Contributors: S. B. Simonsen (Technical University of Denmark), V. R. Barletta (Technical University of Denmark)

Issued by: Technical University of Denmark / Sebastian B. Simonsen

Date: 05/05/2023

Ref: C3S2_312a_Lot4.WP2-FDDP-IS-v1_202212_GMB_ATBD-v4_i1.1

Official reference number service contract: 2021/C3S2_312a_Lot4_EODC/SC1

History of modifications

List of datasets covered by this document

Related documents

Acronyms

General definitions

Brokered Product: A brokered product is a pre-existing dataset to which the Copernicus Climate Change Service (C3S) acquires a license, for the purpose of including it in the Climate Data Store (CDS).

Generated Product: A generated product is a dataset made specifically for C3S, for the purpose of including it in the CDS.

Glacial Isostatic Adjustment (GIA): Glacial isostatic adjustment describes the response of the gravitational field, solid Earth and the ocean to the growth and decay of the global ice sheets.

Gravimetric Mass Balance (GMB): The mass balance of an ice sheet is the net difference between mass gained from snow deposition and mass lost by melting or iceberg calving. This is essentially the same as the mass change of the ice sheet. When mass balance is derived from measured changes in the Earth's gravitational field, this is referred to as a gravimetric mass balance.

Scope of the document

The Copernicus Ice Sheets and Ice Shelves service addresses three essential climate variables (ECVs) by providing four separate products.

• Ice velocity is given for Greenland in product WP2-FDDP-IV-CDR
• Gravimetric mass balance is given for Greenland and Antarctica in product WP2-FDDP-GMB-CDR
• Surface elevation change is given for:
  • Antarctica in product WP2-FDDP-SEC-CDR-AntIS
  • Greenland in product WP2-FDDP-SEC-CDR-GrIS

This document is the Algorithm Theoretical Basis Document (ATBD) for Gravimetric Mass Balance (GMB). The GMB data, as part of the Copernicus Ice Sheets and Ice Shelves service, is brokered from the European Space Agency's (ESA's) Greenland and Antarctic Climate Change Initiative (CCI) projects. The ATBDs from the second phase of the CCI projects (CCI+), Forsberg et al (2021) and Shepherd et al. (2021), provide a full description concerning the scientific approach underlying these products. Only output specifics will be given in this document, other topics will refer to the relevant CCI project's ATBDs. This document will describe the organization of the data processing system and how product updates are implemented.

Executive summary

The Gravimetric mass balance (WP2-FDDP-GMB-CDR) is a brokered product from the ESA CCI programme. For details, the reader is referred to the GMB sections of the ESA Greenland_Ice_Sheet_cci and Antarctic_Ice_Sheet_cci products documentation (see Section 1.2). The focus within the CCI project has been to ensure a seamless continuation of data across the transition from the Gravity Recovery and Climate Experiment (GRACE) to the GRACE follow-on mission. Hence, limited research and development have been conducted within the CCI project in terms of GMB processing algorithms. Thereby, the new C3S product is in essence an update of the observational time series.

In relation to validation, this is not performed within the C3S, as it has been performed previously and is extensively documented within the CCI project. Relevant documentation is available at:

• AntIS: https://climate.esa.int/en/projects/ice-sheets-antarctic/key-documents/

• GrIS: https://climate.esa.int/en/projects/ice-sheets-greenland/key-documents/ ¹

