# Severe Hail Index (SHI) - Severe Hail Index (SHI) - Warning Decision Training Division (WDTD)

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# Severe Hail Index (SHI)

## Short Description

The Severe Hail Index (SHI) is used to compute the Probability of Severe Hail (POSH) and Maximum Estimated Size of Hail (MESH).## Subproducts

None.## Primary Users

None.## Input Sources

3D Reflectivity Cube

Vertical temperature profile from the current operational NCEP/EMC mesoscale model (i.e., the RAP as of 2014).

## Resolution

Spatial Resolution: 0.01^{o} Latitude (~1.11 km) x 0.01^{o} Longitude (~1.01 km at 25^{o}N and 0.73 km at 49^{o}N)

Temporal Resolution: 2 minutes

## Product Creation

This version of SHI is computed using the same cell-based equations as in Witt et al. (1998), except that it is vertically integrated on a multiple-radar 3D grid. Thermodynamic data (0° and -20° C) are integrated from numerical model analysis fields.## Technical Details

To determine the presence of severe hail, an approach similar to the Vertically Integrated Liquid (VIL) algorithm was adopted. The first change involves using a reflectivity-to-hail relation, instead of a reflectivity-to-liquid-water relation as VIL does. The reflectivity data are transformed into flux values of hail kinetic energy (Ė) by:

,

where,

Here, Z is in dBZ, Ė is in J m^{-2} s^{-1}, and the weighting function W(Z) can be used to define a transition zone between rain and hail reflectivities. The default values for this algorithm are Z_{L} = 40 dBZ and Z_{U}= 50 dBZ. While the VIL algorithm filters out the high reflectivities associated with hail by having an upper-reflectivity limit of 55 dBZ, the Z–Ė relation functions in the opposite way, using only the higher reflectivities typically associated with hail and filtering out most of the lower reflectivities typically associated with liquid water (Fig. 1).

**Fig. 1:** Plot of hail kinetic energy flux (solid curve), and liquid water content (used

to calculate VIL; dashed curve), as a function of reflectivity (Witt et al. 1998).

The second change involves using a temperature-weighted vertical integration. Since hail growth only occurs at temperatures < 0°C, and most growth for severe hail occurs at temperatures near -20°C or colder, the following temperature-based weighting function is used:

,

where, H is the height above radar level (ARL), H_{o} is the height ARL of the environmental melting level (i.e., 0°C), and H_{m20} is the height ARL of the -20°C environmental temperature. Both H_{o} and H_{m20} are determined from temperature profiles in numerical model analysis fields.

All of the above leads to the following radar-derived parameter, which is called the Severe Hail Index (SHI). It is defined as:

where, H_{T} is the height of the top of the storm cell and Ė is calculated using the reflectivity profile of the grid point within the 3D Reflectivity Cube. The units of SHI are J m^{-1} s^{-1}.

## References

Witt, A., M. D. Eilts, G. J. Stumpf, J. T. Johnson, E. D. Mitchell, and K. W. Thomas, 1998: An enhanced hail detection algorithm for the WSR-88D.*Wea. Forecasting*,

**13,**286-303.