Hostname: page-component-77f85d65b8-9nbrm Total loading time: 0 Render date: 2026-03-28T13:34:01.904Z Has data issue: false hasContentIssue false
  • English
  • Français

What is the global glacier ice volume outside the ice sheets?

Published online by Cambridge University Press:  06 February 2023

Regine Hock Open the ORCID record for Regine Hock [Opens in a new window] ,
Fabien Maussion Open the ORCID record for Fabien Maussion [Opens in a new window] ,
Ben Marzeion  and
Sophie Nowicki
Regine Hock*
Affiliation:
Department of Geosciences, University of Oslo, Oslo, Norway Geophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska, USA
Fabien Maussion
Affiliation:
Department of Atmospheric and Cryospheric Sciences (ACINN), University of Innsbruck, Innsbruck, Austria
Ben Marzeion
Affiliation:
Institute of Geography and MARUM – Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany
Sophie Nowicki
Affiliation:
Department of Geology, University at Buffalo, Buffalo, USA
*
Author for correspondence: Regine Hock, E-mail: regineho@uio.no
Rights & Permissions [Opens in a new window]

Abstract

A recent study (Millan and others, 2022a, Nature Geoscience 15(2), 124–129) claims that ice volume contained in all glaciers outside the ice sheets and its potential contribution to sea level is 20% less than previously estimated. However, the apparent decrease is largely due to differences in choice of domain, as the study excludes 80% of the glacier area in the Antarctic periphery that was included in previous global glacier volume estimates. The issue highlights the difficulty in separating glaciers from the ice-sheet proper, especially in Antarctica, and the need for both the glacier and ice-sheet communities to develop standards and protocols to avoid double-counting in global ice volume and mass-change assessments and projections. Process-based inversion models have replaced earlier scaling methods, but large uncertainties in global glacier volume estimation remain due to the ill-posed nature of the inversion problem and poorly constrained parameters emphasizing the need for more direct ice thickness observations.

Keywords

Glacier mappingglacier mass balanceglacier volumeice-sheet mass balance

Information

Type
Letter
Information
Journal of Glaciology , Volume 69 , Issue 273 , February 2023 , pp. 204 - 210
Check for updates
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The International Glaciological Society

1. Introduction

Knowledge of total glacier ice volume outside the ice sheets in Antarctica and Greenland is important for a range of studies, such as the assessment of the world's freshwater resources or the potential contribution of glaciers to sea-level change (IPCC, Reference Pörtner, Roberts, Masson-Delmotte, Zhai, Tignor, Poloczanska, Mintenbeck, Alegria, Nicolai, Okem, Petzold, Rama and Weyer2019). However, direct observations of ice thickness based on, for example, ground-penetrating radar or boreholes, are scarce, available only for <5000 of the world's >200 000 glaciers (Pelto and others, Reference Pelto, Maussion, Menounos, Radić and Zeuner2020; Welty and others, Reference Welty2020), and satellites are currently not capable of measuring ice thickness of these glaciers. Thus, global ice volume is estimated indirectly from surrogate variables (see Table 1 for references). Earlier estimates were based on scaling methods, such as volume–area scaling (Bahr and others, Reference Bahr, Meier and Peckham1997). Although the validity of power-law scaling has been demonstrated by dimensional, directional and stretching analyses (Bahr and others, Reference Bahr, Pfeffer and Kaser2015), results characterize the average behavior over a population of glaciers rather than an accurate ice volume of individual glaciers. In the absence of a globally complete inventory, earlier estimates also had to be further upscaled to include all glaciers in a region (e.g. Radić and Hock, Reference Radić and Hock2010). When the globally complete Randolph Glacier Inventory (RGI) became available (Pfeffer and others, Reference Pfeffer2014) including individual glacier outlines mostly around year 2000, Huss and Farinotti (Reference Huss and Farinotti2012) were the first to use a process-based approach to invert the ice thickness distribution of every glacier based on principles of mass conservation and ice flow dynamics. Farinotti and others (Reference Farinotti2019) provided an updated, much refined global-scale ‘consensus’ estimate based on an ensemble of five ice thickness inversion models, which has widely been used in glacier studies (e.g. Watson and others, Reference Watson2020; Rounce and others, Reference Rounce2021).

