WSP04999

• File Number: 8054
• Description: Water Salvage
• State: CO
• Basin: Statewide
• Date: 6/1/1975
• Author: Utah Water Research
• Title: Water Salvage Potentials in Utah - Volume II - Evaporation Suppression by Reservoir Destratification
• Water Supply Pro - Doc Type: Report/Study

rtf'l"Q' I
..;' ~. ' ,) ~ "1'

DETAILED MODEL DESCRIPTION

Format

The complete evaporation suppression model
is summarized as a flow chart in Figure 11. This
figure indicates that the model and its application
to Utah reservoirs required the use of eight
individual computer programs (some of which
could now be combined). Manual checking,
selection of parameters, and modification of data
form is required between sequential use of many of
the programs. The following description of the
model is structured according to the program items
identified in Figure 11. The individual programs
are listed in the Appendices along with a definition
of variables used.

Program 1:
Vapor Preuure/Temperature Fuuctlon

The idealized suppression model represented
by Program 2 requires as input an equation which
determines saturation vapor pressure (es) as a
function of water surface temperature (T). There
are several equations of varying form, complexity,
and accuracy in the literature which define this
relationship. The more complex (and most
accurate) functions were not suitable for this
purpose because a subsequent program also
requires use of the inverse of the function; and a
form which could be solved explicitly for T was
therefore desirable.

Various forms of the vapor pressure equation
were checked for accuracy by comparing computed
values of each with those taken from standard
meteorological tables (List, 1949). The most
accurate form of equation which could also be
expressed in inverse form was derived from an
orothogonal polynomial curve filting program.

Program I simply reads in selected values of es
and corresponding T from the meteorological
table; uses an orthogonal polynomial subroutine to
compute the best fit function coefficients for any
desired order of equation; and then prints
predicted values of vapor pressure and compares
them with input values in order to check for

required accuracy. It was necessary to select input
data only from the range of temperatures which
naturally occur on reservoir surfaces in order to
maximize the accuracy of the function within this
range of interest. It should not be used for very cold
or very warm temperatures. The input data
. consisted of es and T values at an interval of I "F
and a range from 430 to BOO. These were converted
to Celsius (centigrade) temperatures within the
program. The second and third order functions
derived are as follows:

E = .22466 + .34581 (10-') T + .98221 (10-') T'
R' = .9998

E = .17287 + .15028 (10-1) T + .21249 (10-') T'
+ .1S655 (10-')T' R' = 1.0000

The symbol E rather than es is used because vapor
pressure is used as a surrogate for evaporation as
discussed in the next section. The very high
correlation achieved is almost essential because
even with an R' of .9998 the second order equation
produces errors approaching 2 percent near the low
range limit (6eC). The maximum error produced by
the third order equation is 0.3 percent at 6eC (0.1
percent maximum for the balance of the range).
The third order equation is used for all
computations in subsequent programs except
where the inverse form is required, in which case
the second order equation is used.

The program and its predicted values are
given in Appendix C.

Program 2:
Supprallon/ 6. T FnnCdOD

In a previous section the basic relationship
between changes in evaporation and temperature
of the water surface was derived as

Ec

f(Tc)
f(Tn)

f(Tc)
sothat Supp = 1--
f(Tn)

En

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