Investigation of asymmetrical spatial dependence of the regional climate model precipitation using empirical bivariate copulas

Spatial precipitation model which is capable of deriving climate change scenarios at a finer spatial resolution has been playing crucial role in many hydrological applications. Regional climate models (RCMs) are promising tools which can provide projected precipitation data with high spatial and temporal resolutions. This study investigates asymmetrical spatial dependence of precipitation obtained from historical and future RCM simulations on the basis of empirical bivariate copulas. The study regions are located on the south part of Germany namely the states of Bavaria, Baden Württemberg, and Rhine Pfalz using 890 observation stations. RCM grid points are then selected based on nearest grid point to each observation site. Empirical bivariate copulas are constructed by adopting the concept of regionalized of variables in spatial random process assuming that for every selected time interval, precipitation over the region of interest is assumed to be a realization of spatial random process. To get reasonable this assumption, investigation regions are divided into several sub-regions and selected based on homogeneity areas with little topography variation. In order to study behavior of the precipitation fields at different time scales, the data are aggregated into the higher time scales for instance at 5, 10, 15 days, monthly, and quarterly in each different seasons. The asymmetrical dependence is calculated using the deviation between the joint probability of exceeding a quantile 1-u and not exceeding the quantile u for each realization using different values of u (0.1, 0.2, 0.3, 0.4). Positive asymmetric indicates that the high values have a stronger dependence than the low values and vice versa. Gaussian simulation based testing is then applied for counting its degree of uncertainty. Empirical evidences prove that both observations and RCM simulations show an interesting systematic pattern relating to the domination of positive non-symmetrical dependence in short distance and small time steps especially for extreme events in most of different sub-regions and seasons. Precipitations with high intensity tend to exhibit a high spatial clustering behaviour. However, RCM simulations have slight less degree of domination and smaller coverage areas of positive asymmetrical dependence than observations.