A nonlinear preconditioned quasi-Newton method without inversion of a first-guess covariance matrix in variational analyses

Abstract

Aquasi-Newton method developed for adopting a non-diagonal first-guess covariance matrix in nonlinearvariational analyses (i.e. variational analyses adopting a non-quadratic cost function) is presented.As an example, we also show the effect of the nonlinear relationship between temperature and seasurfaceheight in three-dimensional variational ocean analyses.