**Abstract**

In this chapter, we have conducted a statistical study of the annual extreme precipitation (AMP) for 856 grid cells and during the period of 1979–2012 in Algeria. In the first step, we compared graphically the forecasts of the three parameters of the generalized extreme value (GEV) distribution (location, scale and shape) which are estimated by the Spherical model. We used the Cross validation method to compare the two methods kriging and Co-kriging, based on the based on some statistical indicators such as Mean Errors (ME), Root Mean Square Errors (RMSE) and Squared Deviation Ratio (MSDR). The Kriging forecast error map shows low errors expected near the stations, while co-Kriging gives the lowest errors on average at the national level, which means that the method of co-Kriging is the best. From the results of the return periods, we calculate that after 50 years the estimated of the annual extreme precipitation will exceed the maximum AMP is observed in the 33-year.

**Keywords:** extreme precipitations, kriging and Co-kriging, cross validation, return levels
