Assessment of 10 year and 100 year return period monthly rainfall
Research Studies by W. Berolo, Geoazur, UNS, Nice, France.

Tuesday 11 May 2010 by Wanda BEROLO

traduction [English ] [français ]

The statistical analysis of monthly rainfall allows to put forward the characteristic parameters of the observed raingage and to give assessment of the 10 year and 100 year return period monthly rainfall. The raingage is located at 1,140 m elevation in the Saint Etienne de Tinée village. It is running according to the operation criteria recommended by Meteo-France. The available rainfall database covers a 40 year period (1969-2008) and the time series contains no lack. The observed duration is admitted reliable in order to identify the statistical distribution of monthly rainfall in a stable way.

At the monthly scale, the distribution of rainfall events is highly non symmetric and the square root of the variable is Gaussian. The square root normal distribution fitting to monthly rainfall is asserted by QQ plots of the sorted values from the data set versus the expected values of the corresponding quantiles from the square root normal distribution. 

The estimate of the unknown true quantile xF is calculated from the mean and the standard deviation of the observed sample, and the standard normal variable uF associated to the frequency (Eq. 1). Let us remind that an event x with a theoretical frequency F(x)=0.9 and a theoretical return period T=10 years (Eq. 2) is such as each year there is on average one chance among 10 that it is equaled or exceeded, or that it is equaled or exceeded on average once every 10 years. Thus it may occur several times during a time lapse inferior to its return period (as well as a 100 year return period rainfall F(x)=0.99 has on average one chance among 100...).

The 10 year and 100 year return period monthly rainfall are assessed according to a 80% confidence interval at the Saint Etienne de Tinée station. The upper and lower limits of the α% confidence interval are defined by Eq. 3. The estimated values of each month are given in the graphs below. For example one can note that the 10 year return period cumulated rainfall in October is evaluated at 264 mm with 80% of chances that the value does not reach 316 mm. The 100 year return period cumulated rainfall is estimated at 461 mm with 80% probability that it does not reach 562 mm.

with:

  • tα the standard normal variable with the non exceeding frequency 1- ((1-α/100)/2),
  • tF the standard normal variable with the non exceeding frequency F,
  • n the number of observations,
  • σx the standard deviation of the observation series.