A new degree-2190 (10 km resolution) gravity field model for Antarctica developed from GRACE, GOCE and Bedmap2 data

Abstract

The current high-degree global geopotential models EGM2008 and EIGEN-6C4 resolve gravity field structures to $\sim$10 km spatial scales over most parts of the of Earth’s surface. However, a notable exception is continental Antarctica, where the gravity information in these and other recent models is based on satellite gravimetry observations only, and thus limited to about $\sim$80–120 km spatial scales. Here, we present a new degree-2190 global gravity model (GGM) that for the first time improves the spatial resolution of the gravity field over the whole of continental Antarctica to $\sim$10 km spatial scales. The new model called SatGravRET2014 is a combination of recent Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite gravimetry with gravitational signals derived from the 2013 Bedmap2 topography/ice thickness/bedrock model with gravity forward modelling in ellipsoidal approximation. Bedmap2 is a significantly improved description of the topographic mass distribution over the Antarctic region based on a multitude of topographic surveys, and a well-suited source for modelling short-scale gravity signals as we show in our study. We describe the development of SatGravRET2014 which entirely relies on spherical harmonic modelling techniques. Details are provided on the least-squares combination procedures and on the conversion of topography to implied gravitational potential. The main outcome of our work is the SatGravRET2014 spherical harmonic series expansion to degree 2190, and derived high-resolution grids of 3D-synthesized gravity and quasigeoid effects over the whole of Antarctica. For validation, six data sets from the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) database were used comprising a total of 1,092,981 airborne gravimetric observations. All subsets consistently show that the Bedmap2-based short-scale gravity modelling improves the agreement over satellite-only data considerably (improvement rates ranging between 9 and 75 % with standard deviations from residuals between SatGravRET2014 and AntGG gravity ranging between 8 and 25 mGal). For comparison purposes, a degree-2190 GGM was generated based on the year-2001 Bedmap1 (using the ETOPO1 topography) instead of 2013 Bedmap2 topography product. Comparison of both GGMs against AntGG consistently reveals a closer fit over all test areas when Bedmap2 is used. This experiment provides evidence for clear improvements in Bedmap2 topographic information over Bedmap1 at spatial scales of $\sim$80–10 km, obtained from independent gravity data used as validation tool. As a general conclusion, our modelling effort fills—in approximation—some gaps in short-scale gravity knowledge over Antarctica and demonstrates the value of the Bedmap2 topography data for short-scale gravity refinement in GGMs. SatGravRET2014 can be used, e.g. as a reference model for future gravity modelling efforts over Antarctica, e.g. as foundation for a combination with the AntGG data set to obtain further improved gravity information.

Appendix

The fully normalized sinusoidal Legendre weight functions $\overline{K} _{nm}^{2i,2j}$ in Eq. (4) can be computed via various recursive schemes (Claessens 2005)

$$\begin{aligned}&\overline{K} _{nm}^{2i,2j} =\mathop \sum \limits _{k=-1}^1 \overline{K} _{nm}^{2i-2k,2j-2} \overline{K} _{n+2i-2k,m}^{2k,2}\end{aligned}$$

(15)

$$\begin{aligned}&\overline{K}_{nm}^{2i,2j} =\mathop \sum \limits _{k=-1}^1 \overline{K}_{nm}^{2k,2} \overline{K} _{n+2k,m}^{2i-2k,2j-2}\end{aligned}$$

(16)

$$\begin{aligned}&\overline{K} _{nm}^{2i,2j} =\mathop \sum \limits _{k=-1}^1 \overline{K} _{nm}^{2i+2k,2j-2} \overline{K} _{n+2i,m}^{2k,2} \end{aligned}$$

(17)

where (17) follows from (15) and the relation

$$\begin{aligned} \overline{K} _{nm}^{2i,2j} =\overline{K} _{n+2i,m}^{-2i,2j} \end{aligned}$$

(18)

Equations (15)–(17) can all be used to compute the function $\overline{K} _{nm}^{2i,2j}$ for any pair of iand jfrom the initial values

$$\begin{aligned}&\overline{K} _{nm}^{-2,2} =-\sqrt{\frac{( {n^2-m^2})[( {n+1})^2-m^2]}{( {2n-3})( {2n-1})^2(2n+1)}}\end{aligned}$$

(19)

$$\begin{aligned}&\overline{K} _{nm}^{0,2} =\frac{2(n^2+m^2+n-1)}{( {2n-1})(2n+3)}\end{aligned}$$

(20)

$$\begin{aligned}&\overline{K} _{nm}^{2,2} =-\sqrt{\frac{[( {n+1})^2-m^2][( {n+2})^2-m^2]}{( {2n+1})( {2n+3})^2(2n+5)}} \end{aligned}$$

(21)