Contributors: Jacqueline Bannwart (University of Zurich), Inés Dussailan (University of Zurich), Frank Paul (University of Zurich), Michael Zemp (University of Zurich)

Issued by: UZH / Inés Dussaillant, Michael Zemp

Date: 14/08/2023

Ref: C3S2_312a_Lot4.WP2-FDDP-GL-v1_202212_MC_ATBD-v4_i1.1

Official reference number service contract: 2021/C3S2_312a_Lot4_EODC/SC1

History of modifications

List of datasets covered by this document

Related documents

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).

Brokered Product: A brokered product is a pre-existing dataset to which the Copernicus Climate Change Service (C3S) acquires a license, for the purpose of including it in the Climate Data Store (CDS).

Digital elevation model (DEM): An array of numbers representing the elevation of part or all of the Earth's surface as samples or averages at fixed spacing in two horizontal coordinate directions. Digital elevation models are now the preferred means of representing the elevation changes on which mass-balance measurements by geodetic methods are based. The elevation change is calculated by subtracting an earlier DEM from a later DEM (Cogley et al., 2011).

Elevation change: Vertical change in glacier surface elevation (altitude), typically derived from two elevation measurements, adjusted if necessary for the difference of their respective datum surfaces, at the same (or nearly the same) horizontal coordinates (Cogley et al., 2011).

Geodetic method: Any method for determining mass balance by repeated mapping of glacier surface elevations to estimate the volume balance; cartographic method and topographic method are synonyms. The conversion of elevation change to mass balance requires information on the density of the mass lost or gained, or an assumption about the time variations in density (Cogley et al., 2011).

Glaciological method: A method of determining mass balance in-situ on the glacier surface by measurements of accumulation and ablation, generally including measurements at stakes and in snow pits; direct method has long been a synonym. The measurements may also rely on depth probing and density sampling of the snow and firn, and coring. They are made at single points, the results from a number of points being extrapolated and integrated to yield the surface mass balance over a larger area such as an elevation band or the entire glacier (Cogley et al., 2011).

Gravimetric method: A technique in which glacier mass variations are calculated from direct measurements of Earth's gravity field. Satellite gravimetry is at present the most feasible method for determining glacier mass balance from changes in gravity. The Gravity Recovery and Climate Experiment (GRACE) consists of two polar-orbiting satellites separated by about 200 km along-track, and is the primary mission for this work to date (Cogley et al., 2011).

Interferometry: Measurement of the interference of waves, particularly electromagnetic waves, from a common source such as a radar, with the aim of obtaining information about the topography, velocity field and other characteristics of the glacier surface (Cogley et al., 2011).

Remote sensing: Measurement of surface properties with a sensor distant from the surface, such as on an airplane or satellite, or of subsurface properties with a sensor on or distant from the surface, either with a signal emitted by the sensor (Cogley et al., 2011).

Mass change components

Surface ablation (𝐵𝑠𝑓𝑐): Ablation at the surface of the glacier, generally measured as the lowering of the surface with respect to the summer surface, corrected for the increase in density of any residual snow and firn and multiplied by the density of the lost mass (Cogley et al., 2011).

Internal ablation (𝐵𝑖𝑛𝑡): Loss of mass from a glacier by melting of ice or firn between the summer surface and the bed. Internal ablation can occur due to strain heating of temperate ice as the ice deforms. However, the largest heat sources for internal ablation are likely to be the potential energy released by downward motion of the ice and of meltwater (Cogley et al., 2011).

Basal ablation (𝐵𝑏𝑎𝑠): The removal of ice by melting at the base of a glacier (Cogley et al., 2011).

Frontal ablation (Af): Loss of mass from a near-vertical glacier margin, such as a calving front. The processes of mass loss can include calving, subaerial melting and subaerial sublimation, and subaqueous frontal melting (Cogley et al., 2011).

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.

Within C3S, glacier change products (versions 1 to 6) were provided to the CDS as two separate datasets of i) glacier elevation and (ii) mass change time series as extracts from the Fluctuations of Glaciers (FoG) database brokered from the World Glacier Monitoring Service WGMS¹. In C3S2, we now combine these two datasets (product version WGMS-FOG-2022-09) to produce a completely new and unique product of globally distributed gridded glacier mass changes. Consequently, major changes have been applied to the glacier change product algorithms and theoretical basis that are explained in detail in the present document.

The present ATBD document complements the corresponding submission of the glacier mass change CDR towards the end of the first data cycle within C3S2 312a (glacier change product version WGMS-FOG-2022-09, December 2022). The distributed glacier mass-change product builds on the latest Fluctuations of Glaciers Database version released in Sep 2022 by the World Glacier Monitoring Service (WGMS, 2022)².

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).

