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Scientific Index & Meteorological Glossary

Unified Compendium of Empirical Formulations, WMO Quality Bounds & Hydrodynamic Physics

⏱️ 1. Barometric Pressure & Hypsometric Reduction

Station pressure (P_stn) is hypsometrically reduced to Mean Sea Level (MSL / QNH) using the virtual temperature of the intervening column:

P_MSL = P_stn · exp((g₀ · z) / (R_d · T_v)) ∈ [850, 1090] hPa

WMO physical bounds allow normal sea-level pressure between 850 hPa (severe cyclonic eye) and 1090 hPa (continental Siberian anticyclone).

💨 2. Beaufort Wind Scale (WMO Code 1100)

An empirical measure that relates wind speed (10m elevation, 10-minute sustained) to observed sea state conditions and aerodynamic surface drag stress:

Wind Drag Stress: tau = rho_air · C_d · U₁₀² [N/m²]

⚡ 3. Convective Available Potential Energy (CAPE)

Measures atmospheric thermodynamic instability integrated between the Level of Free Convection (LFC) and Equilibrium Level (EL):

CAPE = ∫ g · ((T_v,parcel - T_v,env) / T_v,env) dz [J/kg]

Values > 1,500 J/kg indicate high risk for localized severe thunderstorms, hail, and squall lines.

🌊 4. Kallakkadal Coastal Swell Surges

Sudden coastal flooding events triggered by distant Southern Ocean storms (30°S–60°S) propagating at deep-water group velocity (cg ≈ 1.56 · Tp) across thousands of nautical miles before shoaling abruptly against Indian coastlines.

⚓ 5. Significant Wave Height (Hs)

Defined as the average height of the highest one-third of all recorded waves in an observational window, computed spectrally as:

Hs ≈ 4 · √(m₀) [meters]

📐 6. Green's Law & Shallow-Water Wave Celerity

Decouples phase velocity c = √(g·h) from shoaling amplitude growth A₂ = A₁ · (h₁/h₂)^0.25 to model constant onshore energy flux conservation.

📡 7. Doppler Radar Reflectivity Relations (Z-R)

Regionalized drop-size distribution calibration: Z = 200 · R^1.6 (Stratiform), Z = 300 · R^1.4 (Tropical Convection), Z = 180 · R^1.35 (IMD Monsoon Coastal).