Geoscience Reference
In-Depth Information
@
blk
D
U
n
C
1
U
n
t
U
n
t
U
@t
D
A
j
U
n
j
U
n
C
1
D
ˇ
1
C
ˇ
(11.22)
ˇ
D
A
j
U
n
j
t
and
U
n
C
1
D
U
n
=.1
C
ˇ/
where
.
11.5.1.4
Non-orographic Gravity Wave Drag
The tangent-linear and adjoint versions of the non-linear scheme for non-orographic
gravity waves (in details described by
Orr et al. 2010
) were developed in order
to reduce discrepancies between the full NL and linearized versions of the model,
especially in the stratosphere. The parametrization scheme used in the NL model is
based on
Scinocca
(
2003
). This is a spectral scheme that follows from the
Wa r n e r
and McIntyre
(
1996
) scheme representing the three basic mechanisms that are
conservative propagation, critical level filtering, and non-linear dissipation. Since
the full nonhydrostatic and rotational wave dynamics considered by
Warner and
McIntyre
(
1996
) is too costly for operational models, only hydrostatic and non-
rotational wave dynamics are employed.
The dispersion relation for a hydrostatic gravity wave in the absence of rotation
is
m
2
D
k
2
N
2
!
2
D
N
2
c
2
(11.23)
where
k
,
m
are horizontal and vertical wavenumbers, while
!
D
!
kU
and
c
D
c
U
are the intrinsic frequency and phase speed (with
c
being the ground based
phase speed and
U
the background wind speed in the direction of propagation),
respectively.
The launch spectrum, which is globally uniform and constant, is given by the
total wave energy per unit mass in each azimuth angle
following
Fritts and
VanZandt
(
1993
)as
m
m
s
N
2
!
d
1
m
s
C
3
E.m; !;/
D
B
(11.24)
B
s
d
m
D
2L
where
,
and
are constants, and
is a transitional wavelength.
E.m; !;/
Instead of the total wave energy
, the momentum flux spectral density
!;
) is required. This is obtained through the group velocity rule. In order
to have the momentum flux conserved in the absence of dissipative processes as
the spectrum propagates vertically through height-varying background wind and
buoyancy frequency, the coordinate framework
F.m;
.k;!/
is used instead of
.m; !/
as
shown in
Scinocca
(
2003
).
The dissipative mechanisms applied to the wave field in each azimuthal direction
and on each model level are critical level filtering and non-linear dissipation. After
application of them, the resulting momentum flux profiles are used to derive the
net eastward
F
E
and northward
F
N
fluxes. The tendencies for the (
u
,
v
)wind
Search WWH ::
Custom Search