Diagnosis and tuning of observational error in a quasi‐operational data assimilation setting

Abstract

SUMMARYDesroziers and Ivanov proposed a method to tune error variances used for data assimilation. The implementation of this algorithm implies the computation of the trace of certain matrices which are not explicitly known. A method proposed by Girard, allowing an approximate estimation of the traces without explicit knowledge of the matrices, was then used. This paper proposes a new implementation of the Desroziers and Ivanov algorithm, including a new computation scheme for the required traces. This method is compared to Girard's in two aspects: its use in the implementation of the tuning algorithm, and the computation of a quantification of the observation impacts on the analysis known as Degrees of Freedom for Signal. Those results are illustrated by studies utilizing the French data assimilation/numerical weather-prediction system ARPEGE. The impact of a first quasioperational tuning of variances on forecasts is shown and discussed.

Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis

“…However, it only offers a local analysis (in the vicinity of the minimum). These expressions parallel those obtained in (Chapnik et al, 2006) where the assimilation is of Gaussian nature whereas the model is possibly non-linear. In the Gaussian case, this formula identifies with Eq.…”

Adjoint sensitivity of the model forecast to data assimilation system error covariance parameters

“…which is a common representation used to perform error covariance tuning (Desroziers and Ivanov, 2001;Chapnik et al, 2006;Desroziers et al, 2009). Each of the error covariance parameters is a positive scalar,…”

“…In practice, several simplifying assumptions are necessary to achieve a feasible implementation, and an increased amount of research in numerical weather prediction (NWP) is dedicated to observation-and background-error covariance modelling (Gaspari and Cohn, 1999;Hamill and Snyder, 2002;Lorenc, 2003;Buehner et al, 2005;Frehlich, 2006;Janjić and Cohn, 2006;Bannister, 2008a,b) and to the development of effective techniques for diagnosis, estimation, and tuning of unknown error covariance parameters in both variational and Kalman filter-based assimilation systems (Dee, 1995;Dee and Da Silva, 1999;Desroziers and Ivanov, 2001;Desroziers et al, 2005;Chapnik et al, 2006;Desroziers et al, 2009;Li et al, 2009).…”

Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

“…Quantification of the loss of information as a result of suboptimal weighting, and implementation of efficient procedures to adjust the error covariance parameters to a configuration that improves the forecasts' skill, are areas of active research. Synergistic efforts include the development of error covariance models for NWP applications (Derber and Bouttier, 1999;Gaspari and Cohn, 1999;Lorenc, 2003;Fisher, 2003;Bannister, 2008aBannister, , 2008bFrehlich, 2011;Bishop et al, 2011;Raynaud et al, 2011) and of computationally feasible techniques for diagnosis, estimation, and tuning of the error covariance parameters (Wahba et al, 1995;Dee, 1995;Dee and Da Silva, 1999;Andersson et al, 2000;Desroziers and Ivanov, 2001;Cardinali et al, 2004;Buehner et al, 2005;Chapnik et al, 2006;Zupanski and Zupanski, 2006;Trémolet, 2007;Anderson, 2007;Liu and Kalnay, 2008;Desroziers et al, 2009;Li et al, 2009).…”