Réf. Frei and Schär 2001 - A

Référence bibliographique complète
FREI C. and C. SCHÄR. Detection probability of trends in rare events : Theory and application to heavy precipitations in the Alpine region. Journal of climate, 2001. vol. 14, pp. 1568-1584.

Abstarct : The concept of binomial counts has been employed to quantify the probability with which one can expect to discriminate a long-term trend from the stochastic variations in a count record. The results have exposed serious limitations for trend detection when rare extremes are considered and point toward a careful interpretation of statistically nonsignificant trend results. Calculations of the detection probability for daily events reveal a strong sensitivity upon the rarity of events: in a 100-yr record of seasonal counts, a frequency change by a factor of 1.5 can be detected with a probability of 0.6 for events with an average return period of 30 days; however, this value drops to 0.2 for events with a return period of 100 days. For moderately rare events the detection probability decreases rapidly with shorter record length, but it does not significantly increase with longer record length when very rare events are considered. The statistical method was applied to examine seasonal trends of heavy daily precipitation at 113 rain gauge stations in the Alpine region of Switzerland (1901–94). For intense events (return period: 30 days) a statistically significant frequency increase was found in winter and autumn for a high number of stations. For strong precipitation events (return period larger than 100 days), trends are mostly statistically nonsignificant, which does not necessarily imply the absence of a trend. Substantial long-term changes can be masked by the stochastic fluctuations associated with the small sample size in rare event records.


Heavy daily precipitation records, simulated surrogate trends, statistical framework, detection probability, occurrence thresholds, annual and seasonal count records

Organisme / source

Climate Research, ETH, Zurich, Switzerland. christoph.frei@geo.umnw.ethz.ch

(1) - Paramètre(s) atmosphérique(s) modifié(s)
(2) - Elément(s) du milieu impacté(s)
(3) - Type(s) d'aléa impacté(s)
(3) - Sous-type(s) d'aléa

Heavy precipitation


Pays / Zone
Massif / Secteur
Site(s) d'étude
Période(s) d'observation


Swiss Alps

113 Swiss rain gauge stations    


(1) - Modifications des paramètres atmosphériques

In central Europe an increasing trend of mean wintertime precipitation is observed during this century (Schönwiese et al. 1994). Regionally in the Alpine mountain range this increase amounts to 15%–20% and is statistically significant, but no significant trend is found for other seasons of the year (Widmann and Schär 1997).

For intense precipitation events (return period = 30 days), a seasonally distinct trend signal has been revealed. In spring and summer the trend results in the station sample are roughly balanced between increasing and decreasing estimates and there is only a small number of stations for which the trends are statistically significant. In contrast for winter and autumn the station charts suggest an increasing trend signal with a clear prominence of positive estimates. Trend results for extreme precipitation events show only few series for which trends are statistically significant.

For the winter season there is a strong bias toward increasing trend estimates and a high portion of statistically significant increases in moderate and intense precipitation events. The spatial distribution of the trend is similar between the two event categories. The wintertime trend signal is then gradually less apparent for the more rare strong and extreme events. In the autumn season significant trends are found at a considerable portion of the sites for intense and strong events. In this case the trend analysis did not reveal a trend signal in the occurrence of moderate precipitation events. While the wintertime increase conforms to an increase of mean wintertime precipitation, the trend signal for autumn reflects mutually compensating long-term variations in the frequency distribution. Finally for spring and summer the results of the trend analyses do not exhibit conclusive trend signals at any of the event categories.

For the station samples in the Alps, summer is the main season of heavy precipitation (high threshold values), due to summertime convection and heavy thunderstorms. More frequent heavy events occur to the south of the ridge where local convection and topographic precipitation linked to moist southerly airflows contribute to peak activities in summer and autumn.

For extreme events, the number of stations with a significant trend was low in all four seasons. Yet the results must be considered poorly conclusive, as trends of a large amplitude where estimated without being statistically significant.

