Stochastic Modelling of Daily Precipitation in Semi‐Arid Regions Using Markov Chains and Parametric Distributions

ABSTRACT Synthetic daily rainfall series are essential for agricultural planning, hydraulic infrastructure design and integrated water‐resource management, particularly in semi‐arid regions where observational records are often incomplete or short. This study evaluates two parametric stochastic models, first‐order Markov Chains coupled with gamma (GAM) and mixed exponential (ME) distributions, to generate synthetic rainfall series for three stations in the Agreste mesoregion of Pernambuco, Brazil. Transition probabilities for dry and rainy days were estimated up to third order and optimised via the Bayesian Information Criterion (BIC), which overwhelmingly selected the first‐order chain. A total of 1000 synthetic daily rainfall series were generated for each station to assess distributional fidelity and temporal behaviour. Both GAM and ME adequately reproduced observed daily and monthly precipitation statistics. GAM achieved closer agreement with the observed daily‐series mean precipitation (calculated over the full daily record, including dry days) and with the monthly totals, with deviations below 5% at all stations, while ME more accurately captured extreme rainfall events, reducing the “overdispersion” common in two‐parameter models. These findings demonstrate that combining a first‐order Markov occurrence model with ME is preferable when simulating heavy rainfall extremes, whereas GAM offers robust performance for average and total rainfall estimates. The complementary strengths of these distributions provide a flexible framework for synthetic rainfall generation in data‐scarce, semi‐arid environments, supporting improved hydrological risk assessment and resource planning under variable climatic conditions.