EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 2. Ice sheet flow velocities and their uncertainty estimates in space and time > 2.1 Average horizontal ice flow velocities
---
We begin by plotting the average ice flow velocities for each hydrological year between the beginning and end period that we selected for the velocity data with a defined plotting function. Let us begin with the GrIS:

🚨 **The files can be large! Since the data files to be plotted are of considerable size, this may take a couple of minutes.**

Greenland setup
Extract and preprocess data
Plot Greenland
Colorbar with formatting

*Figure 1. Magnitude of the average horizontal surface flow velocities over Greenland over the defined time period.*

And now also the AIS:

Antarctica setup
Extract and preprocess data
Plot Antarctica
Colorbar with formatting

*Figure 2. Magnitude of the average horizontal surface flow velocities over Antarctica over the defined time period.*

The corresponding data are annually averaged values, and are hence derived from all-year round observations during the glaciological balance year. The annually averaged nature of the data meets the minimum requirement for GCOS (Global Climate Observing System) [[2](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)].

For the GrIS, the dataset shows almost no temporal or spatial (as most have been filled up) data gaps and is presented as gridded values at a spatial resolution of 250 meter (for versions 1.3 to 1.5 as used here), even though spatially filled gaps are not flagged and hence not detectable. The spatial coverage of the data thus approximates 100% and encompasses the entire ice sheet, including peripheral glaciers and ice caps. However, an ice mask is not included and it is thus not possible to exclude non ice-covered pixels from the data. Pixels over ice-free terrain hold non-NaN data and have not been removed, implying that the data exhibits false low velocity measurements and noise over ice-free terrain.

For the AIS, most of the margin is covered by the C3S product, but no values are present over the interior of the ice sheet due to the Sentinel-1 acquisition mask (data is only collected at the margins).

(section-2-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 2. Ice sheet flow velocities and their uncertainty estimates in space and time > 2.2 Ice flow velocity uncertainty: accuracy and precision
---
Let us now consider the unceratinty of the dataset. The total error of an annual ice flow velocity estimate is theoretically given by the sum of the precision (random) and the accuracy (systematic) error:

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

In the ice flow velocity dataset, precision errors are reported as the standard deviation (i.e. the 68% confidence interval) and the accuracy error is not provided. Therefore, in our case, $\delta$ = 0.

Accuracy errors are thus not directly included in the total error estimate of the dataset. To get an idea of the accuracy, the [PQAR](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348656) can be consulted, where the results of a validation study are summarized. The validation process involved comparing the velocity maps with in-situ GPS data from various sites, as well as with NASA's MEaSUREs velocity product [[3](https://nsidc.org/data/nsidc-0777/versions/1)]. Quality assurance furthermore included an algorithm performance assessment in stable terrain (where velocities should equal 0) [[6](https://doi.org/10.1016/j.rse.2017.08.038)]. The results demonstrate a relatively good agreement between the dataset and independent external data.

Quantitative pixel-by-pixel error estimates are, on the other hand, available for the dataset in the form of precision errors and valid measurement counts. The uncertainty characterization is hence quantified by two variables: the standard deviation (i.e. a precision error from a 5x5 pixel neighbourhood) of the velocity estimate with units of m/day, and the valid pixel count (the number of non-NaN observations used in the production of each annual velocity estimate for a certain pixel, or differently stated, the amount of individual displacement estimates (i.e. image pairs) that were used to calculate the annually averaged velocity at that pixel). Let us express the valid pixel count variable with symbol $N_{VP}$.

We will proceed by changing the units of the error $\varepsilon$ to m yr⁻¹ because the GCOS Implementation Plan report advises uncertainty values to be provided in these units [[2](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)]. We will also multiply the standard deviation by 2 because the GCOS assesses precision errors in the form of 2 standard deviations:

$
\varepsilon_{{V_s}}
$
[m yr⁻¹]
$
= 365.25 \cdot (2 \cdot \sigma_{V_{s}})
$

We can now perform some statistics on the error term over all pixels and all years to inspect its overall value for both ice sheets:

Show measurements count


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 2. Ice sheet flow velocities and their uncertainty estimates in space and time > 2.2 Ice flow velocity uncertainty: accuracy and precision
---
$

We can now perform some statistics on the error term over all pixels and all years to inspect its overall value for both ice sheets:

Show measurements count

```text
domain = 'greenland_ice_sheet'
Mean velocity error (2σ) for 2014-2015 CE: 20.42 m/yr
Mean velocity error (2σ) for 2015-2016 CE: 10.93 m/yr
Mean velocity error (2σ) for 2016-2017 CE: 9.92 m/yr
Mean velocity error (2σ) for 2017-2018 CE: 9.19 m/yr
Mean velocity error (2σ) for 2018-2019 CE: 7.90 m/yr
Mean velocity error (2σ) for 2019-2020 CE: 7.14 m/yr
Mean velocity error (2σ) for 2020-2021 CE: 328.67 m/yr
Mean velocity error (2σ) for 2021-2022 CE: 7.69 m/yr
Mean velocity error (2σ) for 2022-2023 CE: 12.84 m/yr
Mean measurement count for 2014-2015 CE: 19.75 estimates/pixel
Mean measurement count for 2015-2016 CE: 61.04 estimates/pixel
Mean measurement count for 2016-2017 CE: 108.80 estimates/pixel
Mean measurement count for 2017-2018 CE: 133.65 estimates/pixel
Mean measurement count for 2018-2019 CE: 138.09 estimates/pixel
Mean measurement count for 2019-2020 CE: 136.80 estimates/pixel
Mean measurement count for 2020-2021 CE: 122.56 estimates/pixel
Mean measurement count for 2021-2022 CE: 78.79 estimates/pixel
Mean measurement count for 2022-2023 CE: 51.34 estimates/pixel

domain = 'antarctic_ice_sheet'
Mean velocity error (2σ) for 2021-2022 CE: 14.09 m/yr
Mean velocity error (2σ) for 2022-2023 CE: 19.45 m/yr
Mean measurement count for 2021-2022 CE: 71.04 estimates/pixel
Mean measurement count for 2022-2023 CE: 45.61 estimates/pixel
```

The threshold (i.e. the minimum requirement to be met to ensure that data are useful) for surface ice flow velocity uncertainty (expressed in terms of 2$\sigma$) proposed by the GCOS is 100 m yr⁻¹, while the "goal" value (i.e. an ideal requirement above which further improvements are not necessary) would be 10 m yr⁻¹ per grid point [[2](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)]. The overall arithmetic mean error over both space and time shows that the minimum threshold is reached for all years but the 2020-2021 period for the GrIS (which will be discussed later).

(section-2-3)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 2. Ice sheet flow velocities and their uncertainty estimates in space and time > 2.3 Spatio-temporal distribution of ice flow velocity uncertainty for the GrIS
---
Let us now plot the spatial distribution of the errors (here thus visualized as 2 times the standard deviation with units in meters per year):

🚨 **The files can be large! Since the data files to be plotted are of considerable size, this may therefore take a couple of minutes.**

Greenland setup
Extract and preprocess data
Plot Greenland
Colorbar with formatting

*Figure 3. Magnitude of the average horizontal surface flow velocity error over Greenland over the defined time period.*

Here, high standard deviation areas suggest lower precision and higher uncertainty. From the images above, it can immediately be seen why the horizontal velocity error for the 2020-2021 period is relatively high when compared to the earlier years: the data for this particular  year have not been masked. High errors prevail over the ocean, which is of course unrealistic, and data even extend further into the Canadian Arctic. We can solve this by masking the data (i.e. by excluding the data outside of the Greenland continent land borders) and recalculating the error:

```text
The masked arithmetic mean precision error (2σ) for the 2020-2021 period is 6.51 m yr⁻¹.
```

Nevertheless, from the figure above, the precision errors seem to be especially higher near the margins of the ice sheet. In these regions, the threshold value of 100 m yr⁻¹ is locally not reached. Let us make this plot a bit clearer by grouping the errors (here averaged over all time periods) with respect to the threshold values proposed by the GCOS:

Create subplots with Polar Stereographic projection
Plot the data
Set extent and plot features
Add colorbar
Apply the function to the velocity standard deviation data
Define bounds and colormap

*Figure 4. Classification of the average horizontal surface flow velocity error over Greenland over the defined time period according to proposed GCOS thresholds.*

When plotted, the error (in the figure above plotted as averaged over all time periods) of the ice velocity product exhibits a significant spatial variability, with higher values generally observed near the ice sheet margins. Here, the terrain complexity, rapidly changing surface conditions (such as high ice melt or any other changes in the terrain that can alter the scattering characteristics of the radar pulse), as well as the relatively high speed of the outlet glaciers, have a direct impact on the absolute error value [[6](https://doi.org/10.1016/j.rse.2017.08.038)]. Conversely, towards the interior of the ice sheet, where there is little or no melt and ice flow speeds are relatively low and stable, the standard deviation is relatively low as well.