1. Instruments

The primary satellite source for the generation of the Gravimetric Mass Balance (GMB) is the Gravity Recovery and Climate Experiment (GRACE) (Tapley et al., 2004) and GRACE Follow-On (GRACE-FO) satellite missions. The GRACE was launched in March 2002 and ended in October 2017. GRACE was a joint effort between the National Aeronautics and Space Administration (NASA) and the German Research Centre for Geosciences (GFZ) (Postdam, Germany), GRACE-FO is the continuation of that mission with almost the same hardware, and it was launched in May 2018. Both missions consist of twin satellites that take measurements of the whole Earth's gravity field once every month. The key principle of GRACE measurement is the K-band microwave ranging system, which accurately measures the changes in the distance between the twin satellites. The two satellites are flying in a polar orbit about 220 km apart and about 500 km above the Earth's surface. The GRACE satellites revolve around the Earth 15 times a day and when the first satellite passes over a gravity anomaly it is pulled or pushed slightly with respect to the trailing satellite. This causes a change in the relative distance and speed of the two satellites, with the range system sensitive enough to detect up to 10 micrometres. Furthermore, the satellites are equipped with very sensitive accelerometers, Global Positioning System (GPS), a magnetometer, and a star camera. All those instruments are necessary to establish the non-gravitational accelerations, the precise position, and the altitude of the satellites. All the information on the satellite's distance, acceleration, and position are combined to infer a map of the Earth's gravity field. Three centres (Center for Space Research: CSR, GFZ, and Jet Propulsion Laboratory: JPL) process the data and produce monthly geopotential models of Earth, called L2 data. These models are distributed from the three centres as spherical harmonic (SH) coefficients with a maximum degree of 60, 90, and 96 respectively. These SH coefficients are used to calculate geoid height, gravity anomalies, and changes in the distribution of mass on Earth's surface.

2. Input/auxiliary data

To produce the GMB for the ESA CCI project, the GRACE L2 data from the CSR processing centre has been used with the spheric harmonics up-to degree 96. The gravity changes are due not only to surface mass changes like the water storage or the ice sheet mass loss, but also to the mass changes induced by the changes in the mantle. The solid Earth changes fast enough to be detected by GRACE are those from the Glacial Isostatic Adjustment (GIA) caused by the last ice age. These changes are modelled, and the GIA model used to correct the Greenland mass balance is Caron et al. 2018. Another auxiliary data is the drainage basin definition that is used to compute the mass changes at basin scale. For the GMB the Zwally (2012) drainage basins are used.

3. Algorithms

The GRACE mission allows fluctuations in ice-sheet mass to be estimated through measurement of their changing gravitational attraction. Advantages of the GRACE method is that it provides regional averages without the need for interpolation, measures the effect of mass fluctuations directly, and permits monthly temporal sampling. However, a key challenge is to discriminate fluctuations in ice-sheet mass from changes in the underlying crust and mantle. The spatial resolution of GRACE observations derived from global spherical harmonic solutions of about 300 km in the Polar Regions is coarse in comparison to that of other geodetic techniques. Hence, a further complicating factor is that signals may leak into regional GRACE solutions because of remote geophysical processes.

In the following, a summary of the CCI data processing is given, for more information on the data use and specific algorithms can be found in:

• For the Antarctic Ice Sheet: Shepherd et al. (2021)
• For the Greenland Ice sheet: Forsberg et al. (2021)

Velicogna and Wahr (2005) published for the first time the possibility of using data from the GRACE mission to determine the mass balance of the Greenland ice sheet. Since then, many mass balance estimates of both Greenland and Antarctica have been published, both on ice sheet scale (Chen et al., 2006; Ramillien et al., 2006; Forsberg and Reeh, 2007; Barletta et al., 2008; Velicogna, 2009; Shepherd et al. 2012) and drainage basin scale (Luthcke et al., 2006; Wouters et al., 2008; Schrama and Wouters, 2011; Sasgen et al., 2012; Barletta et al. 2013, Groh and Horwath 2016).

There are two main ways to derive mass balance from the GRACE mission:

1. Directly use the L1 data to infer the mass variation on the surface of the Earth that caused the changes in the distance between twin satellites. This methodology, called “masscons”, produces a gridded estimate of mass changes in units of liquid water equivalent thickness and is available at JPL's GRACE Tellus website².
2. Use the L2 data, i.e., the spherical harmonics coefficients of the gravity field. With the assumption that all the changes in gravity are happening in a thin layer over the surface of the Earth, in Wahr et al. (1998) a formula is given to directly convert the spherical harmonics coefficients into surface mass balance. This L2 data is then converted into a gridded gravity field at satellite altitude and the field is inverted using a grid of point-like mass sources distributed in the region of interest (Forsberg and Reeh, 2007, Barletta et al. 2013).

