The decomposition-based nonstationary flood frequency analysis

Abstract

• The performance-based NS-FFA is challenged theoretically and practically. • A new decomposition procedure for the decomposition-based NS-FFA is proposed. • The proposed decomposition procedure preserves the stationary component. • The proposed decomposition-based NS-FFA captures the nonstationary process better. • This approach overcomes the previous issues of the NS-FFA and performs competitively. The nonstationary flood frequency analysis (NS-FFA) is conducted when the assumption of stationarity in hydrologic extremes is violated. The commonly used approach is the performance-based NS-FFA, which jointly determines the distribution and the nonstationary structure based upon the model performance. However, this approach is challenged from both theoretical and practical perspectives. An alternative is the herein named decomposition-based NS-FFA, which determines the two NS-FFA model components separately and explicitly uses the available knowledge of the nonstationarity. However, it has been barely implemented in practice. This paper proposed a novel decomposition procedure that strictly follows the theoretical decomposition of nonstationary stochastic processes to advance the decomposition-based NS-FFA. The proposed decomposition procedure was compared with a previously reported method in both an analytical deduction and a simulation study. The proposed decomposition-based NS-FFA was further compared to the performance-based NS-FFA using both synthetic and real datasets from North America, which exhibit different patterns of nonstationarity. The Particle Filter was adopted for uncertainty quantification and parameter estimation. The results revealed that the proposed decomposition-based approach was advantageous in preserving the moments of underlying stochastic component, particularly the higher-order moment (i.e., skewness). In addition, the comparison of the two NS-FFA approaches demonstrated the superiority of the proposed decomposition-based approach in capturing the underlying (known) nonstationary stochastic process and being competitive with the performance-based approach from the performance perspective in real applications. The results from the simulation study and the real application also revealed several caveats of the performance-based approach, including the potential overfitting and equifinality problems as well as the selection of distinct models when adopting different performance metrics. In addition, differing from the performance-based approach, the decomposition-based NS-FFA avoided/alleviated the ergodicity violation. All these results demonstrated the advancements of the proposed decomposition-based NS-FFA and advocated its application in the NS-FFA.