EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 3. Greenland Ice Sheet surface elevation change error estimates > 3.1 Uncertainty estimates: accuracy and precision
---
Let us now consider the errors of the data. The total error of a surface elevation change estimate is theoretically given by the sum of the precision (random) and the accuracy (systematic) error:

$
\varepsilon = a\sigma + \delta
$

where $a$ is the critical z-score related to a certain statistical confidence interval, $\sigma$ is the random error (i.e. standard deviation) and $\delta$ the systematic error.

In the C3S surface elevation change dataset for Greenland, precision errors are reported as the standard deviation (i.e. the 68% confidence interval with $a$ = 1) and the accuracy error is not directly considered in the error estimates provided with the data. Therefore, in our case, $\delta$ = 0, meaning that $\varepsilon_{\frac{dh}{dt}}$ = $\sigma_{\frac{dh}{dt}}$.

Let us now explore a bit more the uncertainty of the data. Quantitative pixel-by-pixel error estimates are namely available for the dataset. Let us begin by plotting a histogram of the error values:

*Figure 3. Histogram of surface elevation change error estimates for the Greenland ice sheet from the SEC dataset on the Climate Data Store.*

Most errors (standard deviations) seem to be situated between 0 and 0.01 m/yr. Given that the GCOS (2022) requires a precision error threshold (expressed as 2$\sigma$) of at least 0.1 m/yr, it can be stated that this requirement is clearly met for the Greenland Ice Sheet [[6](https://library.wmo.int/idurl/4/58111)]. Let us check the spatial and temporal distribution of these errors below.

(section-3-2)=


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 3. Greenland Ice Sheet surface elevation change error estimates > 3.2 Surface elevation change errors in space and time
---
To get a better idea, we can also plot the arithmetic mean values over time for each pixel to check their spatial distribution:

Apply the function to the surface elevation change rate error data
Plot the data

*Figure 4. Spatial distribution of temporarily averaged surface elevation change errors for the Greenland ice sheet from the SEC dataset on the Climate Data Store.*

Let us quantify the ice sheet-wide average value:

```text
The Greenland ice sheet-wide average surface elevation change rate error (standard deviation) between 1992-01-01 and 2023-06-01 is 0.008 m/yr.
```

We can accordingly plot the data as a time series:

*Figure 5. Time series of the spatially averaged surface elevation change error for the Greenland ice sheet from the SEC dataset on the Climate Data Store.*

The highest errors are clearly present around the marginal errors of the ice sheet. Moreover, no clear trend in the average error values is present in the time series. However, given that the GCOS (2022) requires a precision error threshold (expressed as 2$\sigma$) of at least 0.1 m/yr, it can be stated that this requirement is clearly met for the Greenland Ice Sheet [[6](https://library.wmo.int/idurl/4/58111)].

(section-3-3)=


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 3. Greenland Ice Sheet surface elevation change error estimates > 3.3 Link with surface characteristics
---
Let us further investigate this pattern and check whether we can link the amount of missing data to the surface characteristics provided with the data. Therefore, we check how the amount of missing data is linked to the surface slope (i.e. as a proxy for the terrain complexity) and the magnitude of the surface elevation changes at a certain pixel:

Flatten the arrays and remove NaN values for the boxplot
Scatter plot
Remove NaN values for the scatter plot

*Figure 6. Relationship between the surface elevation change error and (left) the slope of the terrain and (right) the magnitude of the ice sheet surface elevation change over Greenland from the SEC dataset on the Climate Data Store.*

The results are displayed in Figure 6. The highest errors are clearly present over complex and steep terrain around the marginal regions, which arise due to processing limitations or challenging data acquisition conditions. The first graph shows that regions with gentle slopes (<2°) have the lowest overall error, indicating better radar performance on flat surfaces. As slopes increase to more than 2 and 5°, the errors increase, reflecting the difficulty of capturing reliable measurements due to slope-induced errors. Moreover, the error also increases with the magnitude of the surface elevation changes themselves, as shown by the right plot. Areas with larger surface elevation changes, often found along ice sheet margins with complex terrain that are more prone to melting, tend to have higher error values. This occurs, amongst others, because radar reflections may occur from different snowpack layers (e.g. from liquid water within the snow or from refrozen ice lenses). This indicates that dynamic regions are harder to monitor consistently. In general, radar altimeters thus tend to perform better in the central, flat regions of Greenland due to simpler topography and relatively stable surfaces, while marginal zones with complex and dynamic terrain (where the most significant SEC occur) exhibit an increased uncertainty.

Let us at last quantify the amount of pixels that do not meet the GCOS precision error requirement of 0.1 m/yr. We therefore multiply the errors accompanying the data by 2 to get a precision error in the form of 2 standard deviations (as proposed by GCOS):

```text
The absolute number of pixels with a surface elevation change rate precision error (2σ) < 0.1 m/yr is 1025570 pixels or 99.41%.
```

As already discussed above, almost all pixels exhibit error values that fall within international proposed thresholds, indicating a robust error characterization of the C3S SEC product for the GrIS.

(section-4)=


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 4. Ice sheet surface elevation and altimetric volume change trends > 4.1 Spatial distribution of linear and quadratic trends
---
With the patterns of the surface elevation changes and their uncertainty known, let us proceed with the analysis. In this subsection, we explore the spatial distribution of surface elevation change rate trends across the Greenland Ice Sheet. Let us start by exploring the linear trends:

Apply the function to the surface elevation change linear trends
Plot the data

*Figure 7. Linear trends of the ice sheet surface elevation change over Greenland from the SEC dataset on the Climate Data Store.*

The maps shows a similar pattern as the multiyear mean surface elevation change rates. The observed patterns highlight regional variability in surface elevation change trends, with coastal areas experiencing more substantial changes compared to interior regions. The data align with expected climate change impacts, where accelerating outlet glaciers and warming temperatures lead to increased melting and surface lowering, particularly in the low-elevation coastal areas [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [3](https://doi.org/10.1016/j.rse.2016.12.012), [5](https://doi.org/10.1029/2020GL091216), [8](https://doi.org/10.5194/tc-5-173-2011), [10](https://doi.org/10.1038/s41586-019-1855-2)].

Let us now consider quadratic trends (accelerations):

Apply the function to the surface elevation change quadratic trends
Plot the data

*Figure 8. Quadratic trends (acceleration) of the ice sheet surface elevation change over Greenland from the SEC dataset on the Climate Data Store.*

Again, the observed patterns highlight a clear regional variability in the acceleration and deceleration of surface elevation change rates. Coastal areas show more substantial changes in the acceleration of elevation change rates compared to central regions, which tend to be more stable.

(section-4-2)=


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 4. Ice sheet surface elevation and altimetric volume change trends > 4.2 Time series of surface elevation and volume change trends
---
Let us now quantify the ice sheet-wide surface elevation change and volume change trends as a time series:

Compute coefficients
Plot trends and print stats

```text
The slope of the ice sheet cumulative average surface elevation change is -0.055 m/yr.
The trend is significant at an alpha level of 0.05, i.e. a monotonic linear trend is present.
The acceleration of the ice sheet cumulative average surface elevation change is -0.004 m/yr^2.
The slope of the ice sheet cumulative altimetric volume change is -94.701 km³/yr.
The trend is significant at an alpha level of 0.05, i.e. a monotonic linear trend is present.
The acceleration of the ice sheet cumulative altimetric volume change is -6.478 km³/yr^2.
```

*Figure 9. Linear and quadratic trends of the cumulative (above) average ice sheet surface elevation change and (below) altimetric volume change over Greenland from the SEC dataset on the Climate Data Store.*

As seen earlier, the significant negative and downward trend, for both the linear and quadratic trend, implies that the surface is generally lowering over the GrIS, and that this lowering has been accelerating over the past several decades. As discussed before, the favorable error characterization and spatial/temporal coverage (with filled-up data gaps) of the C3S GrIS SEC product allow for a reliable and robust statistical analysis. The above-derived trends can thus be interpreted as being credible. Although surface elevation changes are not solely impacted by surface mass balance processes, the observed trends are moreover consistent with the expected impacts of climate change, where accelerating outlet glaciers and rising global temperatures result in increased melting, runoff and surface lowering [e.g. [1](https://doi.org/10.1016/j.epsl.2018.05.015), [4](https://doi.org/10.3189/172756505781829007), [8](https://doi.org/10.5194/tc-5-173-2011), [9](https://doi.org/10.1029/2021JF006505), [10](https://doi.org/10.1038/s41586-019-1855-2)]. Nevertheless, a notable bias exists when comparing the radar altimetry-derived SEC to those from laser altimetry, and the coarse spatial resolution of the C3S product may aid the corresponding underestimation of surface lowering rates as discussed before.

(section-5)=


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > Analysis and results > 5. Short summary and take-home messages
---
When measured over an extended period and over the complete ice sheet, trends in Greenland Ice Sheet surface elevation changes can serve as a clear indicator of global climate change. To ensure these trends are accurate, representative and reliable, the dataset should be sufficiently adequate in terms of its quality and maturity. Hence, the dataset should at least exhibit a comprehensive spatial coverage (i.e. ice sheet-wide), a long and continuous temporal coverage (> 30 years), quantified and transparent pixel-by-pixel uncertainty estimates that meet international proposed thresholds [[6](https://library.wmo.int/idurl/4/58111)], a validation effort, and an adequate spatio-temporal resolution (cfr. the "Maturity Matrix" [[7](https://doi.org/10.1175/BAMS-D-21-0109.1)]).

