Scale considerations in the modeling of temporal rainfall

Abstract

Observations on temporal rainfall are invariably taken in cumulative amounts over disjoint intervals representing different time scales such as hours, days, etc. At these scales a mathematical description of the rainfall process is shown to depend on the scale of measurements. This illustration is carried out employing three stochastic models having different dependence structures which range from complete independence and Markovian dependence to non‐Markovian clustering dependence. The problem of estimating the model parameters is also shown to be tied to the scale of measurements. Hourly and daily rainfall data from Denver, Colorado, and daily rainfall data from Agua Fria, Venezuela, are employed for this illustration.