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where
C N is the neutral drag coefficient, which is a function of the roughness length,
and
g sf .Ri/
is a function of the local Richardson number. Different formulations of
C N and
g sf .Ri/
are used for momentum and heat, according to Louis et al. ( 1982 ).
Regularization
In earlier versions of the model, perturbations of the exchange coefficients were
simply neglected (
K 0
), in order to prevent spurious unstable perturbations
from growing in the linearized version of the scheme ( Mahfouf 1999 ). Later, some
regularization of exchange coefficients was introduced at upper model levels to
allow partial perturbations of these coefficients. This consists in the perturbations
being more significantly reduced around the neutral state (i.e.
D 0
Ri
close to zero)
where both the function of
itself and its derivative exhibit a significant rate of
change. The reduction is eased exponentially away from the neutral state.
Ri
11.5.1.3
Subgrid Scale Orographic Effects
Only the low-level blocking part of the operational non-linear scheme developed
by Lott and Miller ( 1997 ) is taken into account in TL and AD calculations. The
deflection of the low-level flow around orographic obstacles is supposed to occur
below an altitude
Z blk such that
Z 3
N
j U j
d z H n crit
(11.20)
Z blk
where
H n crit
is a critical non-dimensional mountain height,
is the standard
deviation of subgrid-scale orography and
is the Brunt-Vaisala frequency.
The deceleration of wind due to low-level blocking is given by
N
s
@
D C d max
2
U
@t
2 1
Z blk z
z C .B
U j U j
(11.21)
cos 2 ˛ C C
sin 2 ˛/
r ;0
blk
where
C d is the low-level drag coefficient,
is the mean slope of the subgrid-scale
orography, and
˛
is the angle between the low-level wind and the principal axis of
sin 2 ˛/=.
cos 2 ˛ C sin 2 ˛/
cos 2 ˛ C
orography.
r
is determined as
r D .
,where
is the anisotropy of the subgrid-scale orography. The functions
B
,
C
are written as
( Phillips 1984 )
B D 1 0:18 0:04 2
C D 0:48 C 0:3 2 :
and
The final wind tendency produced by the low-level drag parametrization is then
obtained from the following partially implicit discretization of ( 11.21 )
 
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