Initialization for Models Using Sigma as the Vertical Coordinate

Abstract

In using σ as the vertical coordinate there is a need for interpolation of analyzed observations from p- to σ-surfaces in the process of establishing initial fields for a forecast. By employing an equation that establishes balance between the mass and wind fields directly on σ-surfaces (here called alternative b), we need to interpolate temperature alone from p to σ. This procedure appears preferable to the alternative of balancing on p-surfaces by the conventional balance equation followed by an interpolation of both mass and wind fields (called alternative a); how to preserve the established balance in the interpolation procedure is not obvious. The divergence equation is derived from the equations of motion with σ [=p/ps] as the vertical co-ordinate. A comparison of the order of magnitude of the terms is made with the aid of scale analysis. This shows that when the streamfunction for the non-divergent mass flow is introduced in the divergence equation, a consistent approximation to a balance equation results regardless of whether the earth's surface is level or not. A comparison is made between forecasts started from initial fields obtained by the two methods. In case a, pronounced gravity oscillations are present at least during the first 8?12 h, while in case b such oscillations are hardly detectable at any time during the forecast.