Re-inventing Bethlahmy method for estimating probable maximum precipitation

Abstract

The design and risk analysis of large-scale hydraulic structures (e.g., dams) and sensitive installations (e.g., nuclear facilities) downstream of those structures rely on design flood corresponding to probable maximum precipitation (PMP). In areas where there is a sparsity of information on hydrometeorological variables, practitioners use various statistical methods to arrive at a PMP estimate, assuming it to be the possible upper bound for precipitation. However, the assumption is violated in different parts of the world. Hence, there is a need to improve the existing statistical methods and develop their potential alternatives. Against this backdrop, this paper proposes a new variant of a non-parametric method (Bethlahmy) to facilitate the estimation of PMP at locations with sparse records of extreme precipitation. It involves mapping of datapoints in annual maximum series and their ranks to a non-dimensional space (NDS) and using the information on sample size and observed maximum precipitation in the NDS to arrive at a surrogate variable representing PMP, which is eventually mapped back to PMP in the original space. The effectiveness of the proposed Bethlahmy variant over various existing statistical techniques is illustrated through Monte Carlo Simulation experiments and a case study on 37,872 stations from a global precipitation database. The existing techniques include the original Bethlahmy and Hershfield methods, conventional probabilistic approach, and relevant variant(s). Insight is provided into the relative performance of these methods, as there is a dearth of such attempts in the literature. Results indicate that the proposed Bethlahmy variant exhibits better performance than other methods/variants across samples varying in size and extreme precipitation characteristics, making it a promising statistical alternative for PMP estimation.