We can check in what percentage of the pixels the GCOS requirements have been reached or not reached:

```text
The percentage of data points with a velocity precision error value (2σ) less than 10 m yr⁻¹ is 71.03%.
The percentage of data points with a velocity precision error value (2σ) more than 100 m yr⁻¹ is 1.54%.
```

The majority of data therefore meet the uncertainty threshold proposed by the GCOS in the case of the GrIS, which adds credibility to the C3S ice sheet velocity product.

(section-2-4)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 2. Ice sheet flow velocities and their uncertainty estimates in space and time > 2.4 Spatio-temporal distribution of ice flow velocity uncertainty for the AIS
---
Now let us repeat the same procedure for Antarctica. We first plot the average velocity errors:

Antarctica setup
Extract and preprocess data
Plot Antarctica
Colorbar with formatting

*Figure 5. Magnitude of the average horizontal surface flow velocity error over Antarctica over the defined time period.*

In the above figure, we note a very similar pattern as with the GrIS: the flow velocity errors are relatively high near the margins, but are considered small over the interior low-flow zones of the ice sheet. Let us classify them according to the proposed GCOS thresholds:

Create subplots with Polar Stereographic projection
Plot the data
Set extent and plot features
Add colorbar
Apply the function to the velocity standard deviation data
Define bounds and colormap

*Figure 6. Classification of the average horizontal surface flow velocity error over Antarctica over the defined time period according to proposed GCOS thresholds.*

The spatio-temporal pattern of ice sheet velocity errors is therefore similar to that of the GrIS. Let us check in what percentage of the pixels the GCOS requirements have been reached or not reached:

```text
The percentage of data points with a velocity precision error value (2σ) less than 10 m yr⁻¹ is 55.56%.
The percentage of data points with a velocity precision error value (2σ) more than 100 m yr⁻¹ is 1.59%.
```

As with the GrIS, the majority of the pixels exhibit uncertainty values that fall within the thresholds proposed by GCOS. This ensures that the C3S AIS velocity product holds credible data. Next, let us deal with the second measure of error and uncertainty: the valid pixel count.

(section-3)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 3. Valid measurement counts for the surface ice flow velocity > 3.1 Spatio-temporal distribution of ice flow velocity valid pixel counts for the GrIS
---
In the figure below, we plot the averaged pixel-by-pixel valid measurement counts of the horizontal surface velocity for the GrIS:

Greenland setup
Extract and preprocess data
Plot Greenland
Colorbar with formatting

*Figure 7. Average annual valid pixel count of the horizontal surface flow velocity for Greenland over the defined time period.*

In the figure above, the straight edges of different valid pixel counts and the apparent paths of data acquisition are an indicator that the differences in valid pixel count are partly due to the satellite acquisition. However, higher valid pixel counts are clearly observed along the margins of the ice sheet and major outlet glaciers, consistent with areas of fast dynamics that require a more detailed monitoring.

This reflects the fact that generating high-density velocity estimates using SAR-based offset tracking is generally more challenging in the interior of the ice sheet. This difficulty mainly arises because of the relatively slow movement of ice in the interior compared to the faster-flowing edges, which results in smaller displacements between image pairs. It may also be because of less traceable surface features in the interior as compared to the margins, where for example, crevasses are more frequent. This makes it harder to detect and measure them accurately. A drawback to the data is the fact that there is no information given related to the time of the year during which valid measurements were acquired and that no data at a finer temporal resolution than 1 year are present.

(section-3-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 3. Valid measurement counts for the surface ice flow velocity > 3.2 Spatio-temporal distribution of ice flow velocity valid pixel counts for the AIS
---
Let us plot the same for the AIS:

Antarctica setup
Extract and preprocess data
Plot Antarctica
Colorbar with formatting

*Figure 8. Average annual valid pixel count of the horizontal surface flow velocity for Antarctica over the defined time period.*

As with the GrIS, a higher count in the figure above typically indicates a more reliable estimate due to the inclusion of more observations into the velocity estimate. Paths of data acquisition are, however, also clearly visible in the pattern. This suggests that valid pixel counts are also dependent on the satellite acquisition and do not always represent glaciological signals. As with Greenland, a drawback to the data is the fact that there is no information given related to the time of the year during which valid measurements were acquired. Again, no thresholds are proposed by GCOS with respect to valid pixel counts, so no comparison is possible. However, the higher the valid pixel count, the more reliable a velocity estimate can be considered.

(section-4)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 4. Implications for use of horizontal ice flow velocity data in an ice sheet modelling framework > 4.1 Ice sheet model initialisation and tuning of the surface flow velocity field
---
In the following section, we integrate all information derived above (with respect to spatio-temporal coverage and uncertainty) to assess the suitability of the ice sheet surface ice flow velocity dataset to use the velocity product in an ice sheet modelling framework.

At the heart of an ice sheet model is the solution of the time-dependent continuity equation for ice thickness $H$:

$
\dfrac{\partial H}{\partial t} = -\nabla \cdot (\vec{\overline{v}}H) + M - S
$

where $H$ is the ice thickness, $\vec{\overline{v}}$ is the vertically averaged horizontal velocity vector, $M$ is the surface mass balance, and $S$ is the basal mass balance. A calibration procedure involves adjusting, for example, the basal sliding coefficient in Weertman’s basal sliding law in areas with basal temperatures at the pressure melting point and/or to adjust the rate factor in Glen’s flow law for interior regions frozen to bedrock (which impact $\vec{\overline{v}}$). This allows the modelled ice thickness or surface velocity to match the observed one (e.g. [[4](https://doi.org/10.5194/gmd-12-2481-2019), [5](https://doi.org/10.3390/rs11121407)]). This approach is valid as the present-day velocities of the ice sheets are supposedly close to the balance velocities.

In that regard, comparing modelled surface velocity fields to the observed ones provides a tool for the calibration/validation of an ice sheet model. The C3S ice sheet velocity product is particularly well-suited for this purpose. Even though large spatial gaps remain for the AIS product, the most prominent and dynamic regions across the margins are covered. Moreover, the GrIS product practically entirely covers the Greenland continent. Furthermore, the C3S velocity product includes quantitative pixel-by-pixel error estimates, for which the uncertainty characterization is represented by two variables: the standard deviation (i.e. a precision error) and the valid pixel count (the number of observations used to estimate the eventual average pixel value). The inclusion of both variables enhances the product quality and can serve as an important factor to consider when using the velocity product in an ice sheet modelling framework. When tuning an ice sheet model, it can, for example, be beneficial to prioritize high-quality velocity data (i.e. with a low absolute or relative error and a high valid measurement count). This ensures that the model solution is based on the most reliable observations and higher quality data have a greater influence on the eventual solution. One strategy could be to weigh the data using weights based on both the velocity standard deviation and the valid measurement count. This approach involves combining the two variables to form a single weight $w_i$ for each data point $i$:

$w_i = \alpha \cdot (1-\varepsilon_{V_{s},i}^{'}) + \beta \cdot N_{VP,i}^{'}
$

where:
- $\varepsilon_{V_{s},i}^{'}$ are the normalized (relative) errors,
- $N_{VP,i}^{'}$ are the normalized valid measurement counts,
- weights $\alpha$ and $\beta$ for which $\alpha + \beta = 1$.

