AbstractTime series with a significant trend, as is now being the case for the temperature in the course of climate change, need a careful approach for statistical evaluations. Climatological means and moments are usually taken from past data which means that the statistics does not fit to actual data anymore. Therefore, we need to determine the long-term trend before comparing actual data with the actual climate. This is not an easy task, because the determination of the signal—a climatic trend—is influenced by the random scatter of observed data. Different filter methods are tested upon their quality to obtain realistic smoothed trends of observed time series. A new method is proposed, which is based on a variational principle. It outperforms other conventional methods of smoothing, especially if periodic time series are processed. This new methodology is used to test, how extreme the temperature of 2018 in Vienna actually was. It is shown that the new annual temperature record of 2018 is not too extreme, if we consider the positive trend of the last decades. Also, the daily mean temperatures of 2018 are not found to be really extreme according to the present climate. The real extreme of the temperature record of Vienna—and many other places around the world—is the strongly increased positive temperature trend over the last years.
How to correctly apply Gaussian statistics in a non-stationary climate?
