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Acronyms

General definitions

Altimetry: A remote-sensing technique in which surface altitudes (elevations) are estimated as a function of the travel time of a pulse (Cogley et al., 2011).

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Calving (D): The component of ablation consisting of the breaking off of discrete pieces of ice from a glacier margin into lake or sea water, producing icebergs, or onto land in the case of dry calving. Calving excludes frontal melting and sublimation, although in practice it may be difficult to measure the phenomena separately. For example subaqueous frontal melting may lead to the detachment of icebergs by undercutting or by encouraging the propagation of crevasses (Cogley et al., 2011).

Scope of the document

This document is the Algorithm Theoretical Basis Document (ATBD) for the distributed glacier change Climate Data Record (CDR) product provided to the Copernicus Climate Change Service (C3S) Climate Data Store (CDS). It describes the algorithms used to generate the new C3S distributed glacier mass change product, including the scientific justification for the algorithms selected to derive the product, an outline of the proposed approach and a listing of the assumptions and limitations of the algorithm.

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Executive summary

Glacier changes in elevation, volume, and mass can be observed using different methods. As such, in-situ measurements using the glaciological method (c.f Cogley et al., 2011) are carried out at a few hundred glaciers only (WGMS, 2021) but can provide the seasonal to annual variability of glacier mass changes (Zemp et al., 2019) which is well correlated over several hundred kilometers (Letréguilly and Reynaud, 1990; Cogley and Adams, 1998). Differencing of Digital Elevation Models (DEMs) from the geodetic method (c.f Cogley et al., 2011) using airborne and spaceborne sensors can provide glacier elevation and volume changes over multi-annual to decadal periods for thousands of glaciers. In C3S (product versions 1 to 6), we brokered glaciological and geodetic time series for individual glaciers from around the world as available from the WGMS. In recent years, the scientific community develop automated processing chains (e.g. Girod et al., 2017) to apply of the geodetic method over entire mountain ranges (e.g. Brun et al., 2017; Braun et al., 2019; Dussaillant et al., 2019; Menounos et al., 2019) and finally reaching almost global coverage (Hugonnet et al., 2021).

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Instruments

We highlight that our product is not directly derived from any spaceborne instruments. Our product combines time series of glacier mass changes from the glaciological method, obtained from in-situ observations and glacier elevation changes from the geodetic method, obtained via diverse airborne and spaceborne sensors.

With the aim of illustrating the role of the in-situ observations and the spaceborne instruments in the generation of the input data of our glacier change product, this section provides a brief and clear description of both the glaciological and geodetic methods, with particular attention on the generation of DEMs through the use of spaceborne instruments.

Glacier mass-change components

The annual mass change – also called “annual mass balance” – of a glacier is calculated as the difference between snow accumulation (mass gain) and melt of ice and snow (mass loss) over a year, and reflects the prevalent atmospheric conditions. When measured over a long period, trends in mass change are an indicator of climate change. The global net loss of glacier mass contributes to sea-level rise, whereas seasonal melting of ice and snow contributes to runoff. In detail, there are many components that contribute to the mass change of a glacier, summarized in Figure 1.

In a more general way, the mass change 𝛥𝑀 of a glacier can be formulated as:

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Figure 1: Components of the mass balance of a glacier. The arrows have arbitrary widths and do not indicate physical pathways of mass transfer. Source: Cogley et al., (2011).

Glacier mass changes from the glaciological method

The glaciological method (c.f Cogley et al., 2011) usually provides glacier-wide surface mass balance (Bsfc) over an annual period related to the hydrological year. The results are usually reported in meters water equivalent (m w.e.) for the specific mass change (1 m w.e. = 1,000 kg m−2) and in Gigatons (Gt) for the mass change (1 Gt = 1012 kg), with mass balance and mass change as synonymous terms. Results are reported as cumulative values over a period of record or as annual change rates (yr−1). Figure 2 provides a schematic view of a typical glaciological monitoring setup. Interpolation of point balance to glacier-wide estimates are typically done using the contour method or using the profile method ( Cogley et al., 2011). If measurements are performed repeatedly and during an extended period of time, the glaciological method will provide crucial information about the temporal variability of glacier changes.

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Glacier elevation changes from the geodetic method

The geodetic mass balance (i.e. geodetic mass change) (

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The comparison of multi-temporal DEMs, often referred to as the geodetic method, has been used for decades to build maps of elevation changes (dh) on glaciers. In practice, DEM differencing determines elevation and volume changes by repeated mapping and differencing of glacier surface elevations from optical stereo images or Synthetic Aperture Radar (SAR) interferometry. Division by the time separation between the two surveys gives elevation change rates (dh/dt) that can then be converted to mass balance using an assumption on the density of the material gained or lost (Huss, 2013).

