A generalized design flood estimation framework under stationary and non-stationary scenarios

With the ever-ongoing debate over the death of stationarity in flood time series, developing methods for flood frequency analysis that can address both stationarity and non-stationarity simultaneously has become increasingly important for design flood estimation. Existing non-stationary flood frequency analysis (NFFQ) methods are either limited to providing time-varying conditional flood quantile estimates or lack closed-form expression to estimate the design flood over the planning period. We propose a novel framework, MM-NFFQ, that introduces marginal moments (MM) estimation techniques to provide a closed-form expression to estimate design flood under non-stationarity. We demonstrate MM-NFFQ using the LP3 distribution for estimating conditional moments, but in principle, it can work for any 3-parameter distribution. We first show the proposed MM-NFFQ collapses to stationary flood frequency analysis analytically using synthetic data and then demonstrate the MM-NFFQ approach for two basins exhibiting non-stationarity in their flood time series. We further extend the analysis to selected 40 basins across CONUS and find that arid basins exhibit higher deviation from stationarity. Thus, the proposed MM-NFFQ framework can estimate traditional flood frequency curves for both, stationary and non-stationary flood processes, and can also be utilized to analyze the changes in conditional moments and marginal moments over different planning horizons.