EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
0.4
216428   37.7140 -46.8972       19        4  0.528   970  1170  -999    9.6

ASPECT  LMAX                      NAME  \
index
0          346   839                      None
1          162  1197                      None
2          175  2106                      None
3          195  4175                      None
4          181  2981                      None
...        ...   ...                       ...
216424     315   255                      None
216425     200  1130                      None
216426     308  4329                      None
216427     122   106              AQ6C10200013
216428      35    -9  ZA6C40100001 Ice Plateau

geometry
index
0       POLYGON ((-146.81804 63.69081, -146.81768 63.6...
1       POLYGON ((-146.66354 63.40764, -146.66344 63.4...
2       POLYGON ((-146.07232 63.38348, -146.07232 63.3...
3       POLYGON ((-146.14895 63.37919, -146.14881 63.3...
4       POLYGON ((-147.04307 63.55024, -147.04483 63.5...
...                                                   ...
216424  POLYGON ((-37.73275 -53.98779, -37.73328 -53.9...
216425  POLYGON ((-36.13834 -54.82735, -36.13826 -54.8...
216426  POLYGON ((-37.29309 -54.17506, -37.29308 -54.1...
216427  POLYGON ((-90.42751 -68.8649, -90.42719 -68.86...
216428  POLYGON ((37.7162 -46.89403, 37.71674 -46.894,...

[216429 rows x 18 columns]
```

As can be seen above, the data includes attribute information for each individual glacier (i.e. delineated polygon) in the vector-type dataset. Important for this notebook are the `BGNDATE` and `ENDDATE` columns (for version 6.0) or `src_date` (for version 7.0), which contain information about the time of delineation of the specific glacier. If for some glaciers (part of) the attributes are missing, the data are filled by `-9999999`. We will use this information below.

(section-2)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 2. The (area-weighted) mean year of delineation of glacier data > 2.1 Determination of date of delineation for every glacier
---
We can begin to answer the user question by extracting information from the attribute table of the downloaded shapefile. For some glaciers the delineation of the outline is composed from several scenes over multiple years in v6.0, implying that a begin date (attribute "`BGNDATE`") and an end date (attribute "`ENDDATE`") of the outline delineation is given in the attribute table in YYYYMMDD format (if both are available). For v7.0, the acquisition or delineation date is simply given by "`src_date`" in YYYY-MM-DD format:

$
year_t = \textstyle\dfrac{BGNDATE_t + ENDDATE_t}{2}\
$ (version 6.0), or

$
year_t = srcdate_t
$ (version 7.0)

This results in the following plot:

Convert dates from string to datetime, and add digitalization year
Get data from years
Get some statistics

*Figure 1. Time of delineation (date of acquisition) for the glaciers in the glacier extent dataset.*

Let us calculate the percentage of years between some specific periods centered around the year 2000 to stronger emphasize that the large temporal deviations from the year 2000 are not frequent:

```text
In the RGIv6.0 dataset, 92.2% of all acquisitions occurred between 1990 and 2010, of which 65.1% took place between 1995 and 2005.
```

(section-2-2)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 2. The (area-weighted) mean year of delineation of glacier data > 2.2 Spatial distribution of date of delineation
---
Now that we calculated the acquisition dates, let us check the spatial distribution of the year of delineation for each glacier in the dataset. We therefore produce a world map where every dot represents a glacier, that is colored according to its year of delineation. Glaciers with missing data are not plotted:

*Figure 2. Spatial distribution of the time of delineation (date of acquisition) for the glaciers in the glacier extent dataset.*

From the above plots, it becomes clear that not all glaciers are delineated in the year 2000. Although the dataset is intended to be a snapshot of the world’s glaciers as they were near the beginning of the 21$^{st}$ century, the user must keep in mind that the range of delineation dates is substantial. This means that the outlines do not all lie in between the same time frame, which is a main issue of the dataset. The figures above, however, demonstrate that most outlines originate from the period between 2000 and 2010. Nevertheless, for some areas like the western United States or some peripheral glaciers around northern Greenland and the Antarctic Penninsula, the glacier outlines date back to the 1970s or earlier.

(section-2-3)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 2. The (area-weighted) mean year of delineation of glacier data > 2.3 The (area-weighted) mean year of delineation per RGI region
---
Let us now calculate the (area-weighted) mean time of delineation for the 19 different RGI regions (see Figure 5 for the locations of these regions). We do that as follows:

- Arithmetic mean:
$
\overline{year}_a = \textstyle\dfrac{1}{{n\in \text{region}}}{\sum\limits_{i=1}^{n\in \text{region}} year_{t,i}}
$
with
$
n
$
the total number of glaciers and $year_t$ the time of delineation for glacier $i$ as calculated above.

- Area-weighted mean:
$
\overline{year}_w = \left(\dfrac{1}{\sum\limits_{i=1}^{n\in \text{region}} A_i}\right) \sum\limits_{i=1}^{n\in \text{region}} \left(A_i * year_{t,i}\right)
$
where
$
A_i
$
is the glacier area for glacier $i$ [km²].

This results in the following plot:

Extract region number from RGIID
Group by region and calculate total area
Calculate means
Extract region number from o1region
Group by region and calculate total area
Calculate means
Ensure regions are correctly defined as an array
Extract the means
Define bar width and positions
Create the bar plot
Add labels, title, and legend
Add grid and show plot

```text
The global arithmetic mean year of delineation (RGI v6.0) is 2002.8.
The global area-weighted mean year of delineation (RGI v6.0) is 2001.3.
```

*Figure 3. Arithmetic and area-weighted mean year of delineation for the glaciers in each RGI region of the glacier extent dataset.*

We observe that at the global scale, the arithmetic area-weighted average of the year of delineation is close to 2002, which only slightly differs in time from the nominally stated dataset reference time (i.e. 2000). However, the (area-weighted) average of the time of delineation varies notably across the different RGI regions: for RGI region 18, for example, the area-weighted average dates back to the late 1970s, but for RGI regions 1 and 10, the average origin dates are closer to the 2010s.

(section-3)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.1 Recent glacier area and mass/volume change trends
---
Going back to our specific use case, it is worth noting that several methods exist in the literature to derive ice thickness and ice volume estimates of glaciers at different spatial scales, of which the most well-known procedures are the volume-area scaling method, numerical modelling, and the estimation of ice thicknesses from surface characteristics and the principle of ice dynamics. These methods, however, strongly rely on the precise determination of the glacier surface area (and hypsometry) as input data to derive total ice volume estimates.

Farinotti et al. (2019), for example, used the RGIv6.0 dataset to derive a global glacier ice volume of 158.17 ± 41.03 × 10³ km³, noting the heavy reliance on accurate glacier surface area data [[3](https://doi.org/10.1038/s41561-019-0300-3)]. Other studies, including Huss and Farinotti (2012), Marzeion et al. (2012) and GlaMBIE (2025), have similarly highlighted input data uncertainties with respect to the glacier area in ice volume estimates [[4](https://doi.org/10.1029/2012JF002523), [5](https://doi.org/10.5194/tc-6-1295-2012), [14](https://doi.org/10.1038/s41586-024-08545-z)]. The main concern here is that the glacierized area has decreased significantly during the last several decades, with global glacier area decreasing at rates of -0.18% to -0.34% per year and median retreat rates of 7.4 m per year [[6](https://doi.org/10.3189/2015JoG15J017), [7](https://doi.org/10.1016/j.accre.2020.03.003), [8](https://doi.org/10.5194/tc-8-659-2014)]. These changes suggest a potential overestimation of volumes for glaciers delineated before 2000 and an underestimation elsewhere. The suitability of RGI outlines for current volume estimates therefore primarily depends on (1) the deviation of the time since delineation of the outline from 2000 and (2) the significance of glacier area/volume changes during that period, which are influenced by the local climate and specific glacier geometries.

Let us plot the regional glacier mass changes for the different RGI regions from the "[Glacier mass change gridded data from 1976 to present derived from the Fluctuations of Glaciers Database](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview)" dataset on the CDS:

Mask data for RGI regions
Mask data for RGI regions
Compute cumulative fields
Select first and last year explicitly (robust)
Total mass change per region


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.1 Recent glacier area and mass/volume change trends
---
RGI regions
Mask data for RGI regions
Compute cumulative fields
Select first and last year explicitly (robust)
Total mass change per region