When using these weights in model validation, each data point's contribution to the model can be weighed accordingly. For instance, the weighted sum of squared residuals can be compared:

$
\sum_i w_i (y_i - f(x_i))^2
$

where:
- $y_i$ is the observed data (i.e. here the velocities from the dataset)
- $f(x_i)$ is the model prediction for the i$^{th}$ data point
- $w_i$ is the weight for the i$^{th}$ data point

(section-4-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 4. Implications for use of horizontal ice flow velocity data in an ice sheet modelling framework > 4.2 Presence of arteficial 'striping'
---
Apart from quantitive error estimates, another phenomenom deserves special attention. Namely, the presence of 'striping' (i.e. banding or noise in the velocity data that become especially visible in low-flow zones) in SAR offset tracking-based ice velocity estimates can have several significant impacts when using the C3S product for the validation of ice sheet models, especially in interior low-flow zones. In short, these stripes originate from certain specific atmospheric disturbances that interfer with the SAR signal, producing spatially variable unwanted displacements (e.g. [[12](https://doi.org/10.1109/IGARSS.2006.956)]).

The presence of striping reduces the overall quality of the velocity data in low-flow zones and may lead to the misinterpretation of physical processes driving ice flow in these areas. This unrealistic pattern, especially visible in the interior of the ice sheet, may therefore limit the use of the product for slowly moving ice and is hence important to consider when using the data. Mitigating these artefacts involves, for example, noise reduction methods such as spatial averaging or filtering, or the integration of velocities from SAR interferometry, which are generally very accurate for slow-moving ice [[1](https://doi.org/10.3390/rs70709371), [7](https://doi.org/10.3390/rs9101062), [9](https://doi.org/10.1029/2019GL083826)]. Another possible solution is replacing the distorted velocities in these areas by balance velocities or to only use velocities above a certain threshold (i.e. >5 m yr⁻¹) for the relevant procedure.

(section-5)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > Analysis and results > 5. Short summary and take-home messages
---
Satellite-derived ice velocity data provide valuable insight into the flow dynamics of the ice sheets [[11](https://doi.org/10.1016/j.rse.2025.115092)], but users should be aware of specific limitations in the SAR offset tracking-based velocity products. It should be noted that data quality varies across the ice sheet and is best assessed using the provided standard deviation maps (indicating precision errors) and valid measurement count maps (reflecting the number of successful matches used in annual velocity averaging). Challenging regions include the fast-flowing margins, where high absolute errors occur, as well as the interior low-velocity zones, where lower valid pixel counts and artefacts such as striping may occur. Nevertheless, the majority of pixels of the C3S ice sheet velocity dataset meets the GCOS uncertainty target. The product also meets the spatial (250 m) and temporal (annual) resolution thresholds set by GCOS, which further enhances the credibility of the C3S ice sheet velocity product (cfr. the "Maturity Matrix" [[8](https://doi.org/10.1175/BAMS-D-21-0109.1)]). However, significant data gaps remain over the interior of the AIS.

The dataset thus offers a strong spatial/temporal coverage and uncertainty pattern for use in ice sheet model calibration or validation (e.g. [[4](https://doi.org/10.5194/gmd-12-2481-2019), [5](https://doi.org/10.3390/rs11121407), [10](https://doi.org/10.5194/tc-6-1561-2012)]). Validation efforts show a good agreement with independent data, further adding credibility to the C3S dataset. The user can, if desired, prioritize high-quality data (i.e. pixels with low absolute/relative errors and high valid pixel counts) for this purpose. Errors are, however, provided as absolute values, while for flow fields, the relative error is generally considered to be more useful. Other potential limitations include the absence of information on acquisition timing, no flagging of spatially filled pixels or missing data, the lack of an ice mask to exclude non-ice-covered cells with velocity values, and the relatively short temporal span of the dataset. To address these issues, users can, for example, apply custom ice masks and complement the product with external datasets for a more robust velocity estimation.


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > ℹ If you want to know more > Key resources
---
- "[Ice sheet velocity for Antarctica and Greenland derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-greenland-ice-sheet-velocity?tab=overview)" on the CDS
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-greenland-ice-sheet-velocity?tab=documentation) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348656) (Copernicus Knowledge Base).
- [Copernicus climate change indicators: ice sheets](https://climate.copernicus.eu/climate-indicators/ice-sheets)
- [A web article about remote sensing-derived ice velocity acquisition](https://www.esa.int/Applications/Observing_the_Earth/Copernicus/Sentinel-1/Sentinel-1_s_decade_of_essential_data_over_shifting_ice_sheets)
- [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: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > ℹ If you want to know more > References
---
- [[1](https://doi.org/10.3390/rs70709371)] Nagler, T., Rott, H., Hetzenecker, M., Wuite, J. and Potin, P. (2015). The Sentinel-1 Mission: New Opportunities for Ice Sheet Observations. Remote Sensing. 7(7):9371-9389. https://doi.org/10.3390/rs70709371

- [[2](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

- [[3](https://nsidc.org/data/nsidc-0777/versions/1)] Howat, I., Chudley, T., and Noh, M. (2022). MEaSUREs Greenland Ice Velocity: Selected Glacier Site Single-Pair Velocity Maps from Optical Images, https://doi.org/10.5067/b28fm2qvvywy

- [[4](https://doi.org/10.5194/gmd-12-2481-2019)] Le clec'h, S., Quiquet, A., Charbit, S., Dumas, C., Kageyama, M., and Ritz, C. (2019). A rapidly converging initialisation method to simulate the present-day Greenland ice sheet using the GRISLI ice sheet model (version 1.3), Geosci. Model Dev., 12, 2481–2499, https://doi.org/10.5194/gmd-12-2481-2019

- [[5](https://doi.org/10.3390/rs11121407)] Mottram, R., Simonsen, S. B., Svendsen, S. H., Barletta, V. R., Sørensen, L. S., Nagler, T., Wuite, J., Groh, A., Horwath, M., Rosier, J., Solgaard, A., Hvidberg, C. S., and Forsberg, R. (2019). An integrated view of Greenland Ice Sheet mass changes based on models and satellite observations. Remote Sensing, 11(12), 1407. https://doi.org/10.3390/rs11121407

- [[6](https://doi.org/10.1016/j.rse.2017.08.038)] Paul, F., Bolch, T., Briggs, K., Kääb, A., McMillan, M., McNabb, R., Nagler, T., Nuth, C., Rastner, P., Strozzi, T., and Wuite, J. (2017). Error sources and guidelines for quality assessment of glacier area, elevation change, and velocity products derived from satellite data in the Glaciers_cci project, Remote Sensing of Environment, 203, 256-275. https://doi.org/10.1016/j.rse.2017.08.038

- [[7](https://doi.org/10.3390/rs9101062)] Lüttig, C., Neckel, N., and Humbert, A. (2017). A Combined Approach for Filtering Ice Surface Velocity Fields Derived from Remote Sensing Methods, Remote Sensing, 9(10). https://doi.org/10.3390/rs9101062


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: uncertainty_q02  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial variability of velocity-related uncertainties for glaciological applications > ℹ If you want to know more > References
---
A Combined Approach for Filtering Ice Surface Velocity Fields Derived from Remote Sensing Methods, Remote Sensing, 9(10). https://doi.org/10.3390/rs9101062

- [[8](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, https://doi.org/10.1175/Bams-D-21-0109.1

- [[9](https://doi.org/10.1029/2019GL083826)] Mouginot, J., E. Rignot, and B. Scheuchl (2019). Continent-wide, interferometric SAR phase, mapping of Antarctic ice velocity, Geophys. Res. Lett., 46, 9710-9718, https://doi.org/10.1029/2019GL083826

- [[10](https://doi.org/10.5194/tc-6-1561-2012)] Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R., and Vaughan, D. G. (2012). Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model, The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012

- [[11](https://doi.org/10.1016/j.rse.2025.115092)] Wuite, J., Nagler, T., Hetzenecker, M., and Rott, H. (2025). Ten years of polar ice velocity mapping using Copernicus Sentinel-1. Remote Sensing of Environment, 332. https://doi.org/10.1016/j.rse.2025.115092

- [[12](https://doi.org/10.1109/IGARSS.2006.956)] Wegmuller, U., Werner, C., Strozzi, T., and Wiesmann, A. (2006). Ionospheric electron concentration effects on SAR and insar. In Proceedings of the 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA, 31 July–4 August 2006. https://doi.org/10.1109/IGARSS.2006.956


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica
---
Production date: 31-05-2025

Dataset version: 4.0

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


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Quality assessment question
---
* **"How does the spatial coverage of the ice sheet surface elevation change data, aggregated from distinct satellite sensors and missions over time, change and how does it affect estimates of (cumulative) ice sheet surface elevation changes?"**

The C3S surface elevation change (SEC) product quantifies changes in the surface elevation of ice sheets, providing crucial insights into their response to climate change and changing ice sheet dynamics. Satellite remote sensing is a valueable and practical method for regularly monitoring such surface elevation changes over those large, remote ice sheet areas. SEC data on the Climate Data Store (CDS) are derived from satellite radar altimetry, where the time delay between a transmitted pulse from the radar and its surface echo is converted into distance, adjusted for the satellite's known elevation. Repeated measurements of the surface elevation from multiple satellite missions, combined with corrections and interpolation, therefore allows to create a consistent time series of gridded ice sheet surface elevation changes [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [2](https://doi.org/10.5194/tc-13-427-2019)].

