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

Abstract

. In this study it is shown that, by exploiting sensitivity properties that are intrinsic to the analyses derived from a minimization principle, the adjoint-DAS software tools developed at numerical weather prediction centres for observation and background sensitivity may be used to estimate the forecast sensitivity to observation-and background-error covariance parameters and for forecast impact assessment. All-at-once sensitivity to error covariance weighting coefficients and first-order impact estimates are derived as a

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

“…Consequently, the forecast sensitivities to the covariance weight coefficients satisfy the relationship (Daescu and Todling, 2010) ∂e…”

“…may be used to reconcile (55), (57), and (58) with the forecast s o i -and s b -sensitivity equations derived by Daescu and Todling (2010) in terms of the observation sensitivity and the residual y − h(x a ). For completeness, a direct derivation of the s b -sensitivity (57) from the first-order variation (47) is provided in the appendix.…”

“…It is noticed that, as a whole, the observing system information is under-weighted and an increased negative s b -sensitivity indicates that backgrounderror covariance inflation is of potential benefit to the forecasts. Negative s o -sensitivities identify those observation types whose error variance inflation (increasing the assigned σ o ) is of potential benefit to the forecasts, whereas positive s o -sensitivities identify those observation types whose error variance deflation (decreasing the assigned σ o ) is of potential benefit to the forecasts (Daescu and Todling, 2010). Figure 4 displays results of OBSI and forecast sensitivity to the error covariance weight factor for the radiosonde observations (RAOBS) distributed between various pressure levels.…”

“…Daescu (2008) derived the equations of the forecast sensitivity with respect to the observation-error covariance model (R-sensitivity) and to the background-error covariance model (B-sensitivity) in a nonlinear four-dimensional variational (4D-Var) DAS. The practical ability to estimate the forecast sensitivity to R-and B-weight parameters in a 3D-Var DAS was shown by Daescu and Todling (2010).…”

Performance measurement with advanced diagnostic tools of all‐sky microwave imager radiances in 4D‐Var

“…In general, the adjoint methodology can be used to estimate the sensitivity measure with respect to any parameter of importance of the assimilation system. Very recently, Daescu (2008) and Daescu and Todling (2010) derived a sensitivity equation of an unconstrained variational DA system from the first-order necessary condition with respect to the main input parameters: observation, background and their error covariance matrices. The paper provides the theoretical framework for further diagnostic tool development not only to evaluate the observation impact on the forecast but also the impact of the other analysis parameters.…”