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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.
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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.
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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...
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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.