Geoscience Reference
In-Depth Information
(
)
2
4.72 ln
(1
zz
ow
mo
ow
r
=
(23.8)
a
+
0.536
u
)
m
where
u
m
is the wind speed measured at height
z
m
and
z
0
ow
0.00137 m is the
effective value for the aerodynamic roughness for an open water surface that is
implicit in Penman's original equation (Thom and Oliver, 1977). With this value of
z
0
ow
, the Penman-Monteith equation relevant for estimating open water evapora-
tion in mm d
−1
when the daily average wind speed and vapor pressure deficit are
both measured at 2 m becomes:
=
Δ
g
6.43 (1
+
0.536
uD
)
ow
−
1
E
=
(
R
−
A
−
S
)
+
2
(mmd
)
(23.9)
OW
n
h
h
Δ+
g
Δ+
g
l
where
R
n
ow
is the net radiation relevant to an open water surface (preferably
measured over the water surface) in mm d
−1
,
u
2
is the daily average wind speed
in m s
−1
and
D
is the daily average vapor pressure deficit in kPa, both measured
at 2 m, and
S
h
and
A
h
are the estimated changes over the period for which the
evaporation estimate is made in the energy stored in the water body and the energy
advected to the evaporating water body, respectively, both in mm d
−1
. For example,
for a lake:
qT qT pT
(
++
)
(mmd
c
11
0 0
P
−
1
Ar
=
)
(23.10)
h
w w
l
where
r
w
and
c
w
are the density and specific heat of water, respectively,
q
I
and
q
O
are respectively the inflow and outflow per unit area of lake in mm d
−1
,
p
is the
precipitation in mm d
−1
, and
T
I
, T
0
and
T
P
are respectively the temperatures of the
inflow, outflow and precipitation. The term
S
h
has often been neglected and it is
probably reasonable to do so in tropical regions where the rate of change in water
temperature is low. However, at high latitudes this can be a dominant large term
in the energy balance, which is months out of phase with the solar cycle. For exam-
ple, Blanken
et al
. (2000) report that the water in Great Slave Lake in Canada
provided a substantial energy sink throughout most of the spring and summer
before switching to an energy source in the fall and early winter. To overcome the
lack of water temperature measurements Finch and Gash (2002) applied a simple
numerical, finite difference scheme to calculate a running balance of lake energy-
storage which gave good agreement between modeled evaporation loss and
mass-balance measurements of the water loss.
Calculations made using Equation (23.9) require prior calculation of
l
and
from the daily average temperature using Equation (2.1) and Equation (2.18),
respectively, and also
Δ
0.001013
MJ kg
−1
K
−1
. If air pressure is not available as a measurement, it usually is adequate
to estimate it from,
E
l
, the elevation of the site above sea level using:
γ
from Equation (2.25), and the value of
c
p
=
