Time 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.

随着气候变化过程中温度的变化，具有显着趋势的时间序列需要采取谨慎的方法进行统计评估。气候手段和时刻通常取自过去的数据，这意味着统计数据不再适合实际数据。因此，我们需要先确定长期趋势，然后再将实际数据与实际气候进行比较。这不是一件容易的事，因为信号的确定（一种气候趋势）受观测数据的随机散布影响。对不同的滤波方法进行质量测试，以获得观察到的时间序列的实际平滑趋势。提出了一种基于变分原理的新方法。它优于其他传统的平滑方法，尤其是在处理周期性时间序列的情况下。这种新方法用于测试2018年维也纳的实际温度有多极端。如果我们考虑过去几十年的积极趋势，则表明2018年的新年度温度记录不是太极端。此外，根据当前的气候，2018年的日平均气温并没有发现真正极端的情况。维也纳以及世界上许多其他地方的最高气温记录的真正极端是过去几年中正温度趋势大大增加。