Threshold Models for Rainfall and Convection: Deterministic versus Stochastic Triggers

This paper investigates stochastic models whose dynamics switch depending on the state/regime of the system. Such models have been called “hybrid switching diffusions” and exhibit “sliding dynamics” with noise. Here the aim is an application to models of rainfall, convection, and water vapor, where two states/regimes are considered: precipitation and nonprecipitation. Regime changes are modeled with a “trigger function,” and four trigger models are considered: deterministic triggers (i.e., Heaviside function) and stochastic triggers (finite-state Markov jump process), with either a single threshold for regime transitions or two distinct thresholds (allowing for hysteresis). These triggers are idealizations of those used in convective parameterizations of global climate models, and they are investigated here in a model for a single atmospheric column. Two types of results are presented here. First, exact statistics are presented for all four models, and a comparison indicates how the trigger choice influen...

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