Table 1. Summary of published estimates of area and ice volume, and associated sea-level equivalent (SLE) of all glaciers on Earth excluding the ice sheets. Estimates including and excluding the glaciers in the periphery of the Greenland and Antarctica ice sheet are given. Where reported, ocean area (A sea, 106 km2), ice density (ρ ice, kg m−3) and ocean water density (ρ w, kg m−3) used to convert ice volumes to SLE are given. Unless specified otherwise, SLE estimates do not account for the effect of ice below sea level already displacing ocean water. Three estimates (Huss and others, Reference Huss and Farinotti2012; Farinotti and others, Reference Farinotti2019; Millan and others, Reference Millan, Mouginot, Rabatel and Morlighem2022a) are based on thickness inversion using process-based models, while all other estimates are based on scaling methods.

a For studies based on the RGI, the area excluded is defined by RGI primary regions 19 (Antarctic and Subantarctic) and 15 (Greenland periphery). Where not provided in the reference, we computed uncertainties from the regional uncertainties of all RGI regions outside Greenland and Antarctica assuming regional errors either fully correlated (Huss and Farinotti, Reference Huss and Farinotti2012; Farinotti and others, Reference Farinotti2019; Millan and others, Reference Millan, Mouginot, Rabatel and Morlighem2022a, Reference Millan, Mouginot, Rabatel and Morlighem2022b) or independent (Radić and Hock, Reference Radić and Hock2010; Marzeion and others, Reference Marzeion, Jarosch and Hofer2012) consistent with each study's approach.

b Numbers include the corrections reported in Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022b).

c Global estimate excludes 80.3% of glacier area in RGI region 19 (Antarctic and Subantarctic) since these glaciers were considered to belong to the ice sheets.

d Estimates extracted for 2009 from transient mass-balance model run starting in 1901.

2. Have previous studies overestimated global glacier ice volume?

Recently, Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) presented a re-estimation of the global ice volume and its sea-level potential by inverting ice thickness for every glacier based on a novel regional scale (rather than glacier-by-glacier) 2-D inversion scheme. The inversion was driven by surface slope and newly derived, globally almost complete surface ice velocity maps for 2017 and 2018 with an unprecedented sampling resolution of 50 m. The authors conclude that the potential global glacier contribution to sea-level rise is 20% less than the previous estimate by Farinotti and others (Reference Farinotti2019).

However, we note that Millan and others' global estimate excludes large areas in the Antarctic periphery (RGI region 19 ‘Antarctic and Subantarctic’), which were previously included (Fig. 1). Thus, the two estimates are not directly comparable. In total, 106 701 km2 (80.3%) of 132 867 km2 of ice-covered area in this region were excluded by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) (see their Fig. S13), as these glaciers were considered to belong to the ice sheet. If these glacier areas were included, consistent with Farinotti and others (Reference Farinotti2019) and most other previous estimates (Table 1), the difference between these two latest global estimates is just 1 cm sea-level equivalent (SLE) or 4% (0.31 ± 0.10 m SLE by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) versus 0.32 ± 0.08 m SLE by Farinotti and others (Reference Farinotti2019)). Hence the apparent decrease in global glacier potential contribution to sea-level rise postulated in Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) is largely due to relabeling glaciers as ice sheet rather than pointing to an overestimation in the previous estimate, and thus simply a matter of accounting.

Fig. 1. Location of glaciers in the periphery of the (a) Greenland (RGI region 5) and (b) Antarctic ice sheet (RGI region 19) as defined by the RGI 6.0 (RGI Consortium, 2017). All outlines displayed in (b) are obtained from Bliss and others (Reference Bliss, Hock and Cogley2013). In Greenland only RGI glaciers with connectivity levels 0 and 1 (89 717 km2) have been considered in previous RGI-based ice volume estimates. In Antarctica the glaciers in the RGI that were excluded in Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a, M22) are shown in yellow. Subantarctic island glaciers outside the plotted domain cover 3476 km2 (2.6% of total area of 132 867 km2 in RGI 6.0 region 19).

