This thesis develops several unique different precipitation statistics and verification measures that are applicable to scales relevant to global climate models, regional models and hydrological runoff models, through a series of three papers.; The first section of the dissertation is motivated by the fact that climate models are unable to account for the variability of precipitation within a grid box, and that other hydrologically critical precipitation characteristics, such as intensity and frequency, are often times overlooked in the literature. Several issues related to spatial averaging of these two measures are investigated. Rain gauge reports and radar precipitation analyses are used here to address three issues related to the areal estimation of intensity and frequency of precipitation. Differences between the order of spatial and temporal averaging methods are proven to be significant; therefore quantifying these differences is critical for both climate model diagnostics and downscaling applications.; The second section documents spatio-temporal statistics of hourly fine-scale precipitation analyses for the continental U.S. The spatio-temporal coherence of precipitation fields, quantified under the assumption of isotropy, reveals significant seasonal and geographical variations. Anisotropic factors are then considered to obtain estimates of the mean movement and orientation of the precipitating storm systems. The dissertation provides new methodology to quantify the spatio-temporal variability of observed and modeled precipitation that offers new insight into how to correct erroneous model simulations.; The methodologies are used to evaluate the performance of two mesoscale atmospheric forecast models, one with explicit treatment of convection and the other with a convective parameterization scheme. Designed to account for the transient and intermittent character of precipitation, these new verification techniques show that explicit formulation of convection yields spatio-temporal covariance structures that agree closely with observations. The explicit scheme shows however, a systematic tendency to propagate summertime precipitating storm systems to the right of observations, suggesting that the model's convection is too dependent on the source of low-level moisture.
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