With the integration of these regional and global geodetic datasets into the WGMS database (WGMS, 2022) it became – for the first time – feasible to produce a global gridded glacier mass change product with annual resolution from combining glaciological and geodetic methods. Inspired by previous methodological frameworks (Zemp et al., 2019, 2020), we developed a new approach to combine the temporal variability of the glaciological observations (at regional levels) with the long-term change rates (of individual glaciers) of geodetic observations. 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° (hereafter referred to as distributed glacier change product).

In the present document, we provide a very brief summary of the basic instruments used by the community to measure glacier changes in elevation and mass (from the glaciological and geodetic methods) and provide references to further reading (Section 1). While many Essential Climate Variable (ECV) products within C3S are directly derived from one or multiple spaceborne instruments, our glacier product builds on the combination of input data and auxiliary data brokered from international data repositories (described in Section 2). As input data, we use the glaciological and geodetic time series of glacier mass changes and of glacier elevation changes, respectively, as available from the WGMS. As auxiliary dataset, we use the glacier distribution (i.e. area) from the latest version of the Randolph Glacier Inventory (RGI 6.0), which is a community product generated within the RGI working group of the International Association of Cryospheric Sciences (IACS³) and brokered to the C3S CDS (C3S2 glacier Climate Data Record, CDR).

Our algorithm produces a global gridded product in four processing steps described in detail in Section 3. First, we estimate for each glacier of the RGI 6.0 its temporal mass-change variability, calculated as mean annual anomaly (with respect to a given reference period) from nearby glaciological time series. Second, we calibrate this time series with all geodetic observations as available for the corresponding glacier. For each glacier, this results in multiple time series that all come with the temporal variability from the glaciological sample but are calibrated to the long-term trend from the different geodetic surveys. Third, we produce one time series for each glacier calculated as a weighted mean, considering the uncertainty as well as of the temporal coverage of the geodetic surveys. Forth, we aggregate the time series of all glaciers as area-weighted mean for each grid cell.

Our final product provides annual glacier mass changes (in Gigatonnes per year) at global scale with a spatial resolution of 0.5° covering the hydrological years from 1975/76 to 2020/21. An overview of the product and its known limitations is available in Section 4.
  

1. 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.

1.1. 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:

where B is the sum of the surface (sfc), internal (int), and basal (bas) mass-change components, and – in the case of marine-terminating or lacustrine glaciers – of frontal ablation 𝐴𝑓.

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).

1.2. 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.

Time series of glaciological observations are recommended to be checked against and – if required – calibrated with high-quality and high-resolution airborne geodetic surveys (Zemp et al., 2013). Glaciological observations from around the globe are collected in annual calls-for-data by the WGMS (WGMS, 2022, and earlier reports). More details on the glaciological method is found in Kaser et al. (2003), Østrem and Brugman (1991) and in Zemp et al. (2013, 2015) which are made available from the WGMS webpage⁴.

Figure 2: Sketch illustrating the basic observations of the glaciological method at ablation stakes on the glacier tongue and snow pits in the accumulation zone. These point measurements are interpolated to estimate the glacier-wide mass changes (left figure, red and orange lines delineate the glacier outline and the end of summer snow line respectively).

1.3. Glacier elevation changes from the geodetic method

The geodetic mass balance (i.e. geodetic mass change) ( \( B_{geod} \) ) is calculated as volume change \( \Delta V \) , over a survey period between 𝑡0 and 𝑡1, from differencing of DEMs, over the mean glacier area S multiplied by a volume-to-mass conversion factor \( \left(\frac{\overline{\rho}}{\rho_{water}} \right) \)

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.

To ensure a reliable elevation change estimation, a relatively complete coverage of the entire glacier surface is a key aspect of the input DEMs, as high biases may arise if only a fraction of the glacier is surveyed (e.g. only the glacier tongue, Berthier et al., 2010)). The precision of the results is also a function of the time separation between DEMs, where time periods larger than 5 or 10 years are usually preferred to minimize uncertainties. More details on the use of the geodetic method glacier elevation and mass change assessments are found in Zemp et al. (2013, 2015)

Today, there are numerous airborne and spaceborne sensors that can be used for the generation and differencing of DEMs for individual glaciers. In addition, spaceborne altimetry from both radar and lidar, as well as spaceborne gravimetry allows to assess glacier elevation and mass changes at regional scales. For a detailed review on measuring glacier mass changes from spaceborne sensors, we refer the reader to Berthier et al. (2023).

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).

1.4. 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).

Table 1: Summary of main spaceborne instruments currently used by the research community for geodetic glacier elevation change assessments from DEM differencing.

2. Input and auxiliary data

2.1. 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).

Table 2: Summary of the key characteristics of the FoG glacier elevation and mass change input data. Both data set come as time series providing glacier-wide values.

