Environmental Engineering Reference
In-Depth Information
Varying rates of
evaporation
Transpiration
Actual
evaporation
Potential
evaporation
Phreatic line
Water
Figure 6.22
Illustration of the various types of evaporative fluxes.
to evaporation.
Pan evaporation
measurements (i.e., an open
water surface) provide a measure of PE.
Researchers have attempted to develop mathematical rela-
tionships that embrace the primary variables controlling the
rate of evaporation from a free water surface (i.e., PE). Each
proposed PE equation uses specific weather-recorded data.
The calculation of PE can be presented in units of millime-
ters per day, and the range of values is generally between
zero and 10 mm/day. These units of measurement are par-
ticularly useful in geotechnical engineering.
Rowher (1931) incorporated the variables of wind speed,
vapor pressure at the evaporating surface, and vapor pres-
sure above an evaporating surface in an attempt to predict
PE. The vapor pressure gradient between the water sur-
face and the air above the water was seen as the primary
driving mechanism for evaporation. Vapor pressure at the
water surface was assumed to correspond to saturated vapor
pressure conditions which were uniquely related to tem-
perature. The vapor pressure above the evaporating surface
was dependent upon the relative humidity and temperature
of the air.
Sutton (1943) incorporated the variables of wind speed,
vapor pressure at the evaporating surface, vapor pressure
above the evaporating surface, evaporating area, and a con-
stant related to temperature into the prediction of PE.
Following is a summary of some equations that are used
in geotechnical engineering for the estimation of PE.
well as numerous other agricultural and engineering appli-
cations. Daily PE can be written as follows:
0
.
533
L
d
12
N
30
10
T
a
I
a
t
PE
=
(6.19)
where:
PE
=
potential evaporation, mm/day,
L
d
=
length of daylight, h,
N
=
number of days in the month,
mean monthly air temperature,
◦
C,
T
a
=
I
=
summation
for 12 months
of
the
function
=
1
month
=
1
T
a
/
5
1
.
514
,
(T
a
/
5
)
1
.
514
; (i.e.,
I
a
t
=
complex function of
the variable
I
(i.e.,
a
t
=
10
−
7
)I
3
10
−
5
)I
2
(
6
.
75
×
−
(
7
.
71
×
+
(
1
.
79
×
10
−
2
)I
0
.
492
)
, based on correlations to pan
evaporation measurements.
+
6.3.8.2 Penman (1948) Equation
Penman (1948) incorporated a number of variables com-
monly collected at weather stations into the prediction of PE.
The Penman equation combines a Dalton-type formulation
with the heat budget equation, and as a result, the temper-
ature at the evaporating surface is no longer required. The
Penman equation uses the following routine weather data
as input, namely, relative humidity, air temperature, wind
speed, and net radiation. The Penman equation for PE can
be written as follows:
6.3.8.1 Thornthwaite (1948) Equation
The Thornthwaite (1948) equation is commonly used to
assess climatic conditions of aridity and humidity. Thornth-
waite incorporated the variables of length of daylight hours,
mean monthly temperature, and an empirical constant into
the calculation of PE. The Thornthwaite equation has been
extensively used for the classifications of global climate as
Q
n
+
ηE
a
PE
=
(6.20)
+
η
where:
PE
=
potential evaporation, mm/day,
=
slope of saturation vapor pressure versus tempera-
ture curve, kPa/
◦
C,
Search WWH ::
Custom Search