<p>Next Generation Gravity Missions (NGGMs) aim to extend and refine the legacy of Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) by improving the temporal and spatial resolution of gravity field observations. To explore processing strategies for this enhanced data quality, this study presents a unified simulation framework for evaluating mass concentration (mascon) based gravity field recovery under consistent GRACE-like conditions, using Earth System Model (ESM) based synthetic data from October 2002. The Earth’s gravity field is modeled at approximately 222 km resolution. Three mascon approaches, Point Masses (PM), Lumped Spherical Harmonics (LSH), and Spherical Caps (SC), are assessed within a regularized least squares framework. All approaches demonstrate high fidelity in reconstructing the reference signal, with global Root Mean Square Error (RMSE) between 21 and 22 mm in terms of Equivalent Water Height (EWH), suggesting limited impact of the mascon base function on overall performance. However, regional differences emerge. For example, deviations of up to 32 mm in the Amazon Basin highlight a fundamental trade-off between preserving signal amplitude and suppressing artifacts. Finer grids enhance local resolution and reduce leakage but also increase the condition number up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$10^{15}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>15</mn> </msup> </math></EquationSource> </InlineEquation>, requiring stronger regularization. While strong regularization can reduce the condition number by up to 12 orders of magnitude (to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$10^3$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>), similar stability, from <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$3.4 \cdot 10^{7}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.4</mn> <mo>·</mo> <msup> <mn>10</mn> <mn>7</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> to 160.4, can be achieved by coarsening the grid from 222  to 666 km, thus avoiding explicit regularization. This highlights the need for targeted investigation into optimal grid design and regularization. A regional case study over the Amazon Basin demonstrates that tailored grid designs can mitigate typical limitations of global spherical harmonic models, such as signal leakage and global constraints, albeit with increased numerical challenges. The similar performance across methods further emphasizes the point mass approach, which, due to its simplicity and lowest algorithmic complexity, is particularly suitable for high-resolution grids. Overall, model quality depends less on the choice of base function than on the interplay between grid design, regularization, and numerical conditioning, which are key levers for advancing regionalized and application-driven gravity field modeling with future NGGMs data.</p> Graphical Abstract <p></p>

Mascon-based temporal gravity field recovery: evaluation and comparative analysis of different approaches

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2026年3月25日

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Simon Roland Franz Schiller,
Huiyi Wu,
Marius Schlaak,
Roland Pail

摘要

Next Generation Gravity Missions (NGGMs) aim to extend and refine the legacy of Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) by improving the temporal and spatial resolution of gravity field observations. To explore processing strategies for this enhanced data quality, this study presents a unified simulation framework for evaluating mass concentration (mascon) based gravity field recovery under consistent GRACE-like conditions, using Earth System Model (ESM) based synthetic data from October 2002. The Earth’s gravity field is modeled at approximately 222 km resolution. Three mascon approaches, Point Masses (PM), Lumped Spherical Harmonics (LSH), and Spherical Caps (SC), are assessed within a regularized least squares framework. All approaches demonstrate high fidelity in reconstructing the reference signal, with global Root Mean Square Error (RMSE) between 21 and 22 mm in terms of Equivalent Water Height (EWH), suggesting limited impact of the mascon base function on overall performance. However, regional differences emerge. For example, deviations of up to 32 mm in the Amazon Basin highlight a fundamental trade-off between preserving signal amplitude and suppressing artifacts. Finer grids enhance local resolution and reduce leakage but also increase the condition number up to $10^{15}$ $10^{15}$ , requiring stronger regularization. While strong regularization can reduce the condition number by up to 12 orders of magnitude (to $10^3$ $10^{3}$ ), similar stability, from $3.4 \cdot 10^{7}$ $3.4 \cdot 10^{7}$ to 160.4, can be achieved by coarsening the grid from 222 to 666 km, thus avoiding explicit regularization. This highlights the need for targeted investigation into optimal grid design and regularization. A regional case study over the Amazon Basin demonstrates that tailored grid designs can mitigate typical limitations of global spherical harmonic models, such as signal leakage and global constraints, albeit with increased numerical challenges. The similar performance across methods further emphasizes the point mass approach, which, due to its simplicity and lowest algorithmic complexity, is particularly suitable for high-resolution grids. Overall, model quality depends less on the choice of base function than on the interplay between grid design, regularization, and numerical conditioning, which are key levers for advancing regionalized and application-driven gravity field modeling with future NGGMs data.

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