How to correctly apply Gaussian statistics in a non-stationary climate?

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