The counts of intense 24-h precipitation events for the winter seasons of 1901–94 at station Frauenfeld, in north-eastern Switzerland, show a substantial increase in the occurrence of such events (with a threshold of 12.5 mm day-1). The logistic regression model estimates a centennial increase by a factor 2.8, which is significant at a high level of confidence. Notice that the distribution of the data in the count record is substantially skewed and there is a tendency for increasing variance during the period.




Informations complémentaires (données utilisées, méthode, scénarios, etc.)

In this study we present a statistical framework for the assessment of trends in rare weather events. The framework embraces both a trend test (consideration of type I errors) as well as a quantification of the potential/ limitation of trend detectability (type II errors). The methodology is based on the binomial process, which is adopted as a simple stochastic model for annual and seasonal counts of rare events. Trend estimation and testing is conducted using logistic linear regression. The potential of trend detectability, represented in the form of a detection probability, is quantified as a function of record length, trend magnitude, and event rarity. This is accomplished using the binomial process in Monte Carlo simulations of surrogate, ‘‘trendy’’ records.

The dataset for this trend study is composed of daily precipitation series at 113 rain gauge stations in Switzerland. The data embrace all Swiss rain gauges for which a continuous and complete daily record is available throughout the 94-yr period 1901–94.

(2) - Effets du changement climatique sur le milieu naturel

Sensibilité du milieu à des paramètres climatiques
Informations complémentaires (données utilisées, méthode, scénarios, etc.)

(3) - Effets du changement climatique sur l'aléa

Paramètre de l'aléa
Sensibilité du paramètres de l'aléa à des paramètres climatiques
Informations complémentaires (données utilisées, méthode, scénarios, etc.)

(4) - Remarques générales

The detection probability, as a function of the trend magnitude Q for seasonal count records of 100 years, shows an obvious gradual increase with trend magnitude. Moreover the detection probability is remarkably sensitive upon the rarity of the events: for moderate events with a return period of 10 days a centennial change of a few 10% can be detected with reasonable chance, but the detection probability rapidly drops with more rare events. For example a long-term change by a factor of 1.5 in the occurrence of intense events (return period 30 days) is identified with a probability of 0.6, and a similar trend yields a detection probability of 0.2 for events with a return of 100 days. Considering events with a return of 365 days, even a doubling or halving of their occurrence can be identified as statistically significant only with a probability of 0.2.

The observation period is a critical factor for trend detection of intense weather events: while a 60 years period is hardly sufficient to resolve rare event trends for any of the three scenarios, there is a substantial increase of detection probability with increasing record length in the case of an event return period of 30 days. For very rare events improved detectability is only obtained with a substantially longer and in practice unrealistic observation period (or much more dramatic trends).

A substantial decrease of detection probability with the rarity of events has been observed when a similar trend magnitude is assumed. Maximum detection probability is obtained in a range of return periods between 10 and 30 days, that is, for moderately rare events. The decrease toward smaller return periods is the result of a decreasing trend amplitude as prescribed by the scenarios. On the other hand, toward longer return periods, the increasing trend amplitude cannot fully compensate for and is still dominated by the limitations of detectability with increasing event rarity. Hence even in the presence of an intensity progressive trend signal, the detection probability may be more limited for extreme than for intense events.

For similar settings of average return period, record length, and trend magnitude, the detection probability is higher for the annual compared to the seasonal case, which is a result of the increase in sample size. The functional behaviour is similar to the seasonal case.

(5) - Syntèses et préconisations

The findings of this study confirm an earlier report on increasing heavy precipitation frequency in Switzerland. The observed increase of intense precipitation conforms with the ideas of an intensified water cycle and the observed long-term warming.

Références citées :

SCHÖNWIESE, C.-D., J. RAPP, T. FUCHS, and M. DENHARD, 1994: Observed climate trends in Europe 1891–1990. Meteor. Z., 3, 22– 28.

WIDMANN, M., and C. SCHÄR, 1997: A principal component and longterm trend analysis of daily precipitation in Switzerland. Int. J. Climatol., 17, 1333–1356.