Figure 3 provides a schematic view on the main methods and results of the geodetic method.

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Figure 3: Sketch of the main techniques used to estimate glacier mass change from space. DEM differencing first determines glacier volume changes through repeat measurement of the glacier elevations. The sources of elevation data are usually DEMs, commonly derived from satellite stereo images (top right), where two satellites “see” the terrain in 3D just as humans do with their two eyes, or from SAR interferometry (bottom right), which reconstructs the surface terrain from the phase difference of the recorded microwave signal at two SAR satellites that fly very close together. The resulting elevation changes over the glacier (dashed and solid red lines delineate the past and present glacier outline, respectively, and the orange line delineates the end of summer snow line respectively) are combined with uncertainty estimates based on a statistical assessment of elevation differencing over stable terrain (purple zones in left figure).

Spaceborne instruments for Digital Elevation Models (DEMs)

The so called DEM differencing technique was initially applied to DEMs derived from maps (Joerg and Zemp, 2014), aerial photographs (Finsterwalder, 1954; Thibert et al., 2008) and more recently to airborne Lidar data (Echelmeyer et al., 1996; Abermann et al., 2010). Since the early 2000s the onset of satellite imagery has permitted the observation of glacier elevation changes for extended glacierized regions. Satellite DEMs derived from various spaceborne instruments (Table 1) are now widely used not only for local and regional but also for global assessments of glacier elevation change, often in conjunction with older maps or airborne images to assess past periods (Rignot et al., 2003; Berthier et al., 2004; Kääb, 2008). The main sources of spaceborne instruments currently used by the research community for geodetic glacier change assessments from optical stereo imagery and interferometric radar data are summarized in Table 1.

For a more detail summary of the geodetic method and its error sources see Zemp et al., (2013). For further reading on measuring glacier mass changes from space, we refer to the review by Berthier et al. (2022, in review).

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Input and auxiliary data

Input data

The input data for the development of the distributed glacier change product are glacier elevation and mass changes from the Fluctuations of Glaciers database. Table 2 provides a brief summary of the key characteristics of these two datasets. Annual mass balance observations from the glaciological method and multiannual trends of glacier thickness change (i.e. elevation change) from the geodetic method as available from the Fluctuations of Glaciers database are illustrated in Figure 4 and 5 respectively, for glacier Hintereisferner located in the Austrian Alps.

For more detail on the specific input data, auxiliary data, retrieval algorithms and uncertainty estimation of the independent FoG glacier elevation and mass change observations please refer to the previous versions of the C3S glacier product (RD1) as well as to (WGMS, 2021) and Zemp et al. (2015).

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Auxiliary data

To compute the distributed glacier mass change product, we require (i) glacier outlines to spatially locate glaciers and measure their area, and (ii) glacier regions to spatially constrain climatic regions. This auxiliary data is illustrated in Figure 6 and briefly summarized in the sections below.

Figure 6: Global overview of the 19 first-order glacier regions (black outlines) and of the glacier coverage around the year 2000 (dark blue areas). Sources: glacier regions from GTN-G (2017) and glacier outlines from RGI 6.0 (RGI Consortium, 2017).

Glacier outlines

We use the digital glacier outlines from the RGI version 6.0. (RGI Consortium, 2017). This is a globally complete inventory of glacier outlines. It is supplemental to the database compiled by the Global Land Ice Measurements from Space initiative (GLIMS). While GLIMS is a multi-temporal database with an extensive set of attributes, the RGI is intended to be a snapshot of the world's glaciers as they were near the beginning of the 21^st century (although in fact its range of dates is still substantial). Production of the RGI was motivated by the preparation of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5, 2013). The RGI was released initially with little documentation in view of the IPCC's tight deadlines during 2012. More documentation is provided in the current version of this Technical Report. The full content of the RGI has now been integrated into the database of GLIMS. However, work remains to be done to make the RGI a downloadable subset of GLIMS, offering complete one-time coverage, version control and a standard set of attributes.

More detail about this product, which is brokered to the C3S CDS as glacier distribution service, is given in RD2 as well as the related literature (Pfeffer et al., 2014; RGI Consortium, 2017).

Glacier regions

We use the 19 first-order glacier regions as defined in by the Global Terrestrial Network for Glaciers (GTN-G, 2017). This dataset is a joint set of regions recommended by GTN-G Advisory Board, the Global Land Ice Measurements from Space initiative (GLIMS), the Randolph Glacier Inventory (RGI) Working Group of the International Association of Cryospheric Sciences (IACS), and the World Glacier Monitoring Service (WGMS). These glacier regions are implemented in RGI 6.0 (RGI Consortium, 2017) and in the Global Glacier Change Bulletin (WGMS, 2021).

