Cold-Temperature Altimetry Correction Benchmark Matrix
A 5,425-vector computational benchmark comparing the ICAO Doc 8168 PANS-OPS simplified hypsometric layer correction, FAA AIM Table 7-3-1 published lookup values, and the linear 4 ft/°C/1,000 ft rule across multiple airfield elevations and extreme sub-freezing temperature profiles.
Benchmark Distribution ArtifactsDOI: 10.6084/m9.figshare.34065627
Deterministic CSV and JSON artifacts licensed under Creative Commons Attribution 4.0 International.
Representative Calculation Vectors
Sample slices illustrating sea-level calibration nodes, extreme cold departures, and high-elevation airfield layers.
| Elev MSL | Temp (°C) | HAA | Target MSL | ISA Dev | Simplified Model (ft) | FAA Table (ft) | Linear Rule (ft) | FAA vs Model | Corrected Target | Modeled True Alt | Benchmark Note |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 ft | −10.0°C | 1,000 ft | 1,000 ft | −25.00°C | 95.36 ft | 100.0 ft | 100.00 ft | +4.64 ft | 1,095.36 ft | 904.64 ft | Sea Level Published FAA Table Node |
| 0 ft | −30.0°C | 1,000 ft | 1,000 ft | −45.00°C | 185.83 ft | 190.0 ft | 180.00 ft | +4.17 ft | 1,185.83 ft | 814.17 ft | Severe Cold Model Benchmark Point |
| 0 ft | −40.0°C | 5,000 ft | 5,000 ft | −55.00°C | 1,205.10 ft | 1,210.0 ft | 1,100.00 ft | +4.90 ft | 6,205.10 ft | 3,794.90 ft | FAA Table Published Domain Boundary (5,000 ft HAA) |
| 0 ft | −40.0°C | 6,000 ft | 6,000 ft | −55.00°C | 1,452.42 ft | null (Above Tabulated) | 1,320.00 ft | null | 7,452.42 ft | 4,547.58 ft | Aeroway Model Extension (HAA > 5,000 ft; No Published FAA Node) |
| 5,000 ft | −20.0°C | 2,000 ft | 7,000 ft | −25.09°C | 195.95 ft | 280.0 ft | 200.75 ft | +84.05 ft | 7,195.95 ft | 6,804.05 ft | High-Elevation Airfield (5,000 ft MSL Model Point) |
Data Dictionary & Column Schema (13 Variables)
Strictly typed mathematical and atmospheric definitions for every serialized column in the benchmark dataset.
| # | Column Name | Data Type | Units | Nullable | Physical & Computational Definition |
|---|---|---|---|---|---|
| 1 | Airport_Elevation_ft | integer | ft | No | Altimeter setting source aerodrome elevation above MSL (0, 2500, 5000, 7500, 10000 ft). |
| 2 | Surface_Temp_C | float (1 dec) | °C | No | Reported aerodrome surface temperature (−50.0°C to +10.0°C in 2.0°C steps). |
| 3 | Height_Above_Airport_HAA_ft | integer | ft | No | Target procedure altitude height above aerodrome reference: HHAA = Target_MSL − Airport_Elev. |
| 4 | Target_Altitude_MSL_ft | integer | ft | No | Uncorrected published indicated altitude MSL: Airport_Elevation_ft + Height_Above_Airport_HAA_ft. |
| 5 | ISA_Ground_Temp_C | float (2 dec) | °C | No | Standard ISA temperature at airfield elevation: TISA,ground = 15.0 − 0.0019812 · Airport_Elevation_ft. |
| 6 | ISA_Ground_Deviation_C | float (2 dec) | °C | No | Surface temperature departure from standard: ΔTground = Surface_Temp_C − ISA_Ground_Temp_C. |
| 7 | Simplified_Model_Correction_ft | float (2 dec) | ft | No | Analytical correction derived from the ICAO Doc 8168 PANS-OPS simplified hypsometric layer equation. |
| 8 | FAA_Table_731_Correction_ft | float (1 dec) | ft | Yes | Published FAA AIM Table 7-3-1 reference lookup at published nodes / Aeroway piecewise bilinear interpolation between nodes. null for HHAA > 5,000 ft (no directly tabulated FAA reference node; Aeroway does not fabricate direct table entries). |
| 9 | Linear_Rule_Correction_ft | float (2 dec) | ft | No | Linear flight-training rule-of-thumb approximation: 4 · (−ΔTground) · (HHAA / 1000). |
| 10 | FAA_vs_Model_Error_ft | float (2 dec) | ft | Yes | Divergence vector: FAA_Table_731_Correction_ft − Simplified_Model_Correction_ft. null when FAA table is null. |
| 11 | Linear_vs_Model_Error_ft | float (2 dec) | ft | No | Divergence vector: Linear_Rule_Correction_ft − Simplified_Model_Correction_ft. |
| 12 | Modeled_Corrected_Target_MSL_ft | float (2 dec) | ft | No | Indicated barometric altitude to fly under model: Target_Altitude_MSL_ft + Simplified_Model_Correction_ft. |
| 13 | Modeled_True_Altitude_MSL_ft | float (2 dec) | ft | No | Model-derived thermodynamic true altitude if uncorrected barometric indication is flown: Target_Altitude_MSL_ft − Simplified_Model_Correction_ft. Does not represent operational aircraft clearance or terrain distance. |
Mathematical Methodology & Governing Formulations
Theoretical foundations, hypsometric integrations, and comparative models implemented in the benchmark.
