Quantitative assessment of automated threshold selection methods for Generalized Pareto Distribution for modeling precipitation extremes in the Indian subcontinent

Abstract

Extreme Value Theory (EVT) provides a reliable statistical framework for modeling and understanding the behavior of extreme events. Within EVT, the Peak-Over-Threshold (POT) model is a powerful method for estimating the Extreme Precipitation Events (EPEs); however, its application is limited largely due to the challenges in selecting optimal threshold values. The present study critically examines and compares the theoretical underpinnings of several threshold selection methods (such as Anderson Darling (AD), Normality of Differences (ND), Squared Error(SE) and Multiple Threshold Method (MTM)) within the context of the Generalized Pareto Distribution (GPD) model. The comparison of these methods was performed on i) synthetic datasets generated through Monte Carlo simulation and ii) daily and seasonal gridded precipitation datasets from the Indian subcontinent. The evaluation revealed certain theoretical limitations of the existing methods, leading to the development of hybrid threshold selection methods. Results from the synthetic samples also show that the hybrid methods are more accurate and effective in determining critical threshold ranges. Application of the method to Indian precipitation datasets yielded comparable results, with threshold values effectively capturing the spatial pattern of extremes, consistent with regional characteristics. For example, thresholds identified for coastal and northeastern regions often exceed 160 mm/day, while the Rajasthan region exhibits significantly lower thresholds, frequently less than 15 mm/day. These estimated threshold values were subsequently employed to investigate the temporal variability of extreme events within the Indian region. The results indicated a considerable increase in the number of peaks and peak intensity of precipitation events in certain parts of the Southern Peninsular region of India. This study is crucial for providing comprehensive guidelines and improving the reliability of POT-based threshold selection methods for identifying EPEs. The approach is essential for assessing the increasing intensity and frequency of precipitation extremes related to climate change, offering valuable insights for targeted mitigation and disaster risk reduction strategies.