Figure 4: Illustration of the annual mass balance observation from the glaciological method as available from the Fluctuations of Glaciers database. Results belong to glacier Hintereisferner, Austria. Source: WGMS (2022), https://doi.org/10.5904/wgms-fog-2022-09.

 

Figure 5: Illustration of the multiannual trends of glacier thickness change from the geodetic method as available from the Fluctuations of Glaciers database. Results belong to glacier Hintereisferner, Austria. Source: WGMS (2022), https://doi.org/10.5904/wgms-fog-2022-09.

2.2. 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).

2.2.1. 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).

2.2.2. 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).

3. Algorithms

3.1. 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:

• Geodetic elevation change data:

1. Selection of glacier-wide records with available thickness or volume change values,
2. Selection of glacier-wide records with survey periods longer or equal to five years (in view of density conversion uncertainty, cf. Huss (2013)),
3. Calculation of glacier-wide elevation change values from selected thickness or volume change values, under consideration of available area and area change values.

• Glaciological mass change data:
  1. Selection of glacier-wide records with available mass change values.

• Creation of time series from selected data together with glacier coordinates (latitude and longitude of centre point) as well as of corresponding glacier regions.

The selected time series are used for the main processing steps described below.

3.2. 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.

3.2.1.  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)

Direct annual glaciological observations for a given glacier I during year Y, are reported to the FoG database with their relative uncertainties ( \( \sigma_{glac,Y,i} \) ) in the form:

In the case where a glaciological series is missing an uncertainty estimate for a given year, we assume it to be equal to the mean of all valid annual uncertainty estimates within the series. In the case where a glaciological series has no uncertainty estimate, we assume it to be equal to the mean annual uncertainty for all glaciological series from glacier belonging to the same region.

The individual glacier annual anomaly of glacier i is calculated as the glaciological mass balance \( B_{glac} \) value at year Y minus the mean mass balance \( \overline{B}_{glac} \)

during the reference period 2011-2020.

Note that only glaciers with available glaciological observations during the reference period will have a glacier anomaly. We allowed a threshold of at least 8 years within the reference period with glaciological observations to calculate \( \beta_{Y,i}. \)

b Annual spatial anomaly for glacier j (β_{Y,spt, j} ) from a spatially-selected sample of nearby individual glacier annual anomalies

 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).

Figure 8: Spatial-selection of nearby glacier annual anomalies in five radial distance steps search. The purple point represents the location of glacier (i) for which the search is performed.

The annual spatial anomaly for glacier j (β_Y,spt,j) is then calculated as the arithmetic average of the N individual spatially-selected glacier annual anomalies (β_Y,i) located nearby glacier j,

The relative annual spatial anomaly uncertainty for glacier j \( \sigma_{\beta_{Y,spt,j}} \)

is then calculated from the combination of two independent sources of error: the mean uncertainty inherited from the glaciological observations of the spatially-selected glacier sample \( \sigma_{glac_{mean},Y}, \)

and the variability of the individual spatially-selected annual glacier anomalies  \( \sigma_{\beta_{var},Y,spt}. \) These two errors are then combined according to the law of random error propagation as follows:

Where,  \( \sigma_{glac_{mean},Y} = \frac{1}{N} \sum_{i=1}^N \sigma_{B_{glac,Y,i}}. \)  In this equation,  \( \sigma_{B_{glac,Y,i}} \)

corresponds to the glaciological observation uncertainty for a given spatially-selected glacier i and N is the number of spatially-selected glaciological sample (i.e. in form of glacier annual anomalies) located nearby glacier j.

And, \( \sigma_{\beta_{var,Y,R}}=1.96*Stdev \beta_{Y,i} \) Corresponds to the variability, at a 95% confidence interval, of the N individual spatially-selected annual glacier anomalies β_Y,i .

Figure 9: Example glacier j = Hintereisferner (Hf), located in Central Europe (RGI region 11, CEU). (a) Visualization of the spatial-distance search, the purple point shows the location of the Hintereisferner glacier, red crosses correspond to the location of nearby glaciers with available glaciological observations. Within the first distance step of 60 km, 22 glaciers with glaciological observations are located. (b) Only 13 of the 22 glaciers present glaciological observations during the reference period (2011-2020) and therefore their individual glacier anomalies can be calculated. Grey lines correspond to the 13 spatially-selected individual glacier anomalies β_Y,i used to calculate Hintereisferner annual spatial anomaly (β_Y,spt,Hf) and uncertainty (σ_βY,spt,Hf)  (black line and shaded grey at 95% CI, respectively) for the period 1950 to 2021.

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. 