All in all, it can be said that the Greenland Ice Sheet (GrIS) surface elevation change dataset serves a robust indicator of global climate change, as several criteria for certain key quality aspects have been met. The temporal window of the data spams over 30 years at a consistent monthly resolution, which makes the surface elevation change dataset highly applicable for trend analysis. Furthermore, there is a complete spatio-temporal coverage since 1992 with filled-up data gaps. Error estimates (presented as 1-sigma precision errors) align with international proposed thresholds, confirming the dataset's high quality in terms of data uncertainty. Nevertheless, radar altimeters tend to perform better in the central, flat regions of the Greenland Ice Sheet, which have a simpler topography and a more stable surface, compared to the coastal areas with a more complex terrain (with steep slopes, valleys and ridges and large seasonal cycles of melt and accumulation) where errors are generally higher.

However, a notable bias exists when comparing radar altimetry-derived surface elevation changes to laser altimetry, particularly for significant lowering rates (below -0.5 to -1 m/yr), leading to underestimated surface elevation change and volume loss rates [[3](https://doi.org/10.1016/j.rse.2016.12.012)]. Apart from that, the coarse spatial resolution of 25 km is insufficient to capture the very localized mass loss of outlet glaciers, further complicating the data and underestimating surface elevation changes and volume losses to some degree [[5](https://doi.org/10.1029/2020GL091216)]. Users should furthermore note that surface elevation changes do not necessarily equal "actual" ice sheet volume nor mass changes, as processes such as bedrock elevation changes, firn densificaiton and density corrections for volume to mass changes have to be taken into account as well. The surface elevation change data can thus only be converted to "actual" ice sheet volume or mass changes if certain corrections and/or assumptions are made. Users of the C3S GrIS SEC data product are therefore most likely required to implement additional processing to derive glaciologically interpretable volume/mass changes from the provided surface elevation changes [e.g. [1](https://doi.org/10.1016/j.epsl.2018.05.015), [4](https://doi.org/10.3189/172756505781829007), [8](https://doi.org/10.5194/tc-5-173-2011), [9](https://doi.org/10.1029/2021JF006505), [10](https://doi.org/10.1038/s41586-019-1855-2)].


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > ℹ If you want to know more > Key resources
---
- ["Ice sheet surface elevation change rate for Greenland and Antarctica from 1992 to present derived from satellite observations"](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-elevation-change?tab=overview) on the CDS
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-elevation-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355345393) (Copernicus Knowledge Base).
- [Copernicus climate change indicators: ice sheets](https://climate.copernicus.eu/climate-indicators/ice-sheets)
- [An easy-to-read article about ice sheet altimetry](https://blogs.egu.eu/divisions/cr/2023/03/03/ice-radar-altimetry/)
- [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control` prepared by [B-Open](https://www.bopen.eu).


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > ℹ If you want to know more > References
---
- [[1](https://doi.org/10.1016/j.epsl.2018.05.015)] Sørensen, L. S., Simonsen, S. B., Forsberg, R., Khvorostovsky, K., Meister, R., and Engdahl, M. E. (2018). 25 years of elevation changes of the Greenland Ice Sheet from ERS, Envisat, and CryoSat-2 radar altimetry, Earth and Planetary Science Letters. 495. https://doi.org/10.1016/j.epsl.2018.05.015

- [[2](https://doi.org/10.5194/tc-13-427-2019)] Schröder, L., Horwath, M., Dietrich, R., Helm, V., van den Broeke, M.R., and Ligtenberg, S.R.M. (2019). Four decades of Antarctic surface elevation change from multi-mission satellite altimetry. The Cryosphere, 13, p. 427-449. https://doi.org/10.5194/tc-13-427-2019

- [[3](https://doi.org/10.1016/j.rse.2016.12.012)] Simonsen, S. B., and Sørensen, L. S. (2017). Implications of Changing Scattering Properties on Greenland Ice Sheet Volume Change from Cryosat-2 Altimetry. Remote Sensing of Environment. https://doi.org/10.1016/j.rse.2016.12.012

- [[4](https://doi.org/10.3189/172756505781829007)] Zwally, H. J., Giovinetto, M.B., Li, J., Cornejo, H.G, Beckley, M.A., Brenner, A.C., Saba, J.L., and Yi, D. (2005). Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992–2002. J. Glaciol. 51, 509–527, https://doi.org/10.3189/172756505781829007

- [[5](https://doi.org/10.1029/2020GL091216)] Simonsen, S. B., Barletta, V. R., Colgan, W. T., and Sørensen, L. S. (2021). Greenland Ice Sheet mass balance (1992–2020) from calibrated radar altimetry. Geophysical Research Letters, 48(3), e2020GL091216. https://doi.org/10.1029/2020GL091216

- [[6](https://library.wmo.int/idurl/4/58111)] GCOS (Global Climate Observing System) (2022). The 2022 GCOS ECVs Requirements (GCOS-245). World Meteorological Organization: Geneva, Switzerland. doi: https://library.wmo.int/idurl/4/58111

- [[7](https://doi.org/10.1175/BAMS-D-21-0109.1)] Yang, C. X., Cagnazzo, C., Artale, V., Nardelli, B. B., Buontempo, C., Busatto, J., Caporaso, L., Cesarini, C., Cionni, I., Coll, J., Crezee, B., Cristofanelli, P., de Toma, V., Essa, Y. H., Eyring, V., Fierli, F., Grant, L., Hassler, B., Hirschi, M., Huybrechts, P., Le Merle, E., Leonelli, F. E., Lin, X., Madonna, F., Mason, E., Massonnet, F., Marcos, M., Marullo, S., Muller, B., Obregon, A., Organelli, E., Palacz, A., Pascual, A., Pisano, A., Putero, D., Rana, A., Sanchez-Roman, A., Seneviratne, S. I., Serva, F., Storto, A., Thiery, W., Throne, P., Van Tricht, L., Verhaegen, Y., Volpe, G., and Santoleri, R. (2022). Independent Quality Assessment of Essential Climate Variables: Lessons Learned from the Copernicus Climate Change Service, B. Am. Meteorol. Soc., 103, E2032–E2049, doi: 10.1175/Bams-D-21-0109.1.


EQC Quality Assessment: "Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Uncertainty of ice sheet surface elevation change data over Greenland for volume and mass change trend assessments > ℹ If you want to know more > References
---
Lessons Learned from the Copernicus Climate Change Service, B. Am. Meteorol. Soc., 103, E2032–E2049, doi: 10.1175/Bams-D-21-0109.1.

- [[8](https://doi.org/10.5194/tc-5-173-2011)] Sørensen, L. S., Simonsen, S. B., Nielsen, K., Lucas-Picher, P., Spada, G., Adalgeirsdottir, G., Forsberg, R., and Hvidberg, C. S. (2011). Mass balance of the Greenland ice sheet (2003–2008) from ICESat data – the impact of interpolation, sampling and firn density, The Cryosphere, 5, 173–186, https://doi.org/10.5194/tc-5-173-2011

- [[9](https://doi.org/10.1029/2021JF006505)] Khan, S. A., Bamber, J. L., Rignot, E., Helm, V., Aschwanden, A., Holland, D. M., van den Broeke, M., King, M., Noël, B., Truffer, M., Humbert, A., Solgaard, A. M., Box, J. E., Colgan, W. T., Wuite, J., Mouginot, J., Andersen, O. B., Csatho, B., Felikson, D., Fettweis, X., Forsberg, R., Gogineni, P., Joughin, I., Kjeldsen, K. K., Kuschnerus, M., Langen, P. L., Luckman, A., Luthcke, S. B., McMillan, M., Merryman Boncori, J. P., Morlighem, M., Mottram, R., Nagler, T., Nagy, T., Paden, J., Palmer, S., Poinar, K., Shepherd, A., Smith, B., Stearns, L. A., van Angelen, J. H., van der Wal, W., van de Berg, W. J., van Wessem, M., Velicogna, I., Wahr, J., Wendt, A., Wouters, B., & Zwally, H. J. (2022). Greenland mass trends from airborne and satellite altimetry during 2011–2020. Journal of Geophysical Research: Earth Surface, 127(3). https://doi.org/10.1029/2021JF006505

- [[10](https://doi.org/10.1038/s41586-019-1855-2)] The IMBIE Team (2019). Mass balance of the Greenland Ice Sheet from 1992 to 2018. Nature, 579, 233–239. https://doi.org/10.1038/s41586-019-1855-2

- [[11](https://doi.org/10.1038/s41586-018-0179-y)] The IMBIE Team (2018). Mass balance of the Antarctic Ice Sheet from 1992 to 2017. Nature 558, 219–222. https://doi.org/10.1038/s41586-018-0179-y


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets
---
Production date: 31-03-2025

Dataset version: 4.0

Produced by: Yoni Verhaegen and Philippe Huybrechts (Vrije Universiteit Brussel)


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Quality assessment question
---
* **"Is the dataset sufficiently consistent in terms of spatio-temporal completeness to derive multi-year trends in ice sheet mass changes and their corresponding contribution to global sea level rise?"**

Ice sheets are significant contributors to current (and future) global sea-level rise, indicators of climatic changes, and key players regarding feedback mechanisms within the atmosphere, ocean, and cryosphere. Assessing ice sheet mass changes is essential for understanding these mechanisms. At present-day, the gravimetric method from satellite-based remote sensing offers one out of the three feasible ways to regularly and accurately monitor mass changes of the entire ice sheets at a regular basis (the others being the altimetric and input-output method). The ["Gravimetric mass balance data for the Antarctic and Greenland ice sheets from 2003 to 2022 derived from satellite observations"](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) dataset on the Climate Data Store (CDS) therefore provides valuable insights into the ice sheet's mass changes. The dataset uses satellite gravimetry from the GRACE and GRACE-FO missions to detect changes in the Earth's gravitational field. These are then translated into cumulative mass anomalies of ice above buoyancy for the grounded ice of both the Greenland (GrIS) and Antarctic (AIS) ice sheets [[1](https://doi.org/10.1007/s10712-016-9398-7), [2](https://doi.org/10.3390/geosciences9100415)]. This notebook investigates whether the mass change dataset is of sufficient maturity and quality in terms of its spatio-temporal completeness (i.e. coverage and resolution) to derive multi-year trends in ice sheet mass changes and their corresponding contribution to global sea level rise. For that, we use dataset version 4.0.