In addition, the spatial coverage in Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) is not complete in several other regions (see their Table 1), but the regional volume estimates were not upscaled to account for the missing area. The regions with the largest percent volume differences compared to Farinotti and others (Reference Farinotti2019) (North Asia and Low Latitudes, Fig. 2a) are regions with low areal coverage of ice velocity data (63 and 82%, respectively). If volumes were compared over the same glacier area, the differences in these regions would change from −22 to −1% and from −27 to −15%, respectively (see the Supplementary material).

Fig. 2. Published estimates of glacier ice volume. (a) Regional estimates for the primary regions of the RGI 6.0 (RGI Consortium, 2017) sorted by the total glacier area. High Mountain Asia includes RGI regions 13–15. RGI regions 1 (Alaska) and 2 (Western Canada and USA) are combined following Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a). Estimates of sea-level equivalent (SLE) for (b) all glaciers globally and (c) all glaciers excluding the Antarctic and Greenland periphery (Table 1). Studies are sorted by publication year. (d) Global glacier volume as a function of the inventoried or estimated glacier area for the studies shown in (b), abbreviated by first letter of first author and year. The global volume and area estimate by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a)* excludes 80.3% of the area in the Antarctic periphery as defined by the RGI 6.0 (region 19, Fig. 1) and thus is considerably lower than their estimates when this area is included (Table 1). Note that their numbers include the corrections reported in Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022b). Uncertainties are shown where reported.

3. How to distinguish glaciers from the ice sheets?

However, the issue raises the broader question of how to distinguish ‘glaciers’ from the ice-sheet proper. Following IPCC (Reference Stocker, Qin, Plattner, Tignor, Allen, Boschung, Nauels, Xia, Bex and Midgley2013), in this context glaciers are defined as all glacier ice (including ice caps) distinct from the ice sheets. The RGI excludes the ice-sheet proper but it includes the glaciers in their periphery (Fig. 1). In Greenland, the RGI defines three connectivity levels (CL) differentiating entirely unconnected (CL = 0), dynamically weakly connected (CL = 1) and dynamically strongly connected glaciers (CL = 2) to the ice sheet following Rastner and others (Reference Rastner2012). Global glacier assessments (see summary in Hock and Huss, Reference Hock, Huss and Letcher2021) and projections (Hock and others, Reference Hock2019; Marzeion and others, Reference Marzeion2020; Rounce and others, Reference Rounce2023) have only included the glaciers with CL = 0 and 1 (in total 89 717 km2), but excluded those with CL = 2. Also Citterio and Åhlstrøm (Reference Citterio and Ahlstrøm2013) mapped the Greenland ice masses distinguishing ‘local glaciers and ice caps’ from the ice sheet for the mid-1980s (Citterio and Åhlstrøm, Reference Citterio and Ahlstrøm2013).

In Antarctica, the RGI includes only glaciers on the surrounding islands (132 867 km2) excluding ice rises and ice shelves, and any glaciers on the mainland (Fountain and others, Reference Fountain, Basagic and Niebuhr2016; Huber and others, Reference Huber, Cook, Paul and Zemp2017) based on Bliss and others (Reference Bliss, Hock and Cogley2013). Connectivity levels were not defined in this region since the island glaciers were considered separate from the continental ice sheet, although in many cases the ice sheet and island glaciers are connected by ice-sheet-fed ice shelves.