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

a. Geodetic observation sample over a period of record  \( (\overline{B}_{geo,PoR,j,k}) \)

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 \( (\overline{B}_{geo,PoR,j,k}) \)

a given elevation change rate observation k belonging to glacier j over a Period or Record PoR  \( (\overline{dh}_{PoR,j,k}), \) needs to be transformed to specific mass change rate (m w.e., meters water equivalent) by applying a density conversion factor  \( f_{\rho}=850kgm^{-3} \ (Huss, 2013). \)

The relative geodetic mass balance rate uncertainty \( (\sigma_{geo,PoR,j,k}) \)

is then calculated as the combination of two independent sources of error: the uncertainty related to the elevation change rate  \( \sigma_{\overline{dh}_{PoR,j,k}} \) and the uncertainty related to the density conversion factor  \( \sigma_{\rho}=60kgm^{-3} \ (Huss, 2013). \)

These two errors are combined according to the law of random error propagation as follows.

b. Calibrated series  \( (B_{cal,j,k}) \) by calibrating the annual spatial anomaly \( (\beta_{Y,spt,j}) \) over the glacier's geodetic mass balance rates sample \( (\overline{B}_{geo,PoR,j,k}) \)

The calibrated series \( B_{cal,Y,j,k} \)  for a given geodetic mass balance rate k belonging to glacier j is calculated as the sum of the geodetic mass change rate \( \overline{B}_{geo,PoR,j,k} \) and the regional anomaly over the calibration period PoR.

The calibration period corresponds to the period of the geodetic mass balance observation k. Only geodetic observation larger than 5 years are considered for calibration due to the large uncertainties related to the density conversion factor over short period of times (Huss, 2013).

Figure 10: Example glacier j = Hintereisferner (Hf), located in Central Europe (RGI region 11, CEU). Calibration of the Hintereisferner glacier annual spatial anomaly ( \( \beta_{Y,spt,Hf} \) ) over all the Hintereisferner glacier geodetic mass balance observations available from FoG. Red and blue lines represent the geodetic mass balance rates ( \( \overline{B}_{geo,PoR,Hf,k} \) ). Grey lines correspond the calibrated series \( B_{cal,Y,Hf,k} \)  for each geodetic mass balance rate k. Each calibrated series has its own uncertainty \( \sigma_{cal,Y,Hf,k} \)  (a combination between \( \sigma_{\beta_{Y,spt,Hf}} \)   and \( \sigma_{geo,PoR,Hf,k} \) , not represented in the figure). Note that none of the series are calibrated over geodetic mass balance rates with a period of record shorter or equal to 5 years.

The calibrated series uncertainty \( \sigma_{cal,Y,j,k} \)

results as the combination of two independent errors:  the uncertainty inherent to the multi-annual geodetic mass balance rate \( \sigma_{geo,PoR,j,k} \)  and the glacier’s annual spatial anomaly uncertainty \( \sigma_{\beta_{Y,spt,j}} \) . These two errors are combined according to the law of random error propagation as follows:

3.2.3. STEP 3: Observationally calibrated annual mass balance

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

The observational calibrated annual mass balance (B_OC,Y,j)  is calculated as the weighted mean of all available calibrated series available for glacier j (B_cal,j,k)  (i.e. calibrated to each individual geodetic mass balance observation k with PoR longer than 5 year)

Where, \( W_{\sigma_{geo,PoR,j,k}} = \frac{1}{\sigma_{geo,PoR,j,k}} \) Corresponds to the weight relative to the geodetic mass balance uncertainty, i.e. calibrated series are weighted to the inverse ratio of the geodetic rate uncertainty.

And,  \( W_t = \left( \frac{1}{t_Y} \right)^{0.5} \)

Corresponds to the weight relative to the temporal distance to the geodetic rate PoR, i.e. Calibrated series are weighted to the time distance t from the PoR in number of years, y0 and y1 are the initial and end year of the PoR, respectively.

The observationally calibrated annual mass balance uncertainty \( \sigma_{OC,Y,j} \) for glacier j results from two independent sources of error: the variability of the calibrated series  \( \sigma_{cal_{var},Y,k} \)  and the mean of the individual calibrated series uncertainties \( \sigma_{cal_{\Sigma},Y,i} \) . These two errors are combined according to the law of random error propagation as follows:

Where,  \( \sigma_{cal_{mean},Y,j} = \frac{1}{N} \sum_{i=1}^N \sigma_{cal,Y,j,k} \) Corresponds to the arithmetic average of the N individual calibrated series uncertainties available for glacier j. This uncertainty propagates the error inherited from all calibrated series k available for glacier j ( \( \sigma_{cal,Y,j,k} \) ) (i.e. confidence intervals of the individual calibrated series).

