Multivariate Seasonal Design Flood Estimation using Vine Copula Functions

Código

I-EBHE0004

Autores

SHILPA L S, K SRINIVASAN

Tema

WG 1.10: Hydrologic Design - Solutions & Communication

Resumo

Seasonal design floods that can reflect the seasonal variability in flood characteristics (peak, volume, duration, shape) are essential in deriving the seasonal flood mitigation strategies at the reservoir level. The conventional annual flood frequency analysis methods, which are based on univariate distributions of flood peak or flood volume fail to provide a complete description of the flood events and the interdependence of their attributes (Baratti et al., 2012). Hence, design floods should be estimated by taking into consideration their marginals as well as their dependence which can be depicted through a multivariate joint distribution. Further, it is also observed that the severity of a flood event depends not only on the flood magnitudes but also on the shape of the flood hydrograph (Yue et al., 2002). The difference in the shape of the flood hydrograph requires adaptive flood mitigation policies at the reservoir level to achieve same level of flood peak attenuation (Brunner et al., 2017). The study presents an integrated framework to derive seasonal design flood hydrographs which majorly involves two steps (i) estimation of seasonal design flood events, i.e.; identification of targeted design flood characteristic, and (ii) modelling the shape of flood hydrographs. After suitably dividing the flood season into multiple sub-seasons, the annual maximum events sampled from the hourly streamflow record are distributed among the sub-seasons. The flood peak, volume, time to peak and duration are the targeted flood characteristics whose dependence is modelled using Vine Copulas which are flexible statistical tool in multivariate modelling. For each sub-season, suitable four dimensional Vine Copula is used to capture the dependence between the targeted flood characteristics. The best fit vine type and its structure is selected from among the 12 structure combinations each of C-vine and D-vine using the loglikelihood, and information criteria. For the best fit vine copula (includes the vine type and its structure) identified for each sub-season, the joint return periods (JRP) are computed using ?OR? or ?AND? conditions using the equivalent frequency combination method (Yin et al., 2017). The shape of the flood hydrographs are modelled using the typical flood hydrograph (TFH) method. Here, historical flood hydrographs are normalized such that their base and volume are equal to one unit. The resulting normalized TFHs are classified based on their shape factor (ratio of time of peak and duration), which denotes the skewness of the hydrograph. The study addresses the limitation regarding the arbitrary selection of TFH by using the shape factor. From the combination of peak, volume, time to peak and duration, given by a suitable JRP for a given flood sub-season, the design shape factor is computed. The normalized TFH for the given sub-season is sampled based on its closeness to the design shape factor and the same is amplified using the design volume and duration, and the slight difference in peak is modified by multiplying the ordinates around the peak by the ratio of the design peak and the derived peak, to yield the seasonal design flood hydrographs.