Determination of the Adjoint Model of the NMC Global and NGMModels and Their Application to 4-D Data Assimilations

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"Determination of the Adjoint Models for NMC's Global and Nested Grid Models and Their Application to Four Dimensional Data Assimilation" A numerical weather prediction model requires a complete and accurate specification, or analysis, of the state of the atmosphere at the initial time. The process of introducing observations which are distributed in time into a forecast model is known as four dimensional data assimilation. Observations cannot perfectly describe the state of the atmosphere at a given time. Ideally, an assimilation should produce the best "fit" of the data observations while satisfying the dynamical properties of the governing equations as embodied in the model. Under this award, the PI and his colleagues will employ an assimilation method which uses optimal control theory to minimize the differences between the evolution of the observations and the dynamical constraints of the model. This technique requires the determination of the adjoint of the models employed, in this case, models used at the National Meteorological Center (NMC). Determination of the adjoint model of a particular forecast model is a complex numerical problem. The PI has developed a staged approach, working on models of increasing complexity. At each stage, the adjoint method for four dimensional assimilation will be tested in cooperation with NMC scientists. In the course of the research, the PIs will have to develop new methods for dealing with problems introduced by the use of more complex models. For example, determination of the adjoint models requires that quantities be differentiable, but certain physical processes, such as convection, are not. This research is being supported as part of an NSF-NMC cooperative effort to support basic research in numerical weather prediction.