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Evaluation of additional physiographical variables characterising drainage network systems in regional frequency analysis, a Quebec watersheds case-study


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 combination of RFA approaches. Thus, the proposed new variables allow for a better representation of the physical dynamics within the watersheds.

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Basin relief


Mean bias


Canonical correlation analysis


Drainage density


Mean annual degree days below 0 °C


Digital elevation model


Delineation of homogenous regions


Estimated smooth degree of freedom


Extended dataset


Stream frequency


Generalized additive model


Infiltration number


Latitude of the centroid of the basin


Log-linear regression model


Longitude of the centroid of the basin


Stream length


Mean annual liquid precipitation


Mean annual solid precipitation


Mean annual total precipitation


Mean basin slope


Main channel length


Mean bifurcation ratio


Mean stream length ratio


Nash efficiency criterion


National Hydro Network


Percentage of the area occupied by forest


Percentage of the area occupied by lakes


Percentage of first-order stream lengths


Percentage of first-order streams


Specific quantile associated to the return period T

QT :

At-site flood quantile corresponding to return period T

R2 :

Coefficient of determination


Bifurcation ratio


Relative mean bias


Circularity ratio


Regional estimation


Regional frequency analysis


Stream length ratio


Root-mean-square error


Ruggedness number


Region of influence


Relative root-mean-square error


Texture ratio


Standard dataset


Stream order


Explanatory variable


Weighted mean bifurcation ratio


RHO coefficient

\(\rho_{{{\text{WMRB}}}}\) :

RHO WMRB coefficient


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Financial support for the present study was graciously provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Research chairs program (CRC) and the University Mission of Tunisia in Montreal (MUTAN). The authors would like to thank Christian Charron for his valuable help and input. The authors are grateful to Natural Resources Canada ( and the USGS ( services for the employed DEM and NHN data. The authors would like also to thank the Ministry of Sustainable Development, Environment, and Fight Against Climate Change (MDDELCC) services for the used dataset (STA). The authors are grateful to the Editor-in-Chief, Dr. George Christakos, and to three anonymous reviewers for their comments which helped improve the quality of the manuscript.

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Msilini, A., Ouarda, T.B.M.J. & Masselot, P. Evaluation of additional physiographical variables characterising drainage network systems in regional frequency analysis, a Quebec watersheds case-study. Stoch Environ Res Risk Assess (2021).

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  • Drainage network characteristics
  • Ungauged basin
  • Canonical correlation analysis
  • Region of influence
  • Generalized Additive Model, Regional frequency analysis