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

Issued by: UZH / Inés Dussaillant, Michael Zemp

Date: 06/03/2024

Ref: C3S2_312a_Lot4.WP2-FDDP-GL-v2_202312_MC_ATBD-v5_i1.1

Official reference number service contract: 2021/C3S2_312a_Lot4_EODC/SC1Contributors
University of Zurich
J. Bannwart
I. Dussaillant
F. Paul
M. Zemp

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History of modifications

List of datasets covered by this document

Related documents 

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rd rd

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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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 2021/22. An overview of the product and its known limitations is available in Section 4.  

We highlight in this document the improvements and updates applied to the glacier mass change dataset product version WGMS-FOG-2023-09 and algorithm with respect to the previous glacier mass change product version WGMS-FOG-2022-09, released in December 2022:

• Data checks and quality improvements of WGMS-FOG-2023-09 database with respect to previous WGMS-FOG-2022-09 database
• Reduced glacier mass change uncertainties: The leave-one-out cross validation analysis results for the previous glacier change product version WGMS-FOG-2022-09 (RD5), shows that our uncertainty assessment using the standard deviation as a measure of the error was too conservative. These results justify the change to the use of the standard error as a measure of the uncertainties. This allows, at the same time, to i) reduce uncertainties and (ii) produce more realistic uncertainties by accounting for the number of observations (i.e. years with less observations get larger errors than years having a larger observation sample). See changes on the algorithm in section 3.2 of this document.
• Addition of three new variables to the .nc4 files: i) Gridded glacier area in square kilometres (km²), (ii) gridded glacier mass change in meters of water equivalent (m w.e.), and (iii) gridded glacier mass change uncertainties in m w.e.. Users are now provided with the glacier area considered per grid point and per year for transformations between Gt and m w.e. (the unit that is most used in Glaciological applications), plus they have a direct value of mass changes and relative uncertainties in both Gt and m w.e..
• Addition of global attributes to the .nc files: "dataset_limitations", "dataset improvements", "comments" explaining issues and referring to documentation.referring to documentation.

Table 1: New New global attributes in glacier product file .ncnc 

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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. 

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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).

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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 (blue points) and snow pits in the accumulation zone (grey rectangles). These point measurements are interpolated to estimate the glacier-wide mass changes (left figure). Blue shadings represent glacier surfaces; red polygon lines delineate individual glacier outlines. The orange line represents the equilibrium line, beneath is the ablation zone and above the accumulation zone of the observed glacier. Red shadings represent ice loss in the ablation zone which is larger (redder) at lower elevations until 0 at the equilibrium line.

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ablation zone which is larger (redder) at lower elevations until 0 at the equilibrium line.

Glacier elevation changes from the geodetic method

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, 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

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

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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) are combined with uncertainty estimates based on a statistical assessment of elevation differencing over stable terrain (purple zones in left figure). Blue shadings represent glacier surfaces; red polygon lines delineate individual glacier outlines. The orange line represents the equilibrium line, beneath is the ablation zone and above the accumulation zone of the observed glacier. Red shadings represent ice loss in the ablation zone which is larger (redder) at lower elevations until 0 at the equilibrium line.

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 2) 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 2.

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

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 3 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 3: 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.

https://doi.org/10.5904/wgms-fog-2023-09^{Image Removed}

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To compute the distributed glacier mass change product, we require i)  glacier 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).

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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).

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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, 2023). 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 website⁷.

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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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 annual 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_i,Y) from glaciological observation sample (B_{i_glac,Y},)

Direct annual glaciological observations for a given glacier I during year Y, are reported to the FoG database with their relative uncertainties (

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B_{i\_glac,Y} \pm \sigma_{B_{i\_glac,Y}} \quad [3]

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}

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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_{i,Y}.

b. Annual spatial anomaly for glacier j (βY,_{j_spt,} j_Y) 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_{j_spt,Y}) is then calculated as the arithmetic average of the N individual spatially-selected glacier annual anomalies (β_i,Y) located nearby glacier j,

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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 samplesample 

(\sigma_{B_{i \_glac\_mean,Y}}),

and the variability of the individual spatially-selected annual glacier anomalies 

(\sigma_{\beta_{i \_var,Y}})

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

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\sigma_{B_{i \_glac\_mean,Y}} = \frac{1}{N} \sum_{i=1}^N \sigma_{B_{i \_glac,Y}}

