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 for radar calibration bias (Ortega 2018: 0.75×) 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 from Dl, calibrated on 37,726 CoCoRaHS observations.
  3. Stone size distribution: Gamma distribution (α = 1.75; Li et al. 2024) between 5 mm and Dl.
  4. Each 1 mm 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 multiplier applied (cap 1.4×).
  6. Ackermann et al. (2024) HDE: surface-occurrence sigmoid Psurface = 1/(1 + e−0.18(MESH−27)). Corrects for hail melting aloft at swath edges.

Validation Benchmark (NCEI)

NCEI billion-dollar loss benchmark for this event: $3.0B. Model output represents roof-loss ground-up across the MRMS swath footprint. NCEI includes all perils, sectors, and loss layers; direct comparison requires applying sector/coverage ratios.

Key Parameters

MRMS radar correction0.75× (Ortega 2018 global baseline)
Gamma shape α1.75 (Li et al. 2024)
Fragility median θ46 mm (~1.8″) — unrated asphalt shingle
Fragility dispersion γ0.25 (lognormal)
HDE sigmoid inflection27 mm MESH (~1.06″)
Storm type multiplierSupercell 1.15× Dl
Roof RCVFootprint × 1.15 slope × $9/sqft

Calibration Signal — Austin Permits

City of Austin re-roof permit filings (Socrata dataset 3syk-w9eu) show a pronounced post-event surge. Re-roof permits in Jun 2024 alone (80) were 3.8× the 2017–2023 baseline of ~21/month. Excess permits Jun–Dec 2024: ~238 above baseline.

Permit rate proxy ≈ 238 / (Austin structures in swath) — provides a weak but independent lower bound on the fraction of buildings with roof damage. Permits undercount actual damage by 3–10× (not all damaged roofs file permits immediately).

References

Grieser, J. & Hill, M. (2019). How to Express Hail Intensity. 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. Int. J. Disaster Risk Reduction 113, 104853.
Ackermann, L. et al. (2024). HDE surface-occurrence probability. Atmos. Meas. Tech. 17, 407–422.
Ortega, K.L. (2018). Evaluating Multi-Radar Multi-Sensor Products for Surface Hailfall Diagnosis. Electronic J. Operational Meteor. 19(1), 1–21.
Buildings colored by hail damage ratio — v1.7 physics, supercell 1.15×, HDE sigmoid. Click a building for model output.
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