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Steven A. Amburn
Peter L. Wolf


In current severe thunderstorm warning operations, forecasters frequently use the vertically integrated liquid water content (VIL) product from the WSR-88D to estimate thunderstorm severity and, particularly, hail size. Since VIL varies greatly based on airmass characteristics, forecasters have typically determined a threshold VIL to be used for each new thunderstorm event. A product that is independent of airmass characteristics, and thus independent of season and geographic location, would be more desirable in an operational warning environment.

It has been observed that high-topped thunderstorms with high VILs do not always produce large hail. It has also been observed that low-topped thunderstorms with low VILs occasionally do produce large hail. However, the maximum reflectivity in both high-topped and low-topped thunderstorms is similar when both produce similar-sized hail. From this, it was hypothesized that dividing the VIL by the echo top would “normalize” the VIL and produce a common value, or range of values, for thunderstorms producing large hail, independent of airmass characteristics. This quotient is defined as VIL density in this study.

To test the hypothesis, thunderstorm VIL and echo tops were recorded over a wide range of airmass characteristics, and VIL density was calculated. The data were correlated to surface-based reports of hail. The results showed a substantial increase in severe hail (≥19 mm, ¾ in.) reports as VIL density increased above 3.5 g m−3. At values greater than 4.0 g m−3, virtually every thunderstorm produced severe-criteria hail, regardless of the actual VIL or the thunderstorm height. At values below 3.5 g m−3, very few thunderstorms produced severe-criteria hail.

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Steven A. Amburn
Andrew S. I. D. Lang
, and
Michael A. Buonaiuto


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 × 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 ( and ). 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.

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