The hydrological frequency analysis (HFA) evaluates the recurrence of extreme flow and precipitation events and guides water-related management and risk assessment. The conventional HFA assumes stationarity in the underlying process. However, climate change and other changes in the watersheds may induce nonstationarity in hydrometeorological variables. Under nonstationary scenarios, the nonstationary HFA (NS-HFA) is the theoretical choice. To implement the NS-HFA with more confidence, further understanding of the impacts of nonstationarity on the analysis and advancements of the existing approaches are desired.

This dissertation, therefore, aimed to improve the understanding of the HFA under nonstationarity and advance the NS-HFA applications by:​ (a) investigating the impacts of ignoring the nonstationarity of different patterns and degrees in the stationary HFA (S-HFA);​ (b) examining the association between the nonstationarity characteristics and estimated flood hazards;​ (c) improving the determination of the NS-HFA model by proposing a novel procedure based on the decomposition of nonstationary stochastic processes;​ (d) enhancing the computational efficiency and numerical stability of the profile likelihood (PL) method, which is theoretically superior to other available methods for quantifying the uncertainty in the NS-HFA;​ and (e) comprehensively assessing the use of the Metastatistical approach and its simplified version to advance the NS-HFA from the perspectives of fitting efficiency, accuracy, and uncertainty.

The results demonstrated that:​ (a) neglecting the nonstationarity in the S-HFA would lead to decreasing the accuracy and increasing the uncertainty of the analysis;​ (b) the nonstationarity patterns and degrees are strongly associated with the hydrological hazards;​ (c) the proposed decomposition-based approach based upon the theoretical decomposition of nonstationary stochastic processes advances the model determination in the NS-HFA from both theoretical and practical perspectives;​ (d) the proposed methods, which incorporate the classical regula-falsi numerical method and the generalized maximum likelihood principle, effectively reduce the computational burden and numerical instability of the PL method, and consequently facilitate its practical applications;​ and (e) compared to the NS-HFA based on the generalized extreme value distribution, the use of the simplified Metastatistical approach yields improved performance from various perspectives. Therefore, this dissertation improved the understanding of the HFA and advanced the NS-HFA for real-world applications.