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Quality assessment statements
---
These are the key outcomes of this assessment

- The ice sheet mass change dataset, making use of the GRACE(-FO) satellite missions, is a useful tool for quantifying the total ice mass change of the Greenland (GrIS) and Antarctic (AIS) ice sheets. The C3S data are presented as a time series of the ice sheet GMB data and exhibits a long temporal extent (> 20 years). The data represent mass changes aggregated from different basins or from an ice sheet-wide coverage at a (quasi) monthly temporal resolution. Since it only captures ice mass changes above buoyancy, ice mass changes from GRACE(-FO) can be directly converted to global sea level contributions, of which the dataset values agree well with values found in the literature from other methods [[9](https://iopscience.iop.org/article/10.1088/1748-9326/aac2f0/meta), [12](https://doi.org/10.1038/s41586-019-1855-2), [13](https://doi.org/10.1038/s41586-018-0179-y)]. The C3S GMB dataset therefore effectively captures the long-term mean, trends and variability of ice sheet mass changes and the corresponding global sea level contributions, and can thus serve as a clear indicator of global climate change and water cycle changes.

- Data limitations include a coarse spatial resolution of the data acquisition and dataset itself (i.e. since there is a lack of gridded data at the pixel level of the final product, the term "spatial resolution" is actually not appropriate for this dataset), undesired signal leakage from adjacent regions (e.g. the nearby Canadian ice caps for the GrIS), and the need for complex data retrieval methods and geophysical corrections resulting in occasionally very high uncertainty values. Furthermore, data gaps exist, notably during 2017-2018 in between the transition of GRACE and its follow-up GRACE-FO. These are not flagged or filled, requiring users to manually identify missing periods. However, for linear trend estimation, gaps (even long ones) in the time series are practically irrelevant, as mass changes occurring during these gaps are still included in the subsequent solution, and secondly, there is no systematic bias between GRACE and GRACE-FO.
```


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Methodology > Dataset description
---
The total mass balance of an ice sheet is the difference between mass gained (mainly from snow accumulation) and mass lost (by ablation or solid ice discharge across the grounding line), which is the same as the net mass change of the ice sheet. Remote sensing techniques, such as the use of satellites, are an important feature to derive and study the mass changes of the ice sheets. The ice sheet mass change dataset provides monthly gravimetric mass balance (GMB) values and their uncertainty for the Greenland (GrIS) and also the Antarctic ice sheet (AIS). The data represent a time series of the cumulative mass changes (mass anomalies) of the ice above buoyancy of the ice sheets and their basins (including ice caps and glaciers) that are derived using satellite gravimetry data from the GRACE(-FO) missions. Data are available as time series for the whole ice sheet, as well as at the basin level, but no gridded data are provided. Data are available since 2002 with units in Gt (Gigatonnes). For a more detailed description of the data acquisition and processing methods, we refer to the [documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348671) (Copernicus Knowledge Base).

The mass changes and their errors derived from GRACE(-FO) are expressed in Gt (Gigatonnes). It can also be translated into a volume, for example one Gt of water (density 1000 kg/m$^3$) is exactly one km$^3$, while one Gt of ice (density 917 kg/m$^3$) in volume becomes 1.091 km$^3$ of ice. GRACE(-FO) data are in fact considered to be the sum of mass changes driven by changing rates of solid ice discharge (i.e. the flux across the grounding line $D$) and mass changes driven by changing rates of ablation and accumulation (mainly the surface mass balance or $SMB$). What GRACE(-FO) actually detects are patterns of mass redistribution, indicating that a material should be redistributed (e.g. by ice dynamics or liquid discharge) in order for GRACE(-FO) to be able to detect gravity anomalies and the corresponding mass changes over certain locations. In that sense, an amount of melted ice being replaced by its mass-equivalent amount of meltwater at the same location would result in zero mass change.

The main advantage of GRACE(-FO) is that all processes directly contributing to ice sheet mass fluctuations are observed directly. Unlike the input-output method, SMB is therefore not involved explicitely in processing and it is not separated from ice flow dynamics. Moreover, gaps in the time series do not affect linear trend estimation as mass changes occurring during these gaps are still included in the subsequent solution. The main drawbacks of this technique are the large footprint of data acquisition and the fact that corrections must be made for mass redistribution in the atmosphere, ocean, soil and solid earth (e.g. glacial isostatic adjustment) in order to isolate mass changes relevant for the ice sheets.


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Methodology > Structure and (sub)sections
---
**[](section-1)**
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* [](section-1-2)
* [](section-1-3)
* [](section-1-4)

**[](section-2)**
* [](section-2-1)
* [](section-2-2)

**[](section-3)**
* [](section-3-1)
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EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 1. Data preparation and processing > 1.2 Define parameters and download
---
Then we define the parameters, i.e. for which ice sheet (or which basins of these ice sheets) we want the mass change data to be extracted:

Then we define requests for download from the CDS and download and transform the glacier mass change data.

```text
100%|██████████| 1/1 [00:00<00:00, 28.68it/s]
```

```text
Downloading done.
```

(section-1-3)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
Let us inspect the data:

```text
<xarray.Dataset> Size: 3kB
Dimensions:      (time: 216)
Coordinates:
  * time         (time) datetime64[ns] 2kB 2002-04-16T20:23:54.375000 ... 202...
Data variables:
    GrIS_total   (time) float32 864B 1.057e+03 1.123e+03 ... -3.762e+03
    AntIS_total  (time) float32 864B 345.6 488.9 467.3 ... -910.0 -843.2 nan
Attributes:
    Title:                GMB for Greenland and Antarctica ice sheets from th...
    institution:          DTU Space - Geodesy and Earth Observations
    reference:            Baratta et al. (2016), Groh and Horwart (2016)
    file_creation_date:   Tue May 16 09:49:32 2023
    region:               Greenland and Antarctica
    missions_used:        GRACE and and GRACE-FO
    time_coverage_start:  Apr-2002
    time_coverage_end:    Dec-2022
    Tracking_id:          ab2360a4-82d5-42f3-babb-90ce976a8a8e
    netCDF_version:       NETCDF4
    product_version:      4.0
    Summary:              This data set is prepared for the C3S project, and ...
```

It is a dataset that consists of time series data, containing cumulative values of the total ice sheet mass change of, in this case, the entire Greenland Ice Sheet (`GrIS_total`) and the entire Antarctic Ice Sheet (`AntIS_total`) since 2002. Mass changes are expressed in units of Gt and the time period between two measurements is variable. Note that no gridded data are given in this dataset, and hence no spatial resolution can be derived.

(section-1-4)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 1. Data preparation and processing > 1.4 Data handling and creating functions
---
Let us perform some data handling before getting started with the analysis. We also define a plotting function to visualize the time series:

Define specific names for the first and second variables
Determine the number of columns needed based on the number of variables
Convert time to pandas datetime for easy handling
Identify large gaps and shade them
Dataset processing
Set custom attributes for variables

With everything ready, let us now start with the analysis:

(section-2)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 2. Quantifying Greenland and Antarctic Ice Sheet mass changes over time > 2.1 Time series of cumulative ice sheet mass changes
---
We begin by plotting the Greenland and Antarctic Ice Sheet cumulative mass change $M_{GRACE}$ between the begin and end period with the defined plotting function, where the shading in the upper part of the plot indicates when the time between two consecutive measurements is more than 1 month:

*Figure 1. Greenland (top) and Antarctic (bottom) ice mass changes from GRACE(-FO), where shaded intervals depict data gaps longer than 1 month. Note the different range of the y-axis.*

The provided graphs show the cumulative mass change of the Greenland Ice Sheet and the Antarctic Ice Sheet since 2002, as measured by GRACE(-FO) satellites. The GrIS shows a clear and consistent decline in mass, having lost approximately 5000 gigatonnes (Gt) over the period. The AIS mass change graph displays more pronounced fluctuations. For Greenland, mass loss is dominated by meltwater runoff, combined with the solid ice discharge towards the ocean across the grounding line of outlet glaciers. For Antarctica, mass loss primarily occurs through the discharge of ice across the grounding line, with surface melting playing a minor role. Here, interactions between the ice sheet and the warming ocean, combined with dynamic responses within the ice sheet itself (e.g. an acceleration of outlet glaciers due to a reduced buttressing from the ice shelves), are central to understanding why Antarctica's mass is currently decreasing [[1](https://doi.org/10.1007/s10712-016-9398-7), [2](https://doi.org/10.3390/geosciences9100415), [3](https://doi.org/10.1126/science.1178176)].

(section-2-2)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 2. Quantifying Greenland and Antarctic Ice Sheet mass changes over time > 2.2 Spatio-temporal resolution and coverage of the GRACE(-FO) mass change estimates
---
Now that we have visualized the temporal patterns of the mass changes, we can investigate the spatio-temporal resolution and extent of the GrIS and AIS mass changes. Let us begin by zooming in more on the temporal data gaps (coverage) and the temporal resolution in the time series:

Get time gaps
Create the plot

*Figure 2. Time period between two consecutive GRACE(-FO) monthly solutions in the ice sheet GMB dataset.*

The plot displays the time gaps in the GRACE(-FO) data collection over time, which are the same for the GrIS and the AIS, highlighting periods of consistent monthly data acquisition and (significant) data gaps. Generally, a temporal resolution of approximately 1 month (which is mostly the case) is observed, aligning with the optimal requirement proposed by GCOS [[5](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)]. More gaps in GRACE data,  however, arise after 2011, which are due to sensor degradation. The most prominent feature is the large time gap around 2017-2018, where the gap extends up to 12 months. This significant gap corresponds to the end of the original GRACE mission and the transition period before the launch of the GRACE Follow-On (GRACE-FO) mission. During this period, there was an inability to acquire data, as the original GRACE satellites were decommissioned and the new GRACE-FO satellites were not yet operational. Because there is no systematic bias between the GRACE and GRACE-FO time series [[4](https://doi.org/10.1029/2020GL087291)], this does not impact the overall trend and magnitude of the time series after 2018. In fact, for linear trend estimation, the presence of gaps (even long ones) scattered over the entire time series are almost irrelevant, as mass changes occurring during these gaps are still included in the subsequent solution. Long-term trend stability is therefore a major advantage of GMB data, as compared to the altimetry and input-output methods for ice mass change estimations.

Let us have the amount of gaps quantified to get an idea of the temporal data availability:

