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Abstract Flood quantile estimation at sites with little or no data is important for the adequate planning and management of water resources. Regional Hydrological Frequency Analysis (RFA) deals with the estimation of hydrological variables at ungauged sites. Random Forest (RF) is an ensemble learning technique which uses multiple Classification and Regression Trees (CART) for classification, regression, and other tasks. The RF technique is gaining popularity in a number of fields because of its powerful non-linear and non-parametric nature. In the present study, we investigate the use of Random Forest Regression (RFR) in the estimation step of RFA based on a case study represented by data collected from 151 hydrometric stations from the province of Quebec, Canada. RFR is applied to the whole data set and to homogeneous regions of stations delineated by canonical correlation analysis (CCA). Using the Out-of-bag error rate feature of RF, the optimal number of trees for the dataset is calculated. The results of the application of the CCA based RFR model (CCA-RFR) are compared to results obtained with a number of other linear and non-linear RFA models. CCA-RFR leads to the best performance in terms of root mean squared error. The use of CCA to delineate neighborhoods improves considerably the performance of RFR. RFR is found to be simple to apply and more efficient than more complex models such as Artificial Neural Network-based models.

Hydrological systems are naturally complex and nonlinear. A large number of variables, many of which not yet well considered in regional frequency analysis (RFA), have a significant impact on hydrological dynamics and consequently on flood quantile estimates. Despite the increasing number of statistical tools used to estimate flood quantiles at ungauged sites, little attention has been dedicated to the development of new regional estimation (RE) models accounting for both nonlinear links and interactions between hydrological and physio-meteorological variables. The aim of this paper is to simultaneously take into account nonlinearity and interactions between variables by introducing the multivariate adaptive regression splines (MARS) approach in RFA. The predictive performances of MARS are compared with those obtained by one of the most robust RE models: the generalized additive model (GAM). Both approaches are applied to two datasets covering 151 hydrometric stations in the province of Quebec (Canada): a standard dataset (STA) containing commonly used variables and an extended dataset (EXTD) combining STA with additional variables dealing with drainage network characteristics. Results indicate that RE models using MARS with the EXTD outperform slightly RE models using GAM. Thus, MARS seems to allow for a better representation of the hydrological process and an increased predictive power in RFA.

Abstract Flow duration curves (FDC) are used to obtain daily streamflow series at ungauged sites. In this study, functional multiple regression (FMR) is proposed for FDC estimation. Its natural framework for dealing with curves allows obtaining the FDC as a whole instead of a limited number of single points. FMR assessment is performed through a case study in Quebec, Canada. FMR provides a better mean FDC estimation when obtained over sites by considering simultaneously all FDC quantiles in the assessment of each given site. However, traditional regression provides a better mean FDC estimation when obtained over given FDC quantiles by considering all sites in the assessment of each quantile separately. Mean daily streamflow estimation is similar; yet FMR provides an improved estimation for most sites. Furthermore, FMR represents a more suitable framework and provides a number of practical advantages, such as insight into descriptor influence on FDC quantiles. Hence, traditional regression may be preferred if only few FDC quantiles are of interest; whereas FMR would be more suitable if a large number of FDC quantiles is of interest, and therefore to estimate daily streamflows.

Quantile estimates are generally interpreted in association with the return period concept in practical engineering. To do so with the peaks‐over‐threshold (POT) approach, combined Poisson‐generalized Pareto distributions (referred to as PD‐GPD model) must be considered. In this article, we evaluate the incorporation of non‐stationarity in the generalized Pareto distribution (GPD) and the Poisson distribution (PD) using, respectively, the smoothing‐based B‐spline functions and the logarithmic link function. Two models are proposed, a stationary PD combined to a non‐stationary GPD (referred to as PD0‐GPD1) and a combined non‐stationary PD and GPD (referred to as PD1‐GPD1). The teleconnections between hydro‐climatological variables and a number of large‐scale climate patterns allow using these climate indices as covariates in the development of non‐stationary extreme value models. The case study is made with daily precipitation amount time series from southeastern Canada and two climatic covariates, the Arctic Oscillation (AO) and the Pacific North American (PNA) indices. A comparison of PD0‐GPD1 and PD1‐GPD1 models showed that the incorporation of non‐stationarity in both POT models instead of solely in the GPD has an effect on the estimated quantiles. The use of the B‐spline function as link function between the GPD parameters and the considered climatic covariates provided flexible non‐stationary PD‐GPD models. Indeed, linear and nonlinear conditional quantiles are observed at various stations in the case study, opening an interesting perspective for further research on the physical mechanism behind these simple and complex interactions.

ABSTRACTThis work explores the ability of two methodologies in downscaling hydrological indices characterizing the low flow regime of three salmon rivers in Eastern Canada: Moisie, Romaine and Ouelle. The selected indices describe four aspects of the low flow regime of these rivers: amplitude, frequency, variability and timing. The first methodology (direct downscaling) ascertains a direct link between large-scale atmospheric variables (the predictors) and low flow indices (the predictands). The second (indirect downscaling) involves downscaling precipitation and air temperature (local climate variables) that are introduced into a hydrological model to simulate flows. Synthetic flow time series are subsequently used to calculate the low flow indices. The statistical models used for downscaling low flow hydrological indices and local climate variables are: Sparse Bayesian Learning and Multiple Linear Regression. The results showed that direct downscaling using Sparse Bayesian Learning surpassed the other a...

Generalized Additive Models (GAMs) are introduced in this study for the regional estimation of low-flow characteristics at ungauged basins and compared to other approaches commonly used for this purpose. GAMs provide more flexibility in the shape of the relationships between the response and explanatory variables in comparison to classical models such as multiple linear regression (MLR). Homogeneous regions are defined here using the methods of hierarchical cluster analysis, canonical correlation analysis and region of influence. GAMs and MLR are then used within the delineated regions and also for the whole study area. In addition, a spatial interpolation method is also tested. The different models are applied for the regional estimation of summer and winter low-flow quantiles at stations in Quebec, Canada. Results show that for a given regional delineation method, GAMs provide improved performances compared to MLR.

Abstract Change point detection methods have an important role in many hydrological and hydraulic studies of river basins. These methods are very useful to characterize changes in hydrological regimes and can, therefore, lead to better understanding changes in extreme flows behavior. Flood events are generally characterized by a finite number of characteristics that may not include the entire information available in a discharge time series. The aim of the current work is to present a new approach to detect changes in flood events based on a functional data analysis framework. The use of the functional approach allows taking into account the whole information contained in the discharge time series of flood events. The presented methodology is illustrated on a flood analysis case study, from the province of Quebec, Canada. Obtained results using the proposed approach are consistent with those obtained using a traditional change point method, and demonstrate the capability of the functional framework to simultaneously consider several flood features and, therefore, presenting a comprehensive way for a better exploitation of the information contained in a discharge time series.