Statistical Analysis of Extreme Daily Rainfall
Research Studies by W. Berolo, Geoazur, UNS, Nice, France.

Tuesday 11 May 2010 by Wanda BEROLO

traduction [English ] [français ]

One extreme daily rainfall may affect significantly statistics whatever the time scale, either the daily or monthly or annual one. The 133.5 mm rainfall event recorded on 4 March 2001 at Saint Etienne de Tinée meets this particular feature (refer to the statistical analysis of annual cumulated rainfall). From further observation, pluviometry data set at shorter time lapses (inferior to 1 day) indicate that extreme rainfall amounts, recorded over a 1 day period, often fall within a few hours.

The data available at Saint Etienne de Tinée from 1969 to 2008 allow performing the statistical analysis of extreme rainfall at the daily time scale. According to studies carried out over small watersheds located in Mediterranean mountains or over large watersheds under a temperate climate (G. Bontron et al, 1999 ; W. Berolo et al, 2005), a statistical approach implementing the Gumbel distribution associated to a higher risk season should be tested. For the present case, the monthly variation of the location and scale parameters (mode and gradex) calculated for the monthly maxima daily rainfall does not allow determining a higher risk season. Furthermore, even if the distribution, depending on the occuring month, of the 40 annual maxima daily rainfall indicates that 42.5% of extreme events fall in October and November, the sample size remains too small in order to define the seasonal distributions in a stable way.

Therefore, the values of the 2 year, 10 year and 100 year return period daily rainfall and the value of the daily gradex are calculated by fitting the Gumbel distribution to the annual extreme daily rainfall. Let us remind that the Gumbel distribution function is defined by Eq. 1 where F(x) is the probability that any event X is inferior or equal to a particular event x (non exceeding frequency). The two parameters to be adjusted are the mode x0 corresponding to the most probable value, and the gradex g or extremes gradient (a heavy gradex value means that extreme rainfall amounts greatly vary from one frequency to another one). They are defined according to the mean and the standard deviation of the observation series as mentionned by Eq. 2.

The QQ plot shows that the sample points follow a linear pattern, including the extreme value equal to 133.5 mm that was recorded on 4 March 2001. The theoretical return period of the event is estimated at 68 years. The table gives the estimates of the mode, gradex and quantiles.

The values encountered at Saint Etienne de Tinée are heavier than the national territory average, nevertheless they do not reach the extremes observed in the Cévennes. For comparison, over North-Eastern France the 10 year return period daily rainfall are around 40 to 90 mm, and the gradex for the higher risk season vary from 10 to 15 mm. In the Cévennes, the daily gradex for the high risk season reach values about 60 mm at Mont Aigoual (P. Bois et al, 1995). The 10 year and 100 year return period daily rainfall calculated for the same season are respectively equal to 250 and 370 mm (after implementing the Weiss correction - the values indicated in the quoted reference have concerned 24h time lapses and not daily ones from 6:00 UTC to 6:00 UTC).