Environmental Engineering Reference
In-Depth Information
where
k
p
is the pan coefficient, which is a func-
tion of pan type, climate, fetch, and the pan
environment relative to nearby surfaces, and
E
pan
is mean daily pan evaporation in mm/d. Values
of k
p
for the standard Class A pan are given in
Doorenbos and Pruitt (
1975
); they range from
0.35 to 1.10 and decrease with increasing wind
speed and decreasing humidity. The method
is simple to apply and data are available from
many weather stations. Pan measurements
themselves, however, can be problematic; birds
and other animals are often attracted to the
pans (Jensen
et al
.,
1990
).
The Thornthwaite (
1948
) method for esti-
mating
PET
requires only air temperature data.
To estimate monthly
PET
in mm/month, the fol-
lowing formula was proposed:
where
s
is the slope of the water vapor satura-
tion curve,
γ
is the psychrometric constant, and
E
a
is a function of wind speed and water vapor
pressure deficit that has taken several forms.
Thom and Oliver (
1977
) proposed the formula:
E
=
0.037(1
+
U
/ 160)(
ee
−
)
(2.33)
a
s
a
where
U
is the windrun in km/d at a 2 m height
and
e
s
and
e
a
are saturated and actual vapor
pressure, respectively, expressed in kPa.
Monteith (
1963
) modified the Penman equa-
tion for vegetated areas to account for the fact
that specific humidity at leaf surfaces is usually
less than saturation. The Penman-Monteith
equation predicts actual
ET
by including resist-
ance terms:
ρ λ γ
(2.34)
where
r
a
and
r
c
are the aerial boundary layer
and the total canopy resistance, respectively,
in units of time over length. The canopy resist-
ance depends on leaf area and environmental
factors such as solar radiation and tempera-
ture in ways that vary from species to species.
So while Equation (
2.34
) is general, application
to specific sites is hampered by a lack of know-
ledge of these resistance terms for a wide var-
iety of species.
The Priestley and Taylor (
1972
) equation is
another widely used variation of the Penman
equation:
ET
= −+ −
{
rsR
(
G
)
c e
(
e
)} /
{
rs
+ +
(
r
r
)}
a
n
ps
a
a
a
c
PET
=
16(
l
/ 12)(
N
/ 30)(10
T
/ )
I
a1
(2.30)
1
a
where
l
1
is length of day in hours,
N
is number
of days in month,
T
a
is mean monthly air tem-
12
perature (ºC),
=
i
is the heat index (
i
is
I
()
T
1.514
a
i
=
1
an index to months), and a1 = 6.75 × 10
-7
I
3
- 7.71
× 10
- 5
I
2
+ 0.0179
I
+ 0.49. According to Rosenberg
et al
. (
1983
), this method can be successful on
a long-term basis, although
PET
tends to be
underestimated during summer periods of
peak radiation.
The Jensen and Haise (
1963
) method pro-
duces daily estimates of
PET
from daily air tem-
perature and solar radiation:
PET
=
α
s R
(
− +
G
) /(
s
γ
)
(2.35)
n
PET
=
R
s
(0.025
T
+
0.08)
(2.31)
where
α
is an empirically derived constant that
was originally set at 1.26.
Allen
et al
. (
1998
) generalized the Penman
equation for a well-watered reference crop of
short grass to obtain what the authors refer to
as reference evapotranspiration,
ET
o
, in mm/d:
where
PET
is in mm/d,
R
s
is daily total solar radi-
ation in units of millimeters of water/day, and
T
is mean daily air temperature (ºC). According to
Rosenberg
et al
. (
1983
), the Jensen-Haise method
seems to give good results under nonadvective
conditions, but may underestimate
PET
under
highly advective conditions (i.e. when high
wind carries warm dry air, and hence energy,
into the study area).
Penman's (
1948
) formula, which requires net
radiation, soil-heat flux, and humidity, was the
first widely used method for estimating
PET
:
ET
=
{0.408 (
s R
−+
G
)
900
γ
u
(
e
−
e
) /
o
n
2s
a
(2.36)
(
T
+ ++
273)} /{
s
γ
(1
0.34
u
)}
2
where
R
n
and
G
are in MJ/m
2
/day,
u
2
is wind
speed at the 2 m height in m/s, and
s
and
γ
are
in kPa/ºC. The concept of reference evapotrans-
piration is similar to that of potential evapo-
transpiration; actual crop evapotranspiration
PET
= −+ +
( (
s R
G
)
γ
E
) /(
s
γ
)
(2.32)
n
a
