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abstract = {Abstract We discuss several classes of improvements to gravity solutions from the Gravity Recovery and Climate Experiment (GRACE) mission. These include both improvements in background geophysical models and orbital parameterization leading to the unconstrained spherical harmonic solution JPL RL05, and an alternate JPL RL05M mass concentration (mascon) solution benefitting from those same improvements but derived in surface spherical cap mascons. The mascon basis functions allow for convenient application of a priori information derived from near-global geophysical models to prevent striping in the solutions. The resulting mass flux solutions are shown to suffer less from leakage errors than harmonic solutions, and do not necessitate empirical filters to remove north-south stripes, lowering the dependence on using scale factors (the global mean scale factor decreases by 0.17) to gain accurate mass estimates. Ocean bottom pressure (OBP) time series derived from the mascon solutions are shown to have greater correlation with in situ data than do spherical harmonic solutions (increase in correlation coefficient of 0.08 globally), particularly in low-latitude regions with small signal power (increase in correlation coefficient of 0.35 regionally), in addition to reducing the error RMS with respect to the in situ data (reduction of 0.37 cm globally, and as much as 1 cm regionally). Greenland and Antarctica mass balance estimates derived from the mascon solutions agree within formal uncertainties with previously published results. Computing basin averages for hydrology applications shows general agreement between harmonic and mascon solutions for large basins; however, mascon solutions typically have greater resolution for smaller spatial regions, in particular when studying secular signals.},
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# Summary
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`GRACE` (Gravity Recovery and Climate Experiment) satellite mission has been mapping mass changes near the surface of the Earth since 2002. One of the major mechanisms of short term mass transport is the redistribution of water, GRACE has significantly influenced Geosciences. GRACE satellite products are typically released at various levels of complexity, often referred to as processing levels. Level 1 is the satellite instrument data that is processed to obtain Level 2 (`L2`) GRACE Spherical Harmonics data. `L2` are further processed to obtain Level 3 products; global gridded mass change estimates (`L3`) expressed as terrestrial water storage anomalies (`TWSA`). The L2 spherical harmonic data are typically noisy, which necessitates the use of spectral filtering. The data also have to be corrected for known artifacts and contaminating geophysical signals, such as solid Earth processes in the case of isolating TWSA. Processing choices, such as filter properties and type, have a significant impact on the accuracy and the resolution of final gridded output. Therefore, most `L3` users must be cautious when using GRACE data for specific applications. The majority of the GRACE data user community is not well versed with `L2` data processing, and most often use the off-the-shelf `L3` products. Here we developed an open-source processing toolbox to provide users with more control over processing choices. A python module, called PySHbundle, was developed to ease the conversion of GRACE `L2` Spherical Harmonics data products to `L3` `TWSA` products. With this contribution, we hope to enable further usage of GRACE data for Earth system science.
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`GRACE` (Gravity Recovery and Climate Experiment) satellite mission has been mapping mass changes near the surface of the Earth since 2002. One of the major mechanisms of short term mass transport is the redistribution of water, GRACE has significantly influenced Geosciences. GRACE satellite products are typically released at various levels of complexity, often referred to as processing levels. Level 1 is the satellite instrument data that is processed to obtain Level 2 (`L2`) the Spherical harmonic coefficients and standard deviations of the static gravity field, for a particular time period. `L2` are further processed to obtain Level 3 products; global gridded mass change estimates (`L3`) expressed as terrestrial water storage anomalies (`TWSA`). The `L2` spherical harmonic data are typically noisy, which necessitates the use of spectral filtering. The data also have to be corrected for known artifacts and contaminating geophysical signals, such as solid Earth processes in the case of isolating TWSA. Processing choices, such as filter properties and type, have a significant impact on the accuracy and the resolution of final gridded output. Therefore, most `L3` users must be cautious when using GRACE data for specific applications. The majority of the GRACE data user community is not well versed with `L2` data processing, and most often use the off-the-shelf `L3` products. Here we developed an open-source processing toolbox to provide users with more control over processing choices. A python module, called PySHbundle, was developed to ease the conversion of GRACE `L2` Spherical Harmonics data products to `L3` `TWSA` products. With this contribution, we hope to enable further usage of GRACE data for Earth system science.