```text
The start date of the time series is 16/04/2002
The  end  date of the time series is 17/12/2022
The amount of months with mass change measurements that is expected between these two dates is 248
The amount of months with mass change measurements that is present between these two dates is 213
For a consistent monthly temporal resolution, the amount of months with missing data is 14.11%.
```

Concerning spatial coverage, a significant challenge in analyzing the ice sheet's mass changes (especially for the GrIS) is deciding whether to include the peripheral glaciers and ice caps. The GRACE(-FO) GMB data include all ice masses in Greenland (and Antarctica), due to the coarse spatial resolution of several hundred kilometers during the data acquisition, which prevents differentiation between closely situated ice bodies. As a result, the mass changes of Greenland's peripheral glaciers and ice caps, which contribute approximately 30-35 Gt/year [[6](https://essd.copernicus.org/articles/15/1597/2023/)], are included in these measurements. To exclude these peripheral areas from the GRACE(-FO) time series, a scaling factor of 0.84 is often used for the GrIS [[7](https://doi.org/10.1016/j.rse.2015.06.016)]. It must be furthermore noted that only mass changes of ice above buoyancy are considered in the GMB dataset (of which the impact is, however, relatively limited for the GrIS but can be significant for the AIS, due to the presence of more floating ice and ice grounded below present-day sea level).

The lack of downloadable gridded data further complicates the spatial resolution issue (in fact, since there are no gridded data, the term "spatial resolution" is not applicable for this C3S dataset), although such pixel-by-pixel data are available from other sources like the TU Dresden website. The currently available data are provided as time series for the entire ice sheet's and their basins, which is too coarse to meet GCOS requirements and poses challenges, for example for ice sheet models that require gridded inputs.

(section-3)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 3. Ice sheet mass change trends and sea level contribution over time > 3.1 Linear and quadratic ice sheet-wide mass change trends
---
With the imformation above, let us now go on and calculate linear and quadratic trends for the ice sheet mass change product:

Compute coefficients
Plot trends and print stats

```text
Cumulative mass change of the Greenland Ice Sheet from GRACE(-FO):
	The slope of the ice sheet mass change is -251.329 Gt/yr.
	The trend is significant at an alpha level of 0.05, i.e. a monotonic trend is present.
	The acceleration of the ice sheet mass change is 3.240 Gt/yr^2.
Cumulative mass change of the Antarctic Ice Sheet from GRACE(-FO):
	The slope of the ice sheet mass change is -89.873 Gt/yr.
	The trend is significant at an alpha level of 0.05, i.e. a monotonic trend is present.
	The acceleration of the ice sheet mass change is -2.354 Gt/yr^2.
```

*Figure 3. Linear and quadratic trends of ice sheet mass changes for the (above) GrIS and (below) AIS from the ice sheet GMB dataset.*

The GRACE(-FO) data plots illustrate the cumulative mass changes of the Greenland and Antarctic Ice Sheets over time. Both the Greenland and Antarctic Ice Sheets  exhibit significant ongoing mass loss, with the statistical significance of the trends underscoring the robustness of these findings. The linear and quadratic trend lines, depicted in red and green respectively, provide a clear visual representation of these trends, highlighting the critical changes occurring in the polar regions.

(section-3-2)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 3. Ice sheet mass change trends and sea level contribution over time > 3.2 Quantifying ice sheet-related global sea level contributions
---
We furthermore note again that GRACE(-FO) cannot detect changes in floating ice and ice below buoyancy for ice grounded below sea level. Mass change processes occurring beyond the grounding line, such as a retreating calving front, ocean-induced melt beneath the ice shelves, as well as changes to the part of the ice that is grounded below sea level (or in other words ice below buouyancy) will therefore not be detectable because it is occupied by the same mass of water. In that regard, GMB measurements by GRACE(-FO) are immediately convertible to sea level contributions. For the contributions of ice sheets, we assume that 361.8 Gt of ice will raise global sea levels by 1 mm [e.g. [11](https://doi.org/10.1038/s41467-024-45726-w)] (where 361.8 Gt of ice is equivalent to 394.67 km$^3$ ice):

$
h_{SLE}
$
[mm]
$
= -\dfrac{M_{GRACE}}{361.8}
$

where $M_{GRACE}$ is the cumulative mass change of the ice sheets measured by GRACE(-FO) in Gt. Let us plot this:

Convert mass change to global sea level change
Plot the data and trends
Compute coefficients
Plot trends and print stats

