A functional framework for flow-duration-curve and daily streamflow estimation at ungauged sites - Requena, Ana Isabel; Chebana, Fateh; Ouarda, Taha B. M. J. (Advances in Water Resources, 2018)
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.

Introduction of the GAM model for regional low-flow frequency analysis at ungauged basins and comparison with commonly used approaches - Ouarda, Taha B. M. J.; Charron, Christian; Hundecha, Yeshewatesfa; St-Hilaire, André; Chebana, Fateh (Environmental Modelling and Software, 2018)
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.