Thermal refuges in rivers are becoming a critical habitat for ectotherm fish, including Atlantic salmon (Salmo salar). In this study, two statistical modelling approaches were used to estimate the areas of potential thermal refuges: generalized additive models (GAM) and multivariate adaptive regression splines (MARS). This allowed for the first development of a reliable statistical model that uses a few relevant predictors (air temperature, river discharge, main river, and tributary temperatures) to estimate tributary plume thermal refuge surface areas. GAM and MARS models were fitted independently for four sites on the Ste-Marguerite River, (Quebec, Canada). Model performances were evaluated using the leave-one-out cross validation (LOOCV) approach and the following criteria: the Akaike information criterion (AIC), rootmean-square error (RMSE), relative root-mean-square error (rRMSE), Nash-Sutcliffe efficiency coefficient (NASH), and finally the bias (BIAS). Using an array of thermographs deployed at the confluence of a cold tributary and the warmer main river stem, refuges were delineated at a daily time step. Model results indicate that the estimated areas are similar to the refuge surfaces interpolated using temperature measurements, with both models and for all sites. Results suggest that MARS performs better than GAM in terms of forecasting and estimating the variability of the area of thermal refuges at all study-stations. This relatively simple approach will be of use to water resources managers faced with the challenge of protecting thermal refuges for fish. K E Y W O R D S daily water temperature, generalized additive model (GAM), multivariate adaptive regression splines (MARS), thermal refuges

Flood frequency analysis at ungauged catchments with the GAM and MARS approaches in the Montreal region, Canada

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 non-linearity 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.

Regional Frequency Analysis (RFA) relies on a wide range of physiographical and meteorological variables to estimate hydrological quantiles at ungauged sites. However, additional catchment characteristics related to its drainage network are not yet fully understood and integrated in RFA procedures. The aim of the present paper is to propose the integration of several physiographical variables characterizing the drainage network systems in RFA, and to evaluate their added value in predicting quantiles at ungauged sites. The proposed extended dataset (EXTD) includes several variables characterising drainage network characteristics. To evaluate the new variables, a number of commonly used RFA approaches are applied to the extended data representing 151 stations in Quebec (Canada) and compared to a standard dataset (STA) that excludes the new variables. The considered RFA approaches include the combination of two neighborhood methods namely the canonical correlation analysis (CCA) and the region of influence (ROI) with two regional estimation (RE) models which are the log-linear regression model (LLRM) and the generalized additive model (GAM). The RE models are also applied without the hydrological neighborhood. Results show that regional models using the extended dataset lead to significantly better flood quantile predictions, especially for large basins. Indeed, the variable selection performed with EXTD consistently includes some of the new variables, in particular the drainage density, the stream length ratio, and the ruggedness number. Two other new variables are also identified and included in the DHR step: the circularity ratio and the texture ratio. This leads to better predictions with relative errors about 29% for EXTD, versus around 42% for STA in the case of the best

<p>Hydrological processes and phenomena are naturally complex and nonlinear. Many physiographical variables such as those dealing with drainage network characteristics may influence streamflow characteristics and should be considered in regional frequency analysis (RFA). These variables have hence a significant impact on the effectiveness of flood quantile estimation techniques. Although many statistical tools are considered to estimate flood quantiles at ungauged sites in the hydrological literature, little attention has been given to the nonlinearity and to the high-dimensionality of physio-meteorological variable space. In this study, the multivariate adaptive regression splines (MARS) approach is introduced in RFA. This model allows to account simultaneously for non-linearity and interactions between variables hidden in high-dimensional data. MARS is hereby applied on two datasets of 151 hydrometric stations located in the southern part of the province of Quebec (Canada): a standard dataset (STA) including commonly used variables and an extended dataset (EXTD) combining STA with additional variables dealing with drainage network characteristics. It is then compared to generalized additive models (GAM), a state-of-the-art method for regional estimation. Numerical results show that MARS outperforms GAM, especially with the extensive database EXTD. The study suggests that MARS may be a promising tool to take into account the complexity of the hydrological phenomena involved and the increasing number of variables used in RFA.</p>