Convergence of Rain Process Models

Abstract

Representing rain in global climate models continues to be a challenge. Currently, models generally rain too often and too little. Additionally, the models have trouble capturing variability in rain data. One possible solution to increasing variability in a model is to use a stochastic process. A variety of stochastic models have been used to describe time series of precipitation or rainfall. Since many of these stochastic models are simplistic, it is desirable to develop connections between the stochastic models and the underlying physics of rain. In this talk, I will describe simple models of rain in a single column model as a stochastic differential equation (SDE) with a switch. The inclusion of this switch leads to a model with hysteresis. I will show how these models are connected by presenting formal derivations and theorems on convergence of SDEs and their Kolmogorov Equations.