A Quasi-Variational Algorithm for Nonlinear Normal-Mode Initialization

Abstract

Balance equations of normal-mode initialization are nonlinear time-independent partial differential equations solved by iterative methods. For the given geopotential, there are regions where these equations are not elliptic, which is reflected in the divergence of iterative algorithms. Variational approaches used to minimize the geopotential changes are more expensive than conventional methods. In this study a simple quasi-variational algorithm is proposed based on different forms of normal-mode initialization equations, which achieves a good balance of atmospheric fields and ensures small changes of geopotential analysis values.