Four-dimensional variational data assimilation
Abstract
The four-dimensional variational (4D-Var) algorithm is an extension of 3D-Var that imposes a nonlinear numerical weather prediction model as a strong constraint while allowing assimilation of observations at their exact times. These are important for fast-evolving systems such as hurricanes and when high temporal resolution data are available. This chapter presents the mathematical formulation of 4D-Var, a gradient calculation using the adjoint model, the penalty method for controlling gravity-wave oscillations, the adjoint of a physical parameterization with “on–off” switches, the development of a full-physics global 4D-Var system and two regional adjoint modeling systems, and the ...
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