Abstract
Abstract. Classical methods of regional frequency analysis (RFA) of hydrological variables face two drawbacks: (1) the restriction to a particular region which can lead to a loss of some information and (2) the definition of a region that generates a border effect. To reduce the impact of these drawbacks on regional modeling performance, an iterative method was proposed recently, based on the statistical notion of the depth function and a weight function φ. This depth-based RFA (DBRFA) approach was shown to be superior to traditional approaches in terms of flexibility, generality and performance. The main difficulty of the DBRFA approach is the optimal choice of the weight function ϕ (e.g., φ minimizing estimation errors). In order to avoid a subjective choice and naïve selection procedures of φ, the aim of the present paper is to propose an algorithm-based procedure to optimize the DBRFA and automate the choice of ϕ according to objective performance criteria. This procedure is applied to estimate flood quantiles in three different regions in North America. One of the findings from the application is that the optimal weight function depends on the considered region and can also quantify the region's homogeneity. By comparing the DBRFA to the canonical correlation analysis (CCA) method, results show that the DBRFA approach leads to better performances both in terms of relative bias and mean square error.
Highlights
Due to the large territorial extents and the high costs associated to installation and maintenance of monitoring stations, it is not possible to monitor hydrologic variables at all sites of interest
This function is used for its simplicity, value interpretability, and for the relationship with the canonical correlation analysis (CCA) approach used in regional frequency analysis (RFA)
The results obtained from the CCA-based approach are first presented and compared to those obtained by the optimized depth-based RFA (DBRFA) approach
Summary
Due to the large territorial extents and the high costs associated to installation and maintenance of monitoring stations, it is not possible to monitor hydrologic variables at all sites of interest. Hydrologists have often to provide estimates of design event quantiles QT, corresponding to a large return period T at ungauged sites In this situation, regionalization approaches are commonly used to transfer information from gauged sites to the target site (ungauged or partially gauged) (e.g., Burn, 1990b; Dalrymple, 1960; Ouarda et al, 2000). The absence of a natural order to classify multivariate data led to the introduction of the depth functions (Tukey, 1975) They are used in many research fields, and were introduced in water science by Chebana and Ouarda (2008). The Mahalanobis depth function is used to sort sites where the deeper the site is the more it is hydrologically similar to the target site This function is used for its simplicity, value interpretability, and for the relationship with the CCA approach used in RFA.
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