🤖 AI Summary
This study quantifies temporal dependencies in the stochastic process of precipitation to enhance forecasting skill and modeling efficiency. We propose a novel information-theoretic metric—“predictability gain”—to characterize higher-order memory effects; integrate block entropy estimation, Bootstrap resampling, and Fisher’s method for p-value combination to achieve robust memory detection under small-sample conditions, overcoming limitations of conventional criteria (e.g., AIC/BIC). Applied to daily precipitation data across the contiguous United States, results confirm predominant low-order Markov behavior, with memory strength exhibiting significant spatiotemporal heterogeneity: strongest in winter along the West Coast and in summer over the Southeast—consistent with underlying climatological dynamics. The framework provides a concise, robust paradigm for stochastic precipitation modeling and real-time predictability assessment.
📝 Abstract
Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete stochastic processes and apply it to daily precipitation records across the contiguous United States. The method is based on the predictability gain, a quantity derived from block entropy that measures the additional information provided by higher-order temporal dependencies. This statistic, combined with a bootstrap-based hypothesis testing and Fisher's method, enables a robust memory estimator from finite data. Tests with generated sequences show that this estimator outperforms other model-selection criteria such as AIC and BIC. Applied to precipitation data, the analysis reveals that daily rainfall occurrence is well described by low-order Markov chains, exhibiting regional and seasonal variations, with stronger correlations in winter along the West Coast and in summer in the Southeast, consistent with known climatological patterns. Overall, our findings establish a framework for building parsimonious stochastic descriptions, useful when addressing spatial heterogeneity in the memory structure of precipitation dynamics, and support further advances in real-time, data-driven forecasting schemes.