Daily Rainfall Probabilities: Conditional upon Prior Occurrence and Amount of Rain

Abstract

A generalization of the chain-dependent process is proposed to describe daily rainfall. The model allows probabilities of rain occurrence to depend on the amount of rain in the day before. The influence of the antecedent amount of rain on the next day occurrence is called “feedback.” A method for identification of feedback effects in a series of observations is derived and application made to rainfall occurrence at Los Angeles. Performance of the model in reproducing other precipitation patterns, such as maximum daily rainfall or total amount of rainfall in successive n-day periods, was checked by the Monte Carlo method.