Threshold Models for Rainfall and Convection: Deterministic Versus Stochastic Trigger

Abstract:

We study two types of convective triggers as idealizations of a general circulation model's convective parametrization trigger. In one model, we use a stochastic trigger that initiates strong convection at a random time after the water vapor has reached a critical value. In the other, the trigger is deterministic and occurs immediately when a fixed threshold is reached. Also, the triggers are considered with either a single threshold for regime transitions or two distinct thresholds (allowing for hysteresis). These four cases are investigated in stochastic models of column water vapor dynamics. Two types of results are presented here. First, exact statistics are presented for all four models, and a comparison indicates how the trigger choice influences rainfall statistics. For example, it is shown that the average rainfall is identical for all four triggers, whereas extreme rainfall events are more likely with the stochastic trigger. Second, the stochastic triggers are shown to converge to the deterministic triggers in the limit of fast transition rates.