XTREND consists of the following methodical Parts. Time interval extraction (Part 1) to analyse different parts of a time series; extreme events detection (Part 2) with robust smoothing; magnitude classification (Part 3) by hand; occurrence rate estimation (Part 4) with kernel functions; bootstrap simulations (Part 5) to estimate confidence bands around the occurrence rate. You work interactively with XTREND (parameter adjustment, calculation, graphics) to acquire more intuition for your data. Although, using “normal” data sizes (less than, say, 1000) and modern machines, the computing time seems to be acceptable (less than a few minutes), parameter adjustment should be done carefully to avoid spurious results or, on the other hand, too long computing times. This Report helps you to achieve that. Although it explains the statistical concepts used, this is generally done with less detail, and you should consult the given references (which include some textbooks) for a deeper understanding.

For the analysis of trends in weather extremes, we introduce a diagnostic variable, the exceedance product, which combines intensity and frequency of extremes. We separate trends in higher moments from trends in mean or standard deviation and use bootstrap resampling to evaluate statistical significances. Application to daily meteorological records from Potsdam (1893–2005) and Prague (1775–2004) reveals that extremely cold winters occurred only until mid-20th century, whereas warm winters show upward trends. These were significant changes in higher moments of the temperature distribution. In contrast, trends in summer temperature extremes (e.g., 2003 European heatwave), can be explained by linear changes in mean or standard deviation. While precipitation at Potsdam does not exhibit pronounced trends, dew point displays an enigmatic change from maximum extremes during the 1960s to minimum extremes during the 1970s. / Zur Untersuchung von Trends vonWetterextremen wird ein neuartiges „Wirkungsmaß” eingeführt, das Produkt der Extremwertübertreffung, welches die beiden Aspekte „Stärke” und „Häufigkeit” miteinander verbindet. Es werden Trends in höheren Momenten von Trends in Mittelwert und Standardabweichung getrennt sowie Bootstrap-Verfahren angewendet, um die statistische Signifikanz auszuwerten. Bei der Verwendung von meteorologischen Daten in täglicher Auflösung von Potsdam (1893–2005) und Prag (1775–2004) zeigt sich, dass extrem kalte Winter nur bis Mitte des 20. Jahrhundert auftraten, wohingegen warme Winter einen Aufwärtstrend aufweisen, welche signifikante Änderungen in höheren Momenten der Temperaturverteilung darstellen. Im Gegensatz dazu kann der Trend von Sommer-Temperaturextremen (z.B. die Hitzewelle im Jahr 2003 in Europa) durch Änderungen in Mittelwert und Standardabweichung erklärt werden. Während der Niederschlag in Potsdam keine ausgeprägte Trends zeigt, weist der Taupunkt einen rätselhaften Übergang von Maximumextremen in den 1960ern zu Minimumextremen in den 1970ern auf.

XTREND consists of the following methodical Parts. Time interval extraction (Part 1) to analyse different parts of a time series; extreme events detection (Part 2) with robust smoothing; magnitude classification (Part 3) by hand; occurrence rate estimation (Part 4) with kernel functions; bootstrap simulations (Part 5) to estimate confidence bands around the occurrence rate. You work interactively with XTREND (parameter adjustment, calculation, graphics) to acquire more intuition for your data. Although, using “normal” data sizes (less than, say, 1000) and modern machines, the computing time seems to be acceptable (less than a few minutes), parameter adjustment should be done carefully to avoid spurious results or, on the other hand, too long computing times. This Report helps you to achieve that. Although it explains the statistical concepts used, this is generally done with less detail, and you should consult the given references (which include some textbooks) for a deeper understanding.