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-title: 'PySHbundle: A Python implementation of GRACE Spherical Harmonics Synthesis MATLAB codes SHbundle'
+title: 'PySHbundle: A Python software to convert GRACE Spherical Harmonic Coefficients to gridded mass change fields'
 tags:
   - Python
   - GRACE
@@ -67,7 +67,7 @@ bibliography: paper.bib
 
 # Introduction
 
-GRACE stands for the Gravity Recovery and Climate Experiment, a joint satellite mission by the National Aeronautics and Space Administration (`NASA`) in the USA, and the Geoforschung Zentrum (`GFZ`) in Germany. GRACE mission launced on 17 March, 2002, and ended on 27 October, 2017. Some details of the GRACE mission are provided in `Table 1`. GRACE has a successor, GRACE-FO, which was successfully launched on 22 May 2018 and is currently operational. GRACE consists of two identical satellites in the same orbit separated by approx. 220 km. The mission measures changes in the intersatellite distance with a microwave ranging system that gives an accuracy in the range of micrometers [@wahr1998time]. When the satellite system comes in the vicinity of a temporal mass anomaly, the relative intersatellite 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]. Some of the unwanted signals, such as the high frequency tidal mass changes in the ocean and the atmosphere, are modelled and removed at level 1 processing `(Flechtner, 2007)`, while noise is still present at level 2 and it requires filtering [@wahr1998time; @vishwakarma2017understanding]. The choice of filter and/or subsequent steps to counter the signal loss due to filtering have an impact on the quality of GRACE products that are of interest to hydrologists [@humphrey2023using; vishwakarma2020monitoring]. The estimated hydrological signal is represented in terms of  `total water storage anomaly` (`TWSA`), which is the change in the water mass over a vertical column. Conventionally, it is represented in terms of `equivalent water height` (`m`). <br>
+GRACE stands for the Gravity Recovery and Climate Experiment, a joint satellite mission by the National Aeronautics and Space Administration (`NASA`) in the USA, and the Geoforschung Zentrum (`GFZ`) in Germany. GRACE mission launced on 17 March, 2002, and ended on 27 October, 2017. Some details of the GRACE mission are provided in `Table 1`. GRACE has a successor, GRACE-FO, which was successfully launched on 22 May 2018 and is currently operational. GRACE consists of two identical satellites in the same orbit separated by approx. 220 km. The mission measures changes in the intersatellite distance with a microwave ranging system that gives an accuracy in the range of micrometers [@wahr1998time]. When the satellite system comes in the vicinity of a temporal mass anomaly, the relative intersatellite 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]. Some of the unwanted signals, such as the high frequency tidal mass changes in the ocean and the atmosphere, are modelled and removed at level 1 processing [@flechtner2007aod1b], while noise is still present at level 2 and it requires filtering [@wahr1998time; @vishwakarma2017understanding]. The choice of filter and/or subsequent steps to counter the signal loss due to filtering have an impact on the quality of GRACE products that are of interest to hydrologists [@humphrey2023using; @vishwakarma2020monitoring]. The estimated hydrological signal is represented in terms of  `total water storage anomaly` (`TWSA`), which is the change in the water mass over a vertical column. Conventionally, it is represented in terms of `equivalent water height` (`m`). <br>
 
 <i>Table 1: Summary of GRACE satellite mission [[source]](https://www2.csr.utexas.edu/grace/mission/mdetail.html)</i>
 
@@ -82,7 +82,7 @@ GRACE stands for the Gravity Recovery and Climate Experiment, a joint satellite
 
 Various research centers provide GRACE data, such as the University of Texas Center for Space Research (`CSR`), Jet Propulsion Laboratory (`JPL`), and the German Research Center for Geosciences (`GFZ`) and so on. `Level 2` data products are the spherical harmonic coefficients representing the mean monthly gravity field of the Earth. `Level 3` consists of gridded mass anomalies or other standardized products, such as the Monthly Ocean/Land Water Equivalent Thickness Surface-Mass Anomaly. Obtaining `level 3` products from `level 2` requires filtering that affects the signal quality and resolution, which is why another suite of products called mass concentration blocks or `mascons` are also available that are designed to take care of signal degradation due to filtering inherently. More details on the mascon approaches for studying gravity fields and the approaches used by the different data centers for generating mascon products may be referred to in [@antoni2022review]. Mascon products from various centres differ due to the difference in the post-processing strategy used by these centres, which emphasizes that the processing choices have an impact of the gridded GRACE data. Processing `Level 2` data gives the user the freedom and the flexibility to explore GRACE data for a specific application over a specific region as per their convenience and belief. <br>
 
