In Pursuit of a cm-Accurate Local Geoid Model for Ohio

Abstract

As part of its strategic plan for 2008–2018 [The NGS Ten Year-Plan, Mission, vision and strategy, 2008–2018], the National Geodetic Survey has resolved to engage in activities which would allow for the development of a 1-cm accurate national gravimetric geoid for the conterminous US. In this regard, the Ohio Department of Transportation has been collaborating with the OSU SPIN Laboratory in height modernization activities for the state of Ohio. Presented in this paper are the results of an investigation used to evaluate the quality of gravity and height data needed to produce a cm-accurate geoid in Ohio.

In this study a local geoid model over Ohio was computed in a remove-restore geoid determination procedure using EGM2008 [Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An earth gravitational model to degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13–18], publicly-available surface gravity data from the PACES website and the GTOPO30 DEM. Terrain corrections (subject to a planar approximation) were evaluated using a 2D FFT algorithm [Forsberg R (1985) Gravity field terrain effect computations by FFT. Bull G odésique 59:342–3601; Forsberg R (1997) Terrain effects in geoid computations. Lecture notes. International School for the Determination and Use of the Geoid, Rio de Janeiro, Sept 1997]. Ohioan terrain being substantially flat (on average about 330 ± 160 m AMSL) produced terrain corrections which were, for the most part, at the sub-mGal level. However, these translated into a geoid contribution of about 0.039 ± 0.038 m in the local model. A 1D FFT technique [Haagmans R, de Min E, von Gelderen M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Manuscripta Geodaetica 18:227–241] was used to evaluate the Stokes’ integral [Heiskanen WA, Moritz H (1967) Physical geodesy, W.H. Freeman, San Francisco, CA] over a 5° × 5° region on a 5′ × 5′ grid encompassing the state of Ohio and its environs.

This local geoid model was used as a reference solution for statistical comparisons made to subsequently computed geoid determinations (over the same region) in which the latter had been evaluated using surface gravity and height data sets subjected to simulated zero-mean Gaussian-distributed random errors of homogeneous spatial distribution. While EGM2008 was assumed to be perfect, the standard deviation of the errors applied to the surface gravity ranged from ±0.1 to ±5 mGal while those associated with the height data (of both the gravity and the DEM) ranged from ±0.5 to ±20 m. For each Gaussian dispersion utilized, 100 simulated error-prone data sets were selected and their associated geoid solutions determined using the same Stokes/FFT algorithms which were used to evaluate the aforementioned reference geoid model. Summary statistics were evaluated for each set of the 100 “randomized” geoid models relative to the reference solution, allowing for an evaluation of the potential impact of random errors present in the input height and gravity data on the local geoid solution in Ohio.

It was found that simulated height errors which were ±10 m or less produced a 1 cm (1σ) accurate local geoid while those in excess did not. RMS differences of 1–1.6 cm occurred on application of gravity errors of ±3 to ±5 mGal, prohibiting the possibility of achieving a cm-accurate geoid. Based on the results of this study, it was concluded that minimum requirements for a cm accurate geoid determination in Ohio would be a combination of gravity and height data accurate up to about the ±3 mGal and ±10 m levels, respectively.

Future studies will be conducted using updated gravity and height data sets. In addition the geoid height error analysis would account for (1) the implementation of a spatially-heterogeneous error modeling scheme based on surface gravity data density and (2) simulated random errors in the global geopotential model used in concert with the surface gravity and height data sets.