While these techniques generally offer extensive spatial and temporal coverage, they also have limitations, such as inconsistencies due to data aggregation from different satellite sensors and missions, and difficulties with data processing and data acquisition over complex terrain. This notebook assesses the suitability of the CDS SEC dataset (version 4.0) as an indicator of ice sheet imbalance under climate change. It specifically evaluates the dataset's maturity and quality related to data completeness, focusing on its spatio-temporal coverage and consistency across time series derived from multiple satellite sources. In this notebook, we only focus on the Antarctic Ice Sheet (AIS).

🚨 **Although this notebook deals with the Antarctic Ice Sheet only, surface elevation change data for the Greenland Ice Sheet are also available.**


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Quality assessment statements
---
These are the key outcomes of this assessment

- Surface elevation change (SEC) detection by radar altimetry is a valuable tool for assessing the impacts of climate change on ice sheets, but it has notable limitations that users should be aware of. The C3S SEC data have been merged from different satellite missions over time, each having their own (dis)advantages in terms of data acquisition limitations and spatio-temporal sampling coverage/frequency. For the C3S AIS SEC dataset in particular, the lack of post-processing to fill remaining data gaps results in a rather immature final product. Even though significant improvements with respect to data completeness have occured during the more recent years, persistent data gaps remain around the polar gap and over complex terrain around the ice sheet margins. Since some of the areas with the most prominent SEC are within the areas of least coverage, special attention is required.
- Without additional processing, the C3S SEC data for the AIS are found to not be suitable for reliable statistical analysis, such as calculating means, variability, trends, due to the high proportion of missing values, noisier data and relatively higher error values when compared to the GrIS SEC dataset. Due to the lack of post-processing, some signals in the SEC time series may therefore reflect changing sampling conditions and/or processing limitations rather than actual SEC. In the context of long-term monitoring and climate change studies, the C3S AIS SEC dataset mostly lacks the robustness and reliability required to accurately track surface elevation changes and estimate cumulative mass changes. Users of the C3S AIS SEC data product are therefore most likely required to implement additional processing to derive glaciologically interpretable surface elevation changes.
```


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Methodology > Dataset description
---
Surface elevation change detection by satellite radar altimetry is a useful tool to grasp the impact of climate change on the ice sheets. In that regard, the C3S dataset on the Climate Data Store (CDS) provides monthly surface elevation change (SEC) values and their uncertainty for the Greenland (GrIS) and Antarctic Ice Sheet (AIS) on a 25 km spatial resolution grid. The core principle involves measuring surface elevations at different times and comparing them to detect changes. In this dataset, they are derived using satellite radar altimetry that contain data from multiple satellite missions, which are grouped together into a consistent time series for each pixel. Surface elevation changes are reported with units of meter per year and are available since 1992. Data are provided in NetCDF format as gridded data and are available for both the GrIS (excluding peripheral glaciers and ice caps) and AIS (including ice shelves).

These ice sheet surface elevation change rates are mathematically expressed as:

$\dfrac{dh}{dt} = \dfrac{h_{t_2}-h_{t_1}}{t_{2}-t_{1}}$

where:
- $h$ is the surface elevation (m)
- $t$ the time (yr)

Note that in the dataset itself, surface elevation changes are, however, actually calculated from linear regressions to a time series. The mentioned time for such a SEC measurement is the center of a 3-year of 5-year moving window (for the GrIS) and a 5-year moving window (for the AIS) used to derive the SEC values. Users should hereby note that not only accumulation or ablation (i.e. the surface mass balance) can cause the surface elevation to increase or decrease. The surface elevation change rate at a certain pixel contains signals from various processes and are generally split up into contributions from the surface mass balance (surface ablation and accumulation), ice-flow dynamics (dynamical thinning or thickening) and other processes:

$\dfrac{dh}{dt}_{obs} = \dfrac{SMB}{\rho_m} + \dfrac{D'}{\rho_i} + $ other

where the first term on the right-hand side ($SMB$ in units kg m$^{-2}$ yr$^{-1}$) includes elevation changes from surface mass balance processes and the second one ($D'$ in units kg m$^{-2}$ yr$^{-1}$) due to ice dynamic processes. The term $\rho_m$ is the density of the material lost or gained (snow, firn or ice) and $\rho_i$ that of ice. Other factors that may affect surface elevation changes are basal mass balance processes (which is generally of less importance when compared to the surface mass balance), as well as firn densification/compaction and vertical bedrock motion (which, however, do not have a direct effect on mass changes of the ice sheet) [[7](https://doi.org/10.5194/tc-5-173-2011), [8](https://doi.org/10.1029/2021JF006505)]. Ice dynamics is furthermore only relevant with respect to mass changes when ice discharge across the grounding line is considered. For the GrIS as a whole, contributions to mass changes are currently driven by both SMB and ice flow dynamics at an approximately equal magnitude (i.e. 60% SMB and 40% ice dynamics), while for the AIS they are almost entirely driven by ice flow dynamics [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [2](https://doi.org/10.5194/tc-13-427-2019), [9](https://doi.org/10.1038/s41586-019-1855-2), [10](https://doi.org/10.1038/s41586-018-0179-y)].

In this notebook, we use version 4.0. 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-elevation-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355345393) (Copernicus Knowledge Base).


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > 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-3)**
* [](section-3-1)
* [](section-3-2)
* [](section-3-3)

**[](section-4)**


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define requests for download from the CDS and download the ice sheet surface elevation change data.

Select the domain: "greenland" or "antarctica"
Define the request
Download the data

```text
domain='antarctica'
```

```text
100%|██████████| 1/1 [00:00<00:00, 20.94it/s]
```

```text
Download completed.
```

(section-1-3)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
We can read and inspect the data. Let us print out the data to inspect its structure:

```text
{'antarctica': <xarray.Dataset> Size: 108MB
 Dimensions:          (y: 180, x: 216, time: 307, bounds: 2)
 Coordinates:
   * time             (time) datetime64[ns] 2kB 1994-11-01T09:21:19.687500 ......
     grid_x_bounds    (bounds, x) float32 2kB -2.6e+06 -2.575e+06 ... 2.8e+06
     grid_y_bounds    (bounds, y) float32 1kB -2.2e+06 -2.175e+06 ... 2.3e+06
     grid_lon_bounds  (bounds, y, x) float32 311kB 229.8 229.5 ... 50.35 50.6
     grid_lat_bounds  (bounds, y, x) float32 311kB -59.37 -59.54 ... -57.51
     time_bounds      (bounds, time) datetime64[ns] 5kB 1992-05-02T06:21:26.71...
   * x                (x) float32 864B -2.588e+06 -2.562e+06 ... 2.788e+06
   * y                (y) float32 720B -2.188e+06 -2.162e+06 ... 2.288e+06
 Dimensions without coordinates: bounds
 Data variables:
     longitude        (y, x) float32 156kB 229.8 229.5 229.2 ... 50.37 50.63
     latitude         (y, x) float32 156kB -59.53 -59.69 -59.85 ... -57.83 -57.66
     sec              (y, x, time) float32 48MB nan nan nan nan ... nan nan nan
     sec_uncert       (y, x, time) float32 48MB nan nan nan nan ... nan nan nan
     sec_ok           (y, x, time) int8 12MB 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0
     surface_type     (y, x) int8 39kB 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0
     high_slope       (y, x) int8 39kB 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0
     grid_projection  |S1 1B b''
 Attributes: (12/13)
     Conventions:    CF-1.7
     title:          Surface Elevation Change Rate of the Antarctic Ice Sheet
     references:     Main: Wingham, Shepherd, Muir and Marshall, Phil Trans R ...
     source:         ESA Radar altimeters: ERS-1, ERS-2, Envisat, CryoSat-2, S...
     institution:    Copernicus Climate Change Service
     contact:        copernicus-support@ecmwf.int
     ...             ...
     creation_date:  2022-12-16T:10:07:43Z
     comment:        Data is geophysically corrected, instruments power correc...
     history:        Product version 4.0
     summary:        Surface elevation change rate derived for Antarctica in 2...
     keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
     license:        C3S general license}
```


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
rate derived for Antarctica in 2...
     keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
     license:        C3S general license}
```

