Computation of a geopotential model from GOCE data using fast spherical collocation — A simulation study

Using a realistic orbit for GOCE, IAG SC7 has created a one month gravity gradient dataset from EGM96 to degree 300, with gradients referring to an instrument frame aligned with the velocity vector and the z-axis in the plane formed by this vector and the position vector. From the second order derivative of the potential V _zz , we subtracted the contribution of EGM96 to degree 24. The resulted (noise free) data set was used to predict radial gravity gradient values in a 0.5° grid, covering the area of the Earth from −83°to + 83° latitude using local Least-Squares Collocation (LSC). The standard deviation of differences between predicted gridded values and values computed from EGM96 (degree 24 – 300) was between 1.0 and 0.5mE (Eötvös unit = E, 1 E=10−9s−2). Correlated noise with a 3 mEU standard deviation and a 35° correlation distance was added to the simulated data and the gridding was repeated. The formal LSC error-estimates were 2 mE. This was confirmed by comparing radial derivatives from EGM96 with the values predicted from the data with noise. The simulated data sets were used to generate spherical harmonic coefficients of the gravity potential to degree 300 using Fast Spherical Collocation (FSC), with a global covariance function. Both, a grid of noise-free data and a grid obtained from the data with noise were used. Both results agreed with EGM96 within the error-bounds of the FSC estimate.