Data requirements for the determination of a sub-centimetre geoid

Abstract

Recent applications in Earth sciences require geoid models to be determined with a sub-centimetre internal error. Regional models of the geoid are usually determined using discrete gravity values measured at and/or outside the Earth, and global models of the Earth gravity field and topographic surface. In this article, we review previous studies that (to some extent) discuss the estimation of the geoid internal error, and provide formulations and methodologies required for a comprehensive formal propagation of errors of gravity data and global models through a mathematical model used for regional geoid determination. The mathematical model is based on combining the inverse Poisson integral equation and the Hotine integral transform in the Helmert harmonic space; also called the one-step integration method. Calculations and tests are performed in one of the most challenging test areas (“the Colorado test area”) using ground and airborne gravity observations, a global digital terrain model (DTM) for topographic effects on gravity and the geoid, and a global Earth gravitational model (EGM) for the long-wavelength components of gravity and the geoid.There are three main contributors to the total internal error of the geoid height, namely those associated with the EGM (for estimating the long-wavelength geoid height), DTM heights (for evaluation of the topographic effects on observed gravity and the geoid height), and gravity observations (for determining the short-wavelength components of the geoid height). The geoid errors stemming from the EGM formal variances of its spherical harmonic coefficients amount to 0.3 cm of the total internal error budget of the geoid. The mean value of the standard deviation of the geoid height stemming from the topographic effects (due to uncertainties of DTM heights) is 1.0 cm. The observation errors and spatial distribution (resolution) of regional ground and airborne gravity observations, i.e., the design of the project, are the dominant contributors to the internal error of the geoid height. The internal error estimate of the geoid model in the Colorado test area computed on a 1′ × 1′ grid is 2.7 cm which agrees with the differences between various geoid models that contributed to the Colorado 1-cm geoid experiment.Determining a regional geoid model with a sub-centimetre internal error in areas of rough topography, such as that of Colorado, requires high-accuracy and high-resolution gravity observations. To assess the accuracy of regional gravity measurements required for sub-centimetre geoid models, we simulate airborne gravity measurements in the Colorado test area at a practical lower flight altitude, and improve the spatial distribution of existing ground gravity observations by filling in gaps using synthetic (EGM-based) gravity disturbances. Results show that carrying out airborne gravity surveys with a gentle drape approach at an average flight altitude between 300 and 500 m above the Earth's surface provides airborne gravity measurements with a mean standard deviation of 0.75 mGal at 2.2 km spatial resolution. Thus, a sub-centimetre regional gravimetric geoid model in the Colorado test area would be achievable using the proposed configuration of the ground and airborne gravity observations and more accurate DTMs.