The version 4.0 is a gridded dataset at a 25 km spatial resolution containing monthly values of the ice sheet surface elevation change rate $\frac{dh}{dt}$ (`sec` in m/yr) and its uncertainty (`sec_uncert` in m/yr) since 1992. The time for a measurement mentioned in the dataset is the center of a 5-year moving window used to derive the surface elevation change values. For the AIS, uncertainties are reported as the sum of the modeling error, the cross-calibration error, and the measurement uncertainties. These can be considered 1-sigma precision errors. A land mask (`surface_type`), slope mask (`high_slope`), validity flags (`sec_ok`) are also included.

Let us check the total temporal extent of the data:

```text
The begin period of the dataset is 1992-05-02 and the end period is 2022-11-01, which is a total of time 30.50 years.
```

(section-1-4)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 1. Data preparation and processing > 1.4 Data handling and creating functions
---
Let us now perform some data handling and define a plotting function before getting started with the analysis:

Select the specific dataset you want to process, e.g., "greenland"
Define plotting function
Create subplots with Polar Stereographic projection
Plot the data
Set extent and plot features
Add colorbar

Now, our dataset array only holds the most important information, such as the multiyear mean surface elevation change rates (`sec`) and the arithmetic mean precision error (`sec_err`). With the function above, we also calculated linear and quadratic trends of surface elevation changes, as well as the amount of missing values.

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

(section-2)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 2. Quantifying Antarctic Ice Sheet surface elevation changes in space and time > 2.1 Spatial distribution of surface elevation changes
---
We begin by plotting the Antarctic multiyear mean surface elevation change rate $\overline {\frac{dh}{dt}}$ between the beginning and end period with the defined plotting function:

Apply the function to the surface elevation change rate data
Define dataset to be plotted

*Figure 1. Multiyear mean surface elevation change (SEC) over Antarctica from all available data in the SEC dataset on the Climate Data Store. It must be noted that the period over which the data are averaged in this figure may differ, depending on available data (e.g. with respect to the varying polar gap or other missing data).*

The figure displays the multiyear mean surface elevation change of the Antarctic ice sheet from 1992 to 2022 in meter per year (m/yr). In many parts of the ice sheet, the pattern, however, exhibits a noisy appearance. A notable data gap is also present around the South Pole (i.e. the well-known 'polar gap', of which the extent varies depending on the satellite mission). It must be noted that the period over which the data are averaged in Figure 1 may differ, depending on the availability of the data (e.g. due to the varying polar gap or other missing data in steep marginal regions). It is therefore only a quick representation of the data and cannot be used for proper glaciological analysis.

Let us quantify the ice sheet-wide average value:

```text
The Antarctic ice sheet-wide average surface elevation change rate value between 1992-05-02 and 2022-11-01 is -0.01691 m/yr.
```

The negative value indicates that the surface of the ice sheet, in general, has been slightly lowering during the last several decades, resulting in net negative values. Again, we note the presence of abundant noisy and missing data (see later for more details), which may impact the robustness of this value.

(section-2-2)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 2. Quantifying Antarctic Ice Sheet surface elevation changes in space and time > 2.2 Time series of surface elevation changes
---
Let us now express the average surface elevation change for the ice sheet as a whole as a time series:

Define the function
Apply mean to all variables
Combine the results
Plot the data

*Figure 2. Time series of (left) ice sheet-wide surface elevation change (SEC) and (right) cumulative ice sheet-wide surface elevation change over Antarctica from the SEC dataset on the Climate Data Store.*

Overall, the surface elevation of the Antarctic Ice Sheet has shown a long-term declining trend. The relatively consistent downward trajectory of the cumulative surface elevation change (SEC) curve in the figure above may therefore serve as a potential indicator of ongoing ice sheet imbalance, assuming that the underlying dataset is of sufficient quality, particularly with regard to spatio-temporal completeness and the consistency of time series derived from multiple satellite missions.

However, one notable anomaly in the SEC curve is the presence of pronounced spikes around ca. 2012 (negative) and 2016 (positive), which may warrant further investigation. Hence, these peaks may not be due to actual elevation changes, but instead may have occurred due to changes in sampling and/or processing limitations, because such sharp peaks in the SEC values around these periods are not noted in other studies for the AIS (e.g. [[2](https://tc.copernicus.org/articles/13/427/2019/), [5](https://doi.org/10.5194/essd-14-3573-2022)]). In order to further investigate this, let us therefore inspect the spatio-temporal data coverage and the amount of missing data in the SEC dataset.

(section-3)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 3. Inspecting spatio-temporal data coverage and missing data > 3.1 Amount of missing data over time
---
Let us now plot the amount of missing data as a time series in order to investigate the data coverage. In the dataset, this can be assessed comparing the amount of pixels with valid data to the (fixed-in-time) land mask (`surface_type`), where pixels with a value larger than 0 represent ice-covered grid points of the main ice sheet body or ice shelves. The time series looks as follows:

*Figure 3. Time series of missing data of the surface elevation change data over Antarctica from the SEC dataset on the Climate Data Store.*

In the figure above, we note several jumps in the curve which are presumably due to changes in the used data acquisition methods (e.g. varying satellite missions), but can also be due to data processing limitations. When inspecting the graph, some notable increases in missing data seem to occur after 2010. Moreover, the periods around ca. 2012 and 2016 are characterized by a drastic switch in missing data, which may also be linked to the spikes in the surface elevation change time series noted earlier in Figure 2. This indicates that some signals in the SEC time series may reflect changing sampling conditions and/or processing limitations, rather than actual SEC, which is hence an important factor to consider when interprating these data due to the lack of applied corrections (such as gap filling).

(section-3-2)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 3. Inspecting spatio-temporal data coverage and missing data > 3.2 Spastial distribution of missing data
---
Let us have the spatial distribution of the missing data plotted:

Apply the function to the surface elevation change missing data
Plot the data

*Figure 4. Spatial distribution of valid data of the surface elevation change data over Antarctica from the SEC dataset on the Climate Data Store.*

The figure above displays the percentage of valid data in the surface elevation change (SEC) data for Antarctica, which further allows to inspect its data completeness. As discussed before, data gaps in the SEC dataset arise primarily from limited satellite coverage beyond certain mission-specific latitudes (i.e. the "polar gap" around the South Pole), and from processing limitations or challenging conditions, such as complex and steep terrain around the marginal regions (e.g. the Antarctic Peninsula and the transantarctic mountains). Both areas are clearly marked by a lesser amount of missing data in the figure above, providing additional insight into the pattern of missing data.

The central Antarctic region near the South Pole exhibits a low coverage due to the so-called “polar gap”, where satellite altimetry coverage is limited. Early satellite missions like ERS-1, ERS-2, and Envisat had coverage limitations south of 81.5°S, creating significant gaps. CryoSat-2 (launched in 2010) improved polar coverage up to 88°S but still left significant gaps in the central polar region and partly around the margins [[2](https://doi.org/10.5194/tc-13-427-2019), [3](https://doi.org/10.1029/2019GL082182), [4](https://climate.esa.int/media/documents/ST-UL-ESA-AISCCI-E3UB-001-v1.0.pdf)]. The Sentinel-3 mission has recently further enhanced the sampling frequency, but coverage is again rather limited in the coastal regions due to the absence of an interferometric SAR. Near the margins, challenging conditions, such as complex and steep terrain, limit the efficient acquisition of sufficient valid data [[4](https://climate.esa.int/media/documents/ST-UL-ESA-AISCCI-E3UB-001-v1.0.pdf)]. Unlike the Greenland SEC dataset, these data gaps for Antarctica have not been filled up during post-processing, resulting in more pronounced areas with missing data.

