EQC Quality Assessment: "Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies"
Dataset: satellite-ozone-v1 [CDS]
Aspect: climate-monitoring_q01  |  Category: Satellite_ECVs
Section: Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies > ℹ If you want to know more > Key resources
---
* CDS catalog entry used in this notebook is the [Ozone monthly gridded data from 1970 to present derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-ozone-v1?tab=overview)
* Data download from CDS is available [here](https://cds.climate.copernicus.eu/datasets/satellite-ozone-v1?tab=download)
* A Product User Guide and Specification is available on the [Satellite Ozone Catalogue Entry of the CDS](https://cds.climate.copernicus.eu/datasets/satellite-ozone-v1?tab=documentation).

Code libraries used:
* [C3S EQC custom function](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: "Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies"
Dataset: satellite-ozone-v1 [CDS]
Aspect: climate-monitoring_q01  |  Category: Satellite_ECVs
Section: Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies > ℹ If you want to know more > References
---
[[1]](https://dast.copernicus-climate.eu/documents/satellite-ozone/C3S2_312a_Lot2_PUGS_O3_latest.pdf) Van Roozendael, M., et al. (2021a). Ozone Product User Guide and Specification (PUGS). Last access: March 27, 2024

[[2]](https://doi.org/10.5194/amt-8-3021-2015) van der A, R.J., et al. (2015). Extended and refined multi sensor reanalysis of total ozone for the period 1970-2012. Atmospheric Measurement Techniques, 8, 3021-3035.

[[3]](https://dast.copernicus-climate.eu/documents/satellite-ozone/C3S2_312a_Lot2_ATBD_O3_latest.pdf) Van Roozendael, M., et al. (2021b). Ozone Algorithm Theoretical Basis Document (ATBD). Last access: March 28, 2024

[[4]](https://doi.org/10.1002/2013RG000448) Butchart, N. (2014). The Brewer-Dobson circulation. Review of Geophysics, 52(2), 157-184.

[[5]](https://doi.org/10.1038/315207a0) Farman, J.C., et al. (1985). Large losses of total ozone in Antarctica reveal seasonal ClO$_x$/NO$_x$ interaction. Nature, 315, 207-210.

[[6]](https://doi.org/10.1126/science.aae0061) Solomon, S., Ivy, D. J., Kinnison, D., Mills, M. J., Neely III, R. R., & Schmidt, A. (2016). Emergence of healing in the Antarctic ozone layer. Science, 353(6296), 269-274.

[[7]](https://doi.org/10.5194/acp-11-9237-2011) Ziemke, J. R., Chandra, S., Labow, G. J., Bhartia, P. K., Froidevaux, L., & Witte, J. C. (2011). A global climatology of tropospheric and stratospheric ozone derived from Aura OMI and MLS measurements. Atmospheric Chemistry and Physics, 11(17), 9237-9251.

[[8]](https://doi.org/10.1029/1999RG900008) Solomon, S. (1999). Stratospheric ozone depletion: A review of concepts and history. Review of Geophysics, 37(3), 275-316.

[[9]](https://ozone.unep.org/sites/default/files/2023-05/Final_20Qs%202022%20full%20document_26April2023_digital%20version-reduced_0.pdf) Ross, J.S., et al. (2023). Twenty Questions and Answers About the Ozone Layer: 2022 Update, Scientific Assessment of Ozone Depletion: 2022, 75 pp., WMO, Geneva, Switzerland.

[[10]](https://doi.org/10.1038/s41467-023-42637-0) Kessenich, H.E., et al. (2023). Potential drivers of the recent large Antarctic ozone holes. Nature Communications, 14, 7259.

[[11]](https://doi.org/10.1029/2022JD037581) Petkov, B.H., et al. (2023. Un Unprecedented Arctic Ozone Depletion Evnet During Spring 2020 and Its Impacts Across Europe. Journal of Geophysical Research: Atmospheres, 128, e2022JD037581.

[[12]](https://doi.org/10.1175/JAS-3338.1) Stolarski, R. S., McPeters, R. D., & Newman, P. A. (2005). The ozone hole of 2002 as measured by TOMS. Journal of the atmospheric sciences, 62(3), 716-720.

[[13]](https://doi.org/10.1029/2010GL046634) Steinbrecht, W., et al. (2011). Very high ozone columns at northern mid-latitudes in 2010. Geophysical research Letters, 38, L06803.


EQC Quality Assessment: "Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies"
Dataset: satellite-ozone-v1 [CDS]
Aspect: climate-monitoring_q01  |  Category: Satellite_ECVs
Section: Temporal and spatial completeness of the satellite-derived Ozone for policy making and variability studies > ℹ If you want to know more > References
---
9/2010GL046634) Steinbrecht, W., et al. (2011). Very high ozone columns at northern mid-latitudes in 2010. Geophysical research Letters, 38, L06803.

[[14]](https://doi.org/10.1029/2020GL087810) Safieddine, S., et al. (2020). Antarctic ozone enhancement during the 2019 sudden stratospheric warming event. Geophysical Research Letters,47,e2020GL087810.

[[15]](https://doi.org/10.1029/2002JD002170) Logan, J.A., et al. (2003). Quasibiennial oscillation in tropical ozone as revealed by ozonesonde and satellite date. Journal of Geophysical Research, 108, 4244(D8).


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring
---
Production date: 31-05-2025

Dataset version: WGMS-FOG-2023-09

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


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Quality assessment question
---
* **"Is the glacier mass change dataset sufficiently adequate in terms of its uncertainty to effectively monitor and evaluate global (cumulative) glacier mass changes over time, including their associated impacts on global sea level rise?"**

Glaciers significantly impact global sea-level rise, freshwater resources, natural hazards, hydro-power generation, recreation and tourism. Assessing glacier mass changes due to climate warming is therefore crucial for addressing these issues. 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)" (version WGMS-FOG-2023-09) on the Climate Data Store (CDS), offers a global coverage of glacier mass changes by integrating in-situ, aerial, and satellite data [[1](https://wgms.ch/), [2](https://doi.org/10.5194/essd-17-1977-2025)]. The gridded glaciers mass change dataset that is on the CDS is currently one of the most complete dataset of glacier mass change data in terms of its spatial coverage. It is generally considered the main reference dataset to determine long-term glacier mass changes across the globe.

When measured over a long period and at extended geographical scales, trends in glacier mass balance can be considered a clear indicator of global climate change [[3](https://doi.org/10.1038/s41586-019-1071-0)]. Despite some known issues, this dataset provides valuable insights into glacier mass changes across spatial and temporal scales. In that regard, this notebook investigates how well the dataset can be used to quantify the link between glacier melt and glacier-related sea level contributions. More specifically, the notebook evaluates whether the dataset is of sufficient maturity and quality for that purpose in terms of its uncertainty (i.e. accuracy and precision).


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Quality assessment statements
---
These are the key outcomes of this assessment

