Hail Vulnerability Model — v1.5 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 for event-specific radar bias (this event: 2.0× LSR/MRMS calibration from 86 reports) and storm type (supercell 1.15×) to estimate the 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. Hit rate decreases with stone size — large-hail events are sparser, not denser.
  3. Stone size distribution follows a truncated Gamma distribution (α = 1.75; Li et al. 2024) between 5 mm and Dl. The majority of impacts are sub-damaging small stones; large stones are rare tail events.
  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; Li et al. 2024).
  5. Aggregate Pfail = 1 − ∏(1 − pi)Ni across all size bins. Duration exposure applied as cap-limited multiplier (max 1.4×).

Key Parameters

Gamma shape α1.75 (Li et al. 2024 central estimate)
Fragility median θ46 mm (~1.8") — unrated asphalt shingle
Fragility dispersion γ0.25 (lognormal)
MRMS bias correction2.0× (LSR/MRMS median, 86 reports)
Storm type multiplierSupercell 1.15× Dl
Minimum stone modeled5 mm (graupel cutoff)

References

Field, P.R., Heymsfield, A.J., Detwiler, A.G. & Wilkinson, J.M. (2019). Normalized Hail Particle Size Distributions from the T-28 Storm-Penetrating Aircraft. J. Appl. Meteor. Climatol. 58, 231–245. DOI: 10.1175/JAMC-D-18-0118.1
Grieser, J. & Hill, M. (2019). How to Express Hail Intensity — Modeling the Hailstone Size Distribution. J. Appl. Meteor. Climatol. 58, 2329–2344. DOI: 10.1175/JAMC-D-18-0334.1
Li, Y., Porter, K. & Goda, K. (2024). Hail hazard modeling with uncertainty analysis and roof damage estimation of residential buildings in North America. Int. J. Disaster Risk Reduction 113, 104853. DOI: 10.1016/j.ijdrr.2024.104853
Buildings colored by hail damage ratio — supercell 1.15× + duration multipliers. Click a building for full model output.
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