Compare AllTrans EGM2008 Calculator Results — Step-by-Step ExamplesThis article explains how to compare results produced by the AllTrans EGM2008 Calculator. It walks through the calculator’s purpose, inputs and outputs, typical sources of discrepancies, and step‑by‑step example comparisons — so you can validate results, troubleshoot differences, and choose the right settings for your application.
What the AllTrans EGM2008 Calculator does
The AllTrans EGM2008 Calculator computes geoid heights (EGM2008 geoid undulations) and related gravity‑model transformations used to convert between ellipsoidal heights (from GNSS) and orthometric heights (height above the geoid). Typical uses include converting GNSS ellipsoidal heights to survey vertical datums, checking levelling results, and processing geodetic networks.
Key output: geoid height (N) — the geoid undulation in meters relative to the reference ellipsoid.
Common complementary outputs: normal gravity corrections, grid/terrain corrections, and metadata about model resolution and interpolation method.
Inputs that matter (and why)
- Latitude and longitude (decimal degrees): direct positional input; small coordinate errors shift N slightly.
- Ellipsoidal height (h): used when converting to orthometric height H via H = h − N.
- Geoid model/version: EGM2008 must be selected; alternate models (e.g., EGM96) produce different N values.
- Model resolution / spherical harmonic truncation: truncation degree/order (e.g., 2190) or grid-based interpolation affects precision.
- Interpolation method: bilinear, bicubic, nearest-neighbor — changes sub‑meter outputs.
- Reference ellipsoid and datum: mismatches (WGS84 vs GRS80) change computed N slightly.
- Height units: meters vs feet — units mismatch introduces large apparent errors.
Why results may differ between runs/tools
- Different implementations: grid lookup vs spherical-harmonic evaluation.
- Grid resolution and smoothing applied by the tool.
- Numerical precision and rounding.
- Different conventions for sign or the definition of orthometric vs ellipsoidal heights.
- Datum/ellipsoid mismatches or outdated model versions.
How to prepare a valid comparison
- Fix inputs: use identical lat, lon, model version (EGM2008), and ellipsoid.
- Use the same interpolation method when possible.
- Ensure consistent units (meters).
- Record tool settings and metadata (model truncation, grid resolution).
- Compare both geoid heights (N) and converted orthometric heights (H = h − N). Present differences as ΔN and ΔH.
Step-by-step Example 1 — Single point, simple check
Purpose: Quick check of two calculators (AllTrans and a reference tool) at a single point.
Inputs:
- Latitude: 48.8566° N
- Longitude: 2.3522° E
- Ellipsoidal height h: 100.00 m
- Model: EGM2008, degree 2190 (where selectable)
- Interpolation: bilinear
Steps:
- Enter lat/lon and select EGM2008 in both tools.
- Use bilinear interpolation and ensure units are meters.
- Record geoid heights: N_AllTrans and N_ref.
- Compute orthometric heights: H_AllTrans = h − N_AllTrans; H_ref = h − N_ref.
- Compute differences: ΔN = N_AllTrans − N_ref; ΔH = H_AllTrans − H_ref.
Interpreting results:
- If |ΔN| < 0.01 m, calculators agree to within 1 cm — excellent.
- If 0.01 m ≤ |ΔN| < 0.10 m, acceptable depending on application.
- If |ΔN| ≥ 0.10 m, investigate interpolation, truncation, or datum mismatches.
Step-by-step Example 2 — Profile of points (coastal gradient check)
Purpose: Compare how geoid undulation changes along a 50 km coastal profile and verify both tools show the same gradient.
Inputs:
- Start: 43.7000° N, 7.2700° E (near Nice, France)
- End: 43.9000° N, 7.2700° E
- 11 equally spaced points (every 0.02° latitude)
- h constant at 50.00 m
- Model: EGM2008, grid interpolation bicubic if available
Steps:
- Generate the 11 lat/lon points.
- Run both calculators for each point, extracting N and computing H.
- Create a table of lat, lon, N_AllTrans, N_ref, ΔN, H_AllTrans, H_ref, ΔH.
- Plot N vs latitude for each tool (or inspect ΔN column).
What to look for:
- Smooth variation in N along the profile.
- ΔN patterns: a systematic bias indicates model/version difference; localized spikes suggest interpolation artifacts or errors in input coordinates.
Step-by-step Example 3 — High-latitude check (numerical stability)
Purpose: Test behavior near the poles where spherical harmonic series and grid interpolation may show larger numerical differences.
Inputs:
- Latitude: 78.0000° N
- Longitude: 15.0000° E
- h = 0.00 m
- Model: EGM2008, maximum resolution available
Steps:
- Query both tools for N at the point.
- Confirm whether the tool uses grid extrapolation or harmonic evaluation near high latitudes.
- Compare N and ΔN; note any larger deviations than lower-latitude comparisons.
Interpretation:
- Larger ΔN (>0.05–0.10 m) can occur near poles due to model edge effects or interpolation limits. Use harmonic evaluation or higher-resolution grids if accuracy is critical.
Step-by-step Example 4 — Batch comparison vs known benchmarks
Purpose: Validate AllTrans outputs against authoritative benchmark geoid values (e.g., published control points).
Inputs:
- A set of 20 survey control points with published geoid heights (N_bench) and ellipsoidal heights.
- Model: EGM2008.
Steps:
- Run AllTrans for each benchmark point to get N_AllTrans.
- Compute residuals: Res_i = N_AllTrans_i − N_bench_i.
- Compute statistics: mean bias, standard deviation, RMS.
- Map residuals geographically to identify spatial patterns.
Acceptable results:
- Mean bias near zero indicates no systematic offset.
- RMS shows typical random error; aim for RMS within published model uncertainty (often a few cm to decimeters depending on region).
Troubleshooting differences
- Confirm the same geoid model (EGM2008) and truncation used.
- Check interpolation method: switch to a higher-order interpolation if available.
- Verify ellipsoid and datum (WGS84 vs other realistic mismatches).
- Re-run with increased numeric precision setting if tool allows.
- For persistent local discrepancies, compare against local geoid models or levelling data.
Practical tips for surveyors and geodesists
- Always archive the exact tool settings used for each conversion (model version, truncation, interpolation).
- For legal/official heights, prefer workflows that reference the national vertical datum and its recommended geoid model.
- Use batch comparisons against benchmarks to detect systemic offsets before large projects.
- When sub‑centimeter accuracy is required, combine GNSS, gravimetric data, and local leveling.
Example summary checklist (quick validation)
- Inputs consistent (lat, lon, h, units).
- Same geoid model and truncation.
- Same interpolation method.
- Compare both N and H.
- Compute ΔN and ΔH and check against tolerance thresholds.
If you want, I can:
- Run a simulated comparison table for the single‑point example above with hypothetical numbers; or
- Create a ready-to-run spreadsheet template to perform batch comparisons and compute statistics.
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