- The C3S glacier mass change dataset is a mature and quality-rich dataset that allows users to capture the changing state of glaciers on a local, regional and global scale. The data come with a quantitative pixel-by-pixel error estimate in the form of precision errors (reported as 1.96 times the standard deviation), that generally decrease in magnitude over time. As a consequence, the most recent years (after 2000) meet proposed international standards of uncertainty thresholds proposed by GCOS. The uncertainty that comes with the data is, however, highly spatially and temporally variable, with areas like the peripheral glaciers in Greenland and Antarctica exhibiting higher glacier mass change errors. Hence, not all pixels meet the minimum uncertainty threshold proposed by GCOS, of which users should take note. However, when seen as a whole, the majority of the pixels meet the proposed thresholds for uncertainty.
- The dataset is highly suitable to monitor and derive global (cumulative) mass changes over time and to, for example, assess the corresponding impact of their shrinkage. The dataset furthermore has sufficient quality in terms of its consistency with respect to spatial (i.e. global) and temporal (i.e. since 1975-76) coverage for climate change monitoring to become useful and to be able to draw reliable conclusions. Some potential key limitiations include the lack of detailed sampling information, the limited use for individual glacier-scale (smaller than the pixel-scale) applications, and the fact that not all mass changes considered in the dataset directly contribute to sea-level changes (which is nevertheless assumed to be the case). Due to variations in data collection methods and sources, data consistency along the data may furthermore be affected.
```


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Methodology > Dataset description
---
The mass balance of a glacier is the difference between mass gained (mainly from snow accumulation) and mass lost (by meltwater runoff or solid ice discharge into lakes/the ocean), which is the same as the net mass change of a glacier over its surface area $A$:

$\Delta{M} = \dfrac{1}{A} \int\limits_{A} b_a dA - \dfrac{1}{A} \int\limits_{P} d_a dP$

where:

$b_a = \int\limits^{t_1}_{t_0}b_s dt$, with $b_s = ACC - ABL$ [kg m$^{-2}$ yr$^{-1}$]

$d_a = \int\limits^{t_1}_{t_0}d_g dt$, with $d_g = \rho_{i} \cdot H \cdot \overline{V_P}$ [kg m$^{-1}$ yr$^{-1}$]

The first term represents the the total annual surface mass balance (i.e. the difference between accumulation and ablation), whereas the second term encompasses the total annual ice discharge across the grounding line $g$ with perimeter $P$. Here, $\rho_{i}$ is the ice density, $H$ ice thickness and $\overline{V_P}$ the gate-perpendicular vertically averaged horizontal velocity at the grounding line location. The latter term is considered zero for land-terminating glaciers. Other terms can be included as well, such as the basal and internal mass balances.

In general, the basis for the derived gridded mass changes are individual measurements (mainly glaciological in-situ local annual surface mass balance measurements) and geodetic air or spaceborne elevation change data (a surface elevation/ice thickness change or an ice volume change over time). These data are converted into an averaged specific mass balance value (i.e. mostly reported with units of meter water equivalent and often shortened to m w.e.) for an individual glacier. Afterwards, the data are submitted to the World Glacier Monitoring Service (WGMS). Further processing of the data results in a glacier mass change product reported over a 0.5° global grid dating back until the 1975-76 hydrological year. Each grid cell therefore contains a time series of total glacier mass change (in Gt yr⁻¹) or mass balance data (in m w.e. yr⁻¹) of all glaciers within the specific grid cell. In this notebook, we use version WGMS-FOG-2023-09. For a more detailed description of the data acquisition and processing methods, we refer to the [documentation on the CDS](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (Copernicus Knowledge Base).

It is important to note that the glaciers with an annual glaciological sample (ca. 500 glaciers) form the basis for the determination of annual mass changes from the remaining glaciers through a complex algorithm of spatial/temporal interpolation and (area-weighted) averaging of these mass change data [[2](https://essd.copernicus.org/preprints/essd-2024-323/)]. Hence, not all glaciers in the dataset exhibit a time series of directly measured annual in-situ mass balance observations, but most glaciers in the dataset are either unobserved or only have (limited and mostly multi-annual) geodetic mass change data available. Glacier mass change data with these geodetic samples are also more prone to uncertainties in general, for example due to uncertainties related to volume to mass conversions.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > 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-3)**
* [](section-3-1)
* [](section-3-2)
* [](section-3-3)

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

**[](section-5)**


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define the parameters, i.e. for which years we want the glacier mass change data to be downloaded:

This line validates that both period_start and period_stop meet specific criteria:
They contain an underscore ("_") and their length is exactly 9 characters.

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

Download glacier mass change data

```text
Downloading glacier mass change data...
```

```text
100%|██████████| 1/1 [00:06<00:00,  6.66s/it]
```

```text
Downloading done.
```

(section-1-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data structure
---
Lastly, we can read and inspect the glacier mass change data. Let us print out the data to inspect its structure:

```text
<xarray.Dataset> Size: 487MB
Dimensions:                  (time: 47, latitude: 360, longitude: 720)
Coordinates:
  * time                     (time) datetime64[ns] 376B 1976-01-01 ... 2022-0...
  * latitude                 (latitude) float64 3kB 89.75 89.25 ... -89.75
  * longitude                (longitude) float64 6kB -179.8 -179.2 ... 179.8
Data variables:
    glacier_mass_change_gt   (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    glacier_mass_change_mwe  (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    glacier_area_km2         (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    uncertainty_gt           (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    uncertainty_mwe          (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
Attributes:
    title:                 Global gridded annual glacier mass changes
    data_version:          version-wgms-fog-2023-09
    project:               Copernicus Climate Change Service (C3S) Essential ...
    institution:           World Glacier Monitoring Service - Geography Depar...
    created_by:            Dr. Ines Dussaillant - ines.dussaillant@geo.uzh.ch
    references:            Fluctuation of Glaciers (FoG) database version wgm...
    citation:              Dussaillant, I., Bannwart, J., Paul, F., Zemp, M. ...
    conventions:           CF Version CF-1.8
    dataset_description:   Horizontal resolution: 0.5° (latitude - longitude)...
    dataset_limitations:   Grid-point artefact in polar regions: see Algorith...
    dataset_improvements:  Improvements of product version WGMS-FOG-2023-09 w...
    comments:              Conversions between annual grid point mass change ...
```

It is a gridded dataset at a 0.5 by 0.5 degree spatial resolution containing annual values of the total glacier mass change (in Gt yr$^{-1}$) of a grid cell (`glacier_mass_change_gt`) and its uncertainty (`uncertainty_gt`) since the 1975-76 hydrological year. Mass changes and their uncertainty can also be extracted in units of m w.e. yr$^{-1}$ (`glacier_mass_change_mwe` and `uncertainty_mwe`). The parameterized absolute glacier surface area is furthermore also available in this dataset by the variable `glacier_area_km2`. For conversion purposes, glacier mass changes (in Gt yr$^{-1}$) can be converted into glacier mass balances (in m w.e. yr$^{-1}$) by dividing the mass changes (in Gt yr$^{-1}$ multiplied by $1*10^{12}$ to get values in kg yr$^{-1}$) by the product of the density of water (1000 kg m$^{-3}$) and the glacier area (in km$^{2}$ multiplied by $1*10^6$ to get values in m$^2$).

Let us perform some data handling before getting started with the analysis:

Customize attributes in glacier mass change file
Add glacier RGI region based on slope of glacier area change parameterization
Group grid points by RGI region (assuming 'rgi_region' is a coordinate in the dataset)
Compute regional sums assuming spatial correlation within each region
Compute regional uncertainties assuming full spatial correlation within each region
Compute global sums assuming uncorrelated regional estimates
Compute global uncertainty assuming uncorrelated regions
Sum over time
Add results to dataset

(section-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 2. Glacier mass changes and their uncertainty estimates in space and time > 2.1 Glacier mass change uncertainties: accuracy and precision
---
The total error of an annual glacier mass change estimate is theoretically given by the sum of the precision (random) and the accuracy (systematic) error:

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

In the glacier mass change dataset, precision errors are reported as 1.96 times the standard deviation and the accuracy error is not considered [[2](https://doi.org/10.5194/essd-17-1977-2025)]. Therefore, in our case, $a$ = 1.96 and $\delta$ is 0. In the following section below, we will thus consider the uncertainty of the dataset as being $1.96 \sigma$.

Let us now explore a bit more the uncertainty of the data. The pixel-by-pixel quantitative uncertainties that accompany the data arise from different sources, of which the most important ones are the input data measurement uncertainties, the density conversion for geodetic mass balances, and errors related to absolute glacier areas and their changes over time. All these processes and parameters thus play a key role in determining the final estimate of the glacier mass changes. The errors from these various sources are combined in the final product and the authors report these uncertainty values as being precision errors in the form of $1.96 \sigma$ (i.e. equivalent to a 95% confidence interval for a normal distribution) with units in Gt yr⁻¹ or m w.e. yr⁻¹.

In the following, we will, however, change the units of the error to kg m⁻² yr⁻¹ because GCOS advises glacier mass change uncertainty values to be provided in these units [[4](https://library.wmo.int/idurl/4/58111)]:

$
\varepsilon_{\Delta{M}}
$
[kg m⁻² yr⁻¹]
$
= 1 \cdot 10^{6} * \left(\dfrac{1.96 \sigma}{A}\right)
$

where $1.96 \sigma$ is the pixel mass change uncertainty [Gt yr⁻¹] from `uncertainty_gt` and $A$ the pixel glacier surface area [km²] from `glacier_area_km2`.

We can plot a histogram of the error term over all pixels and all years to inspect its distribution:

Plot the histogram

*Figure 1. Histogram of pixel-by-pixel glacier mass change errors in the glacier mass change dataset.*

Let us plot some statistics:

```text
The overall arithmetic mean precision error over all pixels and all years is 530.69 kg m⁻² yr⁻¹ with a maximum of 5083.96 kg m⁻² yr⁻¹.
```

(section-2-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 2. Glacier mass changes and their uncertainty estimates in space and time > 2.2 Glacier mass change errors over time
---
The overall arithmetic mean error over both space and time exhibits a moderate magnitude, and the majority of errors seem to be situated close to 200-500 kg m⁻² yr⁻¹. The threshold (i.e. the minimum requirement to be met to ensure that data are useful) for glacier mass change uncertainty (expressed in terms of 2$\sigma$) proposed by the GCOS is 500 kg m⁻² yr⁻¹, while the "breakthrough" value (i.e. the level at which specified uses within climate monitoring become possible) would be 200 kg m⁻² yr⁻¹ per grid point [[4](https://library.wmo.int/idurl/4/58111)].

As an extra step, we can calculate the overall arithmetic mean glacier mass change precision error for each hydrological year to get a general idea of the overall magnitude of the errors. This is simply calculated as the spatial arithmetic mean of all pixels for each year $t$:

$\overline{\varepsilon_{\Delta{M}}}_{x,y}
$
[kg m⁻² yr⁻¹]
$ = \dfrac{1}{n} \sum\limits^{{{x,y}}} (\varepsilon_{\Delta{M_{x,y}}})$ with $x,y$ the spatial domain size and $n$ is the total amount of latitude/longitude pixels (NaN pixels with no glaciers are excluded).

This results in the following:

Calculate area-weighted mean error for each year
Flatten the arrays to perform the weighted mean calculation
Calculate the area-weighted mean error
Convert to a numpy array or xarray DataArray if needed

*Figure 2. Time series of annual spatially averaged (arithmetic) glacier mass change errors in the glacier mass change dataset. The red dotted line represents the minimum uncertainty threshold proposed by GCOS [[4](https://library.wmo.int/idurl/4/58111)].*

(section-2-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 2. Glacier mass changes and their uncertainty estimates in space and time > 2.3 Glacier mass change errors in space
---
Next, let us check the spatial distribution of the mean overall error over time per grid point, which is simply calculated as the temporal arithmetic mean over all years for each pixel $x,y$:

$\overline{\varepsilon_{\Delta{M_{t}}}}
$
[kg m⁻² yr⁻¹]
$ = \dfrac{1}{n} \sum\limits_{i={1976}}^{{{1976+n-1}}} (\varepsilon_{\Delta{M_i}})$ with $n$ is the total amount of years in the time series.

This results in the following:

Plot the gridded data

*Figure 3. Spatial distribution of temporally averaged glacier mass change errors for each pixel in the glacier mass change dataset.*

Let us make this plot a bit clearer by grouping these errors with respect to the threshold values proposed by GCOS [[4](https://library.wmo.int/idurl/4/58111)]:

Define the boundaries for the colorbar
Plot the data

*Figure 4. Spatial distribution of temporally averaged glacier mass change errors for each pixel in the glacier mass change dataset, classified by proposed GCOS thresholds [[4](https://library.wmo.int/idurl/4/58111)].*

Green pixels indicate areas where the breakthrough value of (an uncertainty of 200 kg m⁻² yr⁻¹ or lower), as proposed by GCOS, has been reached, whereas red grid points exhibit temporally arithmetic mean error values that exceed the threshold value (500 kg m⁻² yr⁻¹ or more) for the data to be useful. This confirms our statement from above: especially the Greenland and Antarctic peripheral glaciers and parts of the Andes exhibit error values that are clearly too high. Extra care from the user is required in these regions since the threshold value has not been reached. Other regions, such as High Mountain Asia and the majority of Alaskan and European glaciers, have precision error values that allow for a reliable and high-quality data analysis. Possible reasons for this pattern are sparse data coverage, complex terrain, and gridded data limitations.

Let us quantify the percentage of data (over all pixels and all years) that do and do not reach the threshold values:

Quantify the percentage of data that do and do not reach the threshold values

```text
The percentage of data points with a glacier mass change error value less than 200 kg m⁻² yr⁻¹ is 21.79%.
The percentage of data points with a glacier mass change error value more than 500 kg m⁻² yr⁻¹ is 38.36%.
```

Now, let us plot the global annual mass change data over time and propagate its error throughout the time series.

(section-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 3. Quantifying global (cumulative) glacier mass changes and their error estimates since 1975-1976 > 3.1 Global glacier mass changes
---
In the following section, we plot the global annual (and cumulative) glacier mass change over time. For the annual values, we therefore sum the gridded mass change product over the entire spatial domain for each individual year to get spatially summed values in Gt yr⁻¹, and calculate the glacier area-weighted mean to get a mass balance value in m w.e. yr⁻¹:

$\Delta M_i
$
[Gt yr⁻¹]
$ = \sum\limits^{x,y}\Delta {M_{x,y,i}}$

where $\Delta {M_{x,y,i}}$ is the glacier mass change (from `glacier_mass_change_gt`, in Gt yr⁻¹) at pixel $x,y$ during a certain year $i$, and

${\Delta B_i}
$
[m w.e. yr⁻¹]
$ = \textstyle\dfrac{1}{\sum\limits^{x,y} A_{x,y,i}} {\sum\limits^{x,y} (A_{x,y,i} * \Delta {B_{x,y,i}})}$

where $\Delta {B_{x,y,i}}$ is the glacier mass balance (from `glacier_mass_change_mwe`, in m w.e. yr⁻¹) and $A_{x,y,i}$ the glacier area [km$^2$] at pixel $x,y$ (from `glacier_area_km2`) during a certain year $i$.

This results in the following plot:

Plot the data

*Figure 5. Annual global (left) glacier mass changes (expressed in Gt yr⁻¹) and (right) mass balances (expressed in m w.e. yr⁻¹) from the glacier mass change dataset.*

The mass changes in the left plot above are expressed in Gt yr$^{-1}$ (Gigatonnes per year). Since Gt is a unit of mass, the mass of 1 Gt of ice is exactly the same as the mass of 1 Gt of water. The value can, however, also be translated into a volume. For example, 1 Gt of water (density 1000 kg/m³) is exactly 1 km³ water, while 1 Gt of ice (density 917 kg/m³) becomes 1.091 km³ of ice in volume.

(section-3-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 3. Quantifying global (cumulative) glacier mass changes and their error estimates since 1975-1976 > 3.2 Global glacier mass change error estimates
---
By making use of the laws of error propagation, we can also determine how the glacier mass change errors propagate throughout the time series. For error propagation, we assume that:
* Errors are spatially correlated within a certain RGI region, but are uncorrelated in between RGI regions
* Errors are uncorrelated in time

The corresponding annual mass change uncertainty is calculated by assuming that errors are spatially correlated within a certain RGI region. To create the global error estimate, we assume uncorrelated/independent errors between the 19 RGI regions [[2](https://doi.org/10.5194/essd-17-1977-2025)]. For error propagation, we also divide the uncertainty estimates by 1.96 since errors values are reported as 1.96 times the standard deviation in the original dataset:

$
\sigma_{\Delta{M_i}}
$
[Gt yr⁻¹]
$= \sqrt{\sum\limits^{19}_{region=1}({\sigma_{ \Delta{M_{region,i}}}})^2}
$
, where
$ {\sigma_{ \Delta{M_{region,i}}}} = \sum\limits^{x,y \in \text{region}}({\sigma_{ \Delta{M_{x,y,i}}}})
$

and $\sigma_{ \Delta{M_{x,y,i}}}$ is the mass change standard deviation (from `uncertainty_gt` divided by 1.96, in Gt yr⁻¹) at pixel $x,y$ during a certain year $i$ in a certain RGI region, and

$
\sigma_{{\Delta{B_i}}}
$
[m w.e. yr⁻¹]
$= \sqrt{\sum\limits^{19}_{region=1}({\sigma_{ \Delta{B_{region,i}}}})^2}
$
, where
${\sigma_{ \Delta{B_{region,i}}}} = {\sum\limits^{x,y \in \text{region}} \left( \dfrac{A_{x,y,i}}{\sum\limits^{x,y \in \text{region}} A_{x,y,i}} * {\sigma_{{\Delta{B}_{x,y,i}}}} \right) }
$

where $\sigma_{{ \Delta{B_{x,y,i}}}}$ is the mass balance standard deviation (from `uncertainty_mwe` divided by 1.96, in m w.e. yr⁻¹) at pixel $x,y$ during a certain year $i$ and $A_{x,y,i}$ the glacier area [km$^2$] (from `glacier_area_km2`).

Plotting these data reveals the following:

Plot the data

*Figure 6. Annual global glacier mass change errors from the glacier mass change dataset expressed in units of (left) Gt yr⁻¹ (mass changes) and (right) m w.e. yr⁻¹ (mass balances).*

It can be seen from the plot that the global glacier mass change uncertainty has been decreasing over time, with a sudden drop around 2000 CE. The data can also be plotted in a cumulative way:

$
{M}
$
[Gt]
$
= \sum\limits_{i={1976}}^{{{1976+n-1}}} (\Delta M_i)
$
, or

$
{{B}}
$
[m w.e.]
$
= \sum\limits_{i={1976}}^{{{1976+n-1}}} ({\Delta B_i})
$

with the global annual glacier mass change (in Gt yr⁻¹) or balance (m w.e. yr⁻¹) at a certain year $i$ (as calculated above) and $n$ the number of years in the time series.

The corresponding uncertainty is calculated by assuming uncorrelated errors over time:

$
\sigma_{{M}}
$
[Gt]
$
= \sqrt{\sum\limits_{i={1976}}^{{1976+n-1}} (\sigma_{\Delta{M_i}})^2}
$
, or

$
\sigma_{{{B}}}
$
[m w.e.] =
$
\sqrt{\sum\limits_{i={1976}}^{{1976+n-1}} (\sigma_{{\Delta{B_i}}})^2}
$

with the global annual mass change (in Gt yr⁻¹) or balance (m w.e. yr⁻¹) uncertainty at a certain year $i$ (as calculated above) and $n$ the number of years in the time series.

(section-3-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 3. Quantifying global (cumulative) glacier mass changes and their error estimates since 1975-1976 > 3.3 Time series of global cumulative glacier mass changes and their error estimate
---
The corresponding plot looks as follows:

Plot the data

*Figure 7. Annual global cumulative (left) glacier mass changes (expressed in Gt yr⁻¹) and (right) mass balances (expressed in m w.e. yr⁻¹), with error propagation (shaded).*

From the image above, it can be seen that glaciers clearly have been losing mass during the observational period, especially since the 1990s, which is in line with findings in the literature (e.g. [[8](https://doi.org/10.1038/s41586-024-08545-z)]). The final estimate of the glaciers mass change at the end of the time series is:

