Solving for Temperature Using Unnaturally Latticed Hydrostatic Equations

Abstract

Analyzing and balancing wind and mass fields on constant pressure surfaces and then interpolating the results to model coordinates cause significant errors, which lower verification scores and create inertial gravity noise. Although interpolation of geopotential to model coordinates produces less error, the computation of temperature with the model finite difference equations may lead to very large errors, as demonstrated by computation with standard atmosphere profiles. The solution for temperature using a variational formalism together with the model hydrostatic equation provides a method that greatly decreases the error in computation of pressure height by the model. The procedure is derived and results given for two different forms of Arakawa's hydrostatic equation. One of these forms an ill-conditioned equation set when geopotential is used to compute temperature. The results show that a significant decrease in the errors of geopotential produced by the model occurs when the variational procedure is used.