A Simplified System of Equations for Simulation of Tropical Cyclones

Abstract

A simplified system of equations which can simulate the development and mature stages of tropical cyclones is presented. The model is similar to that presented by Ooyama, except that the assumption of incompressible fluid layers is relaxed. Instead, the governing equations for a compressible fluid in isentropic coordinates are discretized vertically by considering three fluid layers with constant potential temperature. This makes the inclusion of thermodynamic processes more straightforward. The governing equations in the adiabatic case are mathematically equivalent to the equations used by Ooyama, except with an extra term in the pressure gradient force. The model equations are solved using a spectral method where the basis functions are the normal modes of the linearized equations. Numerical simulations show that the model sensitivity to vertical stability, sea surface temperature and midlevel moisture are similar to results from more general models. The sensitivity to these factors can be explained qualitatively by consideration of the vertical stability factor used in the cumulus parameterization. The sensitivity to latitude is investigated in more detail in previous work. Low-latitude storms are smaller than high-latitude storms, but intensify more rapidly initially. This difference is related to the radial positioning of the diabatic heating which is much closer to the storm center for low-latitude storms. This occurs since the air in the boundary layer can penetrate closer to the storm center when the Coriolis force is smaller. The model is also initialized with climatological values of sea surface temperature as a function of latitude appropriate for the Western Pacific. Despite its simplicity, the model can reproduce the observed variations of storm size and intensity with latitude.