Analytical Hypsometric Layer Model
In accordance with ICAO Doc 8168 (*Procedures for Air Navigation Services — Aircraft Operations*, PANS-OPS, Volume I, Part III, Section 1, Chapter 4, Appendix), the simplified analytical correction applied to an altitude layer above the altimeter setting source is:
- H: Height above altimeter setting source (HAA, ft).
- H_ss: Altimeter setting source elevation above MSL (ft).
- t₀: Reporting station temperature adjusted to sea level: tground + L₀ · Hss (°C).
- L₀: Standard tropospheric lapse rate (0.0019812 °C/ft or 0.0065 °C/m).
Published Table & Cockpit Heuristic
FAA AIM Table 7-3-1: Audited published correction values across 7 temperatures (+10°C to −50°C) and 14 HAA levels (200 to 5,000 ft HAA). Bilinear interpolation is used between published nodes as an Aeroway comparative modeling method.
- Linear Rule: 4 ft of correction per °C below standard per 1,000 ft HAA.
- 5,000-ft Table Boundary: FAA AIM guidance states that the 5,000-ft column or mathematical extrapolation may be used for heights above 5,000 ft. In this research benchmark,
nullis assigned for H > 5,000 ft to reflect the absence of a directly tabulated FAA reference node without fabricating direct table entries. - Transport Canada Reference: Evaluated alongside Transport Canada AIM (AIR 2.12) as a separate national reference baseline.
Two-Tier Computational Validation & Calibration Results
Automated regression testing verifies published FAA table calibration points, model invariants, and physical monotonicity across all 5,425 records.
- −10°C / 1,000 ft HAA:100 ft (Published Table Node Match)
- −30°C / 1,500 ft HAA:280 ft (Published Table Node Match)
- −50°C / 3,000 ft HAA:890 ft (Published Table Node Match)
- −50°C / 4,000 ft HAA:1,190 ft (Published Table Node Match)
- HAA > 5,000 ft (No Tabulated Node):Strict Null Invariant Verified
- Standard Day (ΔT ≥ 0):Δh ≡ 0.00 ft (Passed)
- HAA Monotonicity (∂Δh/∂H > 0):100% Invariant Compliant
- Cold Monotonicity (t₁ < t₂):100% Invariant Compliant
- NaN / Infinity Detection:0 Instances Across 5,425 Rows
- Deterministic Regeneration:Byte-for-Byte Reproducible
1. No Terrain Clearance Representation: The field Modeled_True_Altitude_MSL_ft represents exclusively the thermodynamic calculation of geometric altitude in non-standard sub-freezing air. The dataset contains no digital elevation model (DEM) or terrain proximity database and does NOT evaluate obstacle clearance, minimum vectoring altitudes (MVA), or required obstacle clearance (ROC) buffers.
2. No Operational Certification: This benchmark is an engineering reference and academic dataset. It does NOT constitute operational flight clearance, certified Flight Management System (FMS) temperature compensation logic, or legal authorization to modify published ATC minimums. Flight crews must apply cold-temperature corrections in strict compliance with 14 CFR § 91.103, FAA Terminal Procedures Publications (TPP) Cold Temperature Airport procedures, Transport Canada AIM RAC § 9.17.1, or applicable national AIP directives.