A Statistical Approach to the Kain-Fritsch Convective parameterization

Convective parameterization is one of the most important aspects of numerical modeling of the atmosphere, especially for the numerical weather forecasting. We have implemented a stochastic trigger function for convective initiation in the Kain-Fritsch (KF) scheme within the Penn State/NCAR Mesoscale Model version 5 (MM5). In our approach, convective initiation within MM5 is modeled by Bernoulli random variables. The probability of initiation is then modeled through a probit transformation in terms of the standard KF trigger variables, but with random parameters. The distribution of these random parameters is obtained through a Bayesian importance sampling Monte Carlo procedure informed by radar reflectivities. Kernel density estimates of these distributions are then incorporated into the KF trigger function, giving a meaningful stochastic (distributional) parameterization. We demonstrate this approach with several case studies.