Regional Frequency Analysis at Ungauged Sites with Multivariate Adaptive Regression Splines

AbstractHydrological 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.

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Regional Frequency Analysis at Ungauged Sites with the Generalized Additive Model

Journal of Hydrometeorology ◽

10.1175/jhm-d-14-0060.1 ◽

2014 ◽

Vol 15 (6) ◽

pp. 2418-2428 ◽

Cited By ~ 32

Author(s):

F. Chebana ◽

C. Charron ◽

T. B. M. J. Ouarda ◽

B. Martel

Keyword(s):

Linear Regression ◽

Frequency Analysis ◽

Generalized Additive Model ◽

Additive Model ◽

Nonlinear Effects ◽

Regional Model ◽

Regional Frequency Analysis ◽

Ungauged Sites ◽

Log Linear ◽

Regional Frequency

Abstract The log-linear regression model is one of the most commonly used models to estimate flood quantiles at ungauged sites within the regional frequency analysis (RFA) framework. However, hydrological processes are naturally complex in several aspects including nonlinearity. The aim of the present paper is to take into account this nonlinearity by introducing the generalized additive model (GAM) in the estimation step of RFA. A neighborhood approach using canonical correlation analysis (CCA) is used to delineate homogenous regions. GAMs possess a number of advantages such as flexibility in shapes of the relationships as well as the distribution of the output variable. The regional model is applied on a dataset of 151 hydrometrical stations located in the province of Québec, Canada. A stepwise procedure is employed to select the appropriate physiometeorological variables. A comparison is performed based on different elements (regional model, variable selection, and delineation). Results indicate that models using GAM outperform models using the log-linear regression as well as other methods applied to this dataset. In addition, GAM is flexible and allows for the inclusion and presentation of nonlinear effects of explanatory variables, in particular, basin area effect (scale). Another finding is the reduced effect of CCA delineation when combined with GAM.

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