The hot rainy season marked by local scattered thunderstorms from June to September is typical of most of the lower elevations of the Sonoran and Chihuahuan regions of south‐western North America. This rainy season is analyzed by using long‐term historical daily records to obtain insight concerning the underlying stochastic process. By using historical data from three scattered points in this region, we computed the discrete series of daily Bernoulli parameters and daily first‐order Markov transition probabilities. The hypothesis of sequential independence versus a first‐order Markov dependence hypothesis is tested by comparison of analytically derived distributions for dependent random variables generated by the nonstationary processes. These include wet and dry run lengths, occurrence of the first wet day in the season, number of runs per season, and total number of rainfall days per season. The comparative analysis of historical data indicates that (1) the Markov chain model is generally significantly superior to the Bernoulli model (which extends results of similar analyses by others from regions of largely frontal‐type storms) and (2) year‐to‐year variations in the process require additional probabilistic descriptions, indicated by annual variance in number of rain days and significant annual changes in autocorrelati
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