Estimating reliable Probable Maximum Precipitation at data-sparse locations

Flood estimates corresponding to probable maximum precipitation (PMP) are desirable for planning, designing and risk assessment of large hydraulic structures, such as spillways of large dams, whose failure may have catastrophic consequences on ecology, economy, and the environment. In practice, PMP estimates are obtained using hydrometeorological or/and statistical methods as per the recommendations of the World Meteorological Organization. In regions where data of hydrometeorological variables (e.g., precipitation, temperature, relative humidity) are limited or unavailable, practitioners often resort to various statistical methods which require only precipitation records to estimate PMP. Among statistical methods, the Hershfield method is widely used when records from several sites in a region are available whereas conventional probabilistic approach is preferred for at-site analysis. However, arriving at reliable PMP estimates at data-sparse locations is still a challenge. Thus, there is a growing need to improve the existing statistical methods and develop/explore alternate methods. Against this backdrop, this study proposes a new variant of Bethlahmy method, which is a non-parametric method, to facilitate the estimation of PMP at locations with sparse records of extreme precipitation.

The proposed Bethlahmy variant involves (i) mapping of datapoints and corresponding ranks of target site’s annual maximum precipitation series to a non-dimensional space (NDS), (ii) using the mapped information to arrive at a surrogate estimate for PMP in the NDS, and (iii) mapping the surrogate estimate to PMP in the original space. The efficacy of the proposed Bethlahmy variant over various existing statistical techniques is demonstrated 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). Results revealed that the proposed Bethlahmy variant outperforms other methods/variants across samples varying in size and extreme precipitation characteristics, making it a promising statistical alternative for PMP estimation.