Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. I: Theory

TLDR

The study develops a variational approach to assimilate meteorological observations by finding the model solution that minimizes a distance metric between the model and the available data. The method employs the model’s adjoint equations to compute gradients through a forward–backward integration pair, feeding these gradients into a descent algorithm to iteratively adjust initial conditions, and is applied to the vorticity equation. The approach successfully computes explicit gradients and achieves effective assimilation in numerical experiments on a Haurwitz wave.

Abstract

Abstract The following variational approach is taken to the problem of assimilation of meteorological observations: find the solution of the assimilating model which minimizes a given scalar function measuring the ‘distance’ between a model solution and the available observations. It is shown how the ‘adjoint equations’ of the model can be used to compute explicitly the ‘gradient’ of the distance function with respect to the model's initial conditions. the computation of one gradient requires one forward integration of the full model equations over the time interval on which the observations are available, followed by one backward integration of the adjoint equations. Successive gradients thus computed are introduced into a descent algorithm in order to determine the initial conditions which define the minimizing model solution. The theory is applied to the vorticity equation. Successful numerical experiments performed on a Haurwitz wave are described.