Hail Vulnerability Model — v1.7 Physics

Damage probability is computed using a physically grounded stone-population model. Rather than mapping peak MESH directly to a damage ratio, the model distributes stone impacts across the realistic hail size spectrum — where the largest stones are rare outliers, not the norm.

Algorithm

  1. Peak MRMS MESH is corrected with Ortega (2018) 0.75× universal correction and storm type multiplier (supercell 1.15×) to estimate effective largest stone diameter Dl.
  2. Grieser & Hill (2019) power-law fits give average stone diameter Da, storm duration T, and hit rate Hr as functions of Dl, calibrated on 37,726 CoCoRaHS ground-truth observations.
  3. Stone size distribution follows a truncated Gamma distribution (α = 1.75; Li et al. 2024) between 5 mm and Dl.
  4. Each 1mm size bin is assigned a damage probability via a lognormal fragility curve for unrated asphalt shingle (θ = 46 mm, γ = 0.25).
  5. Aggregate Pfail = 1 − ∏(1 − pi)Ni. Duration exposure applied as cap-limited multiplier (max 1.4×). Ackermann et al. (2024) HDE sigmoid applied for atmospheric path loss.

Key Parameters

Ortega MESH correction0.75× (universal)
Storm type multiplierSupercell 1.15× Dl
Fragility median θ46 mm (~1.8") — unrated asphalt shingle
Fragility dispersion γ0.25 (lognormal)
Industry benchmark~$6.0B insured (PCS estimate)

References

Grieser, J. & Hill, M. (2019). How to Express Hail Intensity. J. Appl. Meteor. Climatol. 58, 2329–2344.
Li, Y., Porter, K. & Goda, K. (2024). Hail hazard modeling with uncertainty analysis. Int. J. Disaster Risk Reduction 113, 104853.
Ackermann, M. et al. (2024). Hail damage efficiency. Nat. Hazards Earth Syst. Sci.
Buildings colored by hail damage ratio — supercell 1.15× + duration multipliers. Click a building for full model output.
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