GR2Analyst‎ > ‎Reference‎ > ‎Algorithms‎ > ‎

### POSH/MEHS

Probability of Severe Hail (POSH) and Maximum Estimate Hail Size (MEHS) are the hail algorithm outputs from GR2Analyst. The algorithm is described below, and also in more detail in the powerpoint presentation GR2Analyst Algorithms in WFO Operations (Lincoln, 2012), which is the source of this page's images/tables.

The hail algorithm is based upon:

Witt, Arthur, Michael D. Eilts, Gregory J. Stumpf, J. T. Johnson, E. De Wayne Mitchell, Kevin W. Thomas, 1998: An Enhanced Hail Detection Algorithm for the WSR-88D. Wea. Forecasting, 13, 286–303.

## Overview

Compares radar representation to the environment, from that creates Severe Hail Index (SHI)
SHI used as basis for Probability of Severe Hail (POSH) and Maximum Estimated Hail Size (MEHS)

## Severe Hail Index Technique from Witt et al (1998)

The Severe Hail Index (SHI) is calculated by the equation:

Where:

SHI is the Severe Hail Index in J/m/s
WT is temp weighting function; hail forms at <0°C, most severe hail forms at <-20°C
H is height above radar level (km)
E is energy flux based on radar reflectivity; weighted based on transition zone from water (40dbZ) and ice (50dbZ). E is closely related to hail damage potential.
H0 and HT are height of freezing level and height of storm top, respectively

SHI values were then compared to actual hail events. A strong correlation was found between SHI, freezing level (H0), and hail occurrence. A warning threshold for SHI was created from value with highest critical success index (CSI). Correlation between warning threshold and H0 was ~0.80, although this varied based upon the verification time window (how much time before/after radar indication of hail to look for reports).

The Warning Threshold is calculated by the equation:

Where:

WT is the Warning Threshold in J/m/s
H0 is the height of the freezing level

### Probability of Severe Hail from SHI

Probability of severe hail (POSH) function created from warning threshold and SHI such that when SHI=WT, POSH=50%. POSH is calculated by the equation:

Where:

POSH is the Probability of Severe Hail (as a dimensionless ratio)
SHI is the Severe Hail Index in J/m/s
WT is the Warning Threshold in J/m/s

The reliability diagrams for POSH are shown below. The plot on the left is from the cases used to develop the POSH equation. The plot on the right is from the set of verification
cases.  The table below the reliability diagrams shows the statistics for the algorithm in different parts of the United States.

### Maximum-Estimate Hail Size from SHI

Maximum Estimated Hail Size (MEHS) function created from SHI such that 75% of hail reports will be smaller than MEHS. MEHS is calculated by the equation:

Where:
MEHS is the Maximum Estimated Hail Size in mm
SHI is the Severe Hail Index in J/m/s

A reliability diagrams for MEHS is shown below. Due to the substantial uncertainty in estimating hail size, further statistics were not calculated in the paper.

Hail icons have their color and size dependent upon the max. estimated hail size. Icons are centered on the highest MEHS value.
Icons can be configured in:
File -> Configure Hail Icons

Increment determines usage of icon sizes and icons colored based upon color from MEHS color table.

## Sources of Uncertainty

### SHI in Witt et al (1998)

Environment Data
Equation-fitting to data with issues (StormData)
POSH algorithm worked best in S. Plains and was worse in Florida test region. Paper authors attribute some of this to lower quality of reports due to less frequent severe weather and lower population density. Due to large uncertainty in maximum hail size reports, MEHS errors were not quantified.

### GR2Analyst Implementation of SHI

GR2Analyst does not implement the algorithm based on the storm-centroid, but it is instead implemented on a gridded cell-by-cell basis. The integration is done for each radar pixel, stacked vertically. Note: Because of this, storm motion is important!

Environment data comes from latest RUC analysis profile valid for radar location. If no profile available, the values are set to defaults of: 0°C = 10,000ft and -20°C = 20,000ft
Note: This might cause issue when looking at archived data if the profiles were not downloaded to that computer either automatically (during the event) or manually (after the event). The RUC analysis is applied to entire radar range; causes most error in situations with strong fronts or varying airmasses.