Error analysis of the NGS’ surface gravity database

Abstract

Are the National Geodetic Survey’s surface gravity data sufficient for supporting the computation of a 1 cm-accurate geoid? This paper attempts to answer this question by deriving a few measures of accuracy for this data and estimating their effects on the US geoid. We use a data set which comprises ${\sim }1.4$ million gravity observations collected in 1,489 surveys. Comparisons to GRACE-derived gravity and geoid are made to estimate the long-wavelength errors. Crossover analysis and $K$-nearest neighbor predictions are used for estimating local gravity biases and high-frequency gravity errors, and the corresponding geoid biases and high-frequency geoid errors are evaluated. Results indicate that 244 of all 1,489 surface gravity surveys have significant biases ${>}2$ mGal, with geoid implications that reach 20 cm. Some of the biased surveys are large enough in horizontal extent to be reliably corrected by satellite-derived gravity models, but many others are not. In addition, the results suggest that the data are contaminated by high-frequency errors with an RMS of ${\sim }2.2$ mGal. This causes high-frequency geoid errors of a few centimeters in and to the west of the Rocky Mountains and in the Appalachians and a few millimeters or less everywhere else. Finally, long-wavelength (${>}3^{\circ }$) surface gravity errors on the sub-mGal level but with large horizontal extent are found. All of the south and southeast of the USA is biased by +0.3 to +0.8 mGal and the Rocky Mountains by $-0.1$ to $-0.3$ mGal. These small but extensive gravity errors lead to long-wavelength geoid errors that reach 60 cm in the interior of the USA.