AN ADJOINT EXAMINATION OF A NUDGING METHOD FOR DATA ASSIMILATION

A regional adjoint modeling system is modified to determine the sensit ivities of data assimilation and forecast results with respect to pert urbations of the nudging fields and coefficients A generalized linear system is used to explain the sensitivities both mathematically and ph ysically. A linearized shallow-water model is utilized to show that th e dynamics determining the sensitivities can be well described in term s 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 a nd forecasts to a given observed variable, and thus to gain insight in to what kinds of information are most (or least) effectively assimilat ed by the nudging method. The results of the adjoint study reveal that the nudging terms contribute significantly to the prognostic tendenci es, even if the values of the nudging coefficient are smaller than tho se commonly used. When either all dynamic fields or only wind fields a re nudged, the assimilation result is much more sensitive to the analy zed data at a later time. The sensitivity of the variance of the diffe rence between the assimilation result and the analyzed data at the fin al time within various bands of horizontal and vertical spatial scales shows that little scale interaction is evident in this study. The qua litative comparison of the sensitivity results for nudging only wind o r temperature or both are apparently well explained by referring to re sults of a sensitivity analysis for a nudged, linear shallow-water mod el. The latter results-indicate that nudging high-frequency gravity wa ves toward an analysis that varies on a much slower timescale had litt le effect on the final assimilation fields, aside from damping. The sa me was not true for either rotational modes or slowly propagating iner tial-gravitational modes. The sensitivity analysis of the shallow wate r model also explains why nudging temperature alone does not produce d esirable results. All the results indicate that the advection is being overwhelmed by the nudging even when the value of the nudging coeffic ient is half as large as commonly used, but geostrophic and dissipativ e adjustment are acting effectively. For larger values of the nudging coefficients, the effects of advection are diminished more.