(section-3-3)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 3. Inspecting spatio-temporal data coverage and missing data > 3.3 Link with satellite mission and 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 outside of the polar gap (taken as 81.5°S) 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
ax1.set_yscale('log')
Scatter plot
Remove NaN values for the scatter plot
ax2.set_yscale('log')

*Figure 5. Relationship between the percentage missing data and (left) the slope of the terrain and (right) the magnitude of the ice sheet surface elevation change of a certain pixel over Antarctica from the SEC dataset on the Climate Data Store.*

The graphs above display the data quality of radar altimetry-derived surface elevation changes over the AIS, highlighting challenges in areas with higher surface slopes and high surface elevation changes. The first graph shows that regions with gentle slopes (<2°) have the least missing data, indicating better radar performance on flat surfaces. As slopes increase to more than 5°, practically all data are missing, reflecting the difficulty of capturing reliable measurements due to slope-induced errors in complex terrain. The second graph illustrates the relationship between the magnitude of surface elevation change at a certain pixel and the percentage of missing data in that same pixel. Areas with larger elevation changes, often found along ice sheet margins with complex, high-slope terrain, tend to have higher data gaps, indicating that dynamic regions are harder to monitor consistently. This relationship, however, is obviously not deterministic, as some significant of scatter remains.

Overall, the graphs reveal that flatter, more stable regions provide more reliable radar data, while steeper and dynamic regions are more prone to significant amounts of missing data. Recognizing these limitations is crucial for accurately interpreting SEC data and assessing climate change impacts on ice sheets.

Let us inspect how varying satellite missions perform with respect to the amount of missing data in the C3S product based on the time period that they are/were active:

Define Antarctica dataset
Define missing data per time period
Broadcast flagged_pixels over time
Count of pixels with surface_type >0 per timestep
Among them, how many are NaN in sec
Average over time steps

*Figure 6. Average percentage of missing data for various satellite missions (time periods) over Antarctica from the SEC dataset on the Climate Data Store.*

The graphs above clearly show the different missing data characteristics of the various satellite missions, which are due to changes in the used data acquisition methods/spatial coverage and data processing limitations (e.g. the size of the polar gap, the susceptibility to slope-induced errors over complex terrain, etc.). The highest amount of missing data are found in the oldest period during the epoch of ERS-1/2. The most recent period, which combines data from CryoSat-2 and Sentinel-3, shows the lowest percentage of missing data, reflecting advancements in radar altimetry technology and data processing methods. Again, these findings display the progressive improvement in the observational capability of remote sensing-derived surface elevation changes over Antarctica, while also underlining the persistent challenges in obtaining complete records.

(section-4)=


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > Analysis and results > 4. Short summary and take-home messages
---
The C3S SEC data represent surface elevation changes of the AIS acquired by satellite radar altimetry that have been merged from different satellite missions over time. Each of those satellite missions are characterized by their own (dis)advantages. The time series of the ice sheet-wide average SEC rate and the cumulative SEC changes show a general trend of surface elevation lowering, reflecting an overall net lowering of the surface. Using the C3S Antarctic Ice Sheet (AIS) surface elevation change (SEC) time series as an indicator for the Antarctic ice sheet imbalance, however, presents several implications.

For example, the varying spatio-temporal coverage of the data that are being fed into these trends should be considered for proper evaluation and interpretation. The most important causes of persistent data gaps in the C3S SEC product for the AIS are the polar gap around the South Pole and complex terrain around the margins. However, combining CryoSat-2 and Sentinel-3 during the more recent years has improved the spatio-temporal coverage of the product greatly, even though unfilled gaps remain in some areas. This is especially the case in high-slope and complex marginal regions. These persistent and unfilled data gaps significantly complicate the robustness and data completeness of SEC measurements of the C3S AIS product. Since some of the areas with the most prominent surface elevation changes are consequently within the area of least coverage, special attention is required. Users of C3S AIS SEC data product are therefore most likely required to implement additional processing to derive glaciologically interpretable surface elevation changes.

In general, radar altimeters tend to perform better in the central, flat regions of Antarctica due to simpler topography and relatively stable surfaces, while marginal zones with complex and dynamic terrain (where the most significant SEC occur) exhibit a higher invalid data acquisition and an increased uncertainty. These gaps pose challenges for assessing radar altimetry-derived volume and mass changes, making C3S SEC data for Antarctica generally less reliable. To address these limitations, integrating multiple datasets, such as gap-filling through laser altimetry over the margins and sloped terrain (e.g. ICESat/ICESat-2) or by ice sheet model output, can improve the robustness of surface elevation change estimates. Additionally, higher-resolution datasets, regional studies, and advanced data processing techniques (e.g. machine learning) can help fill data gaps and enhance the accuracy and reliability of SEC measurements, providing a more comprehensive understanding of the current changes of the surface of the AIS [[2](https://doi.org/10.5194/tc-13-427-2019), [3](https://doi.org/10.1029/2019GL082182), [5](https://doi.org/10.5194/essd-14-3573-2022), [6](https://doi.org/10.1029/2020GL090572)].


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > 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: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > 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/10.1029/2019GL082182)] Shepherd, A., Gilbert, L., Muir, A.S., Konrad, H., McMillan, M., Slater, T., Briggs, H.K., Sundal, A. V., Hogg A.E., and Engdahl, M.E. (2019). Trends in Antarctic Ice Sheet elevation and mass. Geophysical Research Letters, 46, p. 8174-8183. https://doi.org/10.1029/2019GL082182

- [[4](https://climate.esa.int/media/documents/ST-UL-ESA-AISCCI-E3UB-001-v1.0.pdf)] Shepherd, A., Fantin, D., and Engdahl, M. (2020). ESA Climate Change Initiative (CCI+)
Essential Climate Variable (ECV): Antarctic_Ice_Sheet_cci+ (AIS_cci+) End-to-end Uncertainty Budget (E3UB), ST-UL-ESA-AISCCI+-E3UB-001. https://climate.esa.int/media/documents/ST-UL-ESA-AISCCI-E3UB-001-v1.0.pdf

- [[5](https://doi.org/10.5194/essd-14-3573-2022)] Nilsson, J., Gardner, A. S., and Paolo, F. S. (2022). Elevation change of the Antarctic Ice Sheet: 1985 to 2020, Earth Syst. Sci. Data, 14, 3573–3598, https://doi.org/10.5194/essd-14-3573-2022

- [[6](https://doi.org/10.1029/2020GL090572)] Brunt, K. M., Smith, B. E., Sutterley, T. C., Kurtz, N. T., and Neumann, T. A. (2021). Comparisons of satellite and airborne altimetry with ground-based data from the interior of the Antarctic ice sheet. Geophysical Research Letters, 48, e2020GL090572. https://doi.org/10.1029/2020GL090572

- [[7](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


EQC Quality Assessment: "Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica"
Dataset: satellite-ice-sheet-elevation-change [CDS]
Aspect: consistency-assessment_q02  |  Category: Satellite_ECVs
Section: Spatio-temporal data completeness and consistency of remote sensing-derived ice sheet surface elevation changes over Antarctica > ℹ If you want to know more > References
---
data – the impact of interpolation, sampling and firn density, The Cryosphere, 5, 173–186, https://doi.org/10.5194/tc-5-173-2011

- [[8](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

- [[9](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

- [[10](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: "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
---
Production date: 31-05-2025

Dataset version: 5.0

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


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 > Quality assessment question
---
* **"How adequate are the ice sheet surface elevation change data in terms of their uncertainty and how does it affect estimates of ice sheet volume/mass changes, variability and trends?"**

The C3S surface elevation change (SEC) product quantifies changes in the surface elevation of ice sheets, providing crucial insights into their response to climate change and changing ice sheet dynamics. Satellite remote sensing is a valueable and practical method for regularly monitoring such surface elevation changes over those large, remote ice sheet areas. SEC data on the Climate Data Store (CDS) are derived from satellite radar altimetry, where the time delay between a transmitted pulse from the radar and its surface echo is converted into distance, adjusted for the satellite's known elevation. Repeated measurements of the surface elevation from multiple satellite missions, combined with corrections and interpolation, therefore allows to create a consistent time series of gridded ice sheet surface elevation changes [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [2](https://doi.org/10.5194/tc-13-427-2019)].

