Conditioning General Extreme Value Distribution for Rainfall on Rainfall Dynamics

Rainfall return frequency often is modeled by general extreme value distribution with parameters estimated using annual maximum rainfall series. However, estimation can be difficult with sparse data that also contains large variability. The shape variable, in particular, shows high sensitivity, leaving the analyst a great deal of interpretation for determining factors that create homogenous samples.

An alternative approach is to condition general extreme value distribution for rainfall on weather variables. This approach is tested for rainfall across the North Central United States. Daily water budget variables are selected for conditional extreme value modeling, because it is well known that rainfall efficiency, defined as the ratio of rainfall to water flux, varies considerably from the Great Plains into the Ohio Valley. Thus, it is reasonable to expect maximum annual rainfall to depend upon the relative magnitude of daily water budget components.

A hierarchical model is proposed, and its uniqueness is the spatial process model for general extreme value parameters uses combinations of water budget components as covariates. In the Great Plains, water storage is found to have higher correlation than water vapor convergence. By comparison, in the Midwest, water storage has lower correlation than water vapor convergence. Model evaluation is underway to examine the relative importance of spatial modeling for each of the three parameters, though early results indicate the spatial process model informs most the shape parameter.