Precipitation Forecasting with Gamma Distribution Models for Gridded Precipitation Events in Eastern Oklahoma and Northwestern Arkansas*

An elegant and easy to implement probabilistic quantitative precipitation forecasting model that can be used to estimate the probability of exceedance (POE) is presented. The model was built using precipitation data collected across eastern Oklahoma and northwestern Arkansas from late 2005 through early 2013. The dataset includes precipitation analyses at 4578 contiguous, 4 km x 4 km grid cells for 1800 precipitation events of 12 h. The dataset is unique in that the meteorological conditions for each 12-h event were relatively homogeneous when contrasted with single-point data obtained over months or years where the meteorological conditions for each rain event could have varied widely. Grid cells were counted and stratified by precipitation amount in increments of 0.05 in. (1.27 mm) up to 10 in. (254 mm), yielding histograms for each event. POEs were computed from the observed precipitation distributions and compared to POEs computed from two gamma probability density functions The errors between the observed POEs and gamma-computed POEs ranged between 2% and 10%, depending on the threshold POE selected for the comparison. This accuracy suggests the gamma models could be used to make reasonably accurate estimates of POE, given the percent areal coverage and the mean precipitation over the area. Finally, it is suggested that the areal distribution for each event is representative of the distribution at any point in the area over a large number of similar events. It then follows that the gamma models can be used to make forecasts for the probability of exceedance at a point, given the probability of rain and the expected mean rainfall at that same point.