A complete overview of all the different methodologies used in the ESA CCI project and their performance comparison can be found in Groh et al. (2019).

However, the processing of the C3S brokered product is following the algorithm described in Barletta et al. (2013), which is a point-like mass inversion method that uses the reconstruction of the gravity field at the satellite altitude, including a pre-processing phase that mitigates the contamination to the gravity field due to sources outside Greenland. Barletta et al. (2013) dedicate special attention to the uncertainty estimates, and add several components to the total error estimate, namely the propagation of the formal errors from the GRACE L2 data, the uncertainty from the degree one, the GIA correction, the ocean and atmospheric model uncertainty.

4. Output data

The brokered data from the two-ice sheet CCIs have been interpolated onto a common timeframe to provide a consistent product for both hemispheres. Hence, we provide one file containing data for both hemispheres, following the naming convention: C3S_GMB_versV.nc, where V is the version number (current version: 3). Within the file is the monthly mass balance for the major drainage basins of the Greenland and Antarctic ice sheets (e. g. Greenland basin 1 variable is GrIS_1) given. Additional fields are also given for the total ice sheet mass balance. Each of the mass balance estimates is associated with an uncertainty estimate (e.g. GrIS_1_er). Figure 1 shows the mass balance time series for the entire Greenland ice sheet and a summary of the GMB single NetCDF-file main variables is presented in Table 1.

Table 1: Summary of variables in the output fields, as given in the NetCDF-file for the GMB in C3S_GMB_GRACE_vers3.nc. The variable GrIS_total is also shown in Figure 1.

Figure 1: Greenland mass balance time-series (variable "GrIS_total" as function of observation number) as precented in the C3S_GMB_GRACE_vers3.nc file. The observation number can be interpreted from the variable "time". Note that the timeseries have a gap between October 2017 and May 2018, not reflected in the observation number.

References

Barletta, V. R., Bordoni, A., and Sabadini, R.: Isolating the PGR signal in the GRACE data: impact on mass balance estimates in Antarctica and Greenland, Geophys. J. Int., 172, 18–30, doi:10.1111/j.1365- 246X.2007.03630.x, 2008.

Barletta, V. R., Sørensen, L. S., and Forsberg, R.: Scatter of mass changes estimates at basin scale for Greenland and Antarctica. The Cryosphere, 7(5), 1411–1432, 2013

Caron, L., Ivins, E. R., Larour, E., Adhikari, S., Nilsson, J., and Blewitt, G.: GIA model statistics for GRACE hydrology, cryosphere, and ocean science. Geophysical Research Letters, 45(5), 2203-2212., 2018

Chen, J. L., Wilson, C. R., Blankenship, D. D., and Tapley, B. D.: Antarctic mass rates from GRACE, Geophys. Res. Lett., 33, L11502, doi:10.1029/2006GL026369, 2006.

Forsberg, R. and Reeh, N.: Mass change of the Greenland Ice Sheet from GRACE, in: Proceedings, Gravity Field of the Earth – 1st meeting of the International Gravity Field Service, Harita Dergisi, Ankara, vol. 73, avaialble at: http://www.igfs.net, 2007

Forsberg, R., et al, Algorithm Theoretical Baseline Document (ATBD) for the Greenland Ice Sheet CCI+ Project, version 1.4, ST-DTU-ESA-GISCCI+ ATBD001, 2021 (https://climate.esa.int/media/documents/ST-DTU-ESA-GISCCI-ATBD-001_v1.4.pdf [URL resource last viewed 05^th May 2023])

Groh, A., and Horwath, M.: The method of tailored sensitivity kernels for GRACE mass change estimates. Geophysical Research Abstracts, 18, EGU2016-12065, 2016

Groh, A., Horwath, M., Horvath, A., Meister, R., Sørensen, L.S., Barletta, V.R., Forsberg, R., Wouters, B., Ditmar, P., Ran, J., and Klees, R.: Evaluating GRACE mass change time series for the Antarctic and Greenland Ice Sheet—Methods and results. Geosciences, 9(10), p.415., 2019

Luthcke, S. B., Zwally, H. J., Abdalati, W., Rowlands, D. D., Ray, R. D., Nerem, R. S., Lemoine, F. G., McCarthy, J. J., and Chinn, D. S.: Recent Greenland ice mass loss by drainage system from satellite gravity observations, Science, 314, 1286–1289, 2006.