```text
Cumulative global sea level contribution of the Greenland Ice Sheet from GRACE(-FO):
	The slope of the global sea level contribution is 0.695 mm/yr.
	The trend is significant at an alpha level of 0.05, i.e. a monotonic trend is present.
	The acceleration of the global sea level contribution is -0.009 mm/yr^2.
Cumulative global sea level contribution of the Antarctic Ice Sheet from GRACE(-FO):
	The slope of the global sea level contribution is 0.248 mm/yr.
	The trend is significant at an alpha level of 0.05, i.e. a monotonic trend is present.
	The acceleration of the global sea level contribution is 0.007 mm/yr^2.
```

*Figure 4. Contribution of ice sheet mass changes to global sea level for the (above) GrIS and (below) AIS from the ice sheet GMB dataset.*

The linear trends and their significance show a consistent ongoing increase in sea level contributions, with Greenland contributing more significantly compared to Antarctica. The trends and their magnitudes observed in the GRACE(-FO) data for both the Greenland and Antarctic Ice Sheets are broadly consistent with the findings reported in the literature from other mass change estimation methods (e.g. [[9](https://iopscience.iop.org/article/10.1088/1748-9326/aac2f0/meta), [12](https://doi.org/10.1038/s41586-019-1855-2), [13](https://doi.org/10.1038/s41586-018-0179-y)]), highlighting the reliability and quality-richness of GRACE(-FO) data with respect to capturing significant ice mass changes and their impact on global sea level rise.

(section-4)=


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > Analysis and results > 4. Short summary and take-home messages
---
GRACE(-FO) data provide a valuable long-term dataset for detecting trends in ice sheet mass changes, making them a reliable indicator of climate change. With over 20 years of (mostly) continuous data, the dataset enables the assessment of long-term variations in ice sheet mass balance at the basin and ice sheet-wide scales. Unlike other remote sensing methods that infer mass changes indirectly, GRACE(-FO) directly measures gravitational anomalies, capturing mass redistribution patterns across both the GrIS and AIS. Although the IPCC standard for climate normals is 30 years, the dataset's continuity from GRACE (2002–2017) to GRACE-FO (2018–present) ensures that clear temporal patterns can be identified, making it a crucial tool for climate and global water cycle studies.

However, GRACE(-FO) has limitations, including a coarse spatial resolution (several hundred kilometers), which restricts its ability to resolve small-scale variations and separate closely situated ice bodies (e.g. Greenland and its peripheral glaciers/ice caps, including the adjacent Canadian ice caps). Additional uncertainties arise mainly from complex processes such as signal leakage and geophysical corrections [[10](https://tc.copernicus.org/articles/7/1411/2013/)]. The dataset also lacks pixel-level (gridded) mass change and error estimates, limiting its applicability to grid-based assessments. Additionally, users should also acknowledge what GRACE(-FO) ice mass changes represent. GRACE(-FO) only considers patterns of mass redistribution by ice masses above buoyancy (i.e. solid ice discharge and changing rates of runoff/accumulation), meaning floating ice and ice grounded below sea level do not contribute to the measured mass change. For the GrIS, peripheral glaciers and ice caps are included, whereas for the Antarctic Ice Sheet AIS, ice shelves beyond the grounding line are excluded.

Despite occasional data gaps and relatively high uncertainty values in some measurements, GRACE(-FO) remains a powerful tool for quantifying the mean, variability, and trends in ice mass changes because (1) the amount of missing data is relatively limited and these data gaps do not impact the values of consecutive cumulative mass anomalies, (2) the temporal resolution is mostly consistent at 1-monthly spaced time intervals, (3) the number of consecutive years is generally sufficient to filter out inter and intrayearly variability, and (4) the presence of data gaps in the time series do not impact the overall trend and magntiude of the mass changes and sea level contributions (e.g. [[4](https://doi.org/10.1029/2020GL087291)]). The dataset’s ability to directly convert ice mass changes into sea level contributions makes it a convenient tool for climate change monitoring and global water cycle assessments. Trends in ice sheet mass changes and sea level contributions from the C3S product furthermore agree well with general findings in the literature from other mass change estimation methods [[8](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter09.pdf), [9](https://iopscience.iop.org/article/10.1088/1748-9326/aac2f0), [12](https://doi.org/10.1038/s41586-018-0179-y), [13](https://doi.org/10.1038/s41586-019-1855-2)], further adding credibility to the data. While certain limitations are thus present, its role as a direct measurement tool for ice sheet mass loss makes it essential for evaluating ice sheet stability and contributions to sea level rise.


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > ℹ If you want to know more > Key resources
---
- "[Gravimetric mass balance data for the Antarctic and Greenland ice sheets from 2003 to 2022 derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview)" on the CDS.
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348671) (Copernicus Knowledge Base).
- [Copernicus climate change indicators: ice sheets](https://climate.copernicus.eu/climate-indicators/ice-sheets)
- The data portal with GMB data from the data provider (TU Dresden) [for the GrIS](https://data1.geo.tu-dresden.de/gis_gmb/index.html) and [the AIS](https://data1.geo.tu-dresden.de/gis_gmb/index.html).
- [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control` prepared by [B-Open](https://www.bopen.eu).


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > ℹ If you want to know more > References
---
- [[1](https://doi.org/10.1007/s10712-016-9398-7)] Forsberg, R., Sørensen, L.S. and Simonsen, S.B. (2017). Greenland and Antarctica Ice Sheet Mass Changes and Effects on Global Sea Level. Surv. Geophys., 38, 89–104. https://doi.org/10.1007/s10712-016-9398-7

- [[2](https://doi.org/10.3390/geosciences9100415)] Groh, A., Horwath, M., Horvath, A., Meister, R., Sørensen, L.S., Barletta, V.R., Forsberg, R., Wouters, B., Ditmar, P., Ran, J., Klees, R., Su, X., Shang, K., Guo, J., Shum, C.K., Schrama, E., and Shepherd, A. (2019). Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet, Geosciences, 9(10). https://doi.org/10.3390/geosciences9100415

- [[3](https://doi.org/10.5194/tc-10-1933-2016)] van den Broeke, M., Enderlin, E. M., Howat, I. M., Kuipers Munneke, P., Noël, B. P. Y., van de Berg, W. J., van Meijgaard, E., and Wouters, B. (2016). On the recent contribution of the Greenland ice sheet to sea level change, The Cryosphere, 10, 1933–1946, https://doi.org/10.5194/tc-10-1933-2016

- [[4](https://doi.org/10.1029/2020GL087291)] Velicogna, I., Mohajerani, Y., A, G., Landerer, F., Mouginot, J., Noel, B., Rignot, E., Sutterley, T., van den Broeke, M., van Wessem, M., and Wiese, D. (2020). Continuity of Ice Sheet Mass Loss in Greenland and Antarctica from the GRACE and GRACE Follow-On Missions. Geophys. Res. Lett. 47. https://doi.org/10.1029/2020GL087291

- [[5](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)] GCOS (Global Climate Observing System) (2022). The 2022 GCOS ECVs Requirements (GCOS-245). World Meteorological Organization: Geneva, Switzerland. doi: https://library.wmo.int/idurl/4/58111


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > ℹ If you want to know more > References
---
(GCOS-245). World Meteorological Organization: Geneva, Switzerland. doi: https://library.wmo.int/idurl/4/58111

- [[6](https://essd.copernicus.org/articles/15/1597/2023/)] Otosaka, I. N., Shepherd, A., Ivins, E. R., Schlegel, N.-J., Amory, C., van den Broeke, M. R., Horwath, M., Joughin, I., King, M. D., Krinner, G., Nowicki, S., Payne, A. J., Rignot, E., Scambos, T., Simon, K. M., Smith, B. E., Sørensen, L. S., Velicogna, I., Whitehouse, P. L., A, G., Agosta, C., Ahlstrøm, A. P., Blazquez, A., Colgan, W., Engdahl, M. E., Fettweis, X., Forsberg, R., Gallée, H., Gardner, A., Gilbert, L., Gourmelen, N., Groh, A., Gunter, B. C., Harig, C., Helm, V., Khan, S. A., Kittel, C., Konrad, H., Langen, P. L., Lecavalier, B. S., Liang, C.-C., Loomis, B. D., McMillan, M., Melini, D., Mernild, S. H., Mottram, R., Mouginot, J., Nilsson, J., Noël, B., Pattle, M. E., Peltier, W. R., Pie, N., Roca, M., Sasgen, I., Save, H. V., Seo, K.-W., Scheuchl, B., Schrama, E. J. O., Schröder, L., Simonsen, S. B., Slater, T., Spada, G., Sutterley, T. C., Vishwakarma, B. D., van Wessem, J. M., Wiese, D., van der Wal, W., and Wouters, B. (2023). Mass balance of the Greenland and Antarctic ice sheets from 1992 to 2020, Earth Syst. Sci. Data, 15, 1597–1616, https://doi.org/10.5194/essd-15-1597-2023

- [[7](https://doi.org/10.1016/j.rse.2015.06.016)] Colgan, W., Abdalati, W., Citterio, M., Csatho, B., Fettweis, X., Luthcke, S., Moholdt, G., Simonsen, S.B., and Stober, M. (2015). Hybrid glacier Inventory, Gravimetry and Altimetry (HIGA) mass balance product for Greenland and the Canadian Arctic. Remote Sensing of Environment, 168, 24–39. https://doi.org/10.1016/j.rse.2015.06.016

- [[8](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter09.pdf)] Fox-Kemper, B., H.T. Hewitt, C. Xiao, G. Aðalgeirsdóttir, S.S. Drijfhout, T.L. Edwards, N.R. Golledge, M. Hemer, R.E. Kopp, G. Krinner, A. Mix, D. Notz, S. Nowicki, I.S. Nurhati, L. Ruiz, J.-B. Sallée, A.B.A. Slangen, and Y. Yu (2021). Ocean, Cryosphere and Sea Level Change. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K. Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 1211–1362, https://doi.org/110.1017/9781009157896.011


EQC Quality Assessment: "Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Gravimetric mass balance data from satellite observations: utility analysis for mass change monitoring of the ice sheets > ℹ If you want to know more > References
---
B. Zhou (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 1211–1362, https://doi.org/110.1017/9781009157896.011

- [[9](https://iopscience.iop.org/article/10.1088/1748-9326/aac2f0)] Bamber, J. L., Westaway, R. M., Marzeion, B., and Wouters, B. (2018). The land ice contribution to sea level during the satellite era. Environ. Res. Lett. 13, https://doi.org/10.1088/1748-9326/aac2f0

- [[10](https://tc.copernicus.org/articles/7/1411/2013/)] Barletta, V. R., Sørensen, L. S., and Forsberg, R. (2013). Scatter of mass changes estimates at basin scale for Greenland and Antarctica, The Cryosphere, 7, 1411–1432, https://doi.org/10.5194/tc-7-1411-2013

- [[11](https://doi.org/10.1038/s41467-024-45726-w)] Ludwigsen, C.B., Andersen, O.B., Marzeion, B., Malles, J.H., Müller Schmied, H., Döll, P., Watson, C., and King, M.A. (2024). Global and regional ocean mass budget closure since 2003. Nat. Commun. 15, 1416 (2024). https://doi.org/10.1038/s41467-024-45726-w

- [[12](https://doi.org/10.1038/s41586-019-1855-2)] The IMBIE Team (2019). Mass balance of the Greenland Ice Sheet from 1992 to 2018. Nature, 579, 233–239. https://doi.org/10.1038/s41586-019-1855-2

- [[13](https://doi.org/10.1038/s41586-018-0179-y)] The IMBIE Team (2018). Mass balance of the Antarctic Ice Sheet from 1992 to 2017. Nature 558, 219–222. https://doi.org/10.1038/s41586-018-0179-y


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications
---
Production date: 31-05-2025

Dataset version: 4.0

Produced by: Yoni Verhaegen and Philippe Huybrechts (Vrije Universiteit Brussel)


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Quality assessment question
---
* **"Is the C3S Greenland ice sheet mass balance dataset sufficiently adequate in terms of its spatio-temporal resolution and uncertainty to be used in glaciological modeling efforts?"**

Ice sheets are significant contributors to current (and future) global sea-level rise, indicators of climatic changes, and key players regarding feedback mechanisms within the atmosphere, ocean, and cryosphere. Assessing ice sheet mass changes is essential for understanding these mechanisms. At present-day, the gravimetric method from satellite-based remote sensing offers one out of the three feasible ways to regularly and accurately monitor mass changes of the entire ice sheets at a regular basis (the others being the altimetric and input-output method). The ["Gravimetric mass balance data for the Antarctic and Greenland ice sheets from 2003 to 2022 derived from satellite observations"](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) dataset on the Climate Data Store (CDS) therefore provides valuable insights into the ice sheet's mass changes. The dataset uses satellite gravimetry from the GRACE and GRACE-FO missions to detect changes in the Earth's gravitational field. These are then translated into cumulative mass anomalies of ice above buoyancy for the grounded ice of both the Greenland (GrIS) and Antarctic (AIS) ice sheets [[1](https://doi.org/10.1007/s10712-016-9398-7), [2](https://doi.org/10.3390/geosciences9100415)]. This notebook evaluates the dataset’s maturity for monitoring Greenland ice mass changes in the 21st century. More specifically, we will check whether the data are sufficiently adequate in terms of its spatio-temporal resolution and uncertainty to be applicable in glaciological modeling applications. For that, we use the dataset version 4.0.


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Quality assessment statements
---
These are the key outcomes of this assessment

- Mass change detection by GRACE(-FO) is a useful tool to quantify the total ice mass change of the GrIS (and AIS), and is one of the three main data acquisition methods that can extract ice mass change data from large spatial scales, such as the complete ice sheets, at a regular basis. GRACE(-FO) directly captures all relevant processes for ice mass change (from both mass balance and ice dynamics), but it also has its limitations of which the user should take note before using the product. A large problem with the C3S dataset is that no gridded mass change and error products are included for the ice sheets, as well as the presence of (occasionally very) high error/uncertainty values, primarily due to the large data acquisition footprint and corrections needed for mass redistribution in the atmosphere, ocean, soil and solid earth. Data gaps are also present (e.g. during the transition period between GRACE and GRACE-FO in 2017-2018 CE). These are not filled up or flagged, users need to identify them themselves.
- Concerning the specific use case and user question, the C3S GRACE(-FO) data are found to be inadequate to be used in most "traditional" glaciological modeling efforts because it is (1) only a spatially aggregated time series and has no gridded data, (2) does not include a surface mass balance component separately (which is, for example, needed in the prognostic continuity equation for ice thickness changes), and (3) has (very) high uncertainty in certain months. The GRACE(-FO) data can, on the other hand, be used for other purposes. The data are particularly well-suited for the direct calculation and monitoring of ice sheet mass changes and sea level contribution, and/or the validation of mass change estimates from other independent methods (e.g. the input-output method or the validation of the temporal variability of a surface mass balance model from a regional climate model).
```