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# Introduction
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The NASA/DLR GRACE and NASA/GFZ GRACE-FO twin satellite missions measure changes in the Earth's gravitational field by measuring their inter-satellite distance. Changes in the local gravity field affect the orbit of each satellite, which is recorded with the onboard ranging system [@wahr1998time]. When the satellite pair comes in the vicinity of a temporal mass anomaly, the relative inter-satellite distance changes and it can be inverted to estimate the mass change near the surface of the Earth. Over the continental land surface, the hydrological processes are the major driver of the variation in mass anomaly at monthly to decadal scales. However various other signals such as oceanic and atmospheric variations, high frequency tidal mass changes, systemic correlated errors, etc. are also part of the obtained GRACE signals [@humphrey2023using].
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Several researchers in Geosciences use level three GRACE data, which is obtained from `L2` Spherical harmonic coefficients, except JPL MASCONS which are derived from Level-1B satellite ranges. The procedure to convert `L2` to `L3` is called spherical harmonic synthesis. However, there are several pre-processing steps; such as anomaly calculation, replacing poor quality low degree coefficients, filtering, and correcting for signal damage due to filtering.
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Several researchers in Geosciences use level three GRACE data, which is obtained from `L2` Spherical harmonic coefficients, except JPL MASCONS which are derived from Level-1B satellite ranges@watkins2015mascons. The procedure to convert `L2` to `L3` is called spherical harmonic synthesis. However, there are several pre-processing steps; such as anomaly calculation, replacing poor quality low degree coefficients, filtering, and correcting for signal damage due to filtering.
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A few GRACE data processing tools are available based on the python programming language. These include [`gravity-toolkit`](https://gravity-toolkit.readthedocs.io/en/latest/)[@gravity-toolkit], [`ggtools`](https://pypi.org/project/ggtools/1.1.0/)[@ggtools] and [`shxarray`](https://github.com/ITC-Water-Resources/shxarray)[@shxarray]. General tools for spheric harmonic analysis are also available, such as [`SHTools`](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GC007529)[@wieczorek2018shtools]. [`SHbundle`](https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle) provide MATLAB scripts for Spheric Harmonic Synthesis and Spherical Harmonic Analysis. The first version of the code was developed in 1994 while the latest version was released in 2021.
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A few GRACE data processing tools are available based on the Python programming language. These include [`gravity-toolkit`](https://gravity-toolkit.readthedocs.io/en/latest/)[@gravity-toolkit], [`ggtools`](https://pypi.org/project/ggtools/1.1.0/)[@ggtools] and [`shxarray`](https://github.com/ITC-Water-Resources/shxarray)[@shxarray]. General tools for spheric harmonic analysis are also available, such as [`SHTools`](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GC007529)[@wieczorek2018shtools]. [`SHbundle`](https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle) provide MATLAB scripts for Spheric Harmonic Synthesis and Spherical Harmonic Analysis. The first version of the code was developed in 1994 while the latest version was released in 2021.
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# Statement of need
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4.`shutils`: Helper scripts for applying `pysh_core`.
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Based on the main modules, we provide examples as jupyter notebooks for understanding and using spherical harmonics data and the package.
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The accuracy of the core capabilites of pyshbundle was evaluated against the MATLAB software SHbundle. For more details please see the jupyter notebook `examples/validation_pyshbundle.ipynb` and the corresponding python unit tests in `tests/`.
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# Acknowledgements
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The authors would like to thank Dr.-Ing. Markus Antoni and Clara Buetzler, Institute of Geodesy, University of Stuttgart, Germany, for early feedback. We are grateful for the financial support from IISc-ISRO Space Technology Cell for funding the project titled "Improving the spatial resolution of GRACE TWS for India using remote sensing datasets and modeling approach" under grant number STC0437. BDV would like to acknowledge the financial support from Science and Engineering Research Board, Government of India, under the grand agreement number SRG/2022/000625 for the MATRA project.
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The authors would like to thank Dr.-Ing. Markus Antoni and Clara Buetzler, Institute of Geodesy, University of Stuttgart, Germany, for early feedback. We are grateful for the financial support from IISc-ISRO Space Technology Cell for funding the project titled "Improving the spatial resolution of GRACE TWS for India using remote sensing datasets and modeling approach" under grant number STC0437. BDV would like to acknowledge the financial support from Science and Engineering Research Board, Government of India, under the grant agreement number SRG/2022/000625 for the MATRA project.
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