While these techniques offer extensive spatial and temporal coverage, they also have limitations, such as inconsistencies due to data aggregation from different satellite sensors and missions, and difficulties with data acquisition over complex terrain. In that regard, this notebook investigates how well the dataset on the CDS (here we use version 5.0) can be used to monitor the spatial distribution of Greenland Ice Sheet (GrIS) surface elevation changes over the last several decades, as well as to derive reliable values for the (inter/intra-annual) variability and temporal trends of the ice sheet surface elevation, volume and mass changes. More specifically, the notebook evaluates whether the dataset is of sufficient maturity and quality for that purpose in terms of its spatio-temporal uncertainty.

🚨 **Although this notebook deals with the Greenland Ice Sheet only, surface elevation change data for the Antarctic Ice Sheet are also available.**


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 > Quality assessment statements
---
These are the key outcomes of this assessment

- Surface elevation change (SEC) detection by radar altimetry is a valuable tool for assessing the impacts of climate change on ice sheets, but has notable (dis)advantages that users should be aware of. The C3S Greenland Ice Sheet (GrIS) surface elevation change (SEC) dataset consists of mature and quality-rich data, covering a time period of over 30 years with a consistent monthly temporal resolution, filled-up data gaps, and meeting minimum international proposed error thresholds for nearly all pixels. This makes it suitable for detecting reliable climate change signals, trends, and variability at local (pixel) to ice sheet-wide scales. Radar altimeters generally provide more robust surface elevation change measurements in the flat, stable regions of the GrIS compared to the coastal areas, which feature complex terrain. Error estimates therefore tend to be slightly higher around the margins.
- Users should note that SEC cannot be readily converted to volume nor mass changes of the "actual" ice sheet, because converting SEC to volume and mass changes requires adjustments for bedrock uplift, firn densification, and material density differences. Users should also note that biases remain, where radar altimetry tends to underestimate surface lowering rates compared to laser altimetry. This underestimation is aided by the coarse spatial resolution (25 km) of the C3S product, which does not meet minimum thresholds and prevents capturing very localized high mass losses. Despite a favorable error characterization and spatial/temporal coverage, users of the C3S GrIS SEC data product are most likely required to implement additional processing to derive glaciologically interpretable volume/mass changes from the surface elevation changes.
```


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 > Methodology > Dataset description
---
Surface elevation change detection by satellite radar altimetry is a useful tool to grasp the impact of climate change on the ice sheets. In that regard, the C3S dataset on the Climate Data Store (CDS) provides monthly surface elevation change (SEC) values and their uncertainty for the Greenland (GrIS) and Antarctic Ice Sheet (AIS) on a 25 km spatial resolution grid. The core principle involves measuring surface elevations at different times and comparing them to detect changes. In this dataset, they are derived using satellite radar altimetry that contain data from multiple satellite missions, which are grouped together into a consistent time series for each pixel. Surface elevation changes are reported with units of meter per year and are available since 1992 at monthly-spaced intervals. Data are provided in NetCDF format as gridded data and are available for both the GrIS (excluding peripheral glaciers and ice caps) and AIS (including ice shelves).

These ice sheet surface elevation change rates are mathematically expressed as:

$\dfrac{dh}{dt} = \dfrac{h_{t_2}-h_{t_1}}{t_{2}-t_{1}}$

where:
- $h$ is the surface elevation (m)
- $t$ the time (yr)

The time for a measurement mentioned in the dataset is the center of a 3-year of 5-year moving window (for the GrIS) and a 5-year moving window (for the AIS) used to derive the SEC values. Users should hereby not that not only ablation or accumulation (i.e. the surface mass balance) can cause the surface elevation to increase or decrease. The surface elevation change rate at a certain pixel contains signals from various processes:

$\dfrac{dh}{dt}_{obs} = \dfrac{SMB}{\rho_m} + \dfrac{BMB}{\rho_i} + \dfrac{D'}{\rho_i} + w_C + w_B$

where the first term on the right-hand side ($SMB$ in units kg m$^{-2}$ yr$^{-1}$) includes elevation changes from surface mass balance processes (i.e. climatically-driven accumulation and melt/runoff), the second one ($BMB$ in units kg m$^{-2}$ yr$^{-1}$) due to basal mass balance processes at the ice-bedrock interface, the third one ($D'$ in units kg m$^{-2}$ yr$^{-1}$) due to ice dynamic processes (e.g. dynamical thinning or thickening), the fourth one ($w_C$) is the vertical velocity due to snow and/or firn compaction (i.e. the transformation and densification of snow towards firn and in a later stage ice), and the last one ($w_B$) due to bedrock elevation  changes (e.g. glacial isostatic adjustment) [[8](https://doi.org/10.5194/tc-5-173-2011), [9](https://doi.org/10.1029/2021JF006505)]. The term $\rho_m$ is the density of the material lost or gained (snow, firn or ice) and $\rho_i$ that of ice. The two latter terms do not contribute to actual mass changes of the ice sheet, while ice dynamics is only relevant with respect to mass changes when ice discharge across the grounding line is considered. For the GrIS as a whole, contributions to mass changes are currently driven by both SMB and ice flow dynamics at an approximately equal magnitude (i.e. 60% SMB and 40% ice dynamics), while for the AIS they are almost entirely driven by ice flow dynamics [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [2](https://doi.org/10.5194/tc-13-427-2019), [10](https://doi.org/10.1038/s41586-019-1855-2), [11](https://doi.org/10.1038/s41586-018-0179-y)].

In this notebook, we use version 5.0. 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-elevation-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355345393) (Copernicus Knowledge Base).


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

**[](section-4)**
* [](section-4-1)
* [](section-4-2)

**[](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 > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define requests for download from the CDS and download the ice sheet surface elevation change data.

Select the domain: "greenland" or "antarctica"
Define the request
Download the data

```text
domain='greenland'
```

```text
100%|██████████| 1/1 [00:00<00:00,  6.93it/s]
```

```text
Download completed.
```

(section-1-3)=


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 > 1. Data preparation and processing > 1.3 Display and inspect data
---
We can read and inspect the data. Let us print out the data to inspect its structure:

```text
{'greenland': <xarray.Dataset> Size: 76MB
 Dimensions:          (time: 378, y: 123, x: 65)
 Coordinates:
   * time             (time) datetime64[ns] 3kB 1992-01-01 ... 2023-06-01
   * x                (x) float32 260B -7.393e+05 -7.143e+05 ... 8.607e+05
   * y                (y) float32 492B -3.478e+06 -3.453e+06 ... -4.281e+05
 Data variables: (12/15)
     start_time       (time) datetime64[ns] 3kB 1991-08-01 ... 2014-08-01
     end_time         (time) datetime64[ns] 3kB 1996-10-31 ... 2023-07-31
     grid_projection  |S1 1B b''
     lat              (y, x) float32 32kB 58.0 58.04 58.09 ... 81.55 81.35 81.14
     lon              (y, x) float32 32kB -57.0 -56.61 -56.21 ... 17.87 18.55
     dh               (y, x, time) float32 12MB nan nan nan nan ... nan nan nan
     ...               ...
     dhdt_stabil      (y, x, time) float32 12MB nan nan nan nan ... nan nan nan
     dhdt_ok          (y, x, time) int8 3MB 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0
     dist             (y, x, time) float32 12MB nan nan nan nan ... nan nan nan
     land_mask        (y, x) int8 8kB 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
     high_slope       (y, x) int8 8kB 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
     area             (y, x) float32 32kB nan nan nan nan nan ... nan nan nan nan
 Attributes: (12/32)
     Title:                Surface Elevation change of the Greenland ice sheet...
     institution:          Copernicus Climate Change Service, DTU Space - Div....
     reference:            Simonsen and Sørensen (2017), Sørensen et al. (2018)
     contact:              copernicus-support@ecmwf.int
     file_creation_date:   2023-12-15 16:56:53.584072
     project:              C3S_312b_Lot4_ice_sheets_and_shelves
     ...                   ...
     netCDF_version:       NETCDF4
     product_version:      v5
     Conventions:          CF-1.7
     keywords:             EARTH SCIENCE CRYOSPHERE GLACIERS/ICE SHEETS/GLACIE...
     license:              C3S general license
     summary:              Surface elevation change rate derived for Greenland...}
```

The version 5.0 is a gridded dataset at a 25 km spatial resolution containing monthly values of the ice sheet surface elevation change rate $\frac{dh}{dt}$ (`dhdt` in m/yr) and its uncertainty (`dhdt_uncert` in m/yr), as well as the surface elevation change between two measurements $dh$ (`dh` in m, and hence not normalized to "per year") of a grid cell since 1992. The uncertainties are here reported as 1-sigma precision errors or standard deviations. A land mask (`land_mask`), slope mask (`high_slope`), validity flags (`dhdt_ok`) and the surface area of a grid cell (`area`) are also included. The time for a measurement mentioned in the dataset is the center of a 3-year or 5-year moving window used to derive the surface elevation change values.

Let us check the total temporal extent of the data:


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 > 1. Data preparation and processing > 1.3 Display and inspect data
---
area`) are also included. The time for a measurement mentioned in the dataset is the center of a 3-year or 5-year moving window used to derive the surface elevation change values.

Let us check the total temporal extent of the data:

```text
The begin period of the dataset is 1992-01-01 and the end period is 2023-06-01, which is a total of time 31.41 years.
```

(section-1-4)=


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 > 1. Data preparation and processing > 1.4 Data handling and creating functions
---
Let us now perform some data handling and define a plotting function before getting started with the analysis:

Select the specific dataset you want to process, e.g., "greenland"
Define plotting function
Create subplots with Polar Stereographic projection
Plot the data
Set extent and plot features
Add colorbar
Define the function for plotting a time series
Apply mean to all variables except 'dvol', which will use sum
Combine the results

Now, our dataset array only holds the most important information, such as the multiyear mean surface elevation change rates (`sec`) and the arithmetic mean precision error (`sec_err`). With the function above, we also calculated linear and quadratic trends of surface elevation changes, as well as the amount of missing values.

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

(section-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 > 2. Greenland Ice Sheet surface elevation and altimetric volume changes in space and time > 2.1 Multiyear mean surface elevation changes
---
We begin by plotting the Greenland multiyear mean surface elevation change $\overline {\frac{dh}{dt}}$ between the beginning and end period with the defined plotting function:

Apply the function to the surface elevation change rate data
Define dataset to be plotted

*Figure 1. Multiyear mean surface elevation change (SEC) over Greenland from the SEC dataset on the Climate Data Store.*

Overall, the map provides a visual representation of the changes of the surface elevation of Greenland's ice sheet over the last several decades. The red regions, particularly around the margins, indicate areas of significant surface lowering, which is consistent with observations of accelerated glacier flow and ice thinning in these regions [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [3](https://doi.org/10.1016/j.rse.2016.12.012)].

Let us quantify the ice sheet-wide average value:

```text
The Greenland ice sheet-wide average surface elevation change rate value between 1992-01-01 and 2023-06-01 is -0.04856 m/yr.
```

The negative value indicates that the surface of the ice sheet, in general, has been lowering during the last several decades, resulting in net negative values. This is consistent with overall trends in the literature [[1](https://doi.org/10.1016/j.epsl.2018.05.015), [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)].

(section-2-2)=


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 > 2. Greenland Ice Sheet surface elevation and altimetric volume changes in space and time > 2.2 Conversion into altimetric and "actual" volume changes
---
We can also convert the surface elevation change values to cumulative altimetric volume changes $V_a$ (with subscript 'a' meaning altimetric) by combining the variables `dh` and `area`. We therefore have to make the assumption that surface elevation changes due to bedrock uplift and firn compaction rates are unsignificant or unknown:

$dV_{a,i}
$
[m$^{3}$]
$ = \sum\limits^{x,y}{dV_{x,y,i}} = \sum\limits^{x,y}(d{h_{x,y,i}}*A_{x,y})$

where $d{h_{x,y}}$ is the height change between two measurement intervals $i$ (from `dh`, in m) and $A_{x,y}$ the surface area (from `area`, in m$^2$) of pixel $x,y$ .

We then take the cumulative value over time to get the cumulative altimetric volume change:

$
{V_a}
$
[km$^{3}$]
$
= \sum\limits_{i={1}}^{{{n}}} \left(\dfrac{dV_{a,i}}{1 \cdot 10^9}\right)
$

with $dV_{a,i}$ the ice sheet-wide altimetric volume change (in m$^{3}$) between two measurements (as calculated above) and $n$ the number of temporal intervals in the time series.

Let us plot this as a time series:

Given datasets_original is the dataset dictionary
Extract the 'dh' and 'area' variables
Sum over the x and y dimensions and convert to km^3
Plot the resulting time series

*Figure 2. Cumulative altimetric volume change of the Greenland ice sheet from the SEC dataset on the Climate Data Store.*

As expected, the plot shows a downward pattern of the altimetric volume with a clear trend towards volume losses over time, especially during the more recent years. However, the curve should be interpreted with care. Greenland’s bedrock is namely uplifting currently, due to slow mantle-deformation processes and elastic processes associated with the ongoing ice loss today. Especially around the margins, where ice loss is currently highest, bedrock uplift rates are in the order of several mm per year [[9](https://doi.org/10.1029/2021JF006505)]. Effects from near-surface firn density changes are even larger (i.e. up to a few cm per year) but also uncertain [[4](https://doi.org/10.3189/172756505781829007), [9](https://doi.org/10.1029/2021JF006505)]. In order to obtain "actual" ice sheet volume changes, corrections for firn densification (which can lower the surface without actual mass loss) and bedrock uplift (which does not impact ice thickness changes) are required [[4](https://doi.org/10.3189/172756505781829007), [5](https://doi.org/10.1029/2020GL091216), [8](https://doi.org/10.5194/tc-5-173-2011), [9](https://doi.org/10.1029/2021JF006505)]. As such, to derive pixel-by-pixel ice thickness changes $dH/dt$ from surface elevation changes $dh/dt$ over grounded ice, a correction is needed:

$\dfrac{dH}{dt}
$
[m yr$^{-1}$]
$= \dfrac{dh}{dt} - w_C - w_B$

which can then be translated into actual volume changes $dV/dt$ by using the surface area $A$ of a grid cell:

$\dfrac{dV}{dt}
$
[m$^3$ yr$^{-1}$]
$
= A\dfrac{dH}{dt}$

Then, mass changes can be obtained by:

$\dfrac{dM}{dt}
$
[kg yr$^{-1}$]
$
= \rho_m \dfrac{dV}{dt}$

where the value of the density $\rho_m$ depends on the material/physical process involved in the mass change.


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 > 2. Greenland Ice Sheet surface elevation and altimetric volume changes in space and time > 2.2 Conversion into altimetric and "actual" volume changes
---
yr$^{-1}$]
$
= \rho_m \dfrac{dV}{dt}$

where the value of the density $\rho_m$ depends on the material/physical process involved in the mass change.

Moreover, for more significant surface lowering rates (lower than ca. -0.5 to -1 m/yr), there seems to be a bias towards an underestimation of lowering rates by the radar altimetry (as used in the C3S products) when compared to the laser altimeters (see for example the [PQAR](https://confluence.ecmwf.int/pages/viewpage.action?pageId=414590531)). This is presumably related to a variety of factors, including different modes of data acquisition (e.g. varying footprint sizes between radar and laser instruments, a varying penetration depth of the radar pulse into snow), different algorithm applications and settings, or post-processing procedures [[3](https://doi.org/10.1016/j.rse.2016.12.012)]. Additionally, in regions with high surface lowering rates, the coarse resolution of the C3S product (25 km) also tends to aid the underestimation of SEC due to the very localized high mass/volume losses of certain outlet glaciers [[5](https://doi.org/10.1029/2020GL091216)].

In that sense, the dataset on the Climate Data Store (CDS) seems to exhibit a net underestimation of the Greenland surface elevation and volume change rates. All the above processes thus tend to bias the volume change estimates of the "actual" ice sheet, making the curve above less suitable for the determination of actual volume or mass changes of the ice sheet. Users of the C3S GrIS SEC data product are therefore most likely required to implement additional processing to derive glaciologically interpretable mass/volume changes from the provided surface elevation changes.

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