The question of distinguishing glaciers and ice sheets is not just an academic one, but has practical implications. Glaciers are much smaller in size than the ice sheets, often occupying complex mountain topography, and they are generally more sensitive to climate change (Oerlemans and Fortuin, Reference Oerlemans and Fortuin1992; Dyurgerov, Reference Dyurgerov2003; Hock and others, Reference Hock, De Woul, Radić and Dyurgerov2009). Hence, the types of suitable observing systems to assess, and models typically used to simulate large-scale mass changes are generally different for glaciers and ice sheets. Therefore, traditionally glaciers and ice sheets have been treated separately when estimating past (e.g. The IMBIE team, 2018; Hugonnet and others, Reference Hugonnet2021) and projecting future large-scale mass changes (Nowicki and others, Reference Nowicki2016, Reference Nowicki2020; Marzeion and others, Reference Marzeion2020). This separation also enables partitioning of global ice mass change. For example, Horwath and others (Reference Horwath2022) found that 45 ± 2% of the cryospheric mass input into the ocean between 1993 and 2016 originated from glacier mass loss with the remainder coming from the ice sheets.

Glacier and ice-sheet mass-change estimates need to be combined in global sea-level assessments, a central topic, for example, in Assessment Reports of the Intergovernmental Panel on Climate Change (IPCC; e.g. Oppenheimer and others, Reference Oppenheimer, Pörtner, Roberts, Masson-Delmotte, Zhai, Tignor, Poloczanska, Mintenbeck, Alegría, Nicolai, Okem, Petzold, Rama and Weyer2019). However, the separation between glaciers and ice sheets is ambiguous, and care must be taken to avoid double-counting or omissions in global assessments and projections. For example, ice-sheet mass-change assessments based on gravimetry measurements provided by the Gravity Recovery and Climate Experiment (GRACE; e.g. Groh and others, Reference Groh2019; Velicogna and others, Reference Velicogna2020) cannot distinguish unambiguously the glaciers in the ice-sheet periphery from the ice-sheet proper due to methodological limitations (e.g. signal leakage due to limited spatial resolution). In contrast, altimetry-based observations (The IMBIE Team, 2018) allow a clear separation of ice masses. However, which peripheral glaciers exactly are covered, varies among studies (e.g. Schröder and others, Reference Schröder2019; Hanna and others, Reference Hanna2020; Shepherd and others, Reference Shepherd2020; Simonsen and others, Reference Simonsen, Barletta, Colgan and Sørensen2021), hampering unambiguous merging with independent glacier estimates based on the RGI (e.g. Gardner and others, Reference Gardner2013; Hugonnet and others, Reference Hugonnet2021). Hansen and others (Reference Hansen2022) investigated how different ice masks defining the ice-covered area in Antarctica in regional climate models (Mottram and others, Reference Mottram2021) affect the modeled surface mass balance. Despite small differences in the total area (<3%), modeled surface mass balances differed substantially solely due to different ice mask definitions (up to 6% of the ensemble mean balance, which corresponds to the total Antarctic mass imbalance). This finding corroborates generally higher sensitivity of peripheral glaciers to climate change, and thus the need to assess and model these glaciers properly.

A similar problem arises for ice-sheet modeling studies. While recent global glacier projections compute every glacier in the Greenland and Antarctic periphery based on the RGI, and thus the domain is standardized and well-defined, this is not the case for ice-sheet modeling. Some ice-sheet projections include all or some glaciers in the periphery, while others restrict their simulations to the ice-sheet proper (Goelzer and others, Reference Goelzer2020; Seroussi and others, Reference Seroussi2020). Which domain is covered depends on many factors including input dataset, model grid discretization and model initialization procedure (see e.g. model characteristic tables in Goelzer and others, Reference Goelzer2020; Seroussi and others, Reference Seroussi2020). For example, the use of regular grids in some ice-sheet models hampers clear separation where irregularly shaped boundaries between glaciers and ice sheet occur, and the problem is aggravated for coarse grids. Also, long-term interglacial model spin-up may lead to different ice-covered areas than model initializations to present-day ice-sheet extent (Nowicki and others, Reference Nowicki2013a, Reference Nowicki2013b; Goelzer and others, Reference Goelzer2018; Seroussi and others, Reference Seroussi2019).

