41
26.5
29.0
.11
26.4 28.4
-.10 24.9 27.7
-.12 24.7 27.1
-.12 24.0
26.6
-.13 24.0 26.2
-.14 22.9 25.8
-.12 22.7
25.1
24.1 26.5
R
20
35
75
56
28
133
116
88
108
150
132
79
91
96
107
136
30
39
60
63
37
43
43
41
56
Units:
Avg
23
24
20
21
22
18
19
17
16
10
11
12
13
14
15
9
8
7
4
5
6
3
2
1
Time
10
15
11
10
10
10
ii
11
11
10
12
14
14
10
9
9
12
10
8
10
10
6
9
11
7
a
-.02
-.04
-.03
-.03
-.04
-.04
-.03
.39
.02
0
0
0
0
0
.57
.07
.0
.21
.19
.14
.05
.08
.12
.17
-.04
-.05
-.04
-.01
.04
-.04
-.05
-.04
.86
1.09
1.25
1.34
1.35
1,26
1.10
.56
.85
27
0
0
0
0
0
.02
25.0
24.3
24.3
24.3
24.0
25.4
27.7
27.7
27.2
25.3
23.8
24.0
23.5
23.8
23.5
23.3
24.0
24.3
25.3
26.2
26.7
27.5
27.5
27.2
28.2
St rofoam
T
R
n
w
C
9.0
20.1
-. 05
25. 2
19.0
14.3
12.3
11.2
10.5
10.0
20.0
24.8
24,8
24.6
24.5
24.4
23.9
24.3
41.2
41.0
38.8
35.1
30.9
40. 1
37 . 9
26.6
33.5
17 . 2
6.8
5.8
4.5
3.7
3.3
3.9
7.3
24. 3
25.0
25.4
25.1
24.6
25. 1
24.3
23.9
23.7
23.4
23.2
23.2
23.7
23.3
24.4
24.3
24.3
24.8
26.0
25.8
25.8
25.9
25.8
25.6
25.4
25.2
25.2
25.7
25.8
25.4
25.5
25.1
24.9
24.8
24.5
24.3
24.1
24.2
24.5
24.9
25.1
25.1
25.3
Tavg
-.06
-.05
-.05
- .05
-.06
-.05
.01
.07
.02
.12
.19
.26
31
.36
.33
.26
.17
-.07
-.06
-.06
-.06
-.03
- .07
- .06
22.6
22.7
22.6
21.7
22.1
21.3
21.3
21.2
23.4
23.7
23.8
24.0
24.3
24.5
24.5
25.0
24.6
23.9
23.1
24.2
23.8
23.5
23.4
23.1
23.3
16.5
16.0
15.3
14.8
14.4
19.4
22.0
26.0
28.8
30.8
31.5
32.3
31.3
29.4
26.2
22.6
19.0
9.6
9.4
9.6
10.7
17.1
11.4
10.6
10.0
25.1
25.5
25.2
25.1
25.2
24.9
24.8
24.8
24.6
24.6
25. 1
24.7
24.6
24.5
24.2
24.1
23.9
23.8
23.6
23.9
24.1
24.1
24.2
24.5
25.0
St rofoam-12 767
T
Tavg
R
T
n
w
radiatior. ly/min, vapor pressure mb
24.7
24.6
24.6
24.4
24.6
-.05
-.05
-.06
-.05
24.8
25. 0
.01
- .06
25. 1
07
17
.31
36
.33
26
.02
12
19
26
-.03
- . 06
- .06
- . 06
-.07
- .07
-.06
St rofoam-1
76
T
R
T
n
w
C
16.5
12.6
11.1
10.3
9.5
24.8
24.7
24.7
24.3
24.4
24.3
24.2
23.9
24.2
24.3
24.5
24.4
24.5
24.7
24.9
24.9
25.0
Tavg
25 . 0
43.1
44.3
43.5
41.4
38.0
32.5
40. 3
7.0
16.0
27.8
35.5
3.7
2.9
2.4
2.5
3.2
5.3
T
877.)
Wind speed cmlsec, temperature °C
29.0
26.7
24.0
21.5
19.4
24.5
30. 1
34,1
33.7
33.2
32.2
34. 2
13.0
21.5
25.3
28.5
30.6
32.7
34.0
17.7
16.0
14.4
13.1
12.0
11.8
e
August 23, 1968
Meteorological Data
Table 14--Continued
n
- . 12
-. 12
-.11
-. 11
-.10
-.10
.69
.36
19
1.02
1.13
1.18
1.10
.90
.05
.32
.66
.85
-.14
w
21.9
21.4
20.9
20.1
20.2
19.6
19.8
19.8
21.8
22.9
23.5
23.8
24.8
25.4
26.3
26.7
26.9
26.6
24.9
24.5
23.8
23.3
22.6
22.7
23.1
T
0'en Tank
-.15
-.16
-.15
-.15
-.15
R
27.5
27.3
26.9
26.4
26.1
25.7
25.3
27.0
27.8
28.0
28.4
28.3
24.6
24.3
23.9
23.3
23.0
22.4
22.2
22.0
22.7
23.5
24.5
25.3
26.2
Tavg
35
88
131
32
49
31
98
97
160
138
134
127
150
121
83
35
24
21
49
148
164
155
40
48
34
Units:
Avg
22
23
24
20
21
10
11
12
13
14
15
16
17
18
19
9
8
7
3
4
5
6
2
1
Time
U
a
a
14
13
12
ii
12
ii
13
14
12
13
14
12
12
11
12
11
12
12
13
16
14
12
15
14
13
e
0
0
0
0
0
.27
.02
.86
.57
1.08
1.23
1.32
1.33
1.25
1.09
0
0
0
0
0
.01
.25
.55
.85
S
-.02
-.05
-.04
-.03
-.02
-.03
-.03
.03
.10
.15
.16
.14
.16
.14
.07
.01
0
23.8
25.3
24.
