Public and economic interests in climate extremes make representation of their observed long-term amplitude and recurrence in climate models of particular importance in evaluating the value of such models as investigative and predictive tools. In particular, the behavior of extreme events in climate models must be quantitatively and objectively assessed in comparison with the extreme behavior of the observed climate. This assessment only addresses the long-term expectation of these extreme events and not the correspondence of individual simulated and observed events. For a key climate variable, such as precipitation which generally does not have a normal distribution, this is best done by estimating and comparing the underlying observed and model distribution functions.

Statisical methods based on the normal distribution, when applied to non-normally distributed data, converge slowly and generally require more data than is available to obtain robust estimates. For a given amount of data, L-moments give the most robust distribution function estimates when no asymptotic or other theories are applicable.

Using the index-flood procedure based on L-moments of Hosking and Wallis (1997) modified for gridded data, two observed gridded precipitation data sets, CMAP and CAMS, are analyzed and compared with different COLA atmospheric general circulation model (AGCM) versions and several other models covering several decades. Different months and regions are compared. Each model's abilty to represent the statistics of extreme events is discussed.