A generalized method of time series decomposition into significant components including probability assessments of extreme events and application to observational German precipitation data

Abstract

The analysis of climate variability realized in time series of observational data needs adequate statistical methods. In particular, it is important to estimate reliably significant structured components like the annual cycle, trends, the episodic component and extreme events including variations of these components. In this issue estimators are called reliable, if a priori assumed statistical assumptions are fulfilled. However, climate change concerns not only the mean value of meteorological variables, but all parameters of any related frequency distribution. In consequence, a generalized time series decomposition technique is presented allowing a free choice of the underlying probability density function (PDF). The signal (structured components like trends etc.) is detected in two instead of one parameter of a PDF, which can be chosen without any further restriction. So, the scale parameter of any PDF is no longer seen as a constant but rather affected by a deterministic process. The trend and seasonal component reflected in both parameters under consideration are estimated simultaneously in a modified stepwise regression. To deal also with superposed polynomial components and extreme events an iterative procedure is applied that converges to robust estimates of all the components. In particular, the method allows a consistent decomposition of precipitation time series into a statistical and a deterministic component. It arises, that in the special case of 132 time series of monthly precipitation totals 1901-2000, from German stations, the interpretation as a realization of a Gumbel-distributed random variable with time-dependent scale and location parameter reveals a complete analytical description of the time series. In addition to the detection of the components mentioned above, now it is possible to quantify the probability of exceeding optional upper or lower thresholds, respectively, for any time step of the observation period.