Robust trend estimation of observed German precipitation

Summary

Trends in climate time series are habitually estimated on the basis of the least-squares method. This estimator is optimal if the residuals follow the Gaussian distribution. Unfortunately, only a small number of observed climate time series fulfil this assumption. This work introduces a robust method for trend analyses of non-Gaussian climate variables. Robust trend analyses as well as probability assessments of extreme events (Trömel and Schönwiese 2006) represent an application of the generalized time series decomposition technique. Trömel (2005) and Trömel and Schönwiese (2005) applied this decomposition technique to monthly precipitation sums from a German station network of 132 time series covering 1901–2000 in order to achieve a statistical modeling of the time series. The time series under consideration can be interpreted as a realization of a Gumbel-distributed random variable with time-dependent scale and location parameter. More precisely, each observed value can be seen as one possible realization of the estimated probability density function (PDF) with the location and the scale parameter of the respective time step. Consequently, the expected value of the Gumbel-distributed random variable can be estimated for every time step of the observation period and the statistical modeling represents an alternative approach to estimate trends in observational precipitation time series. The method is robust with respect to observed high precipitation values. The influence of relatively high precipitation sums is not larger than justified from a statistical point of view and changes in all parameters (here location and scale parameter) of the distribution can be taken into account. Monte-Carlo-simulations demonstrate the smaller mean squared error of the trend estimator using the statistical modeling. The least-squares estimator often shows a positive bias, while the method introduced provides robust monthly trend estimates taken into account the statistical characteristics of precipitation.