An Inverse Balance Equation in Sigma Coordinates for Model Initialization

Abstract

In many numerical simulation studies there is a need to obtain the balanced initial fields in numerical models with σ as the vertical coordinate. By employing an equation that establishes the balance between the mass and wind fields directly on σ surface, we can obtain mass fields from wind fields, or vice versa. Since the balance equation is generally nonlinear, numerical methods must be used to obtain approximate solutions. However, the term corresponding to the divergence of the pressure gradient in the σ system is more complicated compared to that in pressure or height coordinates. As a result previous studies have made various approximations for this term. In this paper, a relatively accurate and consistent numerical scheme is proposed to solve the inverse balance equation in a coordinates. Several numerical calculations show that the proposed scheme is more accurate and more consistent than that used by Kurihara and Bender and Kurihara et al.