Statistical modelling and cartography of extreme daily rainfall events in Tunisia
The following methodology is based on analytical approaches that have been satisfactorily tested in Tunisia. Temporally, the distribution of annual daily maximum rainfall in Tunisia is skewed because of some extreme values (outliers) measured for the majority of the samples. This skewness is particularly pronounced in the central and southern regions of the country. We propose that the samples be adjusted to fit a two-component statistical law (two-exponential law). This approach simultaneously takes into account the pronounced skewness and the Gumbel law of extremes. The method combines two populations with exponential and Poisson distributions for “ordinary” extreme and very extreme (outliers) rainfall values, respectively. This approach is consistent with our knowledge of the climate in Tunisia, which is at the intersection of two very different climatic areas: the Mediterranean climate from the north and the Saharan climate from the south. Spatially, the drawing of equal value Gradex and ten-year daily rainfall curves depends on point estimates from rainfall collection stations, and takes into account the relief, longitude and latitude, as well as the distance from the sea. Explanatory parameters were carefully chosen so as to be easily measured or calculated for any location. These techniques of statistical adjustment and cartography were applied to 399 samples of annual maximum daily rainfall, distributed throughout Tunisia and observed over 30 years (18,496 station-years). Using these techniques, a Gradex daily rainfall map and a ten-year daily rainfall map of Tunisia were generated.