Four-dimensional variational data assimilation
Four-dimensional variational data assimilation
In this chapter, four-dimensional variational data assimilation (4D-VAR) is discussed in the context of numerical weather prediction (NWP). The analysis step in an NWP data assimilation cycle combines observations with a background forecast. Plausible models of error distributions involve transforms and statistics to describe the structure of errors at one time, plus a forecast model constraining the time evolution. They allow a Bayesian derivation of equations for the optimal analysis, by minimizing a 4D-Var penalty function using an adjoint model. Difficulties with the deterministic best fit of a nonlinear NWP model are discussed and a statistical approach to 4D-VAR based on the extended Kalman filter is presented. Advanced extensions to 4D-VAR can allow for nonlinearities and non-Gaussian distributions, arising from the physical limits to humidity, and from the possibility of erroneous observations. Ensembles provide useful information about likely background errors, which can be used in hybrid ensemble–variational data assimilation.
Keywords: four-dimensional variational data assimilation, 4D-VAR, numerical weather prediction, Bayesian, adjoint model, nonlinearities, hybrid ensemble–variational
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