Variational methods in simultaneous optimum interpolation and initialization

The duality between optimum interpolation and variational objective analysis, is reviewed. This duality is used to set up a variational approach to objective analysis which uses prior information concerning the atmospheric spectral energy distribution, in the variational problem. In the wind analysis example, the wind field is partitioned into divergent and nondivergent parts, and a control parameter governing the relative energy in the two parts is estimated from the observational data being analyzed by generalized cross validation, along with a bandwidth parameter. A variational approach to combining objective analysis and initialization in a single step is proposed. In a simple example of this approach, data, forecast, and prior information concerning atmospheric energy distribution is combined into a single variational problem. This problem has (at least) one bandwidth parameter, one partitioning parameter governing the relative energy in fast slow modes, and one parameter governing the relative weight to be given to observational and forecast data.