paper.md

title	tags	authors	affiliations	date	bibliography
PySHbundle: A Python software to convert GRACE Spherical Harmonic Coefficients to gridded mass change fields	Python GRACE Spherical Harmonic Analysis Spherical Harmonic Synthesis GRACE Data Driven Correction	name orcid equal-contrib corresponding affiliation Vivek Kumar Yadav 0009-0000-7156-4450 true true 1 name orcid equal-contrib affiliation Amin Shakya 0000-0002-4706-826X true 1,2 name orcid equal-contrib affiliation Abhishek Mhamane 0000-0001-9788-0371 true 3 name orcid affiliation Tsungrojungla Walling 0009-0006-9323-1191 4 name affiliation Shard Chander 5 name affiliation Bhaskar R. Nikam 6 name orcid affiliation Nagesh Kumar Dasika 0009-0006-9323-1191 7 name orcid affiliation Bramha Dutt Vishwakarma 0000-0003-4787-8470 2,8	name index Interdisciplinary Centre for Water Research, Indian Institute of Science, India 1 name index Faculty of Geo-Information Science and Earth Observation, University of Twente, the Netherlands 2 name index National Centre for Geodesy, Indian Institute of Technology Kanpur, India 3 name index Undergraduate Programme, Indian Institute of Science, India 4 name index Land Hydrology Division, Space Applications Centre, Indian Space Research Organisation, India 5 name index Earth Observation Applications & Disaster Management Support Programme Office (EDPO), Indian Space Research Organisation, India 6 name index Department of Civil Engineering, Indian Institute of Science, India 7 name index Centre of Earth Science, Indian Institute of Science, India 8	15 November 2023	paper.bib

Summary

GRACE (Gravity Recovery and Climate Experiment) satellite mission has been mapping mass changes near the surface of the Earth since 2002. Since mass redistribution at shorter temporal scales is dominated by water mass transfer, GRACE has transformed 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 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). L2 data are noisy, which are filtered and corrected for known artifacts and signals from solid Earth processes to obtain L3 products that are useful for hydrology. Processing choices, such as filter properties and type, have a significant impact on the accuracy and the resolution of final gridded output. Therefore, L3 users must be cautious when using GRACE data for specific applications. Majority of the GRACE data user community is not well versed with L2 data processing, and often use off the shelf L3 product. Here we developed an open-source processing toolbox to provide users with more control over processing choices. A python module, called PySHbundle, is developed that converts 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.

Introduction

GRACE Satellite mission measures changes in the inter-satellite distance with a microwave ranging system micrometer precision [@wahr1998time]. When the satellite system 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].

several researchers in Jio sciences use level three GRACE data, which is obtained from L2 Spherical harmonic coefficients. 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.

A few GRACE data processing tools are available based on the python programming language. These include gravity-toolkit [@gravity-toolkit], ggtools [@ggtools] and GRACE-filter [@GRACEfilter]. General tools for spheric harmonic analysis are also available, such as SHTools [@wieczorek2018shtools]. 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.

Statement of need

Processing choices introduce subtle differences in the final product, potentially affecting results. Processing L2 data offers flexibility for users to explore GRACE data for specific applications. This software aims to simplify access to L2 products, allowing users to select different processing options.

The software processes widely used L2 products from CSR, JPL, and GFZ. It closely follows the structure of the Matlab-based SHbundle and GRACE Data Driven Correction (GDDC)[@vishwakarma2017data] codes, enabling cross-compatibility between Python and Matlab users.

PySHbundle is modular, offering tools to process GRACE data, including anomaly computation, low-degree coefficient substitution, noise reduction, and signal leakage correction. It supports future development for hydrological applications.

By using Python and the GNU license, the package is accessible globally and aligns with the FAIR principles. We aim to reduce technical and financial barriers, making it useful for researchers, students, and educational programs like the GRACE Hackweek at IIT Kanpur.

Implementation

Mathematical details of the steps involved can be referred in [@vishwakarma2017understanding]. Accordingly, the package consists of four main modules, io, vizutils, pysh_core and shutils.

1. io: extract the L2 coefficients from any of JPl, CSR and ITGZ solutions. Followed by replacing the poorly measured degree 1, 2 and 3 spherical harmonics coefficients with recommended datasets.

2. vizutils: plots the L2 data to visually understand the coefficients, their uncertainties, mathematical functions used for further processing.

3. pysh_core: Scripts for the global spherical harmonics synthesis gshs to convert the L2 data to global gridded TWSA data (L3). Calculating signal leakage (gddc), and basin-scale average (Basinaverage).

4. shutils: Helper scripts for applying pysh_core. Based on the main modules, we provide examples as jupyter notebooks for understanding and using spherical harmonics data and the package.

Acknowledgements

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.

Future Plan

The package will be under continuous development to process data from more research centres, add more filtering and processing algorithms.

References