```text
The total global cumulative glacier mass change between 1975-1976 and 2021-2022 is -10.72 ± 1.12 m w.e. or -7691.70 ± 858.39 Gt.
```

Now, let us use the glacier mass change data to quantify the link between glacier melt and glacier-related contributions to global sea level rise in the context of Earth System modeling and climate change monitoring.

(section-4)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 4. Quantification of glacier-related contributions to global sea level change > 4.1 Computing sea-level rise equivalent from glacier mass loss
---
We can calculate the cumulative contribution of glacier mass changes to global sea level change during the last several decades by making use of the following formula [[5](https://doi.org/10.1038/s41561-019-0300-3)]:

$
h_{SLE}
$
[mm]
$
= 1 \cdot 10^6 * \sum\limits_{i=1976}^{1976+n-1} \left(\dfrac{\Delta V_{i}}{A_s}\right)
$

where
$
\Delta{V_{i}} = \dfrac{\rho_w}{\rho_s} * \sum\limits^{x,y}\left(\dfrac{\Delta {B_{x,y,i}}}{1 \cdot 10^3} * A_{x,y,i}\right)
$.

Here, $\Delta {B}$ is the glacier mass balance (in m w.e. yr⁻¹, divided by 1000 to get units in km) at pixel $x,y$ during a certain year $i$ from `ds["glacier_mass_change_mwe"]`, and $A$ the glacier area [km²] from `ds["glacier_area_km2"]`, so that the annual volume change $\Delta V$ has units of km$^3$ yr$^{-1}$ of water. Furthermore, ${A_{s}}$ is the ocean surface area [km²], $n$ the total number of years in the time series and $\rho$ the respective densities of water $w$ and the sea $s$ [kg m⁻³]. Note that this formulation assumes that all glacier mass or volume losses directly contribute to sea level changes, while this is not necessarily the case (e.g. [[6](https://doi.org/10.1088/1748-9326/aac2f0), [7](https://doi.org/10.5194/tc-14-833-2020)]). Also note that by multiplying the sea level contribution by $\frac{\rho_w}{\rho_s}$, we calculate sea level contributions in ocean water column equivalent.

The corresponding uncertainty is given by:

$
\sigma_{h_{SLE}}
$
[mm] =
$
1 \cdot 10^6 * \left(\dfrac{1}{A_s} \dfrac{{\rho_{w}}}{\rho_{s}}\right) * \sqrt{ \sum\limits_{i={1976}}^{{{1976+n-1}}} (\sigma_{{V_{i}}})^2}
$

where $\sigma_{\Delta{V}}$ is the corresponding volume change uncertainty [km$^{3}$ yr$^{-1}$] calculated from the mass balance uncertainty and the glacier area, again taking into account that uncertainties at the pixel level are given as 1.96 times the standard deviation and that errors within a certain RGI region are correlated, while uncorrelated between RGI regions and over time, as before.

(section-4-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 4. Quantification of glacier-related contributions to global sea level change > 4.2 Time series of glacier-related sea level contribution
---
This ultimately results in the following graph:

Define constants
Compute regional volume change assuming spatial correlation
Compute global volume change by summing over all RGI regions
Compute global sea level equivalent (SLE)
Compute regional uncertainty assuming full spatial correlation within regions
Compute global uncertainty assuming uncorrelated RGI regions
Compute cumulative uncertainty over time
Compute global SLE uncertainty
Plot the data with uncertainty shading

*Figure 8. Cumulative contribution of glacier mass changes to global sea level changes (assuming all glacier mass changes contribute to sea level changes), including the propagation of the error (shaded).*

Let us quantify the total glacier-related contribution to global sea level change since the beginning of the dataset:

```text
The total contribution of glacier mass changes to global sea level change between 1975-1976 and 2021-2022 is 20.64 ± 2.30 mm.
```

The C3S product can be interpreted as glacier mass changes relevant for sea level contributions, as both the glaciological and geodetic approach do not consider ice melt that occurs under the waterline, which already displaces water. In contrast, processes that do contribute to sea level changes – such as liquid runoff from ice above buoyancy and changes in the ice flux across the grounding line – will result in a surface elevation change, which is observed with DEM differencing and hence incorporated in the geodetic method. Even though this consideration is not exact – a precise separation of contributions from ice above buoyancy (which affects sea level changes) and ice below buoyancy (which does not) would require the actual position of the grounding line, as well as values for the ice thickness and bedrock elevation field (e.g. [[7](https://doi.org/10.5194/tc-14-833-2020)]) – it is assumed that the resulting mass change estimates from this approach fall within acceptable uncertainty bounds to consider them relevant for sea level changes [[2](https://doi.org/10.5194/essd-17-1977-2025)]. However, it should also be considered that not all mass changes affect sea levels directly, for example for landlocked glaciers whose meltwater does not reach the ocean [[6](https://doi.org/10.1088/1748-9326/aac2f0), [7](https://doi.org/10.5194/tc-14-833-2020)]).

(section-5)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > Analysis and results > 5. Short summary and take-home messages
---
To be able to use the glacier mass change dataset for reliable climate change analysis/monitoring purposes, the dataset should at least exhibit a comprehensive spatial coverage (i.e. global), 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/idurl/4/58111)], and an adequate spatio-temporal resolution (cfr. the "Maturity Matrix" [[9](https://doi.org/10.1175/BAMS-D-21-0109.1)]).

Since these conditions are generally met, the C3S glacier mass change dataset on the CDS is considered highly suitable for monitoring and deriving global cumulative mass changes over time, as well as assessing their impact on global sea level changes. The dataset, for example, includes pixel-by-pixel error estimates, expressed as precision errors (1.96 times the standard deviation). The corresponding uncertainty furthermore decreases over time, with post-2000 data meeting international GCOS standards. There is, however, a high spatial and temporal variation in the error estimates, implying that not all pixels meet these uncertainty thresholds. Users should therefore exercise caution in certain areas, such as the peripheral glaciers of Antarctica and Greenland, where uncertainties are higher. The dataset furthermore meets GCOS requirements in terms of resolution, spatial coverage (global) and temporal continuity (since 1975-76 without gaps), which demostrates its maturity and reliability for Earth system modeling and climate change monitoring. Data quality is hence considered strong, especially after 2000 and outside the high-uncertainty peripheral regions of the ice sheets.

The glacier mass change data can be considered to be directly transformable to sea level contributions, provided certain assumptions are made [[2](https://doi.org/10.5194/essd-17-1977-2025)]. Additionally, users should note limitations, such as the absence of detailed sampling density information, the fact that data can not be consulted at the individual glacier-scale, and that data are measured and generated by different institutes/research groups and from different methods, which could result in inconsistencies. Moreover, since grid cells are not of the same absolute surface area and decrease in size at higher latitudes, mass change artefacts may arise in polar regions if individual glaciers are larger than the cell size. This may affect glacier mass change representativeness in some areas. Therefore, knowledge of the amount and spatial distribution of glaciers with a consistent and long-term glaciological sample is crucial for assessing the representativeness of the data.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > ℹ If you want to know more > Key resources
---
- [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)
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (Copernicus Knowledge Base)
- [World Glacier Monitoring Service (WGMS)](https://wgms.ch/)
- [Glacier Mass Balance Intercomparison Exercise (GlaMBIE)](https://glambie.org/)
- [Copernicus climate change indicators: glaciers](https://climate.copernicus.eu/climate-indicators/glaciers)
- [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: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > ℹ If you want to know more > References
---
- [[1](https://wgms.ch/)] WGMS (2022). Fluctuations of Glaciers Database. doi: 10.5904/wgms-fog-2022-09.

- [[2](https://doi.org/10.5194/essd-17-1977-2025)] Dussaillant, I., Hugonnet, R., Huss, M., Berthier, E., Bannwart, J., Paul, F., and Zemp, M. (2025). Annual mass changes for each glacier in the world from 1976 to 2023, Earth Syst. Sci. Data, doi: 10.5194/essd-2024-323.

- [[3](https://doi.org/10.1038/s41586-019-1071-0)] Zemp, M., Huss, M., Thibert, E., Eckert, N., McNabb, R., Huber, J., Barandun, M., Machguth, H., Nussbaumer, S. U., Gärtner-Roer, I., Thomson, L., Paul, F., Maussion, F., Kutuzov, S., and Cogley, J. G. (2019). Global glacier mass changes and their contributions to sea-level rise from 1961 to 2016. Nature, 568, 382–386. doi: 10.1038/s41586-019-1071-0.

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

- [[5](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.

- [[6](https://doi.org/10.1088/1748-9326/aac2f0)] Bamber, J. L., Westaway, R. M., Marzeion, B., and Wouters, B. (2018): The land ice contribution to sea level during the satellite era. Environmental Research Letters, 13(6), 063008, doi: 10.1088/1748-9326/aac2f0.

- [[7](https://doi.org/10.5194/tc-14-833-2020)] Goelzer, H., Coulon, V., Pattyn, F., de Boer, B., and van de Wal, R. (2020). Brief communication: On calculating the sea-level contribution in marine ice-sheet models, The Cryosphere, 14, 833–840, doi: 10.5194/tc-14-833-2020.

- [[8](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 (2025). doi: 10.1038/s41586-024-08545-z.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: data-completeness_q01  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: uncertainty analysis for glaciological and climate change monitoring > ℹ If you want to know more > References
---
Community estimate of global glacier mass changes from 2000 to 2023. Nature (2025). doi: 10.1038/s41586-024-08545-z.

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


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis
---
Production date: 31-05-2025

Dataset version: WGMS-FOG-2023-09

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


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Quality assessment question
---
* **"Does the glacier mass change dataset have adequate spatial/temporal resolution, coverage (extent) and sampling density to derive multi-year trends in glacier mass changes, hereby enabling their use as indicators of climate change?"**

Glaciers significantly impact global sea-level rise, freshwater resources, natural hazards, hydro-power generation, recreation and tourism. Assessing glacier mass changes due to climate warming is therefore crucial for addressing these issues. 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)" (version WGMS-FOG-2023-09) on the Climate Data Store (CDS), offers a global coverage of glacier mass changes by integrating in-situ, aerial, and satellite data [[1](https://wgms.ch/), [2](https://doi.org/10.5194/essd-17-1977-2025)]. The gridded glaciers mass change dataset that is on the CDS is currently one of the most complete dataset of glacier mass change data in terms of its spatial coverage. It is generally considered the main reference dataset to determine long-term glacier mass changes across the globe.

When measured over a long period and at extended geographical scales, trends in glacier mass balance can be considered a clear indicator of global climate change [[3](https://doi.org/10.1038/s41586-019-1071-0)]. Despite some known issues, this dataset provides valuable insights into glacier mass changes across spatial and temporal scales. This notebook examines the dataset's suitability as a global climate change indicator, focusing on its resolution, coverage, and ability to reveal long-term trends in glacier mass balance.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Quality assessment statements
---
These are the key outcomes of this assessment

- With its consistent global coverage since 1975-76, annual temporal resolution and a spatial resolution of 0.5° x 0.5°, the dataset meets the minimum international standards concerning spatio-temporal resolution and extent for the data to be useful in climate change analysis and for climate monitoring to become possible [[4](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)]. The dataset thus enables the detection of reliable climate trends and statistical analyses, whereas the gridded format supports monitoring glacier mass changes at the local (pixel), regional, and global scales. Observed trends in glacier mass loss from the dataset furthermore align with theoretical models of the response of glaciers to climate warming, adding further credibility to the dataset. Additionally, majority of pixel-based linear mass change trends have been found to be statistically significant at $\alpha$ = 0.05.
- The product relies on a limited sample of (ca. 500) annual glaciological observations to provide the annual variability of glacier mass changes. However, the annual variability is calibrated to multi-annual or even decadal trends of geodetic mass balance estimates (i.e. glacier elevation change observations, converted to mass change) for more than 200,000 glaciers. Hence, the product may have a lesser pronounced observational coverage with respect to the annual variability of the glacier mass changes, but an excellent coverage with respect to their long-term trend. Product limitations include the fact that mass change are not available at the individual glacier scale, and that mass change artefacts may arise in polar regions if individual glaciers are larger than the cell size.
```


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Methodology > Dataset description
---
The mass balance of a glacier is the difference between mass gained (mainly from snow accumulation) and mass lost (by meltwater runoff or solid ice discharge into lakes/the ocean), which is the same as the net mass change of a glacier over its surface area $A$:

$\Delta{M} = \dfrac{1}{A} \int\limits_{A} b_a dA - \dfrac{1}{A} \int\limits_{P} d_a dP$

where:

$b_a = \int\limits^{t_1}_{t_0}b_s dt$, with $b_s = ACC - ABL$ [kg m$^{-2}$ yr$^{-1}$]

$d_a = \int\limits^{t_1}_{t_0}d_g dt$, with $d_g = \rho_{i} \cdot H \cdot \overline{V_P}$ [kg m$^{-1}$ yr$^{-1}$]

The first term represents the the total annual surface mass balance (i.e. the difference between accumulation and ablation), whereas the second term encompasses the total annual ice discharge across the grounding line $g$ with perimeter $P$. Here, $\rho_{i}$ is the ice density, $H$ ice thickness and $\overline{V_P}$ the gate-perpendicular vertically averaged horizontal velocity at the grounding line location. The latter term is considered zero for land-terminating glaciers. Other terms can be included as well, such as the basal and internal mass balances.

In general, the basis for the derived gridded mass changes are individual measurements (mainly glaciological in-situ local annual surface mass balance measurements) and geodetic air or spaceborne elevation change data (a surface elevation/ice thickness change or an ice volume change over time). These data are converted into an averaged specific mass balance value (i.e. mostly reported with units of meter water equivalent and often shortened to m w.e.) for an individual glacier. Afterwards, the data are submitted to the World Glacier Monitoring Service (WGMS). Further processing of the data results in a glacier mass change product reported over a 0.5° global grid dating back until the 1975-76 hydrological year. Each grid cell therefore contains a time series of total glacier mass change (in Gt yr⁻¹) or mass balance data (in m w.e. yr⁻¹) of all glaciers within the specific grid cell. In this notebook, we use version WGMS-FOG-2023-09. For a more detailed description of the data acquisition and processing methods, we refer to the [documentation on the CDS](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (Copernicus Knowledge Base).