And,  \( \sigma_{\beta_{var},Y,R} = 1.96 \ast Stdev \beta_{Y,i} \) Corresponds to the variability, at a 95% confidence interval, of the N calibrated series for glacier j (B_cal,j,k)

Figure 11: Example glacier j = Hintereisferner (Hf), located in Central Europe (RGI region 11, CEU). Grey lines correspond to the calibrated series \( B_{cal,Y,Hf,k} \)  for each geodetic mass balance rate k available for glacier Hintereisferner. The black line and the grey shadow area depict Hintereisferner glacier observationally calibrated mass balance series ( \( B_{OC,Y,Hf} \) ) and uncertainty ( \( \sigma_{OC,Y,Hf} \) ), respectively.

b. Observationally calibrated annual mass balance for all glaciers in the RGI6.0 with available geodetic observations

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).

3.2.4. 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.

For mass change purposes a glacier must be considered as a whole, all-in-one system which cannot be divided in parts. The best glaciologically correct solution to integrate glacier changes into a grid point is therefore to consider a glacier belonging to a grid point when its geometric centroid lies within the grid point. As naming convention, in the C3S product a grid point is named as the latitude, longitude at the middle of the grid.

a. Grid point specific and total mass balance series and uncertainties

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.

Grid point mass balance (specific), \( B_{grid_{OC},Y} \)

 The observational specific mass balance per grid point \( B_{grid_{OC},Y} \) is calculated as the area weighted mean of the observational calibrated mass balance \( B_{OC,Y,i_{obs}} \)  of the sample of observed glaciers (i_obs) belonging to a given grid point.

Where  \( S_{i_{obs}} \)  is the area of the individual glacier i and  \( S_{tot_{obs}} \)  is the total area of the observed glaciers.

Unobserved glaciers are assumed to be behave as the regional mean B_R,Y, calculated from the full sample of observed glacier N belonging to the same RGI 1^st order region. Their uncertainty \( \sigma_{OCE,Y,i_{unobs}} \)  is expected to be larger than that from the observed glacier sample.

Where,  \( B_{R,Y} = \frac{\sum_{i=1}^N B_{OC,Y,i_{obs}} \ast S_{i_{obs}}}{S_{tot_{obs}}} \)

The uncertainty for unobserved glaciers considers an additional uncertainty term \( \sigma_{R_f} \) , capturing the variability of two different regional interpolation methods of the observed sample: area weighted average \( B_{R,aw,Y} \)  and arithmetic average \( B_{R,mean,Y} \) , measured at a 95% confidence interval (1.96 times the standard deviation).

Where, \( B_{R,Y} = \frac{\sum_{i=1}^N B_{OC,i_{obs}}}{N} \) and \( \sigma_{R_f} = 1.96 \ast StdevB_{R,aw,Y},B_{R,mean,Y} \)

The grid point specific mass balance uncertainty \( \sigma_{B_{grid_{OC},Y}} \)  is then calculated as,

Where \( S_{i_{obs}} \)  is the area of the observed glacier i and  \( S_{grid} \) is the total area of the grid point to which the glacier i belongs. \( S_{grid,i_{obs}} =S_{grid,Y} - S_{grid,i_{obs}} \) , and N is the number of observed glaciers within the point.

Similar to Zemp et al. 2019 we assume that the observed sample is correlated by number of 50 glaciers: 1/(N/50) (i.e. by division by number of independent elements), because  \( \sigma_{B_{grid_{OC},Y}} \) is not independent of the sample size: grids points with higher observation rates should have smaller uncertainties. 

Grid point total mass loss  \( \Delta M_{grid_{OC},Y} \)

The Regional mass loss \( \Delta M_{grid_{OC},Y} \) is obtained by multiplying the grid point specific mass balance \( B_{grid_{OC},Y} \) by the grid point area  \( S_{grid,Y} \) and assuming an area change rate  \( \Delta S_{grid,Y} \) (obtained from Zemp et al. (2019)).

Grid point mass loss uncertainty \( \sigma_{\Delta M_{grid_{OC},Y}} \) is then obtained from the combination of three independent errors: The error relative to the specific regional mass balance \( \sigma_{B_{grid_{OC},Y}} \) , the error relative to the grid point area \( S_{grid,Y} \)  and the error relative to the area change rate \( \sigma_{\Delta S_{grid,Y}} \) . These three errors are combined according to the law of random error propagation.

Where \( \frac{\sigma_{S_{grid,Y}}}{S_{grid,Y}} \) = 5% (Paul et al., 2015) and \( \frac{\sigma_{\Delta S_{grid,Y}}}{\Delta S_{grid,Y}} \) is taken from Zemp et al. (2019)

4. 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

Figure 12: Globally distributed annual glacier changes and uncertainties (in Gt per year). Visualization example of the gridded netCDF 4.0 glacier change product (upper panel) and related uncertainties (bottom panel) for the hydrological year 2016/17, spatially distributed in a global regular grid of 0.5° (latitude/longitude). 


