The Adjoint Sensitivity Guidance to Diagnosis and Tuning of Error Covariance Parameters - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 200

increased tremendously, there is a growing gap between the ability to collect
information and the ability to optimally ingest it into numerical weather prediction
(NWP) models through data assimilation techniques. The high model resolution
and data density must be matched by an improved representation in the data
assimilation system (DAS) of the statistical properties of the errors in the prior
state estimate, model, and observations. Suboptimal information weighting poses a
fundamental limitation on the DAS performance and the development of structured
error covariance models for NWP applications and of computationally efficient
techniques for tuning of error covariance parameters are areas of active research
( Gaspari and Cohn 1999 ; Dee and Da Silva 1999 ; Lorenc 2003 ; Desroziers et al.
2005 ; Buehner et al. 2005 ; Chapnik et al. 2006 ; Bannister 2008a , b ; Li et al. 2009 ;
Frehlich 2011 ).
Adjoint-data assimilation system (adjoint-DAS) techniques provide effective
tools for the analysis and optimization of the observation impact on reducing
the forecast errors. The adjoint-DAS evaluation of the observation sensitivity has
been introduced in NWP by Baker and Daley ( 2000 ) for the analysis and design
of observation targeting strategies. Practical applications include monitoring the
impact of data provided by the global observing system to reduce short-range
forecast errors, data quality diagnostics and guidance to optimal satellite channel
selection, and adaptive observation targeting ( Langland and Baker 2004 ; Langland
2005 ; Cardinali 2009 ; Baker and Langland 2009 ; Gelaro and Zhu 2009 ; Gelaro et al.
2010 ; Cardinali and Prates 2011 ; Lupu et al. 2011 ).
The assessment of the forecast impact as a result of variations in the specification
of observation and background error covariance parameters has been mainly
performed through observing system experiments ( Zhang and Anderson 2003 ;
Joiner et al. 2007 ) and recently, the extension of the adjoint-DAS approach has
been formulated to include the forecast sensitivity to the specification of error
covariance parameters ( Daescu 2008 ; Daescu and Todling 2010 ). This chapter
presents a detailed exposure of the equations to evaluate the sensitivity of a forecast
error aspect with respect to parameters in the observation and background error
covariance representation and recent results obtained with the adjoint versions
of the Naval Research Laboratory Atmospheric Variational Data Assimilation
System - Accelerated Representer (NAVDAS-AR) ( Xu et al. 2005 ; Rosmond
and Xu 2006 ) and the Navy Operational Global Atmospheric Prediction System
(NOGAPS) ( Hogan and Rosmond 1991 ). The chapter is organized as follows below.
Section 9.2 includes a brief review of the adjoint-DAS approach to observation
impact assessment in variational data assimilation. A simple scalar example of
statistical estimation illustrates the suboptimal observation performance in the
presence of misspecified information error statistics. In Sect. 9.3 we present the
theoretical basis to adjoint-DAS forecast sensitivity and first order impact estimation
for observation and background error covariance parameters. A proof-of-concept
to error covariance diagnosis is provided with the Lorenz 40-variable model.
Section 9.4 presents results of observation impact and forecast sensitivity to error
covariance weight parameters obtained with NAVDAS-AR/NOGAPS and their
adjoint versions. The sensitivity analysis provides guidance on the parameter