Ramillien, G., Lombart, A., Cazenave, A., Ivins, E. R., Llubes, M., Remy, F., and Biancale, R.: Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE, Global Planet. Change, 53, 198–208, doi:10.1016/j.gloplacha.2006.06.003, 2006.

Sasgen, I., Broeke, M. v. d., Bamber, J. L., Rignot, E., Sandberg Sørensen, L., Wouters, B., Martinec, Z., Velicogna, I., and Simonsen, S. B.: Timing and origin of recent regional ice-mass loss in Greenland, Earth Planet. Sci. Lett., 333–334, 293–303, doi:10.1016/j.epsl.2012.03.033, 2012.

Schrama, E. J. O. and Wouters, B.: Revisiting Greenland ice sheet mass loss observed by GRACE, J. Geophys. Res., 116, B02407, doi:10.1029/2009JB006847, 2011.

Shepherd, A., Ivins, E. R., Geruo, A., Barletta, V. R., Bentley, M. J., Bettadpur, S., Briggs, K. H., Bromwich, D. H., Forsberg, R., Galin, N., Horwath, M., Jacobs, S., Joughin, I., King, M. A., Lenaerts, J. T. M., Li, J. L., Ligtenberg, S. R. M., Luckman, A., Luthcke, S. B., McMillan, M., Meister, R., Milne, G., Mouginot, J., Muir, A., Nicolas, J. P., Paden, J., Payne, A. J., Pritchard, H., Rignot, E., Rott, H., Sorensen, L. S., Scambos, T. A., Scheuchl, B., Schrama, E. J. O., Smith, B., Sundal, A. V., van Angelen, J. H., van de Berg, W. J., van den Broeke, M. R., Vaughan, D. G., Velicogna, I., Wahr, J., Whitehouse, P. L., Wingham, D. J., Yi, D. H., Young, D., and Zwally, H. J.: A Reconciled Estimate of Ice-Sheet Mass Balance, Science, 338, 1183–1189, 2012.

Shepherd, A., et al: Algorithm Theoretical Baseline Document (ATBD) for the Antarctic Ice Sheet CCI+ Project, version 1.0, ST-UL-ESA-AISCCI+ ATBD001, 2021 (https://climate.esa.int/media/documents/ST-UL-ESA-AISCCI-ATBD-001_v1.0_final.pdf [URL resource last viewed 05^th May 2023])

Tapley, B. D., Bettadpur, S., Watkins, M., and Reigber, C. The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett., 31, L09607, 2004

Velicogna, I. and Wahr, J.: Greenland mass balance from GRACE, Geophys. Res. Lett, 32, L18505, doi:10.1029/2005GL023955, 2005.

Velicogna, I.: Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE, Geophys. Res. Lett, 36, L19503, doi:10.1029/2009GL040222, 2009.

Wahr, J., Molenaar, M., and Bryan, F.: Time variability of the Earth's gravity field: Hydrological and oceanic effects and their possible detection using GRACE. Journal of Geophysical Research: Solid Earth 103.B12, 30205-30229, 1998

Wouters, B., Chambers, D., and Schrama, E. J. O.: GRACE observes small-scale mass loss in Greenland, Geophys. Res. Lett., 35, L20501, doi:10.1029/2008GL034816, 2008.

Zwally: Greenland and Antarctic drainage basins. Dataset available at https://earth.gsfc.nasa.gov/cryo/data/polar-altimetry/antarctic-and-greenland-drainage-systems [URL resource last viewed 05^th May 2023] ,2012 

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