, 

\sigma_{B_{i \_glac,Y}}

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\sigma_{\beta_{i \_var,Y}}=1.96*\frac{1}{\sqrt{n_Y}} \sum_{i=1}^{i=N} Stdev \beta_{Y,i}

Corresponds to the variability, at a 95% confidence interval: the standard deviation of the N individual spatially-selected annual glacier anomalies β_{iduring the common period, divided by the number of observations (nY) at the given year. This allows years with less observations getting larger errors than years having a larger observation sample..}

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_{i,Yused to calculate Hintereisferner annual spatial anomaly (βHf,spt,Y) and uncertainty (σβHf}

(\sigma_{\beta_{Hf,spt,Y}})

 (black line and shaded grey at 95% CI, respectively) for the period 1950 to 2021.

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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}_{k\_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}_{k\_geo,PoR,j,k})

a given elevation change rate observation k belonging to glacier j over a Period or Record PoR 

(\overline{dh}_{k,PoR,j,k}),

needs to be transformed to specific mass change rate (m w.e., meters water equivalent) by applying a density conversion factor 

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\overline{B}_{k\_geo,PoR,j,k} = \overline{dh}_{k,PoR,j,k} \cdot f_{\rho} \quad [7]

The relative geodetic mass balance rate uncertainty

(\sigma_{B_{k\_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}_{k,PoR,j,k}}

and the uncertainty related to the density conversion factor 

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

\sigma_{B_{k\_geo,PoR,j,k}} = |\overline{B}_{k\_geo,PoR,j,k}| \sqrt{ \left( \frac{\sigma_{\overline{dh}_{k,PoR,j,k}}}{\overline{dh}_{k,PoR,j,k}} \right)^2 + \left( \frac{\sigma_{\rho}}{f_{\rho}} \right)^2} \quad [8]

b. Calibrated series 

(B_{k\_cal,j,k})

by calibrating the annual spatial anomaly

(\beta_{Y,j\_spt,jY})

over the glacier's geodetic mass balance rates sample

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

The calibrated series

B_{k\_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}_{k\_geo,PoR,j,k}

and the regional anomaly over the calibration period PoR.

B_{k\_cal,Y,j,k} = \overline{B}_{k\_geo,PoR,j,k} + (\beta_{Y,j\_spt,jY} - \overline{\beta}_{PoR,j\_spt,jPoR}) \quad [9]

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).).

Image Added

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,Hf\_spt,HfY}

) over all the Hintereisferner glacier geodetic mass balance observations available from FoG. Red and blue lines represent the geodetic mass balance rates (

\overline{B}_{k\_geo,PoR,Hf,k}

). Grey lines correspond the calibrated series

B_{k\_cal,Y,Hf,k}

 for each geodetic mass balance rate k. Each calibrated series has its own uncertainty

\sigma_{B_{k\_cal,Y,Hf,k}}

 (a combination between

\sigma_{\beta_{Y,Hf\_spt,HfY}}

  and

\sigma_{B_{k\_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_{B_{k\_cal,Y,j,k}}

results as the combination of two independent errors:  the uncertainty inherent to the multi-annual geodetic mass balance rate

...

\sigma_{\beta_{Y,j\_spt,jY}}

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

\sigma_{B_{k\_cal,Y,j,k}} = \sqrt{(\sigma_{B_{k\_geo,PoR,j,k}})^2 + (\sigma_{\beta_{Y,j\_spt,jY}})^2} \quad [10]

STEP 3: Observationally calibrated annual mass balance

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B_{j \_OCB,Y} = \frac{\sum_{j=1}^N^{j=N} B_{k \_cal,Y,j} \ast W_{\sigma_{B_{k \_geo,PoR,j}}} \ast W_t}{N} \quad [11]

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\sigma_{B_{k \_var,Y,j}} = 1.96 \ast \frac{1}{\sqrt{n_Y}}\sum_{k=1}^{k} Stdev B_{k \_cal,Y,j}

Corresponds to the standard error, at a 95% confidence interval:the standard deviationof the k individual calibrated series B_{k_cal,Y,j} belonging to glacier j divided by the number of calibrated series (n_Y) at the given year.

Figure 11: Example j = glacier Hintereisferner (Hf), located in Central Europe (RGI region 11, CEU). Grey lines correspond to the calibrated series B_{k_cal,Y,Hf}  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_{Hf_OCB,Y}) and uncertainty (σBHf

(\sigma_{B_{Hf \_OCB,Y}})

, respectively. 

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

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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.

...

B_{grid \_{OCB,Y}}

:

The observational specific mass balance per grid point

...

B_{j \_OCB_{obs},Y}

 of the sample (N_{grid_obs}) of observed glaciers (j_OCB_obs) belonging to a given grid point.

B_{grid \_{OCB,Y}} = \frac{\sum_{j=1}^{j=N_{grid\_obs}} \frac{B_{j \_OCB_{obs},Y} \ast S_{j_{obs}}}{S_{obs}} \quad [13]

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Unobserved glaciers are assumed to be behave as the regional mean B_{R_Aw,Y}, calculated from the full sample of observed glacier N_{R_obs} belonging to the same RGI 1^st order region. Their uncertainty

\sigma_{B_{j \_OCB_{unobs},Y}}

 is expected to be larger than that from the observed glacier sample.

...

B_{R \_Aw,Y} = \sum_{j=1}^{j=N_{N_{R \_obs}}} (\frac{B_{j \_OCB_{obs},Y} \ast S_{j_{obs}}}{S_{obs}})

The uncertainty for unobserved glaciers considers an additional uncertainty term

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\sigma_{R_f} = 1.96 \ast StdevB_{R,\_aw,Y},B_{R \_mean,Y}

The grid point specific mass balance uncertainty

...

\sigma_{B_{grid \_OCB,Y}} = \sqrt{\frac{1}{N_{grid \_obs}/50}  \left( \sum_{j=1}^{j=N_{grid \_obs}} (\sigma_{B_{j \_OCB,_{obs},Y}} \ast \frac{S_{jobsj_{obs}}}{S_{grid}})^2 + (\sigma_{B_{j \_OCB,_{unobs},Y}} \ast \frac{S_{junobsj_{unobs}}}{S_{grid}})^2 \right)} \quad [16]

Where

S_{j_{jobsobs}}

 is the area of the observed glacier j and 

...

is the total area of the grid point to which the glacier j belongs:

S_{junobsj_{unobs}} =S_{grid} - S_{jobs}

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 

...

\Delta M_{grid \_OCB,Y}

:

The Regional mass loss

\Delta M_{grid \_OCB,Y}

...

For C3S2, we computed a gridded, annually resolved, global glacier mass change product 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 2021/22. It is based on the glaciological and geodetic time series from the FoG database version 2023-09 (WGMS, 2023) 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 change, glacier change uncertainty (in Gigatonnes per year) and glacier area (in km²) as variables; 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 4 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 4: Overview of C3S distributed glacier mass change product output data fields

Figure 12a12: Globally distributed annual glacier changes and uncertainties (in Gt per year). Visualization example of the gridded netCDF glacier change product (upper panel) and related uncertainties (bottom panel) for the hydrological year 2021/22, spatially distributed in a global regular grid of 0.5° (latitude/longitude).

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f13 f13

 


Figure 13b13: Globally distributed annual glacier changes and uncertainties (in m w.e. per year). Visualization example of the gridded netCDF glacier change product (upper panel) and related uncertainties (bottom panel) for the hydrological year 2021/22, spatially distributed in a global regular grid of 0.5° (latitude/longitude).

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f14 f14

Figure 14c14: Globally distributed annual glacier area (in km² per year). Visualization example of the gridded netCDF glacier area product for the hydrological year 2021/22, spatially distributed in a global regular grid of 0.5° (latitude/longitude).

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f15 f15

Figure 15: Annually resolved global glacier mass changes covering the hydrological years from 1975/76 to 2021/22. Visualization of the temporal component of distributed glacier product and relative uncertainty.

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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 17b 17 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 17b17, part 1left pannel), the grid point where the glacier centroid is located will represent the gridded value of mass gain by the full glacier (Figure 17b17, part 2right pannel) 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

...

17, right panel).

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Figure 16a16: From individual glacier mass change to gridded mass change. (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. (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.

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Figure 17b17: From From individual glacier mass change to gridded mass change. These illustrate how the gridded mass balance integration looks for both the hypothetical and the real case (see also Figure 14a14).

 
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 to this issue would require an increase in 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:

The global gridded annual glacier change product (version WGMS-FOG-2023-09) provides glacier changes for the hydrological years from 1975/76 to 2021/22. 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 to this issue would require an increase in the temporal resolution of the input data to monthly observations, which currently is not feasible. 

Hydrological year periods for the different grid-points:

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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 3021, 20222024].

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.

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