It is important to note that the glaciers with an annual glaciological sample (ca. 500 glaciers) form the basis for the determination of annual mass changes from the remaining glaciers through a complex algorithm of spatial/temporal interpolation and (area-weighted) averaging of these mass change data [[2](https://essd.copernicus.org/preprints/essd-2024-323/)]. Hence, not all glaciers in the dataset exhibit a time series of directly measured annual in-situ mass balance observations, but most glaciers in the dataset are either unobserved or only have (limited and mostly multi-annual) geodetic mass change data available. Glacier mass change data with these geodetic samples are also more prone to uncertainties in general, for example due to uncertainties related to volume to mass conversions.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > 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-3-3)

**[](section-4)**


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 1. Data preparation and processing > 1.2 Define request and download data
---
Then we define the parameters, i.e. for which years we want the glacier mass change data to be downloaded:

Define a function to calculate the sum, linear trend and acceleration:

Define some functions to calculate the sum, linear trends and quadratic trends

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

Download glacier mass change data
Customize some attributes

```text
Downloading and handling glacier mass change data...
```

```text
100%|██████████| 1/1 [00:00<00:00,  6.46it/s]
```

```text
Downloading and data handling done.
```

(section-1-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 1. Data preparation and processing > 1.3 Display and inspect data
---
Let us inspect the data:

```text
<xarray.Dataset> Size: 487MB
Dimensions:                  (time: 47, latitude: 360, longitude: 720)
Coordinates:
  * time                     (time) int64 376B 1976 1977 1978 ... 2020 2021 2022
  * latitude                 (latitude) float64 3kB 89.75 89.25 ... -89.75
  * longitude                (longitude) float64 6kB -179.8 -179.2 ... 179.8
Data variables:
    glacier_mass_change_gt   (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    glacier_mass_change_mwe  (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    glacier_area_km2         (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    uncertainty_gt           (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
    uncertainty_mwe          (time, latitude, longitude) float64 97MB dask.array<chunksize=(1, 360, 720), meta=np.ndarray>
Attributes:
    title:                 Global gridded annual glacier mass changes
    data_version:          version-wgms-fog-2023-09
    project:               Copernicus Climate Change Service (C3S) Essential ...
    institution:           World Glacier Monitoring Service - Geography Depar...
    created_by:            Dr. Ines Dussaillant - ines.dussaillant@geo.uzh.ch
    references:            Fluctuation of Glaciers (FoG) database version wgm...
    citation:              Dussaillant, I., Bannwart, J., Paul, F., Zemp, M. ...
    conventions:           CF Version CF-1.8
    dataset_description:   Horizontal resolution: 0.5° (latitude - longitude)...
    dataset_limitations:   Grid-point artefact in polar regions: see Algorith...
    dataset_improvements:  Improvements of product version WGMS-FOG-2023-09 w...
    comments:              Conversions between annual grid point mass change ...
```

It is a gridded dataset at a 0.5 by 0.5 degree spatial resolution containing annual values of the total glacier mass change (in Gt yr$^{-1}$) of a grid cell (`glacier_mass_change_gt`) and its uncertainty (`uncertainty_gt`) since the 1975-76 hydrological year. Mass changes (mass balances in this case) and their uncertainty can also be extracted in units of m w.e. yr$^{-1}$ (`glacier_mass_change_mwe` and `uncertainty_mwe`). The parameterized absolute glacier surface area is furthermore also available in this dataset by the variable `glacier_area_km2`. For conversion purposes, glacier mass changes (in Gt yr$^{-1}$) can be converted into glacier mass balances (in m w.e. yr$^{-1}$) by dividing the mass changes (in Gt yr$^{-1}$ multiplied by $1*10^{12}$ to get values in kg yr$^{-1}$) by the product of the density of water (1000 kg m$^{-3}$) and the glacier area (in km$^{2}$ multiplied by $1*10^6$ to get values in m$^2$).

(section-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 2. Analysis of spatio-temporal resolution and extent of glacier mass changes > 2.1 Dataset attributes: spatial and temporal resolution
---
Let us print some attributes of the dataset to reveal its spatial and temporal resolution:

```text
Horizontal resolution: 0.5° (latitude - longitude), GCS_WGS_1984Temporal resolution: Annual, hydrological yearTemporal coverage: 1975/76-2021/22Observational sample: 96% of world glaciers with valid observations
```

The dataset has a spatial resolution of 0.5 by 0.5 degrees and a temporal resolution of 1 hydrological year. Although no specific thresholds are given for the spatial resolution of glacier mass change data by GCOS, the annual temporal resolution satisfies the minimum threshold [[4](https://library.wmo.int/records/item/58111-the-2022-gcos-ecvs-requirements-gcos-245)]. The data are not useable to detect mass changes at a finer temporal (e.g. short-term monthly or seasonal changes in glacier mass) or spatial (for individual glaciers) resolution, potentially limiting applications that involve individual glaciers. Note that the usage of a 0.5° grid also implies that not every grid cell has the same absolute surface area. This results in the fact that grid cells are smaller towards the poles, which can result in individual glaciers being larger than the grid surface. This, in turn, may give rise to artificial glacier mass change artefacts in those regions. This would, however, affect only glacier mass changes at local scales (pixels), and not those at the regional or regional spatial scales.

(section-2-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 2. Analysis of spatio-temporal resolution and extent of glacier mass changes > 2.2 Temporal extent/coverage
---
Let us examine the temporal extent of the dataset:

```text
The temporal extent of the glacier mass change dataset is 47 years.
```

To determine whether this temporal extent of the glacier mass change dataset is sufficient to capture reliable temporal trends in global glacier mass changes and to use these trends as indicators of climatic changes, we turn to the literature. The Intergovernmental Panel on Climate Change (IPCC) and World Meteorological Orginization (WMO) often use 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 glacier mass changes. When measured over a long period (> 30 years), trends in glacier mass changes or mass balances can therefore be considered a clear indicator of global climate change. Longer periods, as is here the case, provide even more robust trend estimates and reduce the influence of short-term variability.

We can also determine the number of years that hold non-NaN mass change data for each pixel. If the pixel exhibits complete temporal coverage, the value should equal the number of years in the time dimension `time` of the dataset. Let us have this number quantified:

Determine where values are present
Check where the number of values equals the time dimension of the dataset
Count how many non-NaN values there are

```text
The number of pixels that have a time series of valid glacier mass change data of 47 years, which is the total number of years in the dataset, is 100.00%.
```

Concerning temporal aspects, the dataset thus offers data at regular and consistently spaced annual intervals that are sufficiently long in time to capture long-term glacier mass change trends at a local (individual pixels), regional or global scale. There are no gaps in the temporal data that could affect a trend analysis. In other words, the dataset exhibits a consistently complete temporal resolution and coverage, with no data gaps, which allows for reliable quantifications of glacier mass change trends.

(section-2-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 2. Analysis of spatio-temporal resolution and extent of glacier mass changes > 2.3 Spatial extent/coverage
---
To further assess the spatial coverage of the data, we can make use of the `glacier_area_km2` variable within the dataset. Let us plot the global glacier area over time to get an idea of how this variable looks:

Make the plot

*Figure 1. Total global glacier area over time in the glacier mass change dataset, which results from a parameterization of estimated regional glacier area changes [[3](https://doi.org/10.1038/s41586-019-1071-0)]).*

As can be seen from the plot above, the glacier area results from a linear decrease over time. It is hence not derived from in-situ and/or remote sensing data, but rather inserted into the data as a parameterization (i.e. a linear fit to estimated regional glacier area changes, of which it is assumed that these glacier area change trends remain unchanged over time [[3](https://doi.org/10.1038/s41586-019-1071-0)]). For proper assessment, we can compare the value around 2000 CE to that of the "[Glaciers distribution data from the Randolph Glacier Inventory (RGI) for year 2000](https://cds.climate.copernicus.eu/datasets/insitu-glaciers-extent?tab=overview)" dataset, which is 746088.28 km$^2$ from the vector (shape file) product in RGI v6.0 [[5](https://www.glims.org/RGI/randolph60.html)]:

Calculate the total glacier area for the year 2000
Determine the percentage difference

```text
The total global glacier area in the glacier mass change dataset in 2000 CE is 745153.82 km², which is 99.87% of the glacier area in the RGIv6.0 dataset.
```

(section-2-4)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 2. Analysis of spatio-temporal resolution and extent of glacier mass changes > 2.4 Sampling density
---
Quantitative details about the sampling density (i.e. the number of sampled glaciers per grid point) are not given in the dataset. Nevertheless, a potential scarce observational sample of annual in-situ glaciological mass balance observations can introduce significant biases and uncertainties into the analysis of long-term trends in glacier mass changes. It is thus not possible to determine whether the data are densely sampled enough to ensure that the observed trends are reliable and not affected by sparse data. An indication of the global distribution of glaciological mass change and geodetic elevation change observations from the WGMS Fluctuations of Glaciers database is, however, available from the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (see figure below). While the glaciological sample covers ca. 500 glaciers only, the multi-annual to decadal geodetic sample covers ca. 200,000 glaciers around the globe (in total ca. 96% of the glaciers present in the RGIv6.0 dataset). The other remaining glaciers are unobserved by any means and require the complex algorithm to assign them a mass change value based on the behavior of neighboring observed glaciers.

