Hidden Markov models for modeling daily rainfall occurrence over Brazil

A hidden Markov model (HMM) is used to describe daily rainfall occurrence at ten gauge stations in the state of Ceará in northeast Brazil during the February–April wet season 1975–2002. The model assumes that rainfall occurrence is governed by a few discrete states, with Markovian daily transitions between them. Four “hidden” rainfall states are identified. One pair of the states represents wet vs. dry conditions at all stations, while a second pair of states represents north-south gradients in rainfall occurrence. The estimated daily state-sequence is characterized by a systematic seasonal evolution, together with considerable variability on intraseasonal, interannual and longer time scales. The first pair of states are shown to be associated with large-scale displacements of the tropical convergence zones, and with teleconnections typical of the El Niño-Southern Oscillation and the North Atlantic Oscillation. A trend toward greater rainfall occurrence in the north of Ceará compared to the south since the 1980s is identified with the second pair of states. A non-homogeneous HMM (NHMM) is then used to downscale daily precipitation occurrence at the ten stations, using general circulation model (GCM) simulations of seasonal-mean large-scale precipitation, obtained with historical sea surface temperatures prescribed globally. Interannual variability of the GCM’s large-scale precipitation simulation is well correlated with seasonaland spatial-averaged station rainfall-occurrence data. Simulations from the NHMM are found to be able to reproduce this relationship. The GCM-NHMM simulations are also able to capture quite well interannual changes in daily rainfall occurrence and 10-day dry spell frequencies at some individual stations. It is suggested that the NHMM provides a useful tool (a) to understand the statistics of daily rainfall occurrence at the station level in terms of large-scale atmospheric patterns, and (b) to produce station-scale daily rainfall sequence scenarios for input into crop models etc.