Selecting Markov chain orders for generating daily precipitation series across different Köppen climate regimes

Markov chain models are a commonly used statistical technique to generate realistic sequences of precipitation, but the choice of model order can strongly affect their performance. Although it is widely accepted that a first-order Markov chain reproduces precipitation occurrence in temperate latitudes quite well, it is also well known that first-order models have several shortcomings. These include a limited memory of rare events and inaccurately reproducing the distribution of dry-spell lengths, and their performance outside of temperate regions is less well understood. We present, therefore, the first assessment of model-order optimisation which is both global in extent and which uses four evaluation methods: the Bayesian Information Criterion (BIC) and each model-order's ability to reproduce wet- and dry-spell lengths, and the interannual variability of precipitation occurrence. As well as a global analysis, we also assessed Markov chain performance and model-order selection separately within five climate regimes based on the Köppen classification system: tropical, dry, temperate, continental and polar. These metrics were used to determine the best performing model-order to generate realistic time series of precipitation across the five different climate regimes. We find that the choice of model order is most sensitive to the performance metric and less dependent on the climate regime. Across all regimes, we show that a first-order model performs best when evaluated with BIC and for generating realistic wet-spell distributions across all climate regimes except tropical, where third order performs best. We also find that a third-order model reproduces observed dry-spell distributions the best and second order commonly reproduces the interannual variability of precipitation occurrence across all regimes except tropical, where third order once again performs best. Our findings highlight the benefits of a flexible and tailored approach to the choice of Markov chain order for constructing precipitation series.