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Fig. 6.2
Area over which
forecast error is computed for
Cases 1-3
ratio is even closer to
in Case 3. These results indicate that the lateral boundaries
may effect the ratio calculation, and that the relatively large reduction in Case 1 may
not be entirely due to the inability of the adjoint model to account for parts of the
nonlinear error.
As the COAMPS adjoint model runs backward in time, some information is
transferred from the adjoint model variables to the adjoint lateral boundary condition
variables and is not included in the calculation of
1:0
ıe
f
. Therefore, the calculation of
ıe
f
was updated to include the effects of the lateral boundaries,
x
a
x
a
/;
@J
f
@
x
a
C
@J
g
l
a
l
b
/;
@J
f
@
l
a
C
@J
g
ıe
f
D
.
C
.
:
(6.23)
@
x
b
@
l
b
The updated expression includes a second inner product similar in form to the first
term except that the model space vector
x
has been replaced by a vector of lateral
boundary conditions
l
. As long as the proper lateral boundary fields and gradients
with respect to these fields are stored, the calculation of this second term is trivial.
The value of the second inner product in Eq.
6.23
for each of the three cases
are indicated by the red bars in Fig.
6.3
. With the addition of the lateral boundary
contribution to
ıe
f
(similar to the values observed
in global systems
Langland and Baker 2004
;
Gelaro et al. 2010
). As would be
expected, the red bars are largest for Case 1, and smallest for Case 3.
The ability to quantify the effect of lateral boundary conditions on forecast error
is a nice byproduct of this framework. However, only the information in the first
term of Eq.
6.23
is passed to observation space, so the remainder of the experiments
will be similar to Case 3 to maximize the impact of observations and minimize the
lateral boundary effects.
, the ratios are all above
0:8
6.3.2
Location
Observation impacts for a week of forecasts (Dec 24-31 2010) for three different
locations (continental United States, eastern Pacific Ocean and western United
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