-Converting spherical harmonic coefficients (`level 2`) to gridded field (`level 3`) is called spherical harmonic synthesis and vice-versa is spherical harmonic analysis. `Level 3` products may further be processed to obtain region-averaged timeseries data, labelled as `Level 4` products. Various tools exist to process GRACE data and to analyze it. Some of these are developed in the `MATLAB` programming language: [`SHbundle`](https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle) (`Sneew et al., 2021`), [`GRACE Data Driven Correction`](https://www.gis.uni-stuttgart.de/en/research/downloads/datadrivencorrectionbundle) [@vishwakarma2017understanding],  [`LUH-GRACE2018`](https://www.ife.uni-hannover.de/en/services/luh-grace) [@koch2020luh], [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) [@feng2019gramat], [`SHADE`](https://www.sciencedirect.com/science/article/pii/S0098300418302760) [@piretzidis2018shade], [`GRACETOOLS`](https://www.mdpi.com/2076-3263/8/9/350) [@darbeheshti2018gracetools], [`SSAS GRACE filter`](https://github.com/shuang-yi/SSAS-GRACE-filter)(`Yi & Sneeuw, 2022`), etc. Similarly, some GRACE data processing tools are also available based on the python programming language. These include [`gravity-toolkit`](https://gravity-toolkit.readthedocs.io/en/latest/) `(Sutterley, 2023)`, [`ggtools`](https://pypi.org/project/ggtools/1.1.0/) [@ggtools] and [`GRACE-filter`](https://github.com/strawpants) `(Rietbroek, n.a.)`. 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 `spheric harmonic analysis`. The first version of the code was developed in 1994 while the latest version with upgrades can be found dated 2018. [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) provides a similar MATLAB-based scripts for processing GRACE spherical harmonics data to obtain spatiotemporal global mass variations. The [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) toolbox includes Gaussian smoothening filter to reduce noise that appears strongly as North-South stripes, spherical harmonic analysis and synthesis routines, signal leakage reduction routines, harmonic analysis of times series over regions, and uncertainty analysis of GRACE estimates [feng2019gramat]. [`SHADE`](https://www.sciencedirect.com/science/article/pii/S0098300418302760) provides a MATLAB-based toolbox for the empirical de-correlation of GRACE monthly spherical harmonics (`Piretzidis & Sideris, 2018`). [`Gravity-toolkit`](https://gravity-toolkit.readthedocs.io/en/latest/) is a python-based package meant to handle GRACE L2 data products. Its functionalities include visualization of GRACE and GRACE-FO L2 data products, and the estimation of GRACE and GRACE-FO L2 data product errors. [`Gg-tools`](https://pypi.org/project/ggtools/1.1.0/) too contain similar tools for signal correction and for conversion of GRACE L2 products to L3. `GRACE-filter` provides tool for filtering of GRACE L2 product using DDK filter based on `Kusche et al., (2009)`.
+Converting spherical harmonic coefficients (`level 2`) to gridded field (`level 3`) is called spherical harmonic synthesis and vice-versa is spherical harmonic analysis. `Level 3` products may further be processed to obtain region-averaged timeseries data, labelled as `Level 4` products. Various tools exist to process GRACE data and to analyze it. Some of these are developed in the `MATLAB` programming language: [`SHbundle`](https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle) [@SHbundle], [`GRACE Data Driven Correction`](https://www.gis.uni-stuttgart.de/en/research/downloads/datadrivencorrectionbundle) [@vishwakarma2017understanding],  [`LUH-GRACE2018`](https://www.ife.uni-hannover.de/en/services/luh-grace) [@koch2020luh], [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) [@feng2019gramat], [`SHADE`](https://www.sciencedirect.com/science/article/pii/S0098300418302760) [@piretzidis2018shade], [`GRACETOOLS`](https://www.mdpi.com/2076-3263/8/9/350) [@darbeheshti2018gracetools], [`SSAS GRACE filter`](https://github.com/shuang-yi/SSAS-GRACE-filter)[@yi2022novel], etc. Similarly, some GRACE data processing tools are also 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 [`GRACE-filter`](https://github.com/strawpants) `[@GRACE-filter]`. 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 `spheric harmonic analysis`. The first version of the code was developed in 1994 while the latest version with upgrades can be found dated 2018. [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) provides a similar MATLAB-based scripts for processing GRACE spherical harmonics data to obtain spatiotemporal global mass variations. The [`GRAMAT`](https://link.springer.com/article/10.1007/s12145-018-0368-0) toolbox includes Gaussian smoothening filter to reduce noise that appears strongly as North-South stripes, spherical harmonic analysis and synthesis routines, signal leakage reduction routines, harmonic analysis of times series over regions, and uncertainty analysis of GRACE estimates [@feng2019gramat]. [`SHADE`](https://www.sciencedirect.com/science/article/pii/S0098300418302760) provides a MATLAB-based toolbox for the empirical de-correlation of GRACE monthly spherical harmonics ([@piretzidis2018shade]). [`Gravity-toolkit`](https://gravity-toolkit.readthedocs.io/en/latest/) is a python-based package meant to handle GRACE L2 data products. Its functionalities include visualization of GRACE and GRACE-FO L2 data products, and the estimation of GRACE and GRACE-FO L2 data product errors. [`Gg-tools`](https://pypi.org/project/ggtools/1.1.0/) too contain similar tools for signal correction and for conversion of GRACE L2 products to L3. `GRACE-filter` provides tool for filtering of GRACE L2 product using DDK filter based on [@kusche2009decorrelated].
 
 # Statement of need
 A comprehensive MATLAB code bundle already exists called [`SHbundle`](https://www.gis.uni-stuttgart.de/en/research/downloads/shbundle) developed by [@SHbundle] and distributed under the GNU license. The code bundle can be freely used and modified by anyone giving proper credit to the original developers. However, MATLAB being a proprietary software may have some limitations in terms of accessibility.<br>