![alternatvie text](https://confluence.ecmwf.int/download/attachments/400511869/worddav17d9d5fbc2dc155690254b907459af22.png?version=1&modificationDate=1713359738989&api=v2)

*Figure 2. Distribution of glacier mass change records from the glaciological (red crosses) and geodetic (blue dots) samples over the 19 RGI 1st order regions (shown as black boxes with region number as label) used in the glacier mass change dataset. From: [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (Copernicus Knowledge Base).*

(section-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 3. Glacier mass change trends > 3.1 Spatial distribution of linear mass change trends
---
Let us now express the time series of glacier mass changes at each pixel in the form of linear trends and plot them on a world map:

Plot the gridded data

*Figure 3. Spatial distribution of linear mass change trends (Gt/yr) for each pixel in the glacier mass change dataset.*

Prominent mass loss is evident in regions such as Alaska, the western United States, the Andes, Svalbard, the Alps, and the Himalayas, where red tones (i.e. negative linear trends) dominate. In contrast, areas with mass gain are minimal, shown by isolated blue patches (i.e. positive linear trends). The plot of linear trends above underscores the persistent decrease in glacier mass over recent decades. Let us now check the statistical significance of these trends at $\alpha$ = 0.05:

Plot the gridded data
Define the boundaries for the colorbar
Plot the data

*Figure 4. Statistical significance (alpha=0.05) of linear mass change trends for each pixel in the glacier mass change dataset.*

Let us quantify the number of pixels where a statistically significant negative linear trend prevails:

Check for pixels with negative trend
Check for pixels with statistically significant trend
Count how many there are

```text
The number of pixels with both a negative and statistically significant trend is 3590, which is 76.30% of the total pixels that hold glacier mass change data.
```

The above analysis indicates that the majority of the derived linear mass change trends are negative and statistically significant, adding further credibility to the glacier mass change dataset.

(section-3-2)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 3. Glacier mass change trends > 3.2 Trends in global total glacier mass changes
---
In the following section, we plot the global annual (and cumulative) glacier mass change over time. For the annual values, we therefore sum the gridded mass change product over the entire spatial domain for each individual year to get spatially summed values in Gt yr⁻¹:

$\Delta M_i
$
[Gt yr⁻¹]
$ = \sum\limits^{x,y}\Delta {M_{x,y}}$

where $\Delta {M_{x,y}}$ is the glacier mass change (in Gt yr⁻¹) at pixel $x,y$ during a certain year $i$.

The data can also be plotted in a cumulative way:

$
{\Delta M}
$
[Gt]
$
= \sum\limits_{i={1976}}^{{{1976+n-1}}} (\Delta M_i)
$

with $n$ the total number of years in the time series.

This results in the following plot:

Compute cumulative glacier mass change/balance and area

*Figure 5. Annual (left) and cumulative (right) global glacier mass changes in the glacier mass change dataset.*

The values in the plots above align well with findings in the literature (e.g. [[9](https://doi.org/10.1038/s41586-024-08545-z)]). We can also plot the annual global glacier mass changes in the style of the popular climate [warming stripes](https://showyourstripes.info) for a better visual representation:

Configure the figure
Define a red (negative) to blue (positive) colorscale
Saturate colors
Create a colored rectangle for each year

*Figure 6. Annual global glacier mass changes from the glacier mass change dataset expressed in the form of 'warming stripes'.*

At last, we can calculate the linear and quadratic trends of the global glacier mass change time series:

Extract time and glacier data
Extract most recent 30 years
Calculate linear trend
coeffs[0] is the slope, coeffs[1] is the intercept

```text
The linear trend of the global glacier mass changes between 1975-1976 and 2021-2022 is -167.30 Gt yr⁻¹. During the most recent 30 years, the trend is -257.64 Gt yr⁻¹.
```

Let us have this plotted:

Plot the data

*Figure 7. Cumulative global glacier mass changes from the glacier mass change dataset and the corresponding linear trend.*

Now for the acceleration of the global glacier mass changes:

Extract time and glacier data
Calculate quadratic trend
Extract most recent 30 years
Calculate quadratic trend
coeffs[0] is the quadratic term, coeffs[1] is the linear term, coeffs[2] is the intercept

```text
The acceleration of the global glacier mass changes between 1975-1976 and 2021-2022 is -10.52 Gt yr⁻². During the most recent 30 years, the acceleration is -7.60 Gt yr⁻².
```

Let us have the quadratic trend plotted:

Plot the data

*Figure 8. Cumulative global glacier mass changes from the glacier mass change dataset and the corresponding quadratic trend (acceleration).*

(section-3-3)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 3. Glacier mass change trends > 3.3 Comparison with theoretical models
---
The linear trend of global glacier mass changes from 1975-1976 to 2021-2022 indicates a consistent decline. The quadratic trend shows an accelerating rate of these glacier mass losses. This suggests that the rate of global glacier mass loss has intensified over time, particularly during the more recent decades. The quadratic trend furthermore fits the observed data more closely than the linear trend, highlighting the increasing and non-linear impact of climate change on glacier mass changes. This acceleration was also noted in other glacier mass changes products [[6](https://doi.org/10.1038/s41586-021-03436-z), [7](https://doi.org/10.3389/feart.2019.00096)] and is also what can be expected from theory for a linear climate warming over time (e.g. [[8](https://doi.org/10.1007/s003820050222)]):

$\dfrac{dM}{dt} = -S_T  A_{t_0} \rho_i T'$

where $S_T$ is the mass balance sensitivity to temperature changes (m yr$^{-1}$ K$^{-1}$), $A_{t_0}$ the initial glacier surface area (m$^2$), $\rho_i$ the density of ice (kg m$^{-3}$) and $T'$ the temperature perturbation (K), which gives final units of kg yr$^{-1}$.

By assuming a linear temperature perturbation over time (i.e. $T' = \alpha (t - t_0)$), the equation can be rewritten as (with $\alpha$ in units of K yr$^{-1}$):

$dM = -S_T A_{t_0} \rho_i T' dt = -S_T A_{t_0} \rho_i (\alpha (t - t_0)) dt$

or when integrating over a time period between $t$ and $t_0$:

$ \int\limits^{t}_{t_0} dM = -S_T A_{t_0} \rho_i \int\limits^{t}_{t_0} \alpha (t - t_0)dt$

and by finally assuming ${t_0}$ = 0 and $M(t_0) = 0$, we get:

$M(t) = -\dfrac{1}{2} S_T A_{t_0} \rho_i \alpha t^2$

or $M(t)  \approx  f(-t^2)$

which thus quantifies a quadratic (accelerated) glacier mass decrease over time, as is also noted in the glacier mass change dataset, highlighting the non-linear temperature-driven effects on global glacier mass changes.

(section-4)=


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > Analysis and results > 4. Short summary and take-home messages
---
When measured over long periods and extensive geographical scales, trends in glacier mass changes are clear indicators of global climate change [[3](https://doi.org/10.1038/s41586-019-1071-0), [9](https://doi.org/10.1038/s41586-024-08545-z)]. To be able to derive such trends of glacier mass changes and for climate change analysis/monitoring to become reliable and possible, the glacier mass change dataset should at least exhibit a comprehensive spatial coverage (i.e. global), 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" [[10](https://doi.org/10.1175/BAMS-D-21-0109.1)]).

The [glacier mass change dataset on the CDS](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview) is found to exhibit a consistent suitable spatial (0.5° x 0.5°) and temporal (annual) resolution, as well as an extensive coverage (> 30 years globally), to conduct a meaningful analysis of linear and quadratic trends in glacier mass changes at local (pixel-by-pixel), regional, and global scales. The spatial and temporal resolution/extent of the data furthermore 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. The resulting linear glacier mass change trends show consistent mass loss across most pixels across the globe, while quadratic trends highlight a general accelerating rate of loss over the last several decades. These observations align well with theoretical considerations of the response of glaciers to a linear warming trend [[8](https://doi.org/10.1007/s003820050222)]. The majority of the pixel-based trends are statistically significant at $\alpha$ = 0.05, further enhancing the dataset's credibility and reliability for global climate monitoring. The corresponding glacier mass changes are all assumed to occur above sea level.

Users should, however, keep in mind that mass change artefacts may occur in polar regions due to a variable absolute surface area of the pixels, and that the dataset lacks detailed information on sampling density. The latter is important because annual in-situ glaciological samples (~500 glaciers) form the basis to infer mass changes for a much larger sample of geodetic mass change observations and unobserved glaciers [[2](https://doi.org/10.5194/essd-17-1977-2025)]. This, for example, results in the fact that the product has a less well-pronounced observational coverage with respect to the annual variability of glacier mass changes (which may be less well represented), but an excellent coverage with respect to their long-term trend. Therefore, knowledge of the amount and spatial distribution of glaciers with a consistent and long-term glaciological sample is crucial for assessing the representativeness of the data. Despite sampling density limitations and the related uncertainties, the dataset’s robust temporal/spatial coverage and resolution make it a reliable tool for assessing glacier mass changes as an indicator of global climatic changes.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > ℹ If you want to know more > Key resources
---
- [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)
- [Documentation on the CDS](https://cds.climate.copernicus.eu/datasets/derived-gridded-glacier-mass-change?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/pages/viewpage.action?pageId=355349383) (Copernicus Knowledge Base)
- [World Glacier Monitoring Service (WGMS)](https://wgms.ch/)
- [Glacier Mass Balance Intercomparison Exercise (GlaMBIE)](https://glambie.org/)
- [Copernicus climate change indicators: glaciers](https://climate.copernicus.eu/climate-indicators/glaciers)
- [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: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > ℹ If you want to know more > References
---
- [[1](https://wgms.ch/)] WGMS (2022). Fluctuations of Glaciers Database. doi: 10.5904/wgms-fog-2022-09.

