<p>The existing observation record of satellite gravity missions is already closing in on the minimum time series of 30 years needed to decouple natural and anthropogenic forcing mechanisms according to the Global Climate Observing System (GCOS). The launch of the next generation of gravity field missions [Gravity Recovery and Climate Experiment (GRACE)-Continuity, Next Generation Gravity Mission] is expected within this decade. These missions and their combination (Mass-Change and Geosciences International Constellation [MAGIC)] are setting high anticipation for an enhanced monitoring capability that will significantly improve the spatial and temporal resolution of gravity observations. This study investigates and compares the performance of three different trend estimation strategies for the first time in multi-decadal numerical closed-loop simulations of satellite gravimetry constellations. The considered satellite constellations are a GRACE-type in-line single pair mission and a MAGIC double pair mission with realistic noise assumptions for the key payload, tidal, and non-tidal background model errors. The parameter models used in this study consist of monthly solutions (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>), co-estimation of monthly and trend parameters (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>), and the direct estimation of trend and annual amplitudes (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>). Thirty years of modeled mass transport time series of components of the terrestrial water storage, obtained from future climate projections, form the gravity signal used in the simulations. Our results show the potential of MAGIC’s advanced observation system in estimating a long-term trend. After 10 years, the global root-mean-square error of the trend estimates for the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> parameter model improves from a single pair performance of 59.6–1.2 mm/yr for a double pair constellation. While the improved observation system mainly contributes to the higher resolution, direct trend estimation strategies can achieve minor but visible improvements. Since all three parameter models show globally comparable results, they are further analyzed regionally by dividing the world into 206 hydrological basins. Small basins and areas with low signal-to-noise ratio show slight improvements in the residuals. For example, after 10 years of observation, a single pair shows 1 mm/yr improvements for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> compared to <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. Furthermore, the regional analysis shows that a significant number of basins have a higher signal-to-noise ratio than the global average. These basins would benefit from trend estimates of higher degree and order, which is possible by directly estimating the trend coefficients with <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, but not with the trend estimation from monthly solutions (<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40623_2025_2239_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">${f}_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>).</p> Graphical Abstract <p></p>

Resolving climate-related mass transport trends: a parameter model comparison using closed-loop simulations of current and future satellite gravity missions

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2025年7月1日

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Marius Schlaak,
Roland Pail

摘要

The existing observation record of satellite gravity missions is already closing in on the minimum time series of 30 years needed to decouple natural and anthropogenic forcing mechanisms according to the Global Climate Observing System (GCOS). The launch of the next generation of gravity field missions [Gravity Recovery and Climate Experiment (GRACE)-Continuity, Next Generation Gravity Mission] is expected within this decade. These missions and their combination (Mass-Change and Geosciences International Constellation [MAGIC)] are setting high anticipation for an enhanced monitoring capability that will significantly improve the spatial and temporal resolution of gravity observations. This study investigates and compares the performance of three different trend estimation strategies for the first time in multi-decadal numerical closed-loop simulations of satellite gravimetry constellations. The considered satellite constellations are a GRACE-type in-line single pair mission and a MAGIC double pair mission with realistic noise assumptions for the key payload, tidal, and non-tidal background model errors. The parameter models used in this study consist of monthly solutions ( ${f}_{0}$ $f_{0}$ ), co-estimation of monthly and trend parameters ( ${f}_{1}$ $f_{1}$ ), and the direct estimation of trend and annual amplitudes ( ${f}_{2}$ $f_{2}$ ). Thirty years of modeled mass transport time series of components of the terrestrial water storage, obtained from future climate projections, form the gravity signal used in the simulations. Our results show the potential of MAGIC’s advanced observation system in estimating a long-term trend. After 10 years, the global root-mean-square error of the trend estimates for the ${f}_{0}$ $f_{0}$ parameter model improves from a single pair performance of 59.6–1.2 mm/yr for a double pair constellation. While the improved observation system mainly contributes to the higher resolution, direct trend estimation strategies can achieve minor but visible improvements. Since all three parameter models show globally comparable results, they are further analyzed regionally by dividing the world into 206 hydrological basins. Small basins and areas with low signal-to-noise ratio show slight improvements in the residuals. For example, after 10 years of observation, a single pair shows 1 mm/yr improvements for ${f}_{2}$ $f_{2}$ compared to ${f}_{0}$ $f_{0}$ . Furthermore, the regional analysis shows that a significant number of basins have a higher signal-to-noise ratio than the global average. These basins would benefit from trend estimates of higher degree and order, which is possible by directly estimating the trend coefficients with ${f}_{1}$ $f_{1}$ or ${f}_{2}$ $f_{2}$ , but not with the trend estimation from monthly solutions ( ${f}_{0}$ $f_{0}$ ).

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