Figure 13: Annually resolved global glacier mass changes covering the hydrological years from 1975/76 to 2020/21. Visualization of the temporal component of distributed glacier product and relative uncertainty.

4.1. Known limitations for the distributed glacier product

4.1.1. 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).

Figure 14 (part 1): From individual glacier mass change to gridded mass change. (Top left panel) shows the hypothetical case of two different glaciers located next to each other. The glacier surface color code depicts the typical non-homogeneous spatial distribution of elevation changes experienced by a glacier that is gaining (Glacier A) or loosing (Glacier B) ice during a particular period of time, where blue corresponds to thickness gain and red to thickness loss. The mass change of the glacier for the given period is then calculated as an integrated value considering elevation changes occurring in all the glacier surface: glacier A gained a total of 0.4 Gt and glacier B lost a total of 2.4 Gt during the period. (Top right panel) This shows the real case of glaciers (purple outlines) and their centroids (pink points) in the RGI region Arctic Canada North under 0.5° grid cells. (Bottom panels – in part 2) These illustrate how the gridded mass balance integration looks for both the hypothetical and the real case.

Figure 14 (part 2): From individual glacier mass change to gridded mass change. (Top left panel – in part 1) shows the hypothetical case of two different glaciers located next to each other. The glacier surface color code depicts the typical non-homogeneous spatial distribution of elevation changes experienced by a glacier that is gaining (Glacier A) or loosing (Glacier B) ice during a particular period of time, where blue corresponds to thickness gain and red to thickness loss. The mass change of the glacier for the given period is then calculated as an integrated value considering elevation changes occurring in all the glacier surface: glacier A gained a total of 0.4 Gt and glacier B lost a total of 2.4 Gt during the period. (Top right panel – in part 1) This shows the real case of glaciers (purple outlines) and their centroids (pink points) in the RGI region Arctic Canada North under 0.5° grid cells. (Bottom panels) These illustrate how the gridded mass balance integration looks for both the hypothetical and the real case.

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.

4.1.2. 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.

Abermann, J., Fischer, A., Lambrecht, A., and Geist, T. (2010). On the potential of very high-resolution repeat DEMs in glacial and periglacial environments. The Cryosphere 4, 53–65. doi: 10.5194/tc-4-53-2010.

Berthier, E., Arnaud, Y., Baratoux, D., Vincent, C., and Rémy, F. (2004). Recent rapid thinning of the “Mer de Glace” glacier derived from satellite optical images. Geophys. Res. Lett. 31, L17401. doi: 10.1029/2004GL020706.

Berthier, E., Schiefer, E., Clarke, G. K. C., Menounos, B., and Rémy, F. (2010). Contribution of Alaskan glaciers to sea-level rise derived from satellite imagery. Nature Geoscience 3, 92–95. doi: 10.1038/ngeo737.

Berthier, E., Vincent, C., Magnússon, E., Gunnlaugsson, Á. Þ., Pitte, P., Le Meur, E., et al. (2014). Glacier topography and elevation changes derived from Pléiades sub-meter stereo images. The Cryosphere 8, 2275–2291. doi: 10.5194/tc-8-2275-2014.

Berthier, E., Belart, J., Floriciou, D., Gardner, A.S., Gourmelen, N., Hugonnet, R., Jakob, L., Kääb, A., Krieger, L., Palsson, F., Paul, F., Treichler, D., Wouters, B., and Zemp, M. (in review): Measuring glacier mass changes from space - a review. Reports on Progress in Physics. 

Braun, M. H., Malz, P., Sommer, C., Farías-Barahona, D., Sauter, T., Casassa, G., et al. (2019). Constraining glacier elevation and mass changes in South America. Nature Climate Change 9, 130. doi: 10.1038/s41558-018-0375-7.

Brun, F., Berthier, E., Wagnon, P., Kääb, A., and Treichler, D. (2017). A spatially resolved estimate of High Mountain Asia glacier mass balances from 2000 to 2016. Nature Geoscience 10, 668–673. doi: 10.1038/ngeo2999.

Cogley, J. G., and Adams, W. P. (1998). Mass balance of glaciers other than the ice sheets. J. of Glaciology 44, 315–325. doi: 10.3189/S0022143000002641.

Cogley, J. G., Hock, R., Rasmussen, L. A., Arendt, A. A., Bauder, A., Braithwaite, R. J., et al. (2011). Glossary of Glacier Mass Balance and Related Terms. IHP-VII Technical Documents in Hydrilogy No. 86. IACS Contribution No. 2 UNESCO-IHP, Paris.

