Modeling Daily Rainfall using Markov Chains

Abstract

A number of authors have used Markov chains to model the daily occurrence of rainfall. After the work of Gabriel and Neumann (Gabriel and Neumann,1962) who applied the Markov chain model successfully to describe Tel Aviv daily rainfall data, a number of researchers have applied a similar technique to study rainfall in widely different geographical regions. However, except for a few early studies (Weerasinghe, 1989, Punyawardena and Kulasiri 1998), not much work has been carried out to model the wet and dry spell sequence of daily rainfall observed in Sri Lanka. The main objective of this work is to use Markov chains to study the wet and dry spells of observed at the Colombo meteorological station (1941-2000) based on daily precipitation. In the first order Markov chain probability model, the probability of rain occurring on a given day (wet day) depends solely on the condition of the previous day. The two transitional probabilities can be defined as Hg and 2 H where Hg is the probability of a wet day given the previous day is dry, and 2 H is the probability of a dry day, given the previous day is wet.