- [[2](https://doi.org/10.5194/essd-17-1977-2025)] Dussaillant, I., Hugonnet, R., Huss, M., Berthier, E., Bannwart, J., Paul, F., and Zemp, M. (2025). Annual mass changes for each glacier in the world from 1976 to 2023, Earth Syst. Sci. Data, https://doi.org/10.5194/essd-2024-323

- [[3](https://doi.org/10.1038/s41586-019-1071-0)] Zemp, M., Huss, M., Thibert, E., Eckert, N., McNabb, R., Huber, J., Barandun, M., Machguth, H., Nussbaumer, S. U., Gärtner-Roer, I., Thomson, L., Paul, F., Maussion, F., Kutuzov, S., and Cogley, J. G. (2019). Global glacier mass changes and their contributions to sea-level rise from 1961 to 2016. Nature, 568, 382–386. doi: 10.1038/s41586-019-1071-0.

- [[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://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.

- [[6](https://doi.org/10.1038/s41586-021-03436-z)] Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., Huss, M., Farinotti, D., Dussaillant, I., Brun, F., and Kääb, A. (2021). Accelerated global glacier mass loss in the early twenty-first century. Nature 592, 726–731. doi: 10.1038/s41586-021-03436-z.

- [[7](https://doi.org/10.3389/feart.2019.00096)] Wouters, B., Gardner, A. S., and Moholdt, G. (2019). Global Glacier Mass Loss During the GRACE Satellite Mission (2002-2016). Front. Earth Sci. 7. doi: 10.3389/feart.2019.00096.

- [[8](https://doi.org/10.1007/s003820050222)] Oerlemans, J., Anderson, B., Hubbard, A., Huybrechts, P., Jóhannesson, T., W. H. Knap, M. Schmeits, A. P. Stroeven, R. S. W. van de Wal, J. Wallinga and Z. Zuo  (1998). Modelling the response of glaciers to climate warming. Climate Dynamics 14, 267–274. doi: 10.1007/s003820050222

- [[9](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 (2025). doi: 10.1038/s41586-024-08545-z.


EQC Quality Assessment: "Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis"
Dataset: derived-gridded-glacier-mass-change [CDS]
Aspect: trend-assessment_q02  |  Category: Satellite_ECVs
Section: Glacier mass change data from satellite and in-situ observations: resolution and coverage for trend analysis > ℹ If you want to know more > References
---
IE Team (2025). Community estimate of global glacier mass changes from 2000 to 2023. Nature (2025). doi: 10.1038/s41586-024-08545-z.

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


EQC Quality Assessment: "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
---
Production date: 31-05-2025

Dataset version: 6.0

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


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 > Quality assessment question
---
**"What is the temporal distribution of the delineated glacier outlines, nominally provided for the year 2000, and how well can they be used to estimate regional and global glacier ice volumes?"**

Glaciers are a major contributor to current global sea-level rise, a resource of fresh water, a potential threat of natural hazards, and an important factor for hydro-power production, recreation and tourism. A proper assessment of glacier areas, glacier characteristics, as well as their changes due to warming climatic conditions therefore plays a crucial role in dealing with these issues. In that regard, the "[Glaciers distribution data from the Randolph Glacier Inventory (RGI) for year 2000](https://cds.climate.copernicus.eu/datasets/insitu-glaciers-extent?tab=overview)" dataset on the Climate Data Store (CDS) provides key information with respect to glacier extent and their characteristics. The RGI dataset is a collection of digital glacier and ice cap outlines at the global scale, nominally provided for the year 2000 [[1](https://www.glims.org/RGI/randolph60.html), [2](https://doi.org/10.3189/2014JoG13J176)]. The data are available in both vector (a shapefile with polygons of individual glacier outlines) and raster (as gridded data with the aggregated fractional glacier areas per pixel) format. Although the goal of the dataset is to provide glacier outlines of all glaciers on Earth as close as possible to the year 2000, one of the main known issues of the dataset is the fact that the acquisition date of the delineated glacier data varies substantially. This notebook investigates the corresponding temporal distribution of delineated glacier data in the vector version of the dataset and evaluates its implications for the estimation of current global glacier ice volumes using the examples of Farinotti et al. (2019) [[3](https://doi.org/10.1038/s41561-019-0300-3)] and GlaMBIE (2025) [[14](https://doi.org/10.1038/s41586-024-08545-z)]. Since both studies made use of the RGIv6.0, we also use this version in our notebook.


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

- The RGI dataset, available on the Climate Data Store, is the most comprehensive source of digital glacier area data and provides consistent, static glacier outlines for climatological, hydrological, and glaciological applications at regional to global scales. It holds a snapshot of global glacier area data that is assumed to be representative for the year 2000. However, in reality there is a variation in delineation dates (a certain amount of glaciers were delineated before or after the year 2000). The acquired glacier outlines that deviate from the year 2000 can lead to systematic errors that are apparant for certain applications, such as the use of RGI glacier outlines as input for regional/global glacier volume estimates.
- Nevertheless, the assessment reveals that the (area-weighted) mean acquisition date of all glacier outlines in the dataset is relatively close to 2000, and that the systematic error at the global scale is relatively small compared to the total glacier volume estimates from the glacier community. This makes the dataset reliable to be used as input data for regional and global glacier volume estimates. However, regional and glacier-specific errors can vary significantly due to factors like strongly deviating delineation dates in some areas, varying spatial glacier mass loss rates and glacier response times, and the presence of a supraglacial debris cover (which may cause significant omission errors in glacierized areas). Users should carefully evaluate these factors for specific applications.
```


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 > Methodology > Dataset description
---
The dataset of the glaciers distribution on the Climate Data Store (CDS) is an almost complete collection of digital glacier and ice cap outlines and their geometrical/hypsometrical characteristics from various data sources at the global scale [[1](https://www.glims.org/RGI/randolph60.html), [2](https://doi.org/10.3189/2014JoG13J176)]. The RGI dataset on the CDS is considered a snapshot of glacier outlines around the year 2000, assembled mainly from satellite images, and is currently the most complete dataset of glacier outlines. Simply stated, the glaciers in the dataset were automatically classified using the distinctive spectral reflectance signatures of bedrock and ice. During post-processing, raw glacier outlines are quality checked and manually corrected if required (e.g. in the case of a supraglacial debris cover). The vector part of the dataset divides the glaciers into separate RGI regions, i.e. there are 19 of those regions ("clusters" of glaciers) in RGIv6.0. The raster version of the data contains aggregated fractional glacier areas for each pixel of 1 by 1 degree but does not provide sufficient information to classify glaciers into distinct RGI regions. For a more detailed description of the data acquisition and processing methods, we refer to the [documentation on the CDS](https://cds.climate.copernicus.eu/datasets/insitu-glaciers-extent?tab=overview) and the [ECMWF Confluence Wiki](https://confluence.ecmwf.int/display/CKB/Glacier+Area) (Copernicus Knowledge Base).


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

**[](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 > 1. Data preparation and processing > 1.2 Define request and download
---
Then we define requests for download from the CDS:

🚨 **The files can be large! Since the data files to be downloaded and manipulated have a considerable size, this may take a couple of minutes.**\
🚨 **Insert the correct RGI version number to be downloaded below:**

SELECT THE RGI VERSION TO DOWNLOAD #############
Select correct column names based on RGI version
Glacier extent data
Glacier mass change data

Next, we download the data:

Get glacier extent data: takes a couple of minutes
Download glacier mass change data

```text
Downloading and handling glacier extent data from the CDS, this may take a couple of minutes...
```

```text
100%|██████████| 1/1 [00:00<00:00, 67.66it/s]
```

```text
Downloading glacier mass change data...
```

```text
100%|██████████| 1/1 [00:01<00:00,  2.00s/it]
```

```text
Downloading done.
```

We define the functions to be used:

(section-1-3)=


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