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Methodology > Dataset description
---
The total mass balance of an ice sheet is the difference between mass gained (mainly from snow accumulation) and mass lost (by ablation or solid ice discharge across the grounding line), which is the same as the net mass change of the ice sheet. Remote sensing techniques, such as the use of satellites, are an important feature to derive and study the mass changes of the ice sheets. The ice sheet mass change dataset provides monthly gravimetric mass balance (GMB) values and their uncertainty for the Greenland (GrIS) and also the Antarctic ice sheet (AIS). The data represent a time series of the cumulative mass changes (mass anomalies) of the ice above buoyancy of the ice sheets and their basins (including ice caps and glaciers) that are derived using satellite gravimetry data from the GRACE(-FO) missions. Data are available as time series for the whole ice sheet, as well as at the basin level, but no gridded data are provided. Data are available since 2002 with units in Gt (Gigatonnes). For a more detailed description of the data acquisition and processing methods, we refer to the [documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348671) (Copernicus Knowledge Base).

The mass changes and their errors derived from GRACE(-FO) are expressed in Gt (Gigatonnes). It can also be translated into a volume, for example one Gt of water (density 1000 kg/m$^3$) is exactly one km$^3$, while one Gt of ice (density 917 kg/m$^3$) in volume becomes 1.091 km$^3$ of ice. GRACE(-FO) data are in fact considered to be the sum of mass changes driven by changing rates of solid ice discharge (i.e. the flux across the grounding line $D$) and mass changes driven by changing rates of ablation and accumulation (mainly the surface mass balance or $SMB$). What GRACE(-FO) actually detects are patterns of mass redistribution, indicating that a material should be redistributed (e.g. by ice dynamics or liquid discharge) in order for GRACE(-FO) to be able to detect gravity anomalies and the corresponding mass changes over certain locations. In that sense, an amount of melted ice being replaced by its mass-equivalent amount of meltwater at the same location would result in zero mass change.

The main advantage of GRACE(-FO) is that all processes directly contributing to ice sheet mass fluctuations are observed directly. Unlike the input-output method, SMB is therefore not involved explicitely in processing and it is not separated from ice flow dynamics. Moreover, gaps in the time series do not affect linear trend estimation as mass changes occurring during these gaps are still included in the subsequent solution. The main drawbacks of this technique are the large footprint of data acquisition and the fact that corrections must be made for mass redistribution in the atmosphere, ocean, soil and solid earth (e.g. glacial isostatic adjustment) in order to isolate mass changes relevant for the ice sheets.


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Methodology > Structure and (sub)sections
---
**[](section-1)**
* [](section-1-1)
* [](section-1-2)
* [](section-1-3)
* [](section-1-4)

**[](section-2)**
* [](section-2-1)
* [](section-2-2)
* [](section-2-3)

**[](section-3)**


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define the parameters, i.e. for which ice sheet (or which basins of these ice sheets) we want the mass change data to be extracted:

Then we define requests for download from the CDS and download and transform the glacier mass change data.

```text
100%|██████████| 1/1 [00:04<00:00,  4.46s/it]
```

```text
Downloading done.
```

(section-1-3)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
Let us inspect the data:

```text
<xarray.Dataset> Size: 17kB
Dimensions:        (time: 216)
Coordinates:
  * time           (time) datetime64[ns] 2kB 2002-04-16T20:23:54.375000 ... 2...
Data variables: (12/18)
    GrIS_total     (time) float32 864B 1.057e+03 1.123e+03 ... -3.762e+03
    GrIS_1         (time) float32 864B 54.15 42.37 52.4 ... -440.0 -471.2 -441.5
    GrIS_2         (time) float32 864B 97.2 125.0 43.44 ... 28.75 80.42 17.64
    GrIS_3         (time) float32 864B 219.8 216.2 132.5 ... -467.5 -533.6
    GrIS_4         (time) float32 864B 140.1 152.3 129.0 ... -548.1 -498.9
    GrIS_5         (time) float32 864B 76.06 68.17 53.5 ... -288.9 -316.6 -274.7
    ...             ...
    GrIS_3_er      (time) float32 864B 45.75 25.68 20.46 ... 16.83 18.87 19.34
    GrIS_4_er      (time) float32 864B 42.49 30.83 25.91 ... 18.51 18.26 22.87
    GrIS_5_er      (time) float32 864B 26.84 32.99 18.78 ... 12.84 11.66 11.76
    GrIS_6_er      (time) float32 864B 73.16 41.97 28.93 ... 22.61 24.26 25.49
    GrIS_7_er      (time) float32 864B 57.64 41.52 19.34 ... 23.11 25.23 26.11
    GrIS_8_er      (time) float32 864B 59.26 63.21 45.86 ... 22.68 22.85 21.76
Attributes:
    Title:                GMB for Greenland and Antarctica ice sheets from th...
    institution:          DTU Space - Geodesy and Earth Observations
    reference:            Baratta et al. (2016), Groh and Horwart (2016)
    file_creation_date:   Tue May 16 09:49:32 2023
    region:               Greenland and Antarctica
    missions_used:        GRACE and and GRACE-FO
    time_coverage_start:  Apr-2002
    time_coverage_end:    Dec-2022
    Tracking_id:          ab2360a4-82d5-42f3-babb-90ce976a8a8e
    netCDF_version:       NETCDF4
    product_version:      4.0
    Summary:              This data set is prepared for the C3S project, and ...
```

It is a dataset that consists of several time series data, containing cumulative values of the total ice sheet mass change (cumulative mass anomalies) of, in this notebook, the entire Greenland Ice Sheet (`GrIS_total`) or its basins (`GrIS_{basin_number}`), as well as their uncertainty (`GrIS_total_er` and `GrIS_{basin_number}_er`) since 2002. For basin definitions and delineation, see Zwally et al. (2012) [[3](https://earth.gsfc.nasa.gov/cryo/data/polar-altimetry/antarctic-and-greenland-drainage-systems)]. Mass changes and their uncertainty are expressed in units of Gt and the time period between two measurements is variable but mostly at monthly-spaced intervals. Note that no gridded data are given in this dataset, and hence no spatial resolution can be derived.

(section-1-4)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 1. Data preparation and processing > 1.4 Data handling and creating functions
---
Let us perform some data handling before getting started with the analysis:

Check if the variable name contains a number
Check if the variable name contains a number
Check if the variable name contains a number

We also define a plotting function to visualize the time series:

Create a GridSpec layout with enough rows
Convert time to pandas datetime for easy handling
Plot the first variable, spanning the first row
Define dataset-specific y-axis bounds
Identify large gaps and shade them
Plot the remaining variables, two per row

With everything ready, let us now start with the analysis:

(section-2)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 2. Quantifying Greenland Ice Sheet mass changes and their errors in space and time > 2.1 Time series of cumulative ice sheet mass changes
---
We begin by plotting the GrIS cumulative mass change $M_{GRACE}$ between the begin and end period with the defined plotting function, where the shading in the upper part of the plot indicates when the time between two consecutive measurements is more than 1 month:

*Figure 1. Greenland ice sheet mass changes from GRACE(-FO). The top plot shows the mass changes over the entire ice sheet, where shaded intervals depict data gaps longer than 1 month. The smaller graphs below show the mass changes of the individual basins.*

In the figure above, the first graph on top represents the cumulative mass change of the entire GrIS, while other graphs show the mass changes of its basins. Overall, these graphs depict a significant and widespread loss of ice mass across the practically the entire ice sheet, with different basins showing varying rates and patterns of ice loss. The findings underscore the critical state of the GrIS, serving as a clear indicator of the impacts of climate change [[2](https://doi.org/10.3390/geosciences9100415), [4](https://essd.copernicus.org/articles/15/1597/2023/)].