Hence, in contrast to the glacier modeling community, there is no adopted standard in the ice-sheet modeling community which part of the glacierized area in Greenland and Antarctica should be modeled, and thus targeted in model initialization to the present-day state. Consequently, a wide range of domains have been modeled. For example, in Greenland, modeled domains have ranged from a low estimate including only the main ice sheet (as defined by Rastner and others, Reference Rastner2012) to a high estimate including all peripheral glaciers (Morlighem and others, Reference Morlighem2017; see Fig. 2 in Goelzer and others, Reference Goelzer2020). To ensure that the multiple ice-sheet models were consistent in their definition of the Greenland ice sheet and to avoid double-counting in global sea-level projections, the Ice Sheet Model Intercomparison Project (ISMIP6, Nowicki and others, Reference Nowicki2016, Reference Nowicki2020) normalized ice-sheet mass change per gridcell by the area fraction of the glaciers in the RGI (Goelzer and others, Reference Goelzer2020).

In Antarctica, despite generally fair agreement between simulated and observed ice extents as defined by the Reference Elevation Model of Antarctica (REMA, Howat and others, Reference Howat, Porter, Smith, Noh and Morin2019), modeled present-day areal extents varied by 6% (13.6–14.5 × 106 km2) among the ISMIP6 Antarctica models (Seroussi and others, Reference Seroussi2020), which is more than six times the area of the peripheral glaciers (based on RGI 6.0). Unlike for Greenland, there was no attempt in ISMIP6 to correct for differences in simulated ice-covered area in the Antarctic multi-model ensemble or to avoid possible double-counting with projections by the Glacier Model Intercomparison Project (GlacierMIP; Hock and others, Reference Hock2019; Marzeion and others, Reference Marzeion2020). This decision was based on many factors, including the typically coarser ice-sheet grid used in Antarctic models, and the use of mask datasets that only distinguish between ocean, ice-free land, grounded ice (including glacier) and floating ice (see e.g. Morlighem and others, Reference Morlighem2020).

Due to the different treatment of peripheral glaciers in Greenland and Antarctica in ISMIP6, the IPCC's Sixth Assessment Reports (e.g. IPCC, Reference Pörtner, Roberts, Masson-Delmotte, Zhai, Tignor, Poloczanska, Mintenbeck, Alegria, Nicolai, Okem, Petzold, Rama and Weyer2019, Reference Masson-Delmotte, Zhai, Pirani, Connors, Péan, Berger, Caud, Chen, Goldfarb, Gomis, Huang, Leitzell, Lonnoy, Matthews, Maycock, Waterfield, Yelekçi, Yu and Zhou2021) distinguishes between peripheral glaciers in Greenland but not in Antarctica. While many glaciers in the Antarctic periphery, in particular larger ice caps, appear to be modeled by ISMIP6, it remains unclear in how far their sensitivity to climate change is captured properly by coarse-grid ice-sheet models instead of the glacier-by-glacier modeling approach adopted by GlacierMIP (Hock and others, Reference Hock2019; Marzeion and others, Reference Marzeion2020), and how important any omissions of peripheral glaciers on islands further away from the mainland are.

4. Other causes for discrepancies in global ice volume estimates

Apart from the issue of separating glaciers from the ice sheets, other inconsistencies and methodological issues can contribute to differences between the existing global and regional glacier ice volume estimates (Table 1). For example, ice volume estimates are often reported in SLE, but different approaches (and values for ocean area (Cogley and others, Reference Cogley2012) and ice and water densities) have been used to convert ice volume to SLE (Table 1). Earlier studies simply spread the water equivalent of the ice volume equally over the ocean area, while the most recent two studies account for the displacement of water by ice below sea level, although in different ways. The latter only became possible when estimates of the fraction of ice located below sea level (~15%; Farinotti and others, Reference Farinotti2019) became available. Farinotti and others (Reference Farinotti2019) subtracted the ice volume below sea level from their global ice volume estimate, while Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) adopted a slightly different approach and removed only the ice volume below flotation. The latter is more accurate since a small portion (~10%) of the ice below sea level would contribute to sea-level rise if melted.

