Tests on the recovery of precise geoid height differences from gravimetry

Abstract

To transform Global Positioning System (GPS) derived ellipsoidal height differences, observable to 2–3 ppm of the station separation, into orthometric heights without loss of precision, geoid‐ellipsoid spatial height differences (ΔN) need to be evaluated to this same precision. One of the gravimetric techniques which has been shown, in theory, to be capable of achieving this precision uses ring integration to sense the short wavelength contribution of the local gravity field to ΔN, in combination with a geopotential model to provide the medium to long wavelength contribution. In this paper, comparisons of ΔN, computed by this method, with ΔN values derived from GPS and conventional levelling, have answered many questions relating to computational procedure and have demonstrated the viability of the method. Agreements in ΔN have been accomplished at about 2 to 3 ppm for shorter (<60 km) lines, and at <2 ppm for longer lines. This has been achieved by integrating reduced gravity anomalies over a spherical cap of radius about 1° to find the short wavelength features in ΔN. The gravity anomalies are reduced to a high‐order geopotential model (OSU81, nmax = 180), and this same model is used to generate the longer‐wavelength features of ΔN. It appears that, for a model of this high order, the radius of the cap size is not critical. However, using a lower‐order (e.g., nmax = 90) model as a reference, it appears that the optimum radius, while being in the region of π/nmax, is more critical, although comparisons in ΔN at 2 to 3 ppm are still achievable. The ability of geopotential model OSU81 alone to recover ΔN varies with location and degree. In two of the areas the comparison was at about 10 ppm or worse for nmax = 180, with the fit improving with decrease in nmax. By contrast, the other two tests showed control ΔN at about 3 to 4 ppm for nmax= 180, with the fit deteriorating with decreasing nmax, the behavior one would expect. Apparently the quality of the geopotential model varies with location. It is striking, however, that no matter how poorly the model recovered ΔN, the addition of an inner zone contribution, integrated over a surprisingly small cap size (<0.5°), improved the comparisons and in each case brought them down to the level of 3 to 4 ppm. These tests serve to confirm the viability of the ring integration method for evaluating ΔN, while giving valuable guidance as to the optimum configuration for the technique.