The Adjoint Sensitivity Guidance to Diagnosis and Tuning of Error Covariance Parameters - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 223

For radiosonde temperatures, of 27,063 observations analyzed: 10 % in Q-I, 38.5 %
in Q2, 12 % in Q-III, and 39.5 % in Q-IV. For AMSU-A channel 7, of 22,215
observations analyzed: 13 % in Q-I, 36 % in Q-II, 14 % in Q-III, and 37 % in Q-IV.
A similar distribution was noticed in the analysis of data for other days of the study
period and a throughout investigation of the global observing system remains to be
performed. These results also illustrate that in a given assimilation/forecast episode
tuning an instrument through a single covariance weight coefficient is suboptimal.
For practical applications, a potential use of the combined information derived
from sensitivity and impact estimates is to identify data components and to provide
guidance on the adjustment in the corresponding covariance weight parameters that
are necessary to reduce the errors in a specified forecast aspect.

9.5 Summary and Research Perspectives

The value added by observations to a data assimilation and forecast system is
closely determined by the weight assigned in the DAS to the information provided
by the prior state estimate and measurements. The adjoint-DAS methodology
offers a computationally feasible approach to assess the significance of each DAS
input component to a selected forecast aspect. The evaluation of the observation
sensitivity, observation impact, and forecast R -and B -sensitivity share the same
adjoint-DAS tools and may be performed simultaneously to obtain complementary
information on the DAS performance. The necessary software for these calculations
is currently in place or it is being developed at various NWP centers and new
practical applications remain to be investigated. Valuable insight to the design of
observing system experiments and implementation of parameter tuning procedures
that are effective in reducing the forecast errors may be gained by systematically
monitoring the forecast sensitivity to parameters in the observation and background
error covariance representation. Observation sensitivity calculations provide guid-
ance for observation-space targeting and the practical ability to obtain R -and
B -sensitivity information establishes a basis for extending the traditional targeting
approach from the observation space to the error covariance space.

Acknowledgements The work of D.N. Daescu was supported by the Naval Research Laboratory
Atmospheric Effects, Analysis, and Prediction BAA #75-09-01 under award N00173-10-1-G032
and by the National Science Foundation under award DMS-0914937. Support for the second author
from the sponsor ONR PE-0602435N is gratefully acknowledged.

Appendix

All vectors are represented in column format and the superscript T denotes the
transposition operator. The elementwise (Hadamard) product of two vectors u 2 R n
and v 2 R n is denoted u ı v and is the vector w 2 R n with entries defined as