Information-theoretic analysis of temporal dependence in discrete stochastic processes: Application to precipitation...

Area of Science:

• Hydrology
• Meteorology
• Information Theory

Background:

• Accurate precipitation prediction is crucial for weather forecasting and stochastic rainfall modeling.
• Understanding temporal dependencies in precipitation is essential for improving these models.

Purpose of the Study:

• To develop an information-theoretic approach for quantifying memory effects in discrete stochastic processes.
• To apply this method to daily precipitation records across the contiguous United States.
• To establish a framework for building parsimonious stochastic descriptions of precipitation dynamics.

Main Methods:

• Utilized predictability gain derived from block entropy to measure higher-order temporal dependencies.
• Employed bootstrap-based hypothesis testing and Fisher's method for robust memory estimation from finite data.
• Validated the estimator against Akaike information criterion and Bayesian information criterion using generated sequences.

Main Results:

• Daily rainfall occurrence is effectively modeled by low-order Markov chains.
• Significant regional and seasonal variations in precipitation memory were observed.
• Stronger temporal correlations were found in winter (West Coast) and summer (Southeast).

Conclusions:

• The developed method provides a robust way to estimate memory in precipitation data.
• Findings support the use of low-order Markov chains for describing daily rainfall occurrence.
• The framework aids in addressing spatial heterogeneity in precipitation memory for improved forecasting.