A MARKOV CHAIN ANALYSIS OF RAINFALL PATTERNS IN SOUTHEASTERN WISCONSIN

This study developed a precipitation generator for producing daily precipitation occurrence and amount using the Markov chain model based on historical data from 1995 to 2023 for Milwaukee, Wisconsin. A first order two-state model, relying only on the previous day, has been used in this study. Four transition probabilities were calculated from observed time series data using maximum likelihood estimates. Precipitation occurrence was computed using a transitional matrix and precipitation amount was generated by using monthly two-parameter gamma distribution. The shape (α) and scale (β) parameters were calculated from wet-day only data for each month. The simulated wet and dry spells and average precipitation were then compared with those in the observed time series to assess the role of iterations for comparison between observed and generated precipitation occurrence series.