Variational and Optimization Methods in Meteorology: A Review

Recent advances in variational and optimization methods applied to increasingly complex numerical weather prediction models with larger numbers of degrees of freedom mandate to take a perspective view of past and recent developments in this field, and present a view of the state of art in the field. Variational methods attempt to achieve a best fit between data and model subject to some ‘a priori’ criteria – in view of resolving the undeterminancy problem between the size of the model and the respective number of data required for its satisfactory solution. This review paper presents in a synthesized way the combined views of the authors as to the state of the art of variational and optimization methods in meteorology. Issues discussed include topics of variational analysis, variational initialization, optimal control techniques, variational methods applied for numerical purposes and constrained adjustment, and finally how some of the variational and optimization methods discussed in the review relate to each other.