The Adjoint Sensitivity Guidance to Diagnosis and Tuning of Error Covariance Parameters - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 215

a b

C b correlation in DAS−I C b − sensitivity in DAS−II

40 40

0.1

0.2

0.05

30 30

0

0.1

−0.05

20 20

−0.1 0

10 10

−0.15

−0.1

−0.2

10 20 30 40 10 20 30 40

Fig. 9.4 ( a ) The time-averaged structure of the background error correlations in DAS-I. ( b )Time-
averaged forecast error sensitivity to the background error correlation model in DAS-II. Displayed
is the symmetric part of the C b -sensitivity matrix

2

sensitivity to σ b sensitivity to σ o

1

0

−1

−2

−3

−4

0 5 10 15 20 25 30 35 40

Fig. 9.5 Time-averaged forecast error sensitivity to the b and o specification in DAS-II

A suboptimal specification of the error covariance parameters in a DAS input
component will be reflected in the sensitivities with respect to other input com-
ponents. To illustrate this aspect, Fig. 9.5 displays time-averaged values of the
forecast sensitivity to the specification of the background error standard deviation
b and to the specification of the observation error standard deviation

o in DAS-II.

The negative values associated with the b -sensitivity indicate that in average, the

background information is overweighted in the current configuration of DAS-II
and that an improved performance may be obtained by increasing the assigned
b values (variance inflation). At the same time, positive values associated with
the

o -sensitivity indicate that the information provided by the observing system is
underweighted and that an improved performance of DAS-II may be also obtained