Joint probability of precipitation and discharge deficits in the Netherlands

The Netherlands are situated at the downstream end of the Rhine River. A large part of the country can be supplied with water from the river in the case of precipitation deficits. For drought assessment it is therefore necessary to consider the joint distribution of precipitation and discharge deficits. A transformed bivariate normal distribution as well as a bivariate Gumbel distribution are fitted to this data. In addition, nearest-neighbor resampling is used to estimate joint probabilities of precipitation and discharge deficits. Both the reproduction of the marginal distributions and the dependence structure are explored. It is found that the transformed bivariate normal distribution underestimates the probability that both the precipitation and discharge deficit are extreme due to its asymptotic independence. Nearest-neighbor resampling also underestimates this probability, mainly because the upper tails of the marginal distributions are not properly reproduced by the simulations. From the two fitted bivariate distributions a novel bivariate distribution is constructed with transformed normal marginals and a logistic Gumbel dependence structure, which gives the best description of the upper tail of the joint distribution. The use of a failure region based on economic damage rather than on joint exceedances considerably reduces the differences between the probabilities of drought from the various bivariate models.