An Adjoint Examination of a Nudging Method for Data Assimilation

Abstract A regional adjoint modeling system is modified to determine the sensitivities of data assimilation and forecast results with respect to perturbations of the nudging fields and coefficients. A generalized linear system is used to explain the sensitivities both mathematically and physically. A linearized shallow-water model is utilized to show that the dynamics determining the sensitivities can be well described in terms of the dynamics of geostrophic adjustment, with the added effects of dissipation and nudging terms. The purpose of the study is to reveal the dynamics responsible for the sensitivities of assimilated fields and forecasts to a given observed variable, and thus to gain insight into what kinds of information are most (or least) effectively assimilated by the nudging method. The results of the adjoint study reveal that the nudging terms contribute significantly to the prognostic tendencies, even if the values of the nudging coefficient are smaller than those commonly used. When either ...

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