Model Validation Report

D_eff = D_max × Φ(C) — Applied to NOAA HRRR Data — Nor'easter Feb 22–24, 2026

1. Model Architecture

The atmospheric coherence function Φ(C) is composed of three weighted signals derived from NOAA HRRR analysis grids across five pressure levels (925, 850, 700, 500, 300 mb):

Each component ranges [0, 1]. Higher values indicate more organized atmospheric structure. The weighted sum produces Φ(C) ∈ [0, 1], which directly scales the maximum dimensionality.

2. Bug Discovery: Pressure Stability = 0

Root Cause

This is not atmospheric instability — it is a mathematical artifact of comparing inherently different layer sizes. The function measured the geometry of the atmosphere, not weather-related pressure anomalies.

The Fix

3. Before vs. After Comparison

Impact of the pressure stability fix on Φ(C) values across all seven time steps:

The pressure stability component contributed approximately +0.15 to Φ(C) uniformly. This is consistent with what we'd expect: geopotential heights deviate modestly from the standard atmosphere even during a major storm, contributing a stabilizing signal that was previously zeroed out.

4. Formula Verification

Across all 82,327 data points (7 frames × 11,761 grid points — land + Atlantic extension), D_eff = 5 × Φ(C) was verified:

All errors are due to JSON rounding (3 decimal places for Φ, 2 for D_eff). The formula is mathematically consistent.

5. Component Analysis (Corrected Model)

With pressure stability now active, all three components contribute real atmospheric signal:

Key observation: Wind coherence drives the most variation (range 0.232–0.939), making it the dominant signal for identifying storm location. Temperature consistency is relatively stable (0.787–0.938). Pressure stability now provides a meaningful third axis (0.641–0.961) that properly reflects vertical structure distortion during the cyclone's passage.

6. Storm Track Validation

The 10 lowest-Φ(C) grid points in each frame were averaged to find the coherence degradation center. This was compared against the known nor'easter track:

7. Tier Distribution Evolution

How the atmosphere's coherence state evolved across the event (corrected thresholds):

Peak degradation occurs at Feb 23 7:00 AM (22.0% of grid points in degrading state) — coinciding with the storm's maximum intensity over the most populated area (NY metro). By evening, the atmosphere rapidly recovers to 99.7% stable as the storm departs.

8. Key Conclusions

1. Formula is mathematically consistent. D_eff = 5 × Φ(C) verified across all 82,327 data points (v2: land + Atlantic) with maximum error of 0.005 (rounding only).
2. Three-component Φ(C) recomputation matches stored values to within 0.0008, confirming the weighted sum is correctly implemented.
3. Storm track validation: The lowest-coherence center followed the known nor'easter path from Virginia (37°N) to Maine (45.5°N) over 36 hours.
4. No coherence failure over land (land minimum Φ = 0.593, D_eff = 2.96). Physically correct — the storm center tracked offshore. The v2 Atlantic extension confirmed genuine coherence failure offshore: Φ_min = 0.465, 37 failure points per frame, concentrated in the active storm core southeast of the NJ coast.
5. Pressure stability bug identified and fixed. The original algorithm produced exactly 0.000 everywhere due to comparing inherently different layer sizes. The corrected algorithm uses standard atmosphere deviation, adding a meaningful third signal.
6. Wind coherence is the dominant discriminator (widest range: 0.232–0.939), determining storm location. Temperature consistency is the most stable component. Pressure stability provides vertical structure context.

9. Limitations and Future Work

• HRRR data is clipped to land boundaries — the offshore storm core (where true coherence failure likely occurred) is not captured. Resolved in v2: Atlantic extension added 7,679 ocean grid points, revealing Φ_min = 0.465 and genuine coherence failure offshore.
• Single-model analysis (HRRR only). Cross-validation with GFS, ERA5, or radiosonde observations would strengthen the findings.
• The 0.15 fractional deviation threshold for pressure stability was chosen based on physical reasoning but has not been independently calibrated against multiple storm events.
• D_max = 5 (one per pressure level) is a simplification. True atmospheric degrees of freedom are higher and vary spatially.
• No moisture or precipitation data is included in Φ(C). Adding specific humidity or radar reflectivity as a fourth component could improve resolution of convective zones.