Geoscience Reference
In-Depth Information
Tabl e 5. 2
Forecast error
E.k/
,
z
.k/
W
obser
v
ation
,and
x
f
.k/
W
forecast
k
z
.k/
x
f
.k/
E.k/
W
z
.k/
x
f
.k/
0
1.000
2.000
1:000
1
3.500
4.400
0:900
2
5.375
6.080
0:705
3
6.781
7.256
0:475
0:243
4
7.836
8.079
0:028
5
8.627
8.655
6
9.220
9.059
C
0:161
7
9.665
9.341
C
0:324
8
9.999
9.539
C
0:460
9
10.249
9.677
C
0:572
10
10.437
9.774
C
0:663
11
10.587
9.842
C
0:736
12
10.683
9.889
C
0:794
13
10.762
9.922
C
0:840
14
10.822
9.946
C
0:876
15
10.866
9.962
C
0:904
16
10.900
9.973
C
0:927
17
10.925
9.981
C
0:944
18
10.944
9.987
C
0:957
5.4.3
Experiment 1: Insufficiency of Observations
From the sensitivities displayed in Table
5.1
, air temperature at the last few hours of
forecast is insensitive to the initial air temperature. This insensitivity is even made
apparent when the forecast error is due only to incorrect initial air temperature, i.e.,
2
ı
C
1
ı
C
D
18
is
0:005
ı
C
which is a very
small fraction of the forecast error when all three elements are incorrect (DC
0:957
instead of
. In this case, the error at t
).
The sensitivity of air temperature to turbulent transfer coefficient at the last few
times is also relatively small compared to sensitivity with respect to SST. From the
FSM, it is clear that correction to a given element of control is tied to the fraction
of forecast error due to incorrectness of the given element, i.e., the error relative
to errors in the other elements. In view of this fact, when the four observations are
located at the last four times (t D 15, 16, 17, and 18 h), it is unlikely that meaningful
corrections to
x.0/
can be found. Accordingly, we assume observations at
these last four time steps as the input to Experiment 1.
The components of the gradient of the cost function at the end of the first iteration
are:
and
@J
@x.0/
D
0:011;
@J
@
and
@J
@
D
3:721;
D
0:203
(5.13)
where the philosophy of steepest descent obviously indicates that the control state is
being moved toward a higher SST as expected. But most apparent is the extreme
flatness of the surface along the direction of the initial condition element. The
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