Algorithms

Pre-processing

Time series of glacier elevation and mass changes (cf. Section 2.1) are compiled by the WGMS in annual calls-for-data through a worldwide network of national correspondents and principal investigators (WGMS, 2021). The collected observations run through a basic quality check against the meta-data scheme of the Fluctuations of Glaciers database carried out by the WGMS. After integration of the new, updated, and corrected observations into the Fluctuations of Glaciers database, a new database version is released by the WGMS on its website⁵.
For the present product, we used the glacier-wide time series of glacier elevation and mass changes from the latest available database version (WGMS, 2022). Starting from the downloaded dataset (in csv format), the following pre-processing steps are done in order prepare the data for the main processing:

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Main processing

The new CDS product consists of annual glacier mass changes (in Gigatonnes per year) covering the hydrological years from 1975/76 to 2020/21 and spatially distributed in a 0.5° (latitude, longitude) regular grid. The final product is provided in the file format NetCDF 4.0.

Our algorithm produces a global gridded product of distributed glacier changes in four processing steps summarized in Figure 7 and described in the following sections. First, we estimate for each glacier of the RGI 6.0 its temporal mass-change variability (calculated as the mean annual anomaly with respect to a given reference period) from nearby glaciological time series (Section 3.2.1). Second, we calibrate this mean annual anomaly to the long-term trend from the different geodetic surveys available for the corresponding glacier (Section 3.2.2). Third, we produce an observationally calibrated annual mass change time series, or i.e. one time series for each glacier calculated as a weighted mean of all calibrated time series, considering the uncertainty as well as of the temporal coverage of the geodetic surveys (Section 3.2.3). Finally, we aggregate the time series of all glaciers as area-weighted mean for each grid cell (Section 3.2.4). A detailed description of the algorithms involved in the different processing steps is described below.

Figure 7: Summary illustration of the four main processing steps to produce Global annual glacier mass changes since 1975/76 spatially distributed in a global regular grid.

 STEP 1: Retrieval of the temporal mass change anomaly (i.e. temporal variability) for a given individual glacier.

a Individual glacier annual anomalies (β_Y,i) from glaciological observation sample (B_glac,Y,i)

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 To capture the temporal variability of glacier changes for a given glacier j existing in the RGI6.0 glacier inventory, a spatial search of nearby individual glacier annual anomalies is performed in a five radial distance steps. To ensure a good representativity of the temporal variability of glacier j, a minimum of three time series need to be spatially-selected. The search stops at the distance where this condition is met. In case no individual glacier annual anomalies are found within the 1000 km threshold, glacier anomalies from the same or neighboring RGI 1^st order regions  (Figure 6) are selected manually via expert knowledge (as in Zemp et al. 2019).

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As a general rule all annual spatial glacier anomalies should cover at least the period between the hydrological years from 1975/76 to 2020/21. For glaciers with spatial anomalies not arriving back to 1975/76, the best correlated glaciological series from neighbouring (climatically similar) regions are used to fill in the gap years. Before considering them to calculate the glacier spatial anomaly back in time, the amplitude of the selected neighboring series used is normalized to the amplitude of the glacier anomaly for the reference period (2011-2020). This reduces the effect of possible climatic differences within the neighboring series. The 1975/76 threshold is defined as this is the latest date where all glaciers in all glacier regions contain annual glaciological observations. 

STEP 2: Calibration of the annual spatial anomaly on an individual glacier geodetic sample

a. Geodetic observation sample over a period of record 

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Geodetic observations are reported to the FoG database with their relative uncertainties as rates of elevation change (m, meters) during a period of record (multiannual or decadal). Glaciers may contain multiple individual geodetic observations for different time periods depending on the dates of the DEMs used (see Figure 4 and Figure 10). To obtain the geodetic mass balance rate

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\sigma_{cal,Y,j,k} = \sqrt{(\sigma_{geo,PoR,j,k})^2 + (\sigma_{\beta_{Y,spt,j}})^2} \quad [10]

STEP 3: Observationally calibrated annual mass balance

a. Observationally calibrated annual mass balance for glacier j (B_OC,j)

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Steps 1 to 3 are repeated for all glaciers existing in the RGI6.0 glacier inventory with available geodetic observations (e.g. 205.000 glaciers approximately or 96% of the world glaciers).

STEP 4: Integration at 0.5° (latitude, longitude) regular grid

The final C3S product provides annual glacier mass changes (in Gigatonnes per year) at a global scale with a spatial resolution of 0.5° latitude, longitude. The following equations describe the algorithms used to (a) integrate the observational calibrated annual mass balance series obtained for every glacier in the RGI 6.0 into a global grid of 0.5° latitude, longitude and (b) the transformation from specific mass balance (B in m w.e.) to total mass change (ΔM in Gt) at the grid point. Note that the following equations for specific and total mass change are valid for the integration of individual glacier observationally calibrated estimates into any larger scale region containing multiple glaciers, i.e. regular grid cells of any user requested resolution, hydrological basins, subregions, RGI regions etc.

