Multivariate design in the presence of non-stationarity

• Time dependent bivariate design events are modeled using copulas.
• Influence of marginal distributions and the dependence structure are separately outlined.
• Dominant influence of non-stationary marginal distribution parameters are detected.
• The influence of a time-variant dependence structure is small.

SummaryOver the last decade the number of applications of copula functions for multidimensional modeling of hydrological parameters has significantly increased. However, most of the studies assume stationarity in the marginal distribution parameters as well as in the dependence structure of the variables. This is because the available time series are often too short for using a non-stationary multivariate model. In this study we analyze the joint probability of flood peak and volume based on a discharge time series of the Rhine River providing 191 years of data. We find significant positive trends in the marginal distribution parameters as well as in the dependence measure from analyzing 50-year moving time windows. Fitting time dependent marginal distributions and time dependent copulas to the data sets, and comparing the results with the stationary approach, shows the influence of the non-stationary behavior of the variables. The results are illustrated by calculating the joint probability of the flood peak and volume for four cases: i. considering all parameters as time dependent, i.e. the location, scale and shape parameter of the marginals and the copula parameter, ii. considering the location and scale parameter of the marginals and the copula parameter as time dependent, iii. considering the location parameter of the marginals and the copula parameter as time dependent, and iv. considering only the copula parameter as time dependent. The results highlight that the joint probability, illustrated by the isoline of a given exceedance probability, varies significantly over time when non-stationary models are applied.