Dehecq, A., Gardner, A. S., Alexandrov, O., McMichael, S., Hugonnet, R., Shean, D., et al. (2020). Automated Processing of Declassified KH-9 Hexagon Satellite Images for Global Elevation Change Analysis Since the 1970s. Frontiers in Earth Science 8. doi: 10.3389/feart.2020.566802.

Dussaillant, I., Berthier, E., Brun, F., Masiokas, M., Hugonnet, R., Favier, V., et al. (2019). Two decades of glacier mass loss along the Andes. Nat. Geosci. 12, 802–808. doi: 10.1038/s41561-019-0432-5.

Echelmeyer, Κ. A., Harrison, W. D., Larsen, C. F., Sapiano, J., E, M. J., Mallie, J. D., et al. (1996). Airborne surface profiling of glaciers: a case-study in Alaska. Journal of Glaciology 42, 538–547. doi: 10.3189/S002214300000352X.

Farr, T. G., Rosen, P. A., Caro, E., Crippen, R., Duren, R., Hensley, S., et al. (2007). The Shuttle Radar Topography Mission. Rev. Geophys. 45, RG2004. doi: 10.1029/2005RG000183.

Finsterwalder, R. (1954). Photogrammetry and Glacier Research with Special Reference to Glacier Retreat in the Eastern Alps *. Journal of Glaciology 2, 306–315. doi: 10.3189/S0022143000025119.

Girod, L., Nuth, C., Kääb, A., McNabb, R. W., and Galland, O. (2017). MMASTER: Improved ASTER DEMs for Elevation Change Monitoring. Remote Sensing 9, 704. doi: 10.3390/rs9070704.

GTN-G (2017). GTN-G Glacier Regions. doi: 10.5904/gtng-glacreg-2017-07.

Hirano, A., Welch, R., and Lang, H. (2003). Mapping from ASTER stereo image data: DEM validation and accuracy assessment. ISPRS Journal of Photogrammetry and Remote Sensing 57, 356–370. doi: 10.1016/S0924-2716(02)00164-8.

Howat, I. M., Porter, C., Smith, B. E., Noh, M.-J., and Morin, P. (2019). The Reference Elevation Model of Antarctica. The Cryosphere 13, 665–674. doi: 10.5194/tc-13-665-2019.

Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., et al. (2021). Accelerated global glacier mass loss in the early twenty-first century. Nature 592, 726–731. doi: 10.1038/s41586-021-03436-z.

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

IPCC (2013). Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. , eds. StockerT.F., D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung, et al. Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press.

Joerg, P. C., and Zemp, M. (2014). Evaluating Volumetric Glacier Change Methods Using Airborne Laser Scanning Data. Geografiska Annaler: Series A, Physical Geography 96, 135–145. doi: 10.1111/geoa.12036.

Kääb, A. (2002). Monitoring high-mountain terrain deformation from repeated air- and spaceborne optical data: examples using digital aerial imagery and ASTER data. ISPRS Journal of Photogrammetry and Remote Sensing 57, 39–52. doi: 10.1016/S0924-2716(02)00114-4.

Kaab, A. (2008). Glacier Volume Changes Using ASTER Satellite Stereo and ICESat GLAS Laser Altimetry. A Test Study on EdgeØya, Eastern Svalbard. IEEE Transactions on Geoscience and Remote Sensing 46, 2823–2830. doi: 10.1109/TGRS.2008.2000627.

Kargel, J. S., Leonard, G. J., Bishop, M. P., Kääb, A., and Raup, B. H. (2014). “Digital Terrain Modeling and Glacier Topographic Characterization,” in Global Land Ice Measurements from Space Springer-Praxis., 113–144.

Kaser, G., Fountain, A., and Jansson, P. (2003). A manual for monitoring the mass balance of mountain glaciers by. IHPVI Technical documents in Hydrology 2003, 135.

Korona, J., Berthier, E., Bernard, M., Rémy, F., and Thouvenot, E. (2009). SPIRIT. SPOT 5 stereoscopic survey of Polar Ice: Reference Images and Topographies during the fourth International Polar Year (2007–2009). ISPRS Journal of Photogrammetry and Remote Sensing 64, 204–212. doi: 10.1016/j.isprsjprs.2008.10.005.

Letréguilly, A., and Reynaud, L. (1990). Space and time distribution of glacier mass-balance in the Northern Hemisphere. Arctic and Alpine Research, 43–50.

Menounos, B., Hugonnet, R., Shean, D., Gardner, A., Howat, I., Berthier, E., et al. (2019). Heterogeneous Changes in Western North American Glaciers Linked to Decadal Variability in Zonal Wind Strength. Geophysical Research Letters 46, 200–209. doi: 10.1029/2018GL080942.

