Still Waters - Mathematics and Statistics for the Environment - page 577

20.3.2 e nergy b udget m odel *
The energy budget (Lee and Swancar, 1996) is recognized as the most accurate method for deter-
mining lake evaporation. It is also the most costly and time-consuming method (Mosner and
Aulenbach, 2003). The evaporation rate is given by

= −++−+−
++

QQQQ QQQ
L

s r a ar bs v x

E (20.11)

EB

( 1 RT )

0

where
E EB = Evaporation (cm/day).
Q s = Incident shortwave radiation (cal/cm 2 /day).
Q r = Reflected shortwave radiation (cal/cm 2 /day).
Q a = Incident longwave radiation from atmosphere (cal/cm 2 /day).
Q ar = Reflected longwave radiation (cal/cm 2 /day).
Q bs = Longwave radiation emitted by lake (cal/cm 2 /day).
Q v = Net energy advected by streamflow, ground water, and precipitation (cal/cm 2 /day).
Q x = Change in heat stored in water body (cal/cm 2 /day).
L = Latent heat of vaporization (cal/g).
BR = Bowen ratio (dimensionless).
T 0 = Water surface temperature (°C).

20.3.3 p riestly -t aylor e quation
The Priestly-Taylor equation (Winter et al., 1995) is used to calculate potential evapotranspira-
tion, which is a measure of the maximum possible water loss from an area under a specified set of
weather conditions or evaporation as a function of latent heat of vaporization and heat flux in a water
body. It is defined as

( )

s QQ

L

−

n x

PET =× + α (20.12)

s γ

where
PET = Potential evapotranspiration (cm/day).
α = 1.26, a Priestly-Taylor empirically derived constant (dimensionless).
s = Slope of the saturated vapor pressure gradient (dimensionless).
γ = Psychrometric constant (dimensionless).
Q n = Net radiation (cal/cm 2 /day).
Q x = Change in heat stored in water body (cal/cm 2 /day).
L = Latent heat of vaporization (cal/g).

Note that s and γ are parameters derived from the slope of the saturated vapor pressure-temperature
curve at the mean air temperature.

* Much of the following information is adapted from Mosner, M.S. and Aulenbach, B.T., Comparison of Methods Used
to Estimate Lake Evaporation for a Water Budget of Lake Seminole, Southwestern Georgia and Northwestern Florida ,
U.S. Geological Survey, Atlanta, GA, 2003.