Distribution algorithm in finite difference method and its application to a 2D simulation of temperature inversion

In this article we present a numerical algorithm in a finite difference method coupled with the Schwartz distribution on a surface and its application to 2D simulation of a temperature inversion in meteorology. This phenomenon has been observed in Kyoto in Japan frequently and one of the reasons why the inversion occurs is the radiative cooling on the ground. In order to describe it in a mathematical model, we introduce transmission conditions on the ground and show its distribution formula. The characteristics of our numerical method are based on the direct method and the finite difference approximation of the Schwartz distribution defined on the ground. Through our discussion, a numerical experiment for the inversion of the temperature gradient is presented.