```text
The total glacier mass change in RGI region 1 between 1976 and 2022 is -2445.24 Gt.
The total glacier mass change in RGI region 2 between 1976 and 2022 is -370.94 Gt.
The total glacier mass change in RGI region 3 between 1976 and 2022 is -889.74 Gt.
The total glacier mass change in RGI region 4 between 1976 and 2022 is -794.43 Gt.
The total glacier mass change in RGI region 5 between 1976 and 2022 is -675.07 Gt.
The total glacier mass change in RGI region 6 between 1976 and 2022 is -263.90 Gt.
The total glacier mass change in RGI region 7 between 1976 and 2022 is -424.88 Gt.
The total glacier mass change in RGI region 8 between 1976 and 2022 is -36.70 Gt.
The total glacier mass change in RGI region 9 between 1976 and 2022 is -404.35 Gt.
The total glacier mass change in RGI region 10 between 1976 and 2022 is -50.55 Gt.
The total glacier mass change in RGI region 11 between 1976 and 2022 is -45.34 Gt.
The total glacier mass change in RGI region 12 between 1976 and 2022 is -16.86 Gt.
The total glacier mass change in RGI region 13 between 1976 and 2022 is -415.13 Gt.
The total glacier mass change in RGI region 14 between 1976 and 2022 is -314.62 Gt.
The total glacier mass change in RGI region 15 between 1976 and 2022 is -278.79 Gt.
The total glacier mass change in RGI region 16 between 1976 and 2022 is -24.09 Gt.
The total glacier mass change in RGI region 17 between 1976 and 2022 is -899.90 Gt.
The total glacier mass change in RGI region 18 between 1976 and 2022 is -9.49 Gt.
The total glacier mass change in RGI region 19 between 1976 and 2022 is 601.53 Gt.
```

The above emphasizes the strong negative glacier mass change trends that have been observed across the globe. It, however, creates a systematic bias when using the RGI data for the estimation of regional and global glacier volumes if the acquisition date does not coincide with the year 2000. Let us try to quantify this error with all of the information above.

(section-3-2)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.2 An attempt to quantify potential glacier volume over or underestimation
---
It is difficult to quantify the potential volume over or underestimation due to deviating outlines for each glacier in the dataset. However, we can get an idea of the regional glacier  volume under/overestimation for 2000 CE by using the glacier mass change dataset that is available on the CDS. Our goal here is to obtain values for the regional glacier volume change between the year 2000 and the area-weighted mean year of delineation of that region $\overline{year}_w$ (which is thus equivalent to the potential volume over or underestimation relative to the year 2000), denoted with the symbol $dV_{\text{region}}^{2000,\overline{\text{year}}_w}$.

To get an idea of these potential glacier volume over- or underestimations, we can make use of the glacier mass change dataset that is on the CDS. This dataset estimates the gridded yearly mass change of glacier ice ($dM/dt$) in Gt yr$^{-1}$, which can be converted to glacier volume changes ($dV/dt$) with units of km$^3$ yr$^{-1}$ of ice by making use of the appropriate density. We thus calculate the mass and volume change between 2000 and the area-weighted average year of delineation for a certain RGI region ($\overline{year}_w$) to get a total volume change for that specific RGI region between those two dates $dV_{\text{region}}^{2000,\overline{year}_w}$. If ${{\overline{year}_w}}$ is a decimal (fractional) year, we use linear interpolation to find the interpolated glacier mass and volume change:

$
dV_{\text{region}}^{2000,\overline{year}_w} \text{ [km}^3\text{]} =
\begin{cases}
\left(\sum\limits_{i=2000}^{\lceil \overline{year}_w \rceil} \sum\limits^{\substack{\text{x,y} \\ \text{{region}}}} \left(\frac{1000}{\rho_i} \frac{dM}{dt}\right)\right) - \\ \left[ \left( \lceil \overline{year}_w \rceil - \overline{year}_w \right) * \left( \sum\limits^{\substack{\text{x,y} \\ \text{region}}} \left(\frac{1000}{\rho_i} \frac{dM}{dt}\right)_{\lceil \overline{year}_w \rceil} \right) \right] & \text{if } \overline{year}_w > 2000 \\
\left(\sum\limits_{i=\lfloor \overline{year}_w \rfloor}^{2000} \sum\limits^{\substack{\text{x,y} \\ \text{region}}} \left(\frac{1000}{\rho_i} \frac{dM}{dt}\right)\right) - \\ \left[ \left( \overline{year}_w - \lfloor \overline{year}_w \rfloor \right) * \left( \sum\limits^{\substack{\text{x,y} \\ \text{region}}} \left(\frac{1000}{\rho_i} \frac{dM}{dt}\right)_{\lfloor \overline{year}_w \rfloor} \right) \right] & \text{if } \overline{year}_w < 2000
\end{cases}
$


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.2 An attempt to quantify potential glacier volume over or underestimation
---
{year}_w \rfloor} \right) \right] & \text{if } \overline{year}_w < 2000
\end{cases}
$

Basically, this comes down to "reprojecting" glacier volumes back to the year 2000 from the area-weighted year of data acquisition by making use of known glacier changes in between these two dates. Here, we further assume a density $\rho_i$ of 900 kg m$^{-3}$ for the mass to volume conservation of glaciers, as also chosen by Farinotti et al. (2019) [[3](https://doi.org/10.1038/s41561-019-0300-3), [9](https://doi.org/10.5194/tc-7-877-2013)]. This may look like a complicated formula, but the principle is simple: for each RGI region, we simply sum the mass (and hence volume) changes over all spatial pixels between the year 2000 and the area-weighted year of delineation $(\overline{year}_w)$:
- If $(\overline{year}_w)$ is an integer, the second part of the formula (after the minus sign) drops out.
- If $(\overline{year}_w)$ is not an integer, the formula adjusts for the fractional part of the year:
  - If $(\overline{year}_w)$ > 2000, it uses the fraction between $(\overline{year}_w)$ and $(\lceil \overline{year}_w \rceil)$, where $\lceil \cdot \rceil$ denotes the ceiling function, which rounds a number up to the nearest integer.
  - If $(\overline{year}_w)$ < 2000, it uses the fraction between $(\lfloor \overline{year}_w \rfloor)$ and $(\overline{year}_w)$, where $\lfloor \cdot \rfloor$ denotes the floor function, which rounds a number down to the nearest integer.

Now that we have all information to derive values for $ dV_{\text{region}}^{2000,\overline{year}_w}$, let us apply this to the 19 different RGI regions in the RGIv7.0 data:

Calculate volume under or overestimation
Printing loop

```text
The volume estimate in RGI region  1 for the year 2000 is underestimated by 531.53 km³.
The volume estimate in RGI region  2 for the year 2000 is underestimated by 27.16 km³.
The volume estimate in RGI region  3 for the year 2000 is underestimated by 14.62 km³.
The volume estimate in RGI region  4 for the year 2000 is underestimated by 21.82 km³.
The volume estimate in RGI region  5 for the year 2000 is underestimated by 34.71 km³.
The volume estimate in RGI region  6 for the year 2000 is underestimated by 0.07 km³.
The volume estimate in RGI region  7 for the year 2000 is underestimated by 85.89 km³.
The volume estimate in RGI region  8 for the year 2000 is underestimated by 11.39 km³.
The volume estimate in RGI region  9 for the year 2000 is underestimated by 74.83 km³.
The volume estimate in RGI region 10 for the year 2000 is underestimated by 9.88 km³.
The volume estimate in RGI region 11 for the year 2000 is underestimated by 5.09 km³.
The volume estimate in RGI region 12 for the year 2000 is  overestimated by 1.73 km³.
The volume estimate in RGI region 13 for the year 2000 is underestimated by 49.42 km³.
The volume estimate in RGI region 14 for the year 2000 is underestimated by 2.72 km³.
The volume estimate in RGI region 15 for the year 2000 is underestimated by 25.80 km³.
The volume estimate in RGI region 16 for the year 2000 is underestimated by 2.96 km³.
The volume estimate in RGI region 17 for the year 2000 is underestimated by 17.51 km³.
The volume estimate in RGI region 18 for the year 2000 is underestimated by 2.91 km³.
The volume estimate in RGI region 19 for the year 2000 is underestimated by 219.79 km³.

