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 Akaike Information Criterion and Bayesian Information Criterion. 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.

翻译：理解降水的时间依赖性对于提高天气可预测性和开发高效随机降雨模型至关重要。我们引入了一种信息论方法来量化离散随机过程中的记忆效应，并将其应用于美国本土的日降水记录。该方法基于可预测性增益——一个从块熵导出的量，用于衡量高阶时间依赖性所提供的额外信息。该统计量结合基于自助法的假设检验和费希尔方法，能够从有限数据中获得稳健的记忆估计量。对生成序列的测试表明，该估计量优于其他模型选择准则，如赤池信息准则和贝叶斯信息准则。应用于降水数据的分析表明，日降水发生可由低阶马尔可夫链很好地描述，并呈现出区域性和季节性变化：冬季在西海岸、夏季在东南部相关性更强，这与已知的气候模式一致。总体而言，我们的研究建立了一个构建简约随机描述的框架，该框架在解决降水动态记忆结构中的空间异质性时非常有用，并支持实时数据驱动预测方案的进一步发展。