Joint examination of climate time series based on a statistical definition of multidimensional extreme

The joint examination of the climate time series may be efficient methodology for the characterization of extreme weather and climate events. In general, the main difficulties are connected with the different probability distribution of the variables and the handling of the stochastic connection between them. The first problem can be solved by the standardization procedures, i.e., to transform the variables into standard normal ones. For example, there are the Standardized Precipitation Index (SPI) series for the precipitation sums assuming gamma distribution, or the standardization of temperature series assuming normal distribution. In case of more variables, the problem of stochastic connection can be solved on the basis of the vector norm of the transformed variables defined by their covariance matrix. We will present the developed mathematical methodology and some examples for its meteorological applications.