Improving stochastic rainfall models through event classification

Stochastic rainfall models rely on accurate rainfall distributions. Since rainfall is generated by various processes, rainfall series are composed of events with different distributions. In such cases, the use of mixed distribution approaches has been recommended (e.g., Laaha 2023) based on event separation. However, separating rainfall events into generative types is not straightforward.

We propose clustering based on event characteristics derived from the rainfall series (such as peak magnitude, duration, average intensity, and relative time to peak) to stratify the rainfall series into types of rainfall events. These event characteristics are derived using Yevjevich’s theory of runs, which is commonly used in hydrological drought studies and is adapted here for rainfall event separation to exploit the temporal characteristics of rainfall events. Additionally, a binary lightning index is used to help distinguish between convective and stratiform events.

We compare two methods for event classification. The first method is model-based clustering using a Gamma mixture model. The second method is the robust partitioning method PAM, which uses Gower’s distance to handle the mixed data structure of the event characteristics. Both methods are optimized regarding the number of clusters using state-of-the-art criteria.

The analysis shows that clustering based on rainfall event characteristics and the lightning index is a simple yet effective method to reduce process heterogeneity in rainfall frequency analysis. These characteristics are obtained without additional weather data, which is a major strength of the approach. Finally, we compare the distributions of event types to discuss the value of mixed distribution approaches for stochastic rainfall modeling. In summary, this study encourages a better understanding of statistical assumptions in applied models and enriches the physical knowledge included in environmental statistics, such as stochastic rainfall models.

Reference:

Laaha G (2023). “A Mixed Distribution Approach for Low-Flow Frequency Analysis – Part 1: Concept, Performance, and Effect of Seasonality.” Hydrology and Earth System Sciences, 27(3), 689–701. ISSN 1607-7938. doi:10.5194/hess-27-689-2023.