Gains from modelling dependence of rainfall variables into a stochastic model: application of the copula approach at several sites

Abstract

Since the last decade, copulas have become more and more widespread in the construction of hydrological models. Unlike the multivariate statistics which are traditionally used, this tool enables scientists to model different dependence structures without drawbacks. The authors propose to apply copulas to improve the performance of an existing model. The hourly rainfall stochastic model SHYPRE is based on the simulation of descriptive variables. It generates long series of hourly rainfall and enables the estimation of distribution quantiles for different climates. The paper focuses on the relationship between two variables describing the rainfall signal. First, Kendall's tau is estimated on each of the 217 rain gauge stations in France, then the False Discovery Rate procedure is used to define stations for which the dependence is significant. Among three usual archimedean copulas, a unique 2-copula is chosen to model this dependence for any station. Modelling dependence leads to an obvious improvement in the reproduction of the standard and extreme statistics of maximum rainfall, especially for the sub-daily rainfall. An accuracy test for the extreme values shows the good asymptotic behaviour of the new rainfall generator version and the impacts of the copula choice on extreme quantile estimation

Comparison of Flood Frequency Analysis Methods for Ungauged Catchments in France

“…The development, calibration, regionalisation and validation of this generator have been the object of numerous studies [47,[76][77][78] and are not within the scope of this paper. This generator is included in national guidance for rainfall prediction in France [79].…”

“…This point explains why the stability of the regionalised SHYREG quantiles appears to increase as the return period increases (very stable extreme quantile and variable frequent quantiles), and why these extreme regionalised quantiles are very similar to the calibrated quantiles. In addition, thanks to an extensive work on rainfall analysis [47,76,92,93], SHYREG benefits from an accurate rainfall information [78] even in ungauged sites. It is not the case for other approaches, and it makes it less dependent its regionalised parameter.…”

“…Nevertheless, the SHYREG quantiles largely rely on previous rainfall simulations [47,76,78]; consequently, an application to other areas would still require the availability of rainfall data sets.…”