A complete procedure for multivariate index-flood model application

- A method for multivariate regional hydrological frequency analyses is presented.
- New specific elements to the multivariate regional case are developed.
- An exhaustive description of the steps for margin and copula selection is given.
- Guidelines are pointed, such as selection of a subset of design events.
- The methodology is applied to a case study in Spain.

SummaryMultivariate frequency analyses are needed to study floods due to dependence existing among representative variables of the flood hydrograph. Particularly, multivariate analyses are essential when flood-routing processes significantly attenuate flood peaks, such as in dams and flood management in flood-prone areas. Besides, regional analyses improve at-site quantile estimates obtained at gauged sites, especially when short flow series exist, and provide estimates at ungauged sites where flow records are unavailable. However, very few studies deal simultaneously with both multivariate and regional aspects. This study seeks to introduce a complete procedure to conduct a multivariate regional hydrological frequency analysis (HFA), providing guidelines. The methodology joins recent developments achieved in multivariate and regional HFA, such as copulas, multivariate quantiles and the multivariate index-flood model. The proposed multivariate methodology, focused on the bivariate case, is applied to a case study located in Spain by using hydrograph volume and flood peak observed series. As a result, a set of volume-peak events under a bivariate quantile curve can be obtained for a given return period at a target site, providing flexibility to practitioners to check and decide what the design event for a given purpose should be. In addition, the multivariate regional approach can also be used for obtaining the multivariate distribution of the hydrological variables when the aim is to assess the structure failure for a given return period.