A GNSS receiver at a survey benchmark records an ellipsoidal height

PHYSICS · Subjective · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The shape and gravity of the Earth: potential, geoid, isostasy and flexure

Problem

A GNSS receiver at a survey benchmark records an ellipsoidal height he=68.3 mh_e = 68.3\,\mathrm{m}. A regional geoid model gives the geoid height there as N=+31 mN = +31\,\mathrm{m} (a mass excess). A field technician computes the orthometric height (height above mean sea level) as: "Ho=he+N=68.3+31=99.3 mH_{\rm o} = h_e + N = 68.3 + 31 = 99.3\,\mathrm{m}" Find the error in this working and give the correct orthometric height.

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