Østrem, G., and Brugman, M. M. (1991). Glacier mass-balance measurements: A manual for field and office work.

Paul, F., Bolch, T., Kääb, A., Nagler, T., Nuth, C., Scharrer, K., et al. (2015). The glaciers climate change initiative: Methods for creating glacier area, elevation change and velocity products. Remote Sensing of Environment 162, 408–426. doi: 10.1016/j.rse.2013.07.043.

Pfeffer, W. T., Arendt, A. A., Bliss, A., Bolch, T., Cogley, J. G., Gardner, A. S., et al. (2014). The Randolph Glacier Inventory: a globally complete inventory of glaciers. Journal of Glaciology 60, 537–552. doi: 10.3189/2014JoG13J176.

Porter, C., Morin, P., Howat, I., Noh, M.-J., Bates, B., Peterman, K., et al. (2018). ArcticDEM, Version 3. doi: 10.7910/DVN/OHHUKH.

Rabus, B., Eineder, M., Roth, A., and Bamler, R. (2003). The shuttle radar topography mission—a new class of digital elevation models acquired by spaceborne radar. ISPRS Journal of Photogrammetry and Remote Sensing 57, 241–262. doi: 10.1016/S0924-2716(02)00124-7.

Raup, B. H., Kieffer, H. H., Hare, T. M., and Kargel, J. S. (2000). Generation of data acquisition requests for the ASTER satellite instrument for monitoring a globally distributed target: glaciers. IEEE Transactions on Geoscience and Remote Sensing 38, 8. doi: 10.1109/36.841989.

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.

Rignot, E., Rivera, A., and Casassa, G. (2003). Contribution of the Patagonia Icefields of South America to sea level rise. Science 302, 434–437. doi: 10.1126/science.1087393.

Rizzoli, P., Martone, M., Gonzalez, C., Wecklich, C., Borla Tridon, D., Bräutigam, B., et al. (2017). Generation and performance assessment of the global TanDEM-X digital elevation model. ISPRS Journal of Photogrammetry and Remote Sensing 132, 119–139. doi: 10.1016/j.isprsjprs.2017.08.008.

Shean, D. E., Bhushan, S., Montesano, P., Rounce, D. R., Arendt, A., and Osmanoglu, B. (2020). A Systematic, Regional Assessment of High Mountain Asia Glacier Mass Balance. Frontiers in Earth Science 7. Available at: https://www.frontiersin.org/article/10.3389/feart.2019.00363 [Accessed May 30, 2022].

Surazakov, A., and Aizen, V. (2010). Positional Accuracy Evaluation of Declassified Hexagon KH-9 Mapping Camera Imagery. Photogrammetric Engineering & Remote Sensing 76, 603–608. doi: 10.14358/PERS.76.5.603.

Thibert, E., Blanc, R., Vincent, C., and Eckert, N. (2008). Glaciological and volumetric mass-balance measurements: error analysis over 51 years for Glacier de Sarennes, French Alps. Journal of Glaciology 54, 522–532. doi: 10.3189/002214308785837093.

Wessel, B., Huber, M., Wohlfart, C., Marschalk, U., Kosmann, D., and Roth, A. (2018). Accuracy assessment of the global TanDEM-X Digital Elevation Model with GPS data. ISPRS Journal of Photogrammetry and Remote Sensing 139, 171–182. doi: 10.1016/j.isprsjprs.2018.02.017.

WGMS (2021). Fluctuations of Glaciers Database. doi: 10.5904/wgms-fog-2021-05.

WGMS (2022). Fluctuations of Glaciers Database. doi: 10.5904/wgms-fog-2022-09.

Zemp, M., Frey, H., Gärtner-Roer, I., Nussbaumer, S. U., Hoelzle, M., Paul, F., et al. (2015). Historically unprecedented global glacier decline in the early 21st century. Journal of Glaciology 61, 745–762. doi: 10.3189/2015JoG15J017.

Zemp, M., Huss, M., Eckert, N., Thibert, E., Paul, F., Nussbaumer, S. U., et al. (2020). Brief communication: Ad hoc estimation of glacier contributions to sea-level rise from the latest glaciological observations. The Cryosphere 14, 1043–1050. doi: 10.3929/ethz-b-000408094.

Zemp, M., Huss, M., Thibert, E., Eckert, N., McNabb, R., Huber, J., et al. (2019). Global glacier mass changes and their contributions to sea-level rise from 1961 to 2016. Nature 568, 382. doi: 10.1038/s41586-019-1071-0.

Zemp, M., Thibert, E., Huss, M., Stumm, D., Rolstad Denby, C., Nuth, C., et al. (2013). Reanalysing glacier mass balance measurement series. The Cryosphere 7, 1227–1245. doi: 10.5194/tc-7-1227-2013.

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