26.7
26.5
25,3
25.0
24.8
24.3
8.4
23.8
23.8
23.8
23.8
23.3
23.3
23.8
24.8
24.5
25.3
26.7
27.5
28.4
29.2
27.5
26.7
-.03
-.03
-.04
-.03
-.04
-.04
-.03
20.3
13.1
11.8
11.2
10.8
10.4
22.6
37.1
42.4
45.7
46.8
45.7
42.9
39.3
34.5
28.8
6.6
6.2
5.9
11.1
18.0
30.5
7.2
7.7
c
w
n
Styrofoam (877.)
R
T
T
24.7
24.7
24.7
24.9
24.6
24.5
24.9
24.7
24.5
24.4
24.6
24.4
24.4
24.5
24.4
24.2
24.2
24.2
24.0
24.0
23.9
23.9
24.1
24.2
24.6
Tavg
-.06
-.05
-.05
-.04
-.05
-.05
0
.28
.31
.30
.30
.26
.16
.07
.13
.21
.02
-.05
-.05
-.05
-.05
-.06
-.06
-.03
n
w
C
11.5
22.6
9.4
8.8
8.1
7.6
7.1
7.0
12.0
21.0
28.7
35.2
39.4
42.3
44.2
43.7
40.8
38.0
34.0
29.4
20.6
14.1
13.4
12.8
12.1
T
25.1
25.1
25.0
24.7
24.7
24.7
24.1
24.3
24.3
24.5
24.7
25.2
25.4
25.6
25.5
25.8
25.8
25.7
25.8
26.1
25.9
25.6
25.6
25.4
25.2
Tavg
-.06
-.05
-.05
-.04
-.05
-.05
.07
0
23.5
23.3
23.4
24.0
23.9
23.3
23.3
23.1
23.3
29.5
26.5
20.3
16.4
16.2
15.7
15.5
15.2
21.4
-. 12
-. 12
-.11
25. 2
25 . 2
24.8
24.7
24.7
24.6
-.11
-. 12
15
- .09
25.0
.94
69
.42
1.04
1.12
1.10
1.08
21.7
21.9
23.9
24.8
26.1
26.5
26.9
27.2
27.1
26.6
26.6
25.1
24.8
24.3
24.0
23.4
23.8
21.1
22.6
22.0
21.1
21.1
20.2
20.2
21.0
-.12
-.13
-.12
-.12
-.13
-.12
.06
.32
.64
.88
w
T
Open Tank
n
R
25. 2
25. 1
Styrofoatn-12 (767)
T
T
Tavg
R
n
w
c
13.8 24.5
22.8
-.05
24.5
13.2
22.7
-.05
24.3
22.6
12.8
-.05
22.1
12.2 24. 2
-.05
24.1
11.7
-.06 21.9
11.8 23.9
-.06 21.7
23.8
14.7
-.03 21.8
23.8
.02 21.3
19.7
21.9 24.1 23.9
.13
24.0
23.3 28.3
.21
24.3 31.0 24.4
.28
24.4
25.6 32.7
.31
33.4 24.6
.30 25.5
25. 1
25.1
33.8
.30
.26
24.3 33.5
25.2
.16
24.5
32.0 25. 1
1y/in, vapor pressure mb
23.7
23.4
23.5
23.4
23.2
23.0
23.7
23.2
23.3
23.5
24.6
25.0
25.9
26.0
25.5
25.1
24.6
24.4
24.6
24.9
24.6
24.3
24.0
23.9
24.2
T
Styrofoam-i (767)
R
Wind speed cm/sec, temperature °C, radiatic
18.0
17.2
16.9
16.4
15.7
15.7
18.2
22.3
24.8
28.6
32.0
34.4
35.7
36.4
36.7
36.6
36.1
34.7
32.0
28.0
25.5
24.0
22.8
21.7
26.3
T
August 24, 1968
Meteorological Data
Table 14--Continued
25.3
25.0
24.6
24.2
23.8
23.5
23.1
23.2
23.4
24.0
25.1
26.2
27.2
28.0
28.6
28.8
29.0
28.6
28.1
28.0
27.5
27.1
26.7
26.4
26.1
Tavg
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E. A., and D. R. Baker.
1967.
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Bloch, M. R. and T. Weiss.
1959.
Evaporation rate of water from open
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1926. The ratio of heat losses by conduction and by
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Introduction to Heat
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1967.
Rafts: New way to control evaporation.
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Crops
Conaway, Jack and C. H. M. Van Bavel. 1966. Remote measurement of
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1967.
Evaporation from a wet
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Cruse, Robert R., and G. Earl Harbeck. 1960. Evaporation Control
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106
Stable alkanol dispersion
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Fritschen, Leo J.
1965a.
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Accuracy of evapotranspiration determina1965b.
Fritschen, Leo J.
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Energy balance
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Fritschen, Leo J., and C. H. M. Van Bavel.
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Fritschen, Leo 3., and C. H. M. Van Bavel.
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Fritschen, Leo 3., and C. H. M. Van Bavel.
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Evaporation from
1963c.
Fritschen, Leo J., and C. H. N. Van Bavel.
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1961.
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Jarvis, N. L., and R. E. Kagarise. 1961. Determination of surface
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