Chapter 5. SPATIALLY-COHERENT STRUCTURES
function of elapsed time t since the drifter release. Mean flow advection has
been subtracted. Theoretical dependence (5.20) that follows from the
nonlinear diffusion model is shown for a constant K h = 875 m
2 s
-1 . According
to Figure 5-15, the constant coefficient diffusion law (5.20) appears to be
valid for about 3.5 days. During this time, the RMS distance between drifters
increased to D 0 = 35 km, which is close to the values of the baroclinic
Rossby radius estimated for typical stratification disturbances within the
mixed layer of the tropical sea. On larger horizontal scales, (5.20) is
apparently no longer valid.
The inhomogeneity of the buoyancy (or density) field in the upper ocean
induced by atmospheric forcing can be estimated from a simple budget
relationship as follows:
0
0
Ba
B g
d t
h
W
U
U
§
·
¨
¸
©
¹
³
,
(5.21)
where Ba
) is net the buoyancy flux at the air-sea interface defined by
equation (5.10) and h is the depth of the mixed layer. Respectively, the
variation of the mixed layer density '
U due to precipitation only can be
estimated as follows:
0 0
'
/
P h dt
W
U U
³
(5.22)
Formulas (5.19) and (5.22) then link the horizontal mixing coefficient
with the atmospheric forcing (precipitation):
2 3
2
2
96
h
r
R
g
K
M
L
W
|
.
(5.23)
where
0
r
M
Pdt
W
³
is the cumulative precipitation during rain event.
Rainfalls are in fact the major contributor to the temporal and spatial
intermittency of the buoyancy flux between the atmosphere and ocean in the
warm pool area. During TOGA COARE, the spatial and temporal structure
of the rain rate was known from radar measurements (Figure 5-11) and from
NCAR’s cloud resolving models (Moncrieff et al., 1997; Redelsperger et al.,
2000). For the implementation of the horizontal mixing parameterization in
an ocean general circulation model (GCM), subgrid precipitation statistics
with 1 km resolution can, in principle, be provided by the new generation of
atmospheric cloud resolving models (Grabowski and Smolarkiewicz, 1999;
Randall et al., 2003).
311
)
function of elapsed time t since the drifter release. Mean flow advection has
been subtracted. Theoretical dependence (5.20) that follows from the
nonlinear diffusion model is shown for a constant K h = 875 m
2 s
-1 . According
to Figure 5-15, the constant coefficient diffusion law (5.20) appears to be
valid for about 3.5 days. During this time, the RMS distance between drifters
increased to D 0 = 35 km, which is close to the values of the baroclinic
Rossby radius estimated for typical stratification disturbances within the
mixed layer of the tropical sea. On larger horizontal scales, (5.20) is
apparently no longer valid.
The inhomogeneity of the buoyancy (or density) field in the upper ocean
induced by atmospheric forcing can be estimated from a simple budget
relationship as follows:
0
0
Ba
B g
d t
h
W
U
U
§
·
¨
¸
©
¹
³
,
(5.21)
where Ba
) is net the buoyancy flux at the air-sea interface defined by
equation (5.10) and h is the depth of the mixed layer. Respectively, the
variation of the mixed layer density '
U due to precipitation only can be
estimated as follows:
0 0
'
/
P h dt
W
U U
³
(5.22)
Formulas (5.19) and (5.22) then link the horizontal mixing coefficient
with the atmospheric forcing (precipitation):
2 3
2
2
96
h
r
R
g
K
M
L
W
|
.
(5.23)
where
0
r
M
Pdt
W
³
is the cumulative precipitation during rain event.
Rainfalls are in fact the major contributor to the temporal and spatial
intermittency of the buoyancy flux between the atmosphere and ocean in the
warm pool area. During TOGA COARE, the spatial and temporal structure
of the rain rate was known from radar measurements (Figure 5-11) and from
NCAR’s cloud resolving models (Moncrieff et al., 1997; Redelsperger et al.,
2000). For the implementation of the horizontal mixing parameterization in
an ocean general circulation model (GCM), subgrid precipitation statistics
with 1 km resolution can, in principle, be provided by the new generation of
atmospheric cloud resolving models (Grabowski and Smolarkiewicz, 1999;
Randall et al., 2003).
311
)