Geoscience Reference
In-Depth Information
used the Penman-Monteith equation to calculate surface energy balance for
different prescribed values of surface resistance, with the aerodynamic resist-
ance set to:
⎛⎞
L
1
r
=
ln
(22.26)
⎜
⎝⎠
a
ku
*
0
in which
u
*
and
z
o
are prescribed and the absolute value of the Obukov Length,
L
, was calculated at each model time step. The time evolution of the mean
potential temperature,
q
m
, and specific humidity,
q
m
, in the simulated ABL were
determined by the energy and humidity conservation, as follows:
d
q
dh
(
)
()
r
ch
m
=
Ht
+
r
c
q
−
q
(22.27)
ap
ap s f
dt
dt
dq
dh
r
h
m
=+ −
E t
()
r
(
q
q
)
(22.28)
a
a
s
f
dt
dt
where
h
is the depth of the ABL,
H
(
t
) and
E
(
t
) are the time-dependent modeled
surface sensible heat and evaporation fluxes, respectively, and
q
f
and
q
f
are the
potential temperature and specific humidity of the free atmosphere, respectively.
The rate of growth of the ABL was assumed to be directly related to the surface
buoyancy flux and inversely to
(
, the rate of change of virtual potential
temperature at the top of the ABL, as follows:
∂∂
q
z
)
v
h
dh
H t
( )
+
0.07
l
E t
( )
=
(22.29)
dt
⎛
∂
q
⎞
r
ch
v
⎜
⎟
∂
z
⎝
⎠
ap
h
McNaughton and Spriggs initiated this model run using nine days of data from a
tower site at Cabauw in the humid climate of the Netherlands (Driedonks, 1981;
1982). These nine days included some with weak and some with strong inversions.
Observed profiles of potential temperature and specific humidity measured at
05:45 am were used to initiate the model profiles, and the measured time series of
net radiation minus soil heat flux through the day was used to force surface energy
balance (the growth of boundary layer cloud was not simulated). The surface
evaporation calculated by the model with different prescribed values of average
surface resistance was averaged over the daytime hours when the ABL was grow-
ing. For each value of prescribed area-average surface resistance, the effective
value of the parameter
α
in the equation:
Δ
la
g
E
=
A
(22.30)
Δ+
