Dependence of the stability of semi-implicit atmospheric models on reference temperature profile

Abstract

The linear stability of three-time-level finite-difference semi-implicit schemes is studied for hydrostatic atmospheric models with viscosity terms. The main objective is the investigation of stability dependence on choice of reference temperature profile. Characteristic equation for amplification factor is derived in the case of simplified baroclinic atmospheric numerical model, keeping the implicit approximation for the basic temperature profile and explicit approximation for its deviations. Analytical solutions for amplification factor are found in some special cases and computational experiments are performed for different values of model parameters, such as vertical discretization (number of levels and its distribution), temperature profile (basic and actual), and time step. The influence of the viscosity terms on scheme stability is also studied. Performed analysis confirms two main results obtained numerically in other models: instability generated by inappropriate determination of temperature profile is absolute and computational stability can be recovered if the basic reference profile is chosen to be warmer than the actual one.