We recall the data are expressed as time series of cumulative values (mass anomalies) of the sum of mass changes driven by changing rates of solid ice discharge (i.e. the ice flux across the grounding line) and mass changes driven by changing rates of ablation and accumulation (mainly the SMB) at the basin-scale or ice sheet-wide scale.

(section-2-2)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 2. Quantifying Greenland Ice Sheet mass changes and their errors in space and time > 2.2 Ice sheet mass changes uncertainty estimates
---
The total error of a monthly ice sheet mass change estimate for Greenland is given by the sum of the precision (random) and the accuracy (systematic) error:

$
\varepsilon = a\sigma + \delta
$
where $a$ is the critical z-value related to a certain statistical confidence interval, $\sigma$ is the standard deviation (random error) and $\delta$ the accuracy (systematic) error.

For the GrIS, the product deals with both precision and accuracy errors in its final error estimates [[5](https://tc.copernicus.org/articles/7/1411/2013/)]. The precision error accounts for the statistically distributed random error around one average value. The accuracy error accounts for how much the expected value deviates from the “true” value, dervied from averaging mass change time series obtained with different methods, models and corrections. For the precision error, the 95% confidence interval ($a$ = 1.96) propagated from the data, is provided. Therefore, in the case for the GrIS, the total uncertainty of the data is given by $\varepsilon$. Hence, in the C3S products the most complete error estimate that was evaluated by Barletta et al. (2013) was given [[5](https://tc.copernicus.org/articles/7/1411/2013/)]. In the following section below, we will thus consider the uncertainty of the dataset as being $\varepsilon_{M_{GRACE}}$.

Let us plot a time series of the errors:

*Figure 2. Greenland ice sheet mass change errors from GRACE(-FO). The top plot shows the mass change errors over the entire ice sheet, where shaded intervals depict data gaps longer than 1 month. The smaller graphs below show the mass change errors of the individual basins.*

Note that these values are not normalized to a certain time period, as the time gap between two measurements is (slightly) variable. Uncertainties in GRACE ice mass change estimates are occasionally very high and arise from various sources. These include, amongst others, errors related to measurement noise (e.g. due to leakage of the signal outside the region of interest such as the Canadian ice caps, due to the coarse resolution of GRACE(-FO) data acquisition), uncertainties related to the Earth's gravitational field (e.g. due to the shift of the Earth's center of mass, or due to the influence of the atmosphere and oceans on the Earth's gravity field), and uncertainties related to other mass change signals that may be intertwined in the GRACE(-FO) data (e.g. those related to glacial isostatic adjustment).

We can furthermore calculate the average values (arithmetic means over time):

```text
The arithmetic mean mass change error of the GrIS in total is 76.72 Gt with a maximum of 740.25 Gt.
The arithmetic mean mass change error of the GrIS basin 1 is 58.71 Gt with a maximum of 671.28 Gt.
The arithmetic mean mass change error of the GrIS basin 2 is 42.94 Gt with a maximum of 438.62 Gt.
The arithmetic mean mass change error of the GrIS basin 3 is 23.66 Gt with a maximum of 231.57 Gt.
The arithmetic mean mass change error of the GrIS basin 4 is 22.24 Gt with a maximum of 249.10 Gt.
The arithmetic mean mass change error of the GrIS basin 5 is 13.86 Gt with a maximum of 108.55 Gt.
The arithmetic mean mass change error of the GrIS basin 6 is 33.96 Gt with a maximum of 412.35 Gt.
The arithmetic mean mass change error of the GrIS basin 7 is 24.06 Gt with a maximum of 234.92 Gt.
The arithmetic mean mass change error of the GrIS basin 8 is 33.13 Gt with a maximum of 450.22 Gt.
```


