An at-site flood estimation method in the context of nonstationarity II. Statistical analysis of floods in Quebec

Abstract

Summary This paper, the second of a two-part paper, investigates the nonstationary behaviour of flood peaks in Quebec (Canada) by analyzing the annual maximum flow series (AMS) available for the common 1966–2001 period from a network of 32 watersheds. Temporal trends in the mean of flood peaks were examined by the nonparametric Mann–Kendall test. The significance of the detected trends over the whole province is also assessed by a bootstrap test that preserves the cross-correlation structure of the network. Furthermore, The LM–NS method (introduced in the first part) is used to parametrically model the AMS, investigating its applicability to real data, to account for temporal trends in the moments of the time series. In this study two probability distributions (GEV & Gumbel) were selected to model four different types of time-varying moments of the historical time series considered, comprising eight competing models. The selected models are: two stationary models (GEV0 & Gumbel0), two nonstationary models in the mean as a linear function of time (GEV1 & Gumbel1), two nonstationary models in the mean as a parabolic function of time (GEV2 & Gumbel2), and two nonstationary models in the mean and the log standard deviation as linear functions of time (GEV11 & Gumbel11). The eight models were applied to flood data available for each watershed and their performance was compared to identify the best model for each location. The comparative methodology involves two phases: (1) a descriptive ability based on likelihood-based optimality criteria such as the Bayesian Information Criterion (BIC) and the deviance statistic; and (2) a predictive ability based on the residual bootstrap. According to the Mann–Kendall test and the LM–NS method, a quarter of the analyzed stations show significant trends in the AMS. All of the significant trends are negative, indicating decreasing flood magnitudes in Quebec. It was found that the LM–NS method could provide accurate flood estimates in the context of nonstationarity. The results have indicated the importance of taking into consideration the nonstationary behaviour of the flood series in order to improve the quality of flood estimation. The results also provided a general impression on the possible impacts of climate change on flood estimation in the Quebec province.