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Every glacier with available geodetic observations has an independent Observationally calibrated annual mass balance (Figure 7). Unobserved glaciers are assumed to behave as the regional mean of the observed sample. Hereafter the terminology obs and unobs is used to differentiate the observed glacier sample from the unobserved glacier sample respectively.

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is taken from Zemp et al. (2019)

Output data

For C3S2 (product version WGMS-FOG-2022-09), we computed a gridded, annually resolved, global product of glacier mass changes at a spatial resolution of 0.5°. This product is made available in the CDS as CDR covering the hydrological years from 1975/76 to 2020/21. It is based on the glaciological and geodetic time series from the FoG database version from 2022-09-14 (WGMS 2022) and uses the RGI version 6.0 (RGI 2017; RD2) as auxiliary data.

The final product is provided in NetCDF 4.0 file format as annual individual files containing glacier changes and related uncertainties as variables (in Gigatonnes per year) and time (year), latitude and longitude as dimensions. Files are gridded in a global regular grid with naming convention of the grid point as the center of the grid point. Table 3 shows an overview of the C3S distributed glacier mass change product output data fields and characteristics. A visualization example of both the spatial (0.5° regular grid) and temporal (annual temporal resolution) components of the distributed glacier mass change product and its relative uncertainties is presented in Figure 12 and 13, respectively.

For more details about the product description we refer the user to the Product User Guide and Specification (PUGS, RD3) document. For information about the quality of the product against data requirements we refer to the Product Quality Assessment report (PQAR, RD4).

Table 3: Overview of C3S distributed glacier mass change product output data fields

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Known limitations for the distributed glacier product

Grid-point artefact in polar regions

For mass change purposes a glacier must be considered as a whole; an all-in-one system which cannot be divided in parts (see Section 1.1). The best glaciologically correct solution to integrate glacier changes into a grid point is to consider a glacier belonging to a grid-point when its geometric centroid lies within the grid point.

To illustrate this, Figure 14 represents a hypothetical case of two different glaciers located next to each other. When integrating individual glacier mass balances into a grid cell: if the grid cell is sufficiently large it will include many glaciers and the grid-point mass balance will be calculated as explained in Section 3.2.4. But if the grid cell size is smaller than the surface of the glacier (as the hypothetical and the real case shown in the example Figure 14, part 1), the grid point where the glacier centroid is located will represent the gridded value of mass gain by the full glacier (Figure 14, part 2) even if in reality not all the glacier is contained over the grid point.

At a 0.5° grid point resolution, as used in the C3S distributed glacier mass change product, this integration artifact occurs in polar region above 60° latitude, were latitude, longitude grid points (in WGS-84 projection) are smaller in surface and individual glaciers can be larger than the grid surface. This directly derives into a biased centroid grid point mass change, and consequent neighbor glacierized grid points without a mass change estimate (Figure 14, part 2, right panel).

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Our product is consistent with regard to total glacier mass change at global to regional scales, e.g. 19 GTN-G Glacier Regions. However, it is not able to represent the local to regional mass change distribution in regions where glaciers are larger than the pixel resolution. A solution of this issue would require to increase the spatial resolution of the input data from (currently) glacier-wide averages to distributed mass-change fields, which currently is not feasible for all input datasets.

Calendar year vs Hydrological year:

Our distributed glacier change product (version WGMS-FOG-2022-09) provides glacier changes for the hydrological years from 1975/76 to 2020/21. In a glaciological context, it is a general agreement that the hydrological year starts in winter with the beginning of the accumulation season and finishes at the end of summer or ablation season. Therefore, the hydrological year varies between regions (South and North Hemispheres and Tropics) and is not equal to the calendar year. Note that this issue– inherited from the input data – introduces some inconsistencies and uncertainties that might need to be considered by the user. As such, annual values from a pixel or region on the northern hemisphere are temporally not fully consistent with annual values from a pixel or region on the southern hemisphere. For cumulative values over longer time periods, these differences are less important. A solution for this issue would require an increase in the temporal resolution of the input data to monthly observations, which currently is not feasible.

References

Abdel Jaber, W., Rott, H., Floricioiu, D., Wuite, J., and Miranda, N. (2019). Heterogeneous spatial and temporal pattern of surface elevation change and mass balance of the Patagonian ice fields between 2000 and 2016. The Cryosphere 13, 2511–2535. doi: 10.5194/tc-13-2511-2019.

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