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 2. Quantifying Greenland Ice Sheet mass changes and their errors in space and time > 2.2 Ice sheet mass changes uncertainty estimates
---
of 234.92 Gt.
The arithmetic mean mass change error of the GrIS basin 8 is 33.13 Gt with a maximum of 450.22 Gt.
```

For the entire ice sheet, error values mostly range between 50 and 100 gigatonnes (Gt), with occasional spikes reaching around 400 Gt or more. When comparing the errors to the respective mass change magnitudes, it can be noted that for the majority of the time series, the errors are relative large when compared to the actual changes in mass. This suggests that the data should be handled with care for most periods. The user can decide whether to leave the months with the highest errors out if desired. It is furthermore difficult to compare these errors to GCOS requirements (GCOS, 2022) because (a) the GCOS does not propose thresholds for mass change explicitely, but solely for ice sheet volume changes, (b) the GCOS reformulates error requirements in the form of precision errors (2$\sigma$), while the error in the GrIS mass change product contains an error product that combines precision and accuracy errors [[5](https://tc.copernicus.org/articles/7/1411/2013/)], and (c) the time difference between two GRACE measurements varies over time, and the time series also exhibits time gaps which complicates normalizing the errors to a common timeframe.

Concerning the errors, it must be said that in the C3S GrIS GMB products, the most complete error estimate that could be evaluated is included [[5](https://tc.copernicus.org/articles/7/1411/2013/)]. However, in contrast to other datasets, these errors are not easily formalized as the standard deviation or the 95% confidence interval. Most datasets namely do not usually provide the total error (i.e. they neglect the accuracy error). Apart all complex processes that can introduce uncertainty (as described above), this additionally provides a partial explanation for the relatively high uncertainty values for the ice sheet GMB dataset.

(section-2-3)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 2. Quantifying Greenland Ice Sheet mass changes and their errors in space and time > 2.3 Application to an ice sheet modelling framework
---
Let us now go back to our user question and assess whether the data are sufficiently adequate in terms of its spatio-temporal resolution and uncertainty to be applicable in glaciological modeling applications. Given the nature of the dataset and the above analysis, it is difficult to directly use GrIS (or AIS) GRACE(-FO) ice sheet mass change data into a "traditional" ice sheet model for several reasons:
- Most importantly, ice sheet models that solve the continuity equation for prognostic ice thickness changes require surface mass balance ($SMB$) (and, if desired, basal mass balance ($BMB$)) data (measured in m yr⁻¹ ice equivalents). However, GRACE(-FO) data include mass changes that combine both $SMB$ and solid ice discharge ($D$) across the grounding line, complicating direct integration into models.
- The coarse spatial resolution (actually, since no gridded data are provided, the term "spatial resolution" is not applicable for this dataset) and relatively high uncertainties of GRACE(-FO) data limit their ability to be useful in ice sheet models. GRACE(-FO) data are more suited for basin-scale or ice sheet-wide analyses rather than the fine-scale resolution (pixels or grid-based data) required for pixel-by-pixel modeling in ice sheet models.

To be directly usable in glaciological models, the C3S GRACE(-FO) GMB data would need a downscaling to higher spatial resolutions (i.e. reformatting into gridded products), an integration with SMB models or ice discharge data for component separation, and improved corrections/uncertainty characterization for certain months. The data can, however, be used for other purposes. GRACE(-FO) data are, for example, valuable for the direciton calculation and monitoring of ice sheet mass changes and their sea level contribution, or for the independent validation of ice sheet mass balance estimates from other methods. For example, they can help assess results from the input-output method, which quantifies the surface mass balance ($SMB$) and solid ice discharge ($D$) components seperately [[6](https://essd.copernicus.org/articles/12/1367/2020/), [7](https://tc.copernicus.org/articles/7/469/2013/)], as well as for validating surface mass balance output from regional climate model outputs for Greenland (e.g. [[7](https://tc.copernicus.org/articles/7/469/2013/), [8](https://doi.org/10.1126/science.1178176), [9](https://doi.org/10.5194/tc-10-1933-2016)]). Studies, including Van den Broeke (2016) [[9](https://doi.org/10.5194/tc-10-1933-2016)], have shown that cumulative surface mass balance ($SMB$) minus solid ice discharge ($D$) closely aligns with the trends and variability of GRACE(-FO) mass changes for Greenland, confirming the credibility and reliability of the GRACE(-FO) mass change data, despite the relatively high error/uncertainty values provided with the data.

(section-3)=


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > Analysis and results > 3. Short summary and take-home messages
---
The ice sheet mass change dataset, making use of the GRACE(-FO) satellite missions, is a useful tool for quantifying the total ice mass change of the Greenland (GrIS) Ice Sheet. It is one of the three main data acquisition methods that can extract ice mass change data from large spatial scales, such as the complete ice sheets, at a regular basis (the others being the altimetric and the input-output methods). The C3S ice sheet GMB data, with its long temporal extent (> 20 years), ice sheet-wide coverage and (quasi) monthly temporal resolution, effectively captures the long-term mean, trends and variability of ice sheet mass changes and the corresponding global sea level contributions. The data thus serve as a clear indicator of global climate change and water cycle changes.

Despite its strengths, GRACE(-FO) has certain limitations of which the user should take note, including a low spatial resolution (only ungridded ice-sheet-wide or basin-scale changes) and (occasionally very) high uncertainty values, including for example potential signal leakage from adjacent regions (e.g. the Canadian ice caps or peripheral glaciers and ice caps). Additional uncertainties furthermore arise from necessary geophysical corrections (e.g. glacial isostatic adjustment and intertwined mass changes from outer sources). Some GRACE(-FO) error values exhibit very high values, requiring careful interpretation. Additionally, data gaps (e.g. between the GRACE and GRACE-FO missions) affect the time series continuity, but these do not generally affect the overal trend and magnitude of the cumulative mass changes in the product (e.g. [[10](https://doi.org/10.1029/2020GL087291)]). Nevertheless, unlike the input-output method (where SMB is directly needed) and the altimetric method (where it is necessary to obtain the firn density profiles for the volume-to-mass conversion), the SMB is not explicitly involved in the processing of GRACE(-FO) data, nor is it separated from ice flow dynamics. This independence negates uncertainties due to potential discrepancies between SMB model outputs from different centers and is a significant advantage of this method.

Moreover, due to the nature of the C3S GRACE(-FO) data presented on the CDS, they cannot be used directly as data assimilation into any glaciological model that requires the usage of pixel-based data to model ice thickness changes (e.g. an ice sheet model that solves the prognostic continuity equation on a grid). In essence, the results of this notebook therefore indicate that the product is inadequate to be used in most "traditional" glaciological modelling efforts because it is (1) only a spatially aggregated time series, (2) does not include SMB separately (which is to be used in the prognostic continuity equation for ice thickness changes), and (3) has high uncertainty in certain months. Nevertheless, it certainly has other applications and is highly relevant for the direct calculation and monitoring of ice sheet mass changes and their sea level contribution, and/or the validation of mass change estimates from other independent methods (e.g. the input-output method or the validation of the temporal variability of a surface mass balance model from a regional climate model) (e.g. [[7](https://tc.copernicus.org/articles/7/469/2013/), [8](https://doi.org/10.1126/science.1178176), [9](https://doi.org/10.5194/tc-10-1933-2016)]).


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > ℹ If you want to know more > Key resources
---
- "[Gravimetric mass balance data for the Antarctic and Greenland ice sheets from 2003 to 2022 derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview)" on the CDS.
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ice-sheet-mass-balance?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348671) (Copernicus Knowledge Base).
- [Copernicus climate change indicators: ice sheets](https://climate.copernicus.eu/climate-indicators/ice-sheets)
- [The data portal with GrIS GMB data from the data provider (TU Dresden)](https://data1.geo.tu-dresden.de/gis_gmb/index.html)
- [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control` prepared by [B-Open](https://www.bopen.eu).


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > ℹ If you want to know more > References
---
- [[1](https://doi.org/10.1007/s10712-016-9398-7)] Forsberg, R., Sørensen, L.S. and Simonsen, S.B. (2017). Greenland and Antarctica Ice Sheet Mass Changes and Effects on Global Sea Level. Surv. Geophys., 38, 89–104. https://doi.org/10.1007/s10712-016-9398-7

- [[2](https://doi.org/10.3390/geosciences9100415)] Groh, A., Horwath, M., Horvath, A., Meister, R., Sørensen, L.S., Barletta, V.R., Forsberg, R., Wouters, B., Ditmar, P., Ran, J., Klees, R., Su, X., Shang, K., Guo, J., Shum, C.K., Schrama, E., and Shepherd, A. (2019). Evaluating GRACE Mass Change Time Series for the Antarctic and Greenland Ice Sheet, Geosciences, 9(10). https://doi.org/10.3390/geosciences9100415

- [[3](https://earth.gsfc.nasa.gov/cryo/data/polar-altimetry/antarctic-and-greenland-drainage-systems)] Zwally, H., Giovinetto, M., Beckley, M., and Saba, J. (2012). Antarctic and Greenland drainage systems, GSFC cryospheric sciences laboratory. URL: https://earth.gsfc.nasa.gov/cryo/data/polar-altimetry/antarctic-and-greenland-drainage-systems

- [[4](https://essd.copernicus.org/articles/15/1597/2023/)] Otosaka, I. N., Shepherd, A., Ivins, E. R., Schlegel, N.-J., Amory, C., van den Broeke, M. R., Horwath, M., Joughin, I., King, M. D., Krinner, G., Nowicki, S., Payne, A. J., Rignot, E., Scambos, T., Simon, K. M., Smith, B. E., Sørensen, L. S., Velicogna, I., Whitehouse, P. L., A, G., Agosta, C., Ahlstrøm, A. P., Blazquez, A., Colgan, W., Engdahl, M. E., Fettweis, X., Forsberg, R., Gallée, H., Gardner, A., Gilbert, L., Gourmelen, N., Groh, A., Gunter, B. C., Harig, C., Helm, V., Khan, S. A., Kittel, C., Konrad, H., Langen, P. L., Lecavalier, B. S., Liang, C.-C., Loomis, B. D., McMillan, M., Melini, D., Mernild, S. H., Mottram, R., Mouginot, J., Nilsson, J., Noël, B., Pattle, M. E., Peltier, W. R., Pie, N., Roca, M., Sasgen, I., Save, H. V., Seo, K.-W., Scheuchl, B., Schrama, E. J. O., Schröder, L., Simonsen, S. B., Slater, T., Spada, G., Sutterley, T. C., Vishwakarma, B. D., van Wessem, J. M., Wiese, D., van der Wal, W., and Wouters, B. (2023). Mass balance of the Greenland and Antarctic ice sheets from 1992 to 2020, Earth Syst. Sci. Data, 15, 1597–1616, https://doi.org/10.5194/essd-15-1597-2023

- [[5](https://tc.copernicus.org/articles/7/1411/2013/)] Barletta, V. R., Sørensen, L. S., and Forsberg, R. (2013). Scatter of mass changes estimates at basin scale for Greenland and Antarctica, The Cryosphere, 7, 1411–1432, https://doi.org/10.5194/tc-7-1411-2013


EQC Quality Assessment: "Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications"
Dataset: satellite-ice-sheet-mass-balance [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Gravimetric mass changes from satellite data: assessment of resolution and uncertainty of Greenland ice sheet mass changes for glaciological applications > ℹ If you want to know more > References
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). Scatter of mass changes estimates at basin scale for Greenland and Antarctica, The Cryosphere, 7, 1411–1432, https://doi.org/10.5194/tc-7-1411-2013

- [[6](https://essd.copernicus.org/articles/12/1367/2020/)] Mankoff, K. D., Solgaard, A., Colgan, W., Ahlstrøm, A. P., Khan, S. A., and Fausto, R. S. (2020). Greenland Ice Sheet solid ice discharge from 1986 through March 2020, Earth Syst. Sci. Data, 12, 1367–1383, https://doi.org/10.5194/essd-12-1367-2020

- [[7](https://tc.copernicus.org/articles/7/469/2013/)] Fettweis, X., Franco, B., Tedesco, M., van Angelen, J. H., Lenaerts, J. T. M., van den Broeke, M. R., and Gallée, H. (2013). Estimating the Greenland ice sheet surface mass balance contribution to future sea level rise using the regional atmospheric climate model MAR, The Cryosphere, 7, 469–489, https://doi.org/10.5194/tc-7-469-2013

- [[8](https://doi.org/10.1126/science.1178176)] van den Broeke, M., Bamber, J., Ettema, J., Rignot, E., Schrama, E., van de Berg, W. J., van Meijgaard, E., Velicogna, I., and Wouters, B. (2009). Partitioning recent Greenland mass loss. Science, 326(5955), 984-986. https://doi.org/10.1126/science.1178176

- [[9](https://doi.org/10.5194/tc-10-1933-2016)] van den Broeke, M., Enderlin, E. M., Howat, I. M., Kuipers Munneke, P., Noël, B. P. Y., van de Berg, W. J., van Meijgaard, E., and Wouters, B. (2016). On the recent contribution of the Greenland ice sheet to sea level change, The Cryosphere, 10, 1933–1946, https://doi.org/10.5194/tc-10-1933-2016

- [[10](https://doi.org/10.1029/2020GL087291)] Velicogna, I., Mohajerani, Y., A, G., Landerer, F., Mouginot, J., Noel, B., Rignot, E., Sutterley, T., van den Broeke, M., van Wessem, M., and Wiese, D. (2020). Continuity of Ice Sheet Mass Loss in Greenland and Antarctica from the GRACE and GRACE Follow-On Missions. Geophys. Res. Lett. 47. https://doi.org/10.1029/2020GL087291


EQC Quality Assessment: "Satellite fire burned area completeness for seasonal climatology maps"
Dataset: satellite-fire-burned-area [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Satellite_ECVs
Section: Satellite fire burned area completeness for seasonal climatology maps > Quality assessment question
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* **How well can we disclose what are the spatial patterns of the total burned area per season over the Iberian Peninsula?**

In this Use Case we will access the Fire burned area from 2001 to present derived from satellite observations (henceforth, FIRE) data from the Climate Data Store (CDS) of the Copernicus Climate Change Service (C3S) and analyse the spatial patterns of the FIRE reliability over a given Area of Interest (AoI), considering the Nomenclature of Territorial Units for Statistics, at the level 2, which are used for decision monitoring and decision-making purposes (see section 3)’