MeteoSwiss - Climate Extremes

Weather and climate events take on various scales and amplitudes. We call extreme those that are rare. But how do we know an event is rare? Extreme value analysis is the statistical tool used to determine the frequency of extreme events.

Return period for daily precipitation at la Chaux-de-Fond

Fig. 1: Relation between return period (abscissa) and return level (ordinate) for daily precipitation at la Chaux-de-Fond (blue) in the period 1961-2009. In green: confidence intervals. The grey lines relate the 5 yearly maxima of highest magnitude to the corresponding return periods.

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Figure 1 shows in blue the relationship between the intensity of precipitation and its rarity. The ordinate represents precipitation at la Chaux-de-Fonds, while the abscissa is the so-called return period. The precipitation amount of an event with a return period of 10 years, for instance, has a 1/10 probability of being exceeded in a given year - one or several times. The highest precipitation event between 1961 and 2009 reached 100.8 mm and occurred on August 25th, 2002. Figure 1 shows that it would be expected to recur on average every 70 years. The green lines are confidence intervals that represent the uncertainty of the estimate. Thus, the same event could in fact have a return period between about 20 years and over 300! Note: the confidence intervals are not related to measurement errors.

Who needs to know? We cannot prevent extreme climatic events, but we can mitigate their socio-economic consequences if we know their frequency. The frequency of an event gives us an objective measure of its severity. Compared to the vulnerability or the life cycle of a location or construction, it allows engineers to dimension buildings and constructions, insurances to calculate their premiums, and public services to issue warnings.

Applications: climatology and large-scale event analysis

Fig. 2: Return levels of summer daily precipitation [mm] with a 30-year return period. The size of the dots corresponds to the length of the time series.

Fig. 3: Return periods [years] of a precipitation event on August 8, 2007 (Report MeteoSwiss 222).

Climatology of extremes

The return levels corresponding to a given return period at different measurement stations can be represented on a map. Thus, we can see how extremes are distributed geographically, and compare with our knowledge of the climate. Figure 3 shows the summer daily precipitation with a 30-year return period. The climatic characteristics of the different regions of Switzerland (Tessin, Rhone Valley, pre-Alps) appear clearly.

Analysis of large-scale events

Extreme events are generally not localized, but often sweep across a wide area. Determining the return period corresponding to one particular large-scale event at each measurement station can help identify the regions that were affected in an extreme fashion. An example of such an analysis is shown in figure 3.

How is it done? Statistical tools

Extremes can be defined as the maximum of a parameter (for example precipitation, wind gusts, fresh snow, etc.) over a given period, generally one year. Indeed, the collection of all maxima of a time-series has a known statistical distribution called General Extreme Value (GEV) distribution. In figure 4, for instance, the left panel shows the complete time series of daily precipitation at la Chaux-de-Fonds with red circles around the yearly maxima. The histogram of the same data is represented vertically in the central panel. Here, the maxima can be seen at the top, in the tail of the distribution. A histogram of the maxima alone is represented in the right panel with the fitted GEV distribution in red. Return periods and levels, as well as their confidence intervals, can be computed with the estimated GEV distribution.

Analysis of daily precipitation at la Chaux-de-Fond

Figure 4. Left: time series of daily precipitation at la Chaux-de-Fond with annual maxima circled in red. Middle: histogram of the same data, represented vertically. Right: histogram of annual maxima of daily precipitation at la Chaux-de-Fond. Red line: estimated distribution of the extremes.

Links and Literature

Ceppi P., Della-Marta P.M., Appenzeller C., 2008: Extreme Value Analysis of Wind Speed Observations over Switzerland. MeteoSwiss work reports, 219, 43pp.
Bezzola G.R. und Hegg C. (Ed.) 2007. Ereignisanalyse Hochwasser 2005, Teil 1 - Prozesse, Schäden und erste Einordnung. Bundesamt für Umwelt BAFU, Eidgenössische Forschungsanstalt WSL, Umwelt-Wissen Nr. 0707. 215pp. (in German)
Bezzola G.R., Ruf W. (Ed.), 2009. Ereignisanalyse Hochwasser August 2007. Analyse der Meteo- und Abflussvorhersagen; vertiefte Analyse der Hochwasserregulierung der Jurarandgewässer. Umwelt-Wissen Nr. 0927. Bundesamt für Umwelt, Bern. 209pp. (in German)
Frei, C, 2006. Eine Länderübergreifende Niederschlagsanalyse zum August Hochwasser 2005, Ergänzung zum Arbeitsbericht 211. Arbeitsberichte der MeteoSchweiz, 213, 10pp. (in German)
Frei C, Germann U, Fukutome S, Liniger M, 2008. Möglichkeit und Grenzen der Niederschlagsanalyse zum Hochwasser 2005. Arbeitsberichte der MeteoSchweiz, 221, 21pp. (in German)
MeteoSchweiz (Hrsg.), 2006: Starkniederschlagsereignis August 2005.
Arbeitsberichte der MeteoSchweiz, 211, 63pp. (in German)
MeteoSchweiz (Hrsg.), 2008: Meteorologische Ereignisanalyse des Hochwassers 8. bis 9. August 2007. Arbeitsberichte der MeteoSchweiz, 222, 30pp. (in German)