In addition, ice volumes are rapidly changing in response to climate change, but it is currently impossible to assign a single date to the global glacier ice volume estimates. In particular, the most modern methods (Table 1) require a large array of observational datasets such as ice velocity fields, surface topography, surface slope and area to derive ice thickness, as well as ice thickness observations for calibration. However, available datasets refer to different years, sometimes decades apart, and dates also vary within a region for the same type of data.

Furthermore, ice thickness inversion models are sensitive to the assumptions on model parameters, in particular those related to ice flow, but ice thickness observations are currently too scarce and unevenly distributed between regions to constrain these parameters. The inversion models (Huss and Farinotti, Reference Huss and Farinotti2012; Farinotti and others, Reference Farinotti2019; Werder and others, Reference Werder, Huss, Paul, Dehecq and Farinotti2020; Jouvet and others, Reference Jouvet2022; Van Wyk de Vries and others, Reference Van Wyk de Vries, Carchipulla-Morales, Wickert and Minaya2022; Millan and others, Reference Millan, Mouginot, Rabatel and Morlighem2022a) are constrained by surface data as information on basal conditions is widely lacking. However, despite significant methodological advances, such as by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a), thickness inversions remain ill-posed problems (Bahr and others, Reference Bahr, Pfeffer and Kaser2015), and the ill-posed inversion can exponentially increase any errors due to poorly constrained parameters. In fact, due to ill-posed inversion errors, inversion methods have been found to have the same volume resolution as scaling methods (Bahr and others, Reference Bahr, Pfeffer and Kaser2015). In addition, the shallow-ice approximation adopted in the recent inversion techniques (Table 1) can further increase errors considerably (Bahr and others, Reference Bahr, Pfeffer and Kaser2015), since most of the world's glaciers have geometries and related aspect ratios that are not compatible with the shallow ice approximation. For these reasons, current ice thickness inversions are likely subject to large biases, and far more direct observations on ice thickness and basal boundary conditions from glaciers around the world are urgently needed to better constrain model parameters. Recent developments in airborne radar techniques provide new promising opportunities to increase the number of observations in remote regions (Pritchard and others, Reference Pritchard2020).

In addition, global ice volume estimation depends on the accuracy of glacier outlines in the underlying inventories. For example, Li and others (Reference Li2022) found differences in ice volume of 2–8% in the Tien Shan using two different inventories. The influence of the choice of digital elevation model appeared to be negligible at the regional scale. Another uncertainty is the volume contained in very small glaciers not included in the different glacier inventories used in previous studies. Bahr and Radić (Reference Bahr and Radić2012) showed that in some regions the omission of glaciers <0.01 km2 can lead to errors in regional ice volume in the order of 10% emphasizing the need for regionally complete inventories. The RGI applies a minimum size threshold of 0.01 km2. However, the actual threshold differs regionally and between versions since higher minimum thresholds have been imposed in some of the underlying inventories.

5. Conclusions

Overall, tremendous progress has been made in the last decade in our ability to determine regional and global glacier ice volume as physics-based inversion techniques are replacing empirical scaling methods, and glacier area data with unprecedented accuracy and coverage have become available through the globally complete RGI (RGI Consortium, 2017). However, large uncertainties remain, especially on regional and smaller scales due to the ill-posed nature of current inversion schemes with lack of information on basal conditions, reliance on shallow-ice assumptions and scarcity of ice thickness observations. Since glacier area is a strong prognostic variable for glacier volume, it is likely that future updated glacier inventories will also have an impact on volume estimates (Fig. 2d).

In Greenland and especially in Antarctica significant ambiguities remain with respect to how to separate glaciers from the ice sheets hampering direct comparability of results from different studies as highlighted by the incorrect claim by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022a) of considerably lower global glacier ice volume compared to Farinotti and others (Reference Farinotti2019; Table 1, Fig. 2). While objective separation may be elusive and may also vary depending on purpose or applied observational or modeling tools, care needs to be taken to guarantee direct comparability between studies. As alluded to in Goelzer and others (Reference Goelzer2020) and Hansen and others (Reference Hansen2022), