NWS MESH and POSH Algorithms
Use a reflectivity to hail energy relationship. The hail kinetic energy is integrated with height above the freezing layer. Using a large dataset, the integrated energy is statistically related to:
- MESH (Maximum Expected Size of Hail)
- POSH (Probability of Severe Hail)
The Hail Kinetic Energy (E)
E = 5×10-6 × 100.084 × W(dBZ)
where W(dBZ) is a weight function based on reflectivity; dBZl = 40, dBZu = 50:
- W(dBZ) = 0 for dBZ ≤ dBZl
- W(dBZ) = (dBZ-dBZl)/(dBZu-dBZl) for dBZl < dBZ < dBZu
- W(dBZ) = 1 for dBZ ≥ dBZu
Severe Hail Index (SHI)
SHI = 0.1×∫Wt(H)×E×dH; integrated from from the freezing level (H0) to the height of the -20C (H-20), and all heights are above radar level, where:
- WT(H) = 0 for H ≤ H0
- WT(H) = (H-H0)/(H-20-H0) for H0 < H < H-20
- WT(H) = 1 for H ≥ H-20
MESH and POSH Calculations
MESH = 2.54×√SHI
POSH = 29×ln(SHI/WT)+50
where:
WT is the warning threshold given by: WT = 57.5×H0 - 121; if WT < 20, WT = 20