A new method for determining geoid gradient components from SWOT wide-swath data for marine gravity field

Abstract The Surface Water and Ocean Topography (SWOT) altimeter mission provides a significant opportunity to improve the accuracy of geoid gradients (GGs) and marine gravity fields. This paper presents a new method, namely LSA3, to determine the north and east ( $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> and $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> ) components of GGs from simulated and real SWOT data in the northern South China Sea. To fully use SWOT’s fine-scale sea surface height (SSH) measurements, LSA3 first determines GGs in SWOT along-, cross- and oblique-track directions and constructs a grid for each gradient. Least-squares adjustment (LSA), accounting for correlations of the GGs in three directions, is then employed to point-wisely estimate $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> and $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> components at grid points. The accuracy of estimated $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> and $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> components is assessed using those computed by numerical differentiations. For comparison, GG components are also estimated using least-squares collocation (LSC) and weighted LSA (WLSA) methods with empirically determined data window sizes and without accounting for correlations. Simulated results show that LSA3-estimated GG components achieve the root-mean-square deviation (RMSD) values of 0.43 and 0.47 microrad for $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> and $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> , respectively, outperforming LSC (0.82 and 0.86 microrad) and WLSA (0.49 and 0.54 microrad). The results from the real SWOT data indicate that LSA3 is comparable to LSC with a mean RMSD of 1.88 mgal for marine gravity anomalies when compared to shipborne gravity data, but LSA3 is more computationally efficient than LSC. Compared to the Sandwell V32.1 gravity field, SWOT improves gravity accuracy by an average of 12.0%, with a maximum improvement of 44.3% for a single ship trajectory.