The volume estimate at the global scale for the year 2000 is underestimated by 1136.37 km³.
```

Or when plotted:

Area-weighted estimate
Plot 1 — Raw estimates
Plot 2 — Area-weighted


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.2 An attempt to quantify potential glacier volume over or underestimation
---
The volume estimate at the global scale for the year 2000 is underestimated by 1136.37 km³.
```

Or when plotted:

Area-weighted estimate
Plot 1 — Raw estimates
Plot 2 — Area-weighted

*Figure 4. Total (above) and relative, i.e. volume divided by the total glacier surface area, (below) volume over or underestimation compared to the year 2000 for the glaciers in each RGI region of the glacier extent dataset.*

In the plot above, negative values indicate an underestimation. Underestimations of glacier volumes are noted in all but one regions, which is because the (area-weighted) average origin dates of the outlines are generally later than 2000, together with a general trend of glacier shrinkage during the last several decades [[6](https://doi.org/10.3189/2015JoG15J017)]. It is clear that especially RGI regions 1 (Alaska) and 19 (Antarctic and Subantarctic) exhibit a relatively large underestimation of the total glacier ice volume, mainly due to their large deviation of the area-weighted average year of delineation to the year 2000, as well as the large glacier ice volume changes during this corresponding period. Even though the largest temporal deviation of acquisition dates is noted for RGI region 18 (New Zealand), the total volume underestimation is not significant due to the relatively small glacier changes.

At the global scale, glacier ice volume estimates would exhibit an underestimation of ca. 1150 km³ due to misdated glacier outlines, which is only ca. 0.75% and 0.85% of the total glacier ice volume estimate by Farinotti et al. (2019) and GlaMBIE (2025) respectively [[3](https://doi.org/10.1038/s41561-019-0300-3), [14](https://doi.org/10.1038/s41586-024-08545-z)]. At the global scale, the above obtained deviation related to the misdated glacier outlines from RGIv6.0 is thus relatively low when compared to the total global glacier ice volume estimate from the glacier community, implying that the dataset is well-suited to estimate current global glacier ice volumes for the year 2000. The corresponding systematic error is thus small, but glacier- and region-dependent.

![alternatvie text](https://www.glims.org/rgi_user_guide/_images/global_map_small.jpeg)

*Figure 5. The 19 first-order regions of the RGI version 7.0 and glacier locations in red. From: [GLIMS RGI](https://www.glims.org/rgi_user_guide/welcome.html).*

(section-3-3)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 3. Estimation of global glacier ice volumes around the year 2000 with RGI data > 3.3 Other potential sources of error and uncertainty
---
Several additional factors contribute to the uncertainty in glacier data derived from the RGI dataset. These include low-resolution and poor-quality source data, errors by delineators, and challenges such as shadows, clouds, proglacial lakes, seasonal snowfields, and limited multi-temporal satellite imagery. The most significant source of misdelineation is, however, supraglacial debris, which often results in glacier area underestimation in regions with extensive debris cover (e.g. High Mountain Asia and the Caucasus), due to the spectral similarity between debris and surrounding moraines or bedrock [[10](https://doi.org/10.3189/2013AoG63A296)]. Additionally, ice bodies smaller than 0.01 km², considered below the threshold for ice flow, were excluded, leading to further underestimation of glacier area in some regions [[1](https://www.glims.org/RGI/randolph60.html)].

The interpretation of what constitutes a glacier also varies due to the diverse global community that contributed to the dataset, causing inconsistencies in how features like debris-covered glaciers, tributaries, and peripheral ice bodies in Antarctica and Greenland were handled [[11](https://doi.org/10.1017/jog.2023.1)]. For example, distinguishing debris-covered ice from bedrock or separating outlet glaciers from main ice sheets remains problematic. Other problems are related to geolocation issues, outline artefacts, and ice divides at wrong locations.

Quantitative error estimates are not provided with the downloaded data, but [[2](https://doi.org/10.3189/2014JoG13J176)] noted that relative errors are higher for small glaciers due to their larger outline-to-area ratio. Consequently, the uncertainty in an individual glacier outline depends on the quality of the source material and the specific glacier's characteristics. Users should thus exercise caution, particularly in regions with significant debris cover, small glacier features or around the peripheral glaciers of the Greenland and Antarctic ice sheets (where a clear separation of outlet glaciers from the main ice sheet body may be difficult).

Although this notebook makes use of the RGIv6.0, some notable improvements have been made in the newer RGIv7.0 with respect to area and mapping year estimates. This has ensured that the quality of outlines has substantially improved in many regions due to, amongst others, the inclusion of new updated inventory data and a new largely automated workflow. For example, 35% of all RGIv6.0 outlines were dated to five or more years away from the target year 2000, while this number is down to 23% in RGIv7.0. It is therefore advised for users to utilize the RGIv7.0 in future assessments.

(section-4)=


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > Analysis and results > 4. Short summary and take-home messages
---
The RGI glaciers distribution dataset that is on the CDS is currently the most complete dataset of glacier (and ice cap) outlines, outside of the Greenland and Antarctic Ice Sheets, in terms of its spatial coverage. It aims to capture the spatial distribution and global state of glacier outlines representative for the year 2000. However, the date of delineation (i.e. the time for which the outlines are representative) can significantly deviate from 2000, resulting in a systematic error.

When using the data for certain applications, such as for quantifying current global glacier volumes with RGI glacier areas as input data, this sytematic error has to be taken into account. It is found that the suitability of a RGI outline for current glacier ice volume estimates hence depends on (1) the deviation of the time since delineation from 2000 and (2) the significance of glacier area/volume changes during that period, which are influenced by changes of the local climate and the specific glacier geometries. Nevertheless, the assessment in this notebook revealed that (area-weighted) mean acquisition date of the glacier outlines is relatively close to 2000 at the global scale, although a tendency for delineation dates that are slightly more recent than 2000 is noted. Moreover, when compared to the total global ice volume estimate by Farinotti et al. (2019) and GlaMBIE (2025) [[3](https://doi.org/10.1038/s41561-019-0300-3), [14](https://doi.org/10.1038/s41586-024-08545-z)], the resulting systematic error calculated in this notebook is in the order of <1% only. This makes the dataset reliable to be used as input data for current global glacier volume estimates, but the systematic error is glacier- and region-dependent.

Additional factors to take into account are, amongst others, supraglacial debris, which often leads to an underestimation of the glacierized area in highly debris-covered regions such as High Mountain Asia and the Caucasus. When fed into glaciological and/or hydrological models, users are thus advized to take into account these considerations.


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > ℹ If you want to know more > Key resources
---
- [Glaciers distribution data from the Randolph Glacier Inventory (RGI) for year 2000](https://cds.climate.copernicus.eu/datasets/insitu-glaciers-extent?tab=overview)
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/insitu-glaciers-extent?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/display/CKB/Glacier+Area)
- [Copernicus climate change indicators: glaciers](https://climate.copernicus.eu/climate-indicators/glaciers)
- [RGI website from GLIMS](https://www.glims.org/RGI/) (Global Land Ice Measurements from Space)
- [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: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > ℹ If you want to know more > References
---
- [[1](https://www.glims.org/RGI/randolph60.html)] RGI Consortium (2017). Randolph Glacier Inventory – A Dataset of Global Glacier Outlines: Version 6.0: Technical Report, Global Land Ice Measurements from Space, Colorado, USA. Digital Media. doi: 10.7265/N5-RGI-60.

- [[2](https://doi.org/10.3189/2014JoG13J176)] Pfeffer, W. T., Arendt, A. A., Bliss, A., Bolch, T., Cogley, J. G., Gardner, A. S., Hagen, J. O., Hock, R., Kaser, G., Kienholz, C., Miles, E. S., Moholdt, G., Mölg, N., Paul, F., Radić, V., Rastner, P., Raup, B. H., Rich, J., Sharp, M. J., and Glasser, N. (2014). The Randolph Glacier Inventory: A globally complete inventory of glaciers, Journal of Glaciology, 60(221), 537-552. doi: 10.3189/2014JoG13J176.

- [[3](https://doi.org/10.1038/s41561-019-0300-3)] Farinotti, D., Huss, M., Fürst, J. J., Landmann, J., Machguth, H., Maussion, F., and Pandit, A. (2019). A consensus estimate for the ice thickness distribution of all glaciers on Earth. Nature Geoscience, 12(3), 168-173. doi: 10.1038/s41561-019-0300-3.

- [[4](https://doi.org/10.1029/2012JF002523)] Huss, M., and Farinotti, D. (2012). Distributed ice thickness and volume of all glaciers around the globe, Journal of Geophysical Research, 117, F04010. doi: 10.1029/2012JF002523.

- [[5](https://doi.org/10.5194/tc-6-1295-2012)] Marzeion, B., Jarosch, A. H., and Hofer, M. (2012). Past and future sea-level change from the surface mass balance of glaciers, The Cryosphere, 6, 1295–1322. doi: 10.5194/tc-6-1295-2012.

- [[6](https://doi.org/10.3189/2015JoG15J017)] Zemp, M., Frey, H., Gärtnew-Roer, I., Nussbaumer, S. U., Helzle, M., Paul, F., Haeberli, W., Denzinger, F., Ahlstrøm, A. P., Anderson, B., Bajracharya, S., Baroni, C., Braun, L. N., Cáceres, B. E., Casassa, G., Cobos, G., Dávila, L. R., Delgado Granados, H., Demuth, M. N., Espizua, L., Fischer, A., Fujita, K., Gadek, B., Ghazanfar, A., Hagen, J. O., Holmlund, P., Karimi, N., Li, Z., Pelto, M., Pitte, P., Popovnin, V. V., Portocarrero, C. A., Prinz, R., Sangewar, C. V., Severskiy, I., Sigurdsson, O., Soruco, A., Usubaliev, R., and Vincent, C. (2015). Historically unprecedented global glacier decline in the early 21st century, Journal of Glaciology, 61, 745-762. doi: 10.3189/2015JoG15J017.

- [[7](https://doi.org/10.1016/j.accre.2020.03.003)] Li, Y. J., Ding, Y. J., Shangguan, D. H., and Wang, R. J. (2019). Regional differences in global glacier retreat from 1980 to 2015, Advances in Climate Change Research, 10(4), 203–213. doi: 10.1016/j.accre.2020.03.003.


EQC Quality Assessment: "Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates"
Dataset: insitu-glaciers-extent [CDS]
Aspect: uncertainty_q01  |  Category: Satellite_ECVs
Section: Utility of the Randolph Glacier Inventory (RGI) for regional and global glacier volume estimates > ℹ If you want to know more > References
---
differences in global glacier retreat from 1980 to 2015, Advances in Climate Change Research, 10(4), 203–213. doi: 10.1016/j.accre.2020.03.003.

- [[8](https://doi.org/10.5194/tc-8-659-2014)] Leclercq, P. W., Oerlemans, J., Basagic, H. J., Bushueva, I., Cook, A. J., and Le Bris, R. (2014). A data set of worldwide glacier length fluctuations, Cryosphere, 2014(8), 659–672. doi: 10.5194/tc-8-659-2014.

- [[9](https://doi.org/10.5194/tc-7-877-2013)] Huss, M. (2013). Density assumptions for converting geodetic glacier volume change to mass change, The Cryosphere, 7, 877–887, doi: 10.5194/tc-7-877-2013.

- [[10](https://doi.org/10.3189/2013AoG63A296)] Paul, F., Barrand, N. E., Baumann, S., Berthier, E., Bolch, T., Casey, K., Frey, H., Joshi, S. P., Konovalov, V., Le Bris, R., Mölg, N., Nosenko, G., Nuth, C., Pope, A., Racoviteanu, A., Rastner, P., Raup, B., Scharrer, K., Steffen, S., and Winsvold, S. (2013). On the Accuracy of Glacier Outlines Derived from Remote-Sensing Data. Annals of Glaciology, 54(63), 171–82. doi: 10.3189/2013AoG63A296.

- [[11](https://doi.org/10.1017/jog.2023.1)] Hock, R., Maussion, F., Marzeion, B., and Nowicki, S. (2022). What is the global glacier ice volume outside the ice sheets? Journal of Glaciology, 69(273), 204–10. doi: 10.1017/jog.2023.1.

- [[12](https://doi.org/10.1017/jog.2021.28)] Li, Y. J., Li, F., Shangguan, D. H., Ding, Y. J. (2021). A New Global Gridded Glacier Dataset Based on the Randolph Glacier Inventory Version 6.0. Journal of Glaciology, 67 (2021), 773–76. doi: 10.1017/jog.2021.28.

- [[13](https://doi.org/10.5194/tc-6-1483-2012)] Rastner, P., Bolch, T., Mölg, N., Machguth, H., Le Bris, R., and Paul, F. (2012). The first complete inventory of the local glaciers and ice caps on Greenland, The Cryosphere, 6, 1483–1495, https://doi.org/10.5194/tc-6-1483-2012

- [[14](https://doi.org/10.1038/s41586-024-08545-z)] The GlaMBIE Team (2025). Community estimate of global glacier mass changes from 2000 to 2023. Nature 639, 382–388. https://doi.org/10.1038/s41586-024-08545-z


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications
---
Production date: 31-05-2025

Dataset version: 1.3 to 1.5

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


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Quality assessment question
---
* **"Is the dataset of sufficient spatial/temporal resolution, coverage and completeness to derive multi-year trends of horizontal surface flow velocities and the associated patterns of solid ice discharge?"**

Ice sheets are not static, but instead flow. The total velocity magnitude is the sum of the velocity related to internal ice deformation, and is complemented by basal sliding and bed deformation components. Mapping ice sheet surface flow velocities and their temporal changes provides key information for investigating the dynamic response of the ice sheets to climate change. Remote sensing techniques, such as the use of satellites, are an important feature to derive and study these flow velocities. Satellites are able to inspect directly and repeatedly large areas of ice, and, as such are able to detect the movement of its surface. Remote sensing techniques that use satellite data are therefore considered the only feasible manner to derive accurate surface velocities of the ice sheets on a regular basis. In this dataset, they are derived by applying offset tracking techniques using Sentinel-1 synthetic aperture radar (SAR) satellite data. The main principle of the "[Ice sheet velocity for Antarctica and Greenland derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-greenland-ice-sheet-velocity?tab=overview)" dataset therefore relies on the preservation of surface features or other detectable patterns (e.g. speckle) in between multiple image acquisition periods. The extraction of these features/patterns from images acquired over different time periods is used to detect their displacements, and with further processing this information can be used to derive velocity fields [[1](https://doi.org/10.3390/rs70709371)].

This notebook investigates how well the dataset on the CDS (here we use versions 1.3 to 1.5) can be used to derive mean values, (inter/intra-)annual variability and multi-year trends of ice flow velocities and the associated patterns of solid ice discharge. More specifically, the notebook evaluates whether the dataset is of sufficient maturity and quality for that purpose in terms of its spatio-temporal coverage and resolution and its data completeness.


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Quality assessment statement
---
These are the key outcomes of this assessment

- Surface ice flow velocity (“displacement”) observation by satellites is a useful tool to grasp the overall patterns of flow dynamics of the ice sheets. The C3S dataset exhibits a high spatial resolution, a consistent annual temporal resolution, and a nearly full ice sheet-wide coverage of the Greenland Ice Sheet (GrIS), which complies with international proposed standards. The majority of pixels also exhibit uncertainty values that fall within proposed error thresholds by GCOS. The data are therefore particularly well-suited for visualizing the spatial distribution of horizontal ice flow and for solid ice discharge calculations (i.e. dynamic ice mass loss), but additional datasets (i.e. the grounding line position, the ice thickness at those positions, and a conversion factor to derive vertically averaged horizontal velocities) are required for the latter.
- When using the ice flow velocity data for the GrIS for certain applications, such as for solid ice discharge estimations, users should be aware of the typical strengths and limitations of the C3S SAR offset tracking-based velocity products. For example, the short temporal span (from 2014–2015 onwards) limits its use for detecting long-term trends or reliable climate change signals. Additionally, the ice sheet margins often suffer from higher absolute error values. These regions are nevertheless crucial for solid ice discharge estimates. Another limitation of this product is its yearly temporal resolution, which only captures interannual changes and misses important seasonal variations, making it less suitable for certain detailed studies. This especially holds for the Greenland Ice Sheet, where some outlet glaciers exhibit significant seasonal variations with respect to their dynamics. If desired, the C3S data can be complemented with external datasets to increase its temporal resolution and time span.
```


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Methodology > Dataset description
---
The 'Ice sheet velocity for Antarctica and Greenland derived from satellite observations' dataset, available on the Climate Data Store (CDS), offers annually averaged surface ice flow velocities and their easting and northing components for the Antarctic (AIS) and Greenland (GrIS) Ice Sheets. This data is provided on a spatial resolution grid of either 200 m, 250 m or 500 m, depending on the ice sheet and dataset version. The dataset includes horizontal velocity components in the east and north directions, as well as the total horizontal velocity magnitude and its uncertainty, expressed as 1-sigma precission errors. Surface flow velocities are treated as “displacements”, normalized to true meters per day, and are available for each glaciological year since 2014-2015 for the GrIS and since 2021-2022 for the AIS. The horizontal velocities and their components are derived using offset tracking techniques with Sentinel-1 synthetic aperture radar (SAR) satellite data. The data are provided in NetCDF format as gridded data fields in Polar Stereographic projection, covering the entire GrIS domain, including peripheral glaciers and ice caps.


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Methodology > Structure and (sub)sections
---
**[](section-1)**

* [](section-1-1)
* [](section-1-2)
* [](section-1-3)
* [](section-1-4)

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

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

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

**[](section-5)**


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > 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 GrIS velocity data.

🚨 **The files can be large! Since the data files to be downloaded have a considerable size due to the high spatial resolution, this may take a couple of minutes.**

```text
Downloading ice sheet velocity data, this may take a couple of minutes...
```

```text
100%|██████████| 1/1 [00:00<00:00,  8.78it/s]
100%|██████████| 1/1 [00:00<00:00, 86.43it/s]
100%|██████████| 1/1 [00:00<00:00, 27.16it/s]
100%|██████████| 1/1 [00:00<00:00, 98.45it/s]
100%|██████████| 1/1 [00:00<00:00, 76.81it/s]
100%|██████████| 1/1 [00:00<00:00, 108.28it/s]
100%|██████████| 1/1 [00:00<00:00, 116.87it/s]
100%|██████████| 1/1 [00:00<00:00, 108.75it/s]
100%|██████████| 1/1 [00:00<00:00, 114.07it/s]
```

```text
Downloading completed.
```

(section-1-3)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
We can read and inspect the data. Let us print out the data to inspect its structure:

```text
<xarray.Dataset> Size: 19GB
Dimensions:                              (period: 9, y: 10801, x: 5984)
Coordinates:
  * period                               (period) object 72B '2014_2015' ... ...
  * y                                    (y) float64 86kB -6.556e+05 ... -3.3...
  * x                                    (x) float64 48kB -6.399e+05 ... 8.55...
Data variables:
    crs                                  (period) int32 36B -2147483647 ... -...
    land_ice_surface_easting_velocity    (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_northing_velocity   (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_vertical_velocity   (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_velocity_magnitude  (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_measurement_count   (period, y, x) float64 5GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_easting_stddev      (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
    land_ice_surface_northing_stddev     (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
Attributes: (12/13)
    Conventions:    CF-1.7
    title:          Ice Velocity of the Greenland Ice Sheet
    reference:      Main: Nagler, T.; Rott, H.; Hetzenecker, M.; Wuite, J.; P...
    source:         Copernicus Sentinel-1A and Sentinel-1B
    institution:    Copernicus Climate Change Service
    contact:        copernicus-support@ecmwf.int
    ...             ...
    creation_date:  2024-12-12
    comment:        Ice velocity map of Greenland derived from Sentinel-1 SAR...
    history:        product version 1.3
    summary:        Ice velocity derived for Greenland Ice Sheet gridded at 2...
    keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
    license:        C3S general license
```

The versions 1.3 to 1.5 are a gridded dataset at a 250 m spatial resolution containing annually averaged values of the ice sheet horizontal surface flow velocity $V_s$ (in m/day) of a grid cell (`land_ice_surface_velocity_magnitude`) and its components (`land_ice_surface_easting_velocity` ($V_x$) and `land_ice_surface_northing_velocity` ($V_y$)) since the 2014-2015 hydrological year. The uncertainties (reported as precision errors or standard deviations) of the horizontal components are also given as `land_ice_surface_easting_stddev` ($\sigma_{V_x}$) and `land_ice_surface_northing_stddev` ($\sigma_{V_y}$). Also the vertical component is given as `land_ice_surface_vertical_velocity` ($V_z$), but without a corresponding uncertainty. Next to that, also a variable named `land_ice_surface_measurement_count` is present, which quantifies the total number of valid image pairs used in the annually averaged velocity estimate for a certain pixel.

For clarification, the total horizontal surface velocity magnitude $V_s$ and its uncertainty $\sigma_{V_s}$ are calculated from its components as follows (with subscript 's' referring to the surface):

$
V_s
$
[m day⁻¹]
$
= \sqrt {V_x^2 + V_y^2}
$

$
\sigma_{V_s}
$
[m day⁻¹]
$
= \sqrt {(\sigma_{V_x})^2 + (\sigma_{V_y})^2}
$

where $V_x$ and $V_y$ are respectively the easting and northing components of the horizontal velocity vector.


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
$
= \sqrt {(\sigma_{V_x})^2 + (\sigma_{V_y})^2}
$

where $V_x$ and $V_y$ are respectively the easting and northing components of the horizontal velocity vector.

The flow direction of the ice can be calculated as follows:

$
\theta_{\text{V}_s} = \left( 90^\circ - \left( \arctan2(v_y, v_x) \times \left( \frac{180}{\pi} \right) \right) \right) \mod 360^\circ
$

(section-1-4)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 1. Data preparation and processing > 1.4 Data handling
---
Let us calculate and add the total standard deviation to the data, as well as the flow direction of the ice, so we can work with it easily later on in the notebook. We also perform some data slight manipulations to the data array to improve data handling:

Compute standard deviation
Flow direction
Keep only selected variables (coords like 'source' stay by default)
Apply transformation
Add attributes

Now, our dataset array only holds the most important information: the total horizontal velocity magnitude (`land_ice_surface_velocity_magnitude`), the valid pixel count (`land_ice_surface_measurement_count`), the calculated ice flow direction (`land_ice_flow_direction`), and our calculated standard deviation (`land_ice_surface_stddev`) from the northing and easting components. Let us first make the plotting function before we begin with the analysis:

Circular mean over time for the flow direction
Main plotting function
Auto-detect if this is directional data (degrees)
Take mean over time (period)
Assign cyclic colormap if direction
Create polar plot
Set map extent and features
Colorbar with angular formatting if needed

(section-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 2. Spatial and temporal patterns of ice sheet surface ice flow velocities > 2.1 Average horizontal ice flow velocities
---
We begin by plotting the ice flow velocities averaged over every hydrological year between the beginning and end period that we selected for the velocity data with the defined plotting function.

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

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

The corresponding data are annually averaged values, derived from all year-round observations during the glaciological balance year of the GrIS (1 October to 30 September). The horizontal velocity data effectively highlight the low-flow zones in the interior and the increased velocities near the ice sheet’s margins and outlet glaciers. This pattern aligns with findings from other GrIS velocity maps in the literature (e.g. [[2](https://doi.org/10.1017/jog.2017.73), [3](https://nsidc.org/data/nsidc-0777/versions/1)]). The annually averaged nature meets the minimum requirement set by the Global Climate Observing System (GCOS) [[4](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)], providing a comprehensive overview of ice flow velocities. However, there is no information given related to the time of the year during which valid pixels for the velocity calculation were acquired. Also the spatial resolution of 250 m meets the threshold value proposed by GCOS. In other words, both the spatial and temporal resolution meet the minimum requirement to ensure that data are useful for use in climatological, hydrological and glaciological studies and applications.

(section-2-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 2. Spatial and temporal patterns of ice sheet surface ice flow velocities > 2.2 Average horizontal ice flow direction
---
We can also plot flow directions (i.e. the direction to which the ice flows measured clockwise from the north). For that, we calculate the circular mean:

Apply to flow direction

*Figure 2. Average direction of the horizontal surface flow velocities over Greenland over the defined time period.*

The provided image displays the average ice flow direction for Greenland averaged over all available periods. The color scale indicates the direction of ice flow in degrees, measured clockwise from north (northwards = 0°/360°, eastwards = 90°, southwards = 180°, westwards = 270°). Several ice divides are visible, of which the most prominent one is situated meriodionally over central Greenland where flow directions diverge, leading to different drainage basins. The predominant direction of the ice flow is consistent with the topographical characteristics of the ice sheet (i.e. ice flows parallel to the direction of the steepest surface slope).

Let us now analyze the spatial and temporal resolution and coverage of the dataset.

(section-3)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 3. Analysis of spatio-temporal resolution and extent of ice sheet velocities > 3.1 Temporal extent of the ice sheet velocity dataset
---
We begin our analysis by examining the temporal extent of the dataset:

```text
The temporal extent of the ice sheet velocity dataset for the GrIS is 9 years.
```

To determine whether the temporal extent of the ice sheet velocity dataset is sufficient to capture reliable temporal trends in horizontal surface velocities and to use these trends as indicators of climatic changes, we turn to the literature. The Intergovernmental Panel on Climate Change (IPCC) often uses 30 years as a standard period for climate normals and trend analysis to ensure that the analysis captures meaningful climatic changes rather than short-term (intra/interannual) fluctuations. We therefore consider these guidelines to be likewise applicative for ice flow velocities.

When measured over a long period (> 30 years), significant trends in surface flow velocities can be considered a clear indicator of a disequilibrium of the ice sheet with the environment, for example due to climate change. Longer periods provide even more robust trend estimates and reduce the influence of short-term variability. However, the dataset (as of versions 1.3 to 1.5 with 9 years of data) is clearly not of sufficient temporal extent for this purpose.

(section-3-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 3. Analysis of spatio-temporal resolution and extent of ice sheet velocities > 3.2 Spatial coverage of the ice sheet velocity dataset
---
To have a more extended idea of the temporal and spatial coverage of the gridded dataset, we can plot the total amount of pixels that hold non-NaN velocity data for each year. Let us have this quantified:

Apply the function to the velocity counts
Print values

```text
The total amount of pixels holding non-NaN values for the year 2014-2015 CE is 33048867 counts, which equals a surface area of 2.06555 million km².
The total amount of pixels holding non-NaN values for the year 2015-2016 CE is 34139948 counts, which equals a surface area of 2.13375 million km².
The total amount of pixels holding non-NaN values for the year 2016-2017 CE is 34195665 counts, which equals a surface area of 2.13723 million km².
The total amount of pixels holding non-NaN values for the year 2017-2018 CE is 34146643 counts, which equals a surface area of 2.13417 million km².
The total amount of pixels holding non-NaN values for the year 2018-2019 CE is 34166241 counts, which equals a surface area of 2.13539 million km².
The total amount of pixels holding non-NaN values for the year 2019-2020 CE is 34181540 counts, which equals a surface area of 2.13635 million km².
The total amount of pixels holding non-NaN values for the year 2020-2021 CE is 34210311 counts, which equals a surface area of 2.13814 million km².
The total amount of pixels holding non-NaN values for the year 2021-2022 CE is 34203801 counts, which equals a surface area of 2.13774 million km².
The total amount of pixels holding non-NaN values for the year 2022-2023 CE is 34070897 counts, which equals a surface area of 2.12943 million km².
```

Given that the surface area of the entire continent of Greenland roughly equals 2.165 million km² (of which ca. 80% covered by ice), it is clear that almost the entire continent is covered by the product, including ice-free areas. Let us determine what percentage of the pixels hold a time series of data with a length that is equal to the magnitude of the `time` dimension of the dataset:

```text
The number of pixels that have a time series of valid velocity data of 9 years, which is the total number of years in the dataset, is 32911734 pixels or 96.18%.
```

The amount of missing data can therefore be considered limited.

Let us now check where the missing pixels are. In the plot below, pixels with a time series of valid data that are lower than the time dimension of the data are colored red, else they are colored green:

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

*Figure 3. Presence of missing data of the horizontal surface flow velocities over Greenland over the defined time period.*

The dataset thus offers GrIS velocity data at regular and consistently spaced temporal intervals (e.g. annually averaged data), and there are (almost) no spatial/temporal gaps in the data that could affect a (local or ice sheet-wide) trend analysis. However, the total number of consecutive years in the dataset is too low to perform a reliable temporal trend analysis. In other words, from the above analysis it becomes clear that the dataset exhibits a consistently complete temporal and spatial coverage, with practically no data gaps, which would allow for reliable quantifications of velocity means, variability and trends if the temporal extent would have been sufficient. Moreover, 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. These non-ice values are, however, intentionally retained because the velocity retrievals over stable land are used for the quality assessment of the algorithm, as detailed in the PQAR.

(section-4)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 4. Trends of annually averaged horizontal surface ice flow velocities > 4.1 Linear trends of horizontal ice flow velocities
---
Although the temporal extent is not sufficient to derive reliable values for the mean, variability and trends (as discussed above), we can still plot a time series of annually averaged ice sheet-wide velocity data to get an idea of their magnitudes and their change over time in the dataset. Let us print the average values over the entire ice sheet for each hydrological year:

Print values

```text
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2014-2015 CE is 0.1124 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2015-2016 CE is 0.1113 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2016-2017 CE is 0.1134 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2017-2018 CE is 0.1172 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2018-2019 CE is 0.1164 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2019-2020 CE is 0.1154 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2020-2021 CE is 0.1131 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2021-2022 CE is 0.1132 m/day.
The annually averaged ice sheet-wide horizontal surface ice flow velocity for the year 2022-2023 CE is 0.1156 m/day.
```

Let us now have this plotted on a graph:

Extract time and velocity data
Convert period strings to numerical values (midpoint of each period)
Calculate linear trend
Plot the data

*Figure 4. Linear trend of the ice sheet-wide average horizontal surface flow velocities over Greenland over the defined time period.*

We can quantify the linear trend as follows:

Quantify the linear trend (coeffs[0] is the slope, coeffs[1] is the intercept)

```text
The linear trend of the ice sheet-wide horizontal surface ice flow velocity between 2014-2015 and 2022-2023 is 0.0003 m day⁻¹ yr⁻¹.
```

The provided plot shows the trend of ice sheet-wide horizontal surface ice flow velocities since the period 2014-2015. The linear trend shows an increase in the ice sheet-wide horizontal surface ice flow velocity over time. This means that the ice flow has generally been speeding up over this period. This generally agrees with what can be expected from a warming climate, although the impact of climate change on the GrIS dynamic patterns is complex in both space and time. The outlet glaciers of the GrIS are currently retreating, calving more icebergs, and also flowing faster. Many major outlet glaciers in Greenland (e.g. Jakobshavn Isbræ, Helheim, and Kangerlussuaq) experienced substantial speed-ups during the last several decades. This acceleration was mainly linked to oceanic and atmospheric warming, which led to increased basal sliding and reduced backstress (buttressing), hereby enhancing flow speed (e.g. [[5](https://doi.org/10.5194/tc-6-923-2012), [6](https://doi.org/10.1038/s41586-022-05301-z), [7](https://doi.org/10.1038/s43247-020-0001-2)]). However, studies indicate that this ongoing acceleration cannot simply be extrapolated throughout the 21st century and beyond. In the future, the ice sheet's thinning is expected to slow down the ice due to the inverse relationship between ice thickness and ice velocity, as expected from physical theory (e.g. [[8](https://doi.org/10.5194/tc-9-1039-2015)]).

However, it must be said that the temporal extent of the velocity data is relatively short. Longer-term observations (> 30 years) are necessary to identify persistent trends and separate short-term variability from long-term changes. Moreover, the trend in ice sheet-wide velocity data for Greenland may be influenced by the inclusion of unrealistic velocity data over ice-free terrain, whereas certain zones, such as the glacier margins, may be subject to lower data quality as well [[9](https://doi.org/10.1016/j.rse.2017.08.038)]. Therefore, further investigation and long-term monitoring of velocities over ice-covered areas are essential to accurately and reliably assess and interpret trends of ice flow velocities and their implications for future ice sheet behavior and sea-level rise.

(section-4-2)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 4. Trends of annually averaged horizontal surface ice flow velocities > 4.2 Implications for deriving multi-year trends of surface flow velocities and associated patterns of solid ice discharge
---
Reliable and long-term trends in ice sheet flow velocities are essential for understanding the complex dynamics of ice sheets and the impact of climate change. One of such processes for which ice flow velocities are important is the quantification of solid ice discharge.

Solid ice discharge is the transport of solid ice across the grounding line of an ice sheet. This process represents the loss of grounded ice from the ice sheet to the ocean due to ice flow. The grounding line is the boundary between the grounded ice sheet, where ice rests on bedrock, and the floating ice, which is buoyant. As ice flows from the grounded portion of the ice sheet into the ocean, it contributes to sea-level rise. Solid ice discharge $D$ therefore is a critical component of the total mass balance of an ice sheet [[10](https://essd.copernicus.org/articles/12/1367/2020/)]:

$\Delta M = SMB - D$

where:
- $\Delta M$ is the total mass balance or the total ice mass loss or gain [Gt yr$^{-1}$],
- $SMB$ is surface mass balance (often also supplemented by the basal and internal mass balance) [Gt yr$^{-1}$],
- $D$ is the solid ice discharge (zero for land-terminating glaciers/ice sheets) [Gt yr$^{-1}$].

The solid discharge $D$ can be further expressed as a mass flux as follows:

$D = \rho_i \cdot \overline{V_P} \cdot A = \rho_i \cdot \overline{V_P} \cdot H \cdot w
$

where
- $\rho_i$ is the ice density [kg m$^{-3}$]
- $\overline{V_P}$ the gate-perpendicular vertically averaged horizontal ice flow velocity at the grounding line [m yr$^{-1}$]

≈ $\overline{V}\cdot cos(\theta)$ with $\theta$ the difference between ice flow and gate-perpendicular azimuths and where $\overline{V}$ approximately equals the surface velocity $V_s$
- $H$ the ice thickness at the grounding line [m]
- $A$ the considered cross-sectional area [m]
- $w$ the width of the cross section across the groundling line [m].

Ice flow velocities are thus an important component to assess the solid ice discharge and its trends over time. The dataset provided for monitoring GriS surface flow velocity patterns on the CDS is a relatively mature dataset that can serve as input for solid ice discharge calculations, as it has a suitable spatial resolution for capturing detailed flow patterns, particularly near ice margins and outlet glaciers. The spatial coverage is furthermore comprehensive, encompassing the entire ice sheet, including peripheral glaciers and ice caps, with almost no gaps present. The dataset's completeness thus appears high, with minimal missing values.

However, the temporal coverage only extends from 2014-2015 onwards, which is too short to perform a reliable long-term trend analysis. The dataset's short temporal extent therefore poses a limitation to deduce reliable long-term trends of horizontal surface flow velocities and solid ice discharge. Furthermore, to precisely quantify the solid ice discharge, also other additional and external datasets of other variables are needed, of which the most important ones are the position of the grounding line and the ice thickness at those locations [[10](https://doi.org/10.5194/essd-12-1367-2020)]. Moreover, the dataset provides horizontal surface velocities, while solid ice discharge calculations require vertically averaged horizontal velocities. However, because basal sliding is generally the dominant process that defines the ice velocity at the grounding line, velocities generally do not vary significantly with depth at these locations [[10](https://doi.org/10.5194/essd-12-1367-2020)]. Next, with only yearly maps, this product can only calculate interannual changes in ice discharge, which may not be sufficient for certain users. This may be particularly true for the GrIS, where many outlet glaciers exhibit significantly distinct seasonal variations in ice velocity. The lack of information related to the time of the year of the valid data acquisitions, as well as higher standard deviations near the margins and a missing ice mask that can be used to distinguish between ice-covered and non ice-covered grid cells, further complicate the use of the data. Hence, for comprehensive glaciological studies and solid ice discharge modeling, supplementary datasets with a longer temporal extent (preferably > 30 years) and higher temporal resolution (subannual) should be considered to fully capture the changing patterns of ice flow dynamics.

(section-5)=


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > Analysis and results > 5. Short summary and take-home messages
---
When measured over long periods and extensive geographical scales, trends in GrIS ice sheet flow velocities and solid ice discharge are clear indicators of global climate change [[9](https://doi.org/10.1016/j.rse.2017.08.038), [10](https://doi.org/10.5194/essd-12-1367-2020)]. To be able to derive such trends of ice sheet velocities and for climate change analysis/monitoring to become reliable and possible, the velocity dataset should at least exhibit a comprehensive spatial coverage (i.e. ice sheet-wide), a long and continuous temporal coverage (> 30 years), quantified and transparent pixel-by-pixel uncertainty estimates that meet international proposed thresholds [[4](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)], a validation effort or a comparison to theoretical models, and an adequate spatio-temporal resolution (cfr. the "Maturity Matrix" [[11](https://doi.org/10.1175/BAMS-D-21-0109.1)]).

The [ice sheet velocity dataset on the CDS](https://cds.climate.copernicus.eu/datasets/satellite-greenland-ice-sheet-velocity?tab=overview) is found to exhibit a consistent suitable spatial (250 m) and temporal (annual) resolution, but a less extensive temporal coverage (< 30 years), to conduct a meaningful analysis of linear (and quadratic) trends in ice sheet surface velocities and solid ice discharge. Nevertheless, the spatial and temporal resolution/extent of the data align with international standards such as those proposed by GCOS [[4](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)] and data gaps are practically non-existant in this dataset. An even finer temporal resolution would, however, be beneficial to better capture subannual variations in flow speeds and solid ice discharge estimates. Validation efforts also show encouraging results, as shown in the [PQAR](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355348656). The resulting trends from the C3S dataset show a general speedup of the GrIS over the last few years.

Taking all of the above into account, the SAR offset tracking-based GrIS velocity dataset is generally considered to be relatively well-suited for use in the context of visualizing the spatial patterns of ice flow and for solid ice discharge quantifications (if it is assumed that vertically averaged horizontal velocities approximate the surface velocities near the grounding line) in terms of its spatial/temporal resolution, spatial coverage and data completeness. However, the GrIS velocity data are at this stage found to be less suitable to derive the corresponding long-term trends (climate change signals) and inter/intra-annual variability. Moreover, noise over ice-free terrain and the lack of imformation regarding the time of valid data acquisitions may impact the results of the analysis. Users should thus acknowledge the above-mentioned limitations for this dataset. The derivation of (long-term) surface ice flow velocity trends from C3S data, as well as the associated patterns of solid ice discharge, should therefore be handled with care.


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in 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)
- [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 coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in 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://doi.org/10.1017/jog.2017.73)] Joughin, I., Smith, B. E., and Howat, I. M. (2018). A complete map of Greenland ice velocity derived from satellite data collected over 20 years, J. Glaciol., 64, 1–11, https://doi.org/10.1017/jog.2017.73

- [[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://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

- [[5](https://doi.org/10.5194/tc-6-923-2012)] Bevan, S. L., Luckman, A. J., and Murray, T. (2012). Glacier dynamics over the last quarter of a century at Helheim, Kangerdlugssuaq and 14 other major Greenland outlet glaciers, The Cryosphere, 6, 923–937, https://doi.org/10.5194/tc-6-923-2012

- [[6](https://doi.org/10.1038/s41586-022-05301-z)] Khan, S. A., Choi, Y., Morlighem, M., Rignot, E., Helm, V., Humbert, A., Mouginot, J., Millan, R., Kjær, K. H., and Bjørk, A. A. (2022). Extensive inland thinning and speed-up of Northeast Greenland Ice Stream. Nature, 611, 727–732, https://doi.org/10.1038/s41586-022-05301-z

- [[7](https://doi.org/10.1038/s43247-020-0001-2)] King, M. D., Howat, I. M., Candela, S. G., Noh, M. J., Jeong, S., Noël, B. P. Y., van den Broeke, M. R., Wouters, B., and Negrete, A. (2020). Dynamic ice loss from the Greenland Ice Sheet driven by sustained glacier retreat. Communications Earth & Environment, 1, Article 1. https://doi.org/10.1038/s43247-020-0001-2

- [[8](https://doi.org/10.5194/tc-9-1039-2015)] Fürst, J. J., Goelzer, H., and Huybrechts, P. (2015). Ice-dynamic projections of the Greenland ice sheet in response to atmospheric and oceanic warming, The Cryosphere, 9, 1039–1062, https://doi.org/10.5194/tc-9-1039-2015

- [[9](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


EQC Quality Assessment: "Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications"
Dataset: satellite-greenland-ice-sheet-velocity [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Ice sheet velocity data from satellite observations: temporal and spatial coverage and data completeness for trend analysis in glaciological applications > ℹ If you want to know more > References
---
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

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

- [[11](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


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
---
Production date: 31-05-2025

Dataset version: 1.3 to 1.5

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


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 > Quality assessment question
---
* **"How does the uncertainty of the horizontal ice sheet surface flow velocity vary in space and time and is the dataset sufficiently accurate and precise to be used in an ice sheet modeling framework?"**

Ice sheets are not static, but instead flow. The total velocity magnitude is the sum of the velocity related to internal ice deformation, and is complemented by basal sliding and bed deformation components. Mapping ice sheet surface flow velocities and their temporal changes provides key information for investigating the dynamic response of the ice sheets to climate change. Remote sensing techniques, such as the use of satellites, are an important feature to derive and study these flow velocities. Satellites are able to inspect directly and repeatedly large areas of ice, and, as such are able to detect the movement of its surface. Remote sensing techniques that use satellite data are therefore considered the only feasible manner to derive accurate surface velocities of the ice sheets on a regular basis. In this dataset, they are derived by applying offset tracking techniques using Sentinel-1 synthetic aperture radar (SAR) satellite data. The main principle of the "[Ice sheet velocity for Antarctica and Greenland derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-greenland-ice-sheet-velocity?tab=overview)" dataset therefore relies on the preservation of surface features or other detectable patterns (e.g. speckle) in between multiple image acquisition periods. The extraction of these features/patterns from images acquired over different time periods is used to detect their displacements, and with further processing this information can be used to derive velocity fields [[1](https://doi.org/10.3390/rs70709371), [11](https://doi.org/10.1016/j.rse.2025.115092)].

This notebook investigates how well the dataset on the CDS (here we use versions 1.3 to 1.5) can be used in the context of an ice sheet modelling framework for Greenland and Antarctica. More specifically, the notebook evaluates whether the dataset is of sufficient maturity and quality for that purpose in terms of its spatio-temporal coverage and uncertainty.


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

- Data quality of the C3S ice sheet velocity dataset in terms of error and uncertainty can be assessed by two variables: the standard deviation (as a precision error estimate) and the valid pixel count maps (as the total number of valid measurements used in the annually averaged velocity estimate over 1 year of data acquisition). Consulting the accompanying standard deviation and the valid measurement count maps is therefore recommended to assess the error and uncertainty characterization of the product. The majority of pixels meet the proposed GCOS thresholds in terms of uncertainty. However, data quality can be slightly lower in some regions (due to 'striping', higher error values and/or lower valid measurements). Errors are furthermore provided as absolute values, while for flow fields, the relative error is generally considered to be more useful.
- Due to the high spatial resolution/coverage and the quality-rich uncertainty characterization, the C3S ice sheet velocity dataset is particularly well-suited for the use as a calibration or validation tool within an ice sheet modelling framework. Validation efforts furthermore show good agreement with independent data. The user can, if desired, prioritize high-quality data (i.e. pixels with low absolute or relative errors and/or high valid pixel counts) when adjusting tuning parameters in an ice sheet model, such that the modelled ice thickness or surface velocity matches the observed one as close as possible.
```


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 > Methodology > Dataset description
---
The 'Ice sheet velocity for Antarctica and Greenland derived from satellite observations' dataset, available on the Climate Data Store (CDS), offers annually averaged surface ice flow velocities and their easting and northing components for the Antarctic (AIS) and Greenland (GrIS) Ice Sheets. This data is provided on a spatial resolution grid of either 200 m, 250 m or 500 m, depending on the ice sheet and dataset version. The dataset includes horizontal velocity components in the east and north directions, as well as the total horizontal velocity magnitude and its uncertainty, expressed as 1-sigma precission errors. Surface flow velocities are treated as “displacements”, normalized to true meters per day, and are available for each glaciological year since 2014-2015 for the GrIS and since 2021-2022 for the AIS. The horizontal velocities and their components are derived using offset tracking techniques with Sentinel-1 synthetic aperture radar (SAR) satellite data. The data are provided in NetCDF format as gridded data fields in Polar Stereographic projection, covering the entire GrIS domain, including peripheral glaciers and ice caps.


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 > Methodology > Structure and (sub)sections
---
**[](section-1)**

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

**[](section-2)**
* [](section-2-1)
* [](section-2-2)
* [](section-2-3)
* [](section-2-4)

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

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

**[](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 > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define requests for download from the CDS and download the GrIS and AIS velocity data and immediately perform some data handling to make the dataset more readable.

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

Add period dim
Compute standard deviation
Flow direction
Keep only selected variables

```text
Downloading ice sheet velocity data, this make take a couple of minutes...
domain = 'greenland_ice_sheet'
```

```text
100%|██████████| 9/9 [00:05<00:00,  1.57it/s]
```

```text
domain = 'antarctic_ice_sheet'
```

```text
100%|██████████| 2/2 [00:00<00:00,  5.84it/s]
```

```text
Downloading ice sheet velocity data complete.
```

(section-1-3)=


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 > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
:

```text
{'greenland_ice_sheet': <xarray.Dataset> Size: 12GB
 Dimensions:                              (period: 9, y: 10801, x: 5984)
 Coordinates:
   * period                               (period) <U9 324B '2014-2015' ... '2...
     source                               (period) <U32 1kB '3f623b8825fe15dda...
   * y                                    (y) float64 86kB -6.556e+05 ... -3.3...
   * x                                    (x) float64 48kB -6.399e+05 ... 8.55...
 Data variables:
     land_ice_surface_velocity_magnitude  (period, y, x) float32 2GB dask.array<chunksize=(1, 3601, 1995), meta=np.ndarray>
     land_ice_surface_measurement_count   (period, y, x) float64 5GB dask.array<chunksize=(1, 3601, 1995), meta=np.ndarray>
     land_ice_surface_stddev              (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
     land_ice_flow_direction              (period, y, x) float32 2GB dask.array<chunksize=(1, 1351, 748), meta=np.ndarray>
 Attributes: (12/13)
     Conventions:    CF-1.7
     title:          Ice Velocity of the Greenland Ice Sheet
     reference:      Main: Nagler, T.; Rott, H.; Hetzenecker, M.; Wuite, J.; P...
     source:         Copernicus Sentinel-1A and Sentinel-1B
     institution:    Copernicus Climate Change Service
     contact:        copernicus-support@ecmwf.int
     ...             ...
     creation_date:  2024-12-12
     comment:        Ice velocity map of Greenland derived from Sentinel-1 SAR...
     history:        product version 1.3
     summary:        Ice velocity derived for Greenland Ice Sheet gridded at 2...
     keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
     license:        C3S general license,
 'antarctic_ice_sheet': <xarray.Dataset> Size: 28GB
 Dimensions:                              (period: 2, y: 24580, x: 28680)
 Coordinates:
   * period                               (period) <U9 72B '2021-2022' '2022-2...
     source                               (period) <U32 256B '24d8cbb7053b3957...
   * y                                    (y) float64 197kB 2.458e+06 ... -2.4...
   * x                                    (x) float64 229kB -2.868e+06 ... 2.8...
 Data variables:
     land_ice_surface_velocity_magnitude  (period, y, x) float32 6GB dask.array<chunksize=(1, 4097, 4780), meta=np.ndarray>
     land_ice_surface_measurement_count   (period, y, x) float64 11GB dask.array<chunksize=(1, 4097, 4780), meta=np.ndarray>
     land_ice_surface_stddev              (period, y, x) float32 6GB dask.array<chunksize=(1, 1891, 2207), meta=np.ndarray>
     land_ice_flow_direction              (period, y, x) float32 6GB dask.array<chunksize=(1, 1891, 2207), meta=np.ndarray>
 Attributes: (12/13)
     Conventions:    CF-1.7
     title:          Ice Velocity of the Antarctic Ice Sheet
     reference:      Main: Nagler, T.; Rott, H.; Hetzenecker, M.; Wuite, J.; P...
     source:         Copernicus Sentinel-1A and Sentinel-1B
     institution:    Copernicus Climate Change Service
     contact:        copernicus-support@ecmwf.int
     ...             ...
     creation_date:  2023-12-15
     comment:        Ice velocity map of Antarctica derived from Sentinel-1 SA...
     history:        product version 1.5
     summary:        Ice velocity derived for Antarctic Ice Sheet gridded at 2...
     keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
     license


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 > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
product version 1.5
     summary:        Ice velocity derived for Antarctic Ice Sheet gridded at 2...
     keywords:       EARTH SCIENCE CLIMATE INDICATORS CRYOSPHERIC INDICATORS G...
     license

:        C3S general license}
```


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 > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
```

For the GrIS, the versions 1.3 to 1.5 are a gridded dataset at a 250 m spatial resolution containing annually averaged values of the ice sheet horizontal surface flow velocity $V_s$ (in m/day) of a grid cell (`land_ice_surface_velocity_magnitude`) and its components (`land_ice_surface_easting_velocity` ($V_x$) and `land_ice_surface_northing_velocity` ($V_y$)) since the 2014-2015 hydrological year. The uncertainties (reported as precision errors or standard deviations) of the horizontal components are also given as `land_ice_surface_easting_stddev` ($\sigma_{V_x}$) and `land_ice_surface_northing_stddev` ($\sigma_{V_y}$). Also the vertical component is given as `land_ice_surface_vertical_velocity` ($V_z$), but without a corresponding uncertainty. Next to that, also a variable named `land_ice_surface_measurement_count` is present, which quantifies the total number of valid image pairs used in the annually averaged velocity estimate for a certain pixel.

For the AIS, only version 1.5 is available at a spatial resolution of 200 m since the 2021-2022 period. After the data handling we performed, our dataset array now only holds the most important information: the total horizontal velocity magnitude (`land_ice_surface_velocity_magnitude`), the valid pixel count (`land_ice_surface_measurement_count`), the calculated ice flow direction (`land_ice_flow_direction`), and our calculated standard deviation (`land_ice_surface_stddev`) from the northing and easting components.

For clarification, the total horizontal surface velocity magnitude $V_s$ and its uncertainty $\sigma_{V_s}$ are calculated from its components as follows (with subscript 's' referring to the surface):

$
V_s
$
[m day⁻¹]
$
= \sqrt {V_x^2 + V_y^2}
$

$
\sigma_{V_s}
$
[m day⁻¹]
$
= \sqrt {(\sigma_{V_x})^2 + (\sigma_{V_y})^2}
$

where $V_x$ and $V_y$ are respectively the easting and northing components of the horizontal velocity vector.

The flow direction of the ice can be calculated as follows:

$
\theta_{\text{V}_s} = \left( 90^\circ - \left( \arctan2(v_y, v_x) \times \left( \frac{180}{\pi} \right) \right) \right) \mod 360^\circ
$

Let us begin with the analysis.

(section-2)=