Non- Stationary Hershfield Method for Probable Maximum Precipitation Estimation

Abstract:

Many studies have reported the non-stationary behavior of extreme precipitation in the recent past and in warming future climate. Probable maximum precipitation (PMP), also defined as an upper limit of extreme precipitation, is widely used to arrive at design flood estimate for risk analysis of large hydraulic structures (e.g., dams) whose failure could lead to catastrophic consequences for ecology and environment. Owing to climate change, PMP is also expected to exhibit non-stationarity (NS). A handful of studies have attempted to consider NS in estimation of PMP using moisture maximization and multi fractal methods, but none have been reported in the context of Hershfield method. It is widely used statistical method for estimation of PMP, as it does not require voluminous data on various hydrometerological variables except precipitation, and yet produces reliable estimates close to those obtained from a physical method.

A modification over original Hershfield method is proposed in this study, which takes into account NS in precipitation data. The applicability of proposed method is illustrated over India, where PMP estimates are being considered for risk analyses of several ageing dams among the existing 5264 dams in the country, through aid of world bank, under DRIP (Dam Rehabilitation and Improvement Project). For use in this analysis, 119 years (1901-2019) long precipitation records available at 0.25-degree spatial resolution from IMD (Indian Meteorological Department) were considered. Substantial number of those grids exhibited significant trend and NS in the at-site frequency factors quantified using 60-year long overlapping time windows formed from the data. Analysis of trend was based on Mann-Kendall test, whereas presence of NS was investigated using various tests namely KPSS , ADF and PP. A novel methodology is proposed to arrive at PMP estimates accounting for NS in the frequency factors by considering time as covariate. One-day to 3-day PMP estimates obtained using the new methodology are compared with those estimated using the conventional Hershfield method. The implications of accounting for NS in PMP estimates on the corresponding design flood estimates are demonstrated for Mahanadi river basin in India, which is frequently prone to floods.