Environmental Engineering Reference
In-Depth Information
small wetland in North Dakota and at a small lake in New Hampshire. Mass-transfer
results were within 20 % of energy-budget results 45 and 57 % of the time at the
North Dakota and New Hampshire sites, respectively, and were among the poorest
methods in comparison to energy-budget results (Rosenberry et al.
2004
,
2007
).
3.5.3.4 Combination Methods
Combination methods determine ET based on measuring both available energy and
aerodynamic efficiency. Probably the best known is the Penman method (
1948
),
which often is written as
Δ
Δ þ γ
Q
n
Q
x
λρ
w
þ
γ
Δ þ γ
E
¼
E
a
(3.17)
where
is the slope of the saturation vapor pressure versus temperature curve at the
mean air temperature,
Δ
is the psychrometric constant described in the
Energy-
balance methods
section, and
E
a
is described as the drying power of the air and is
basically a mass-transfer product, as described in the
Aerodynamic methods
section.
The first and second terms on the right side of the equation are the radiation and
aerodynamic terms, respectively; hence, a combination method. Many mass-
transfer products have been associated with the Penman method. A form of the
equation that includes an often-used mass-transfer product in place of
E
a
, along
with a multiplier to convert to units of mm/day, is (Rosenberry et al.
2007
):
γ
Δ
Δ þ γ
Q
n
Q
x
λρ
w
γ
Δ þ γ
E
¼
86
:
4
þ
ð
0
:
26 0
ð
:
5
þ
0
:
54
u
2
Þ
ð
e
sa
e
a
Þ
Þ
(3.18)
where
u
2
(m s
1
) is wind speed measured at 2 m above the water surface,
e
sa
(hPa)
is the saturation vapor pressure at the air temperature, and
e
a
(hPa) is the measured
vapor pressure at 2 m height. One of the benefits of using the Penman equation is
temperature and vapor pressure only need to be measured at one height. Penman
originally formulated this method to use
T
a
as the temperature at which to obtain
Δ
and
e
sa
because
T
s
was considered difficult to measure.
The Penman method requires a lot of data: net radiation, temperature of the
water body at multiple depths, air temperature, vapor pressure of the air, and wind
speed. Numerous simplifying assumptions have been made to reduce the data
requirements. The Priestley-Taylor (
1972
) method is likely the best of these
alternate approaches. It assumes that the aerodynamic portion of the equation is
26 % of the energy term and replaces the aerodynamic term with the coefficient
1.26 applied to the energy term. Therefore, only
T
a
,
Q
n
, and
Q
x
need to be
determined:
26
Δ
Δ þ γ
Q
n
Q
x
E
¼
1
:
(3.19)
λρ
w
