A stochastic design rainfall generator based on copulas and mass curves

Abstract

Abstract. The use of design storms can be very useful in many hydrological and hydraulic practices. In this study, the concept of a copula-based secondary return period in combination with the concept of mass curves is used to generate point-scale design storms. The analysis is based on storms selected from the 105 year rainfall time series with a 10 min resolution, measured at Uccle, Belgium. In first instance, bivariate copulas and secondary return periods are explained, together with a focus on which couple of storm variables is of highest interest for the analysis and a discussion of how the results might be affected by the goodness-of-fit of the copula. Subsequently, the fitted copula is used to sample storms with a predefined secondary return period for which characteristic variables such as storm duration and total storm depth can be derived. In order to construct design storms with a realistic storm structure, mass curves of 1st, 2nd, 3rd and 4th quartile storms are developed. An analysis shows that the assumption of independence between the secondary return period and the internal storm structure could be made. Based on the mass curves, a technique is developed to randomly generate an intrastorm structure. The coupling of both techniques eventually results in a methodology for stochastic design storm generation. Finally, its practical usefulness for design studies is illustrated based on the generation of a set of statistically identical design storm and rainfall-runoff modelling.

A continuous rainfall model based on vine copulas

“…3 illustrates the 10 and 90 % percentile curves of the second-quartile autumn storms. Vandenberghe et al (2010a) showed that these curves are independent of the extremity of the storm. different copula families could be used to describe the dependences between the different variables (see Vandenberghe et al, 2010b).…”

“…Based on the historical time series, it was observed that the increment in cumulative storm depth between two subsequent time instants in a Huff curve is not uniformly distributed (this observation was neglected in Vandenberghe et al, 2010a). Smaller increments occur more often than large increments.…”

“…Any dry period shorter than this threshold is thus considered to be part of a storm (Bonta and Rao, 1988). Similar to Verhoest et al (1997) and Vandenberghe et al (2010aVandenberghe et al ( , b, 2011, a dry period of 24 h was chosen, as this period assures that the arrival times of independent storms are Poisson distributed (Restrepo-Posada and Eagleson, 1982). In this way, 8665 storms were selected and the following characteristics calculated: the onset of a storm (day, month, year), the storm volume V (mm), the storm duration W (h), the dry duration after the storm D (h), and the fraction dry As this is not desirable for a copula-based analysis, in which ranks are important, random noise, uniformly distributed between −0.1and +0.1 mm was introduced to all strictly positive 10 min observations as described and motivated in Vandenberghe et al (2010b).…”

“…As the storm characteristics V , W and D do not reveal any information on the internal storm structure, and p d only gives partial information, Huff curves, as derived in Vandenberghe et al (2010a), are employed to provide statistical information on the internal structure. The idea to use Huff curves to generate an internal storm structure has also been adopted by Candela et al (2014).…”

“…These data were obtained by a Hellmann-Fuess pluviograph, installed in and operated by the Royal Meteorological Institute at Uccle near Brussels, Belgium (Demarée, 2003). This exceptional time series has been used in several studies, albeit with varying lengths, concerning statistical analyses (Vaes et al, 2002;De Jongh et al, 2006;Ntegeka and Willems, 2008;Vandenberghe et al, 2010b) and stochastic rainfall modelling (Verhoest et al, 1997;Vandenberghe et al, 2011;Vanhaute et al, 2012;Evin and Favre, 2013;Pham et al, 2013). For the current study, storms were first selected and their characteristics of interest calculated.…”