When is curvature-level geoid validation feasible? A detectability-and-identifiability design rule, demonstrated on GSVS17

Russell David Moore 

Geoid-model validation campaigns compare observed geoid heights and slopes against models. This work asks what it takes to extend that comparison by one differential order — to curvature, the local change of slope — and gives a predictive design rule for when such a test is worthwhile. The rule rests on the classical fact that plumb-line curvature is a projection of the gravity Hessian, or gravity-gradient tensor, and combines three computable ingredients: a row-space identifiability map, showing which gravity-field curvature components a survey geometry can constrain; a calibrated detectability floor, giving the smallest geoid-height feature resolvable at curvature level as a function of station spacing, height precision, and feature wavelength; and a terrain-confound criterion, giving the DEM resolution needed to control the terrain-driven plumb-line-curvature signal, about 30 arcseconds in rugged relief.
The rule is demonstrated on the public 2017 Geoid Slope Validation Survey (GSVS17), a 222-station line in Colorado. The two independent curvature channels agree on the raw geoid curvature, with correlation 0.90. Against GEOID18, however, the curvature residual is marginal: SNR ≈ 1.8 at 2 km smoothing, crossing SNR ≈ 3 near 3 km. The channel difference is well explained by terrain. An a-priori, fixed-density rectangular-prism model with no fitted scale reproduces the surface-to-geoid deflection difference with correlation 0.75, about 4σ-equivalent above a phase-randomized null. At GSVS17's station spacing and roughly 10 mm per-mark height precision, curvature validation reaches only near the centimetre scale; the test sharpens with denser spacing, better height precision, or astrogeodetic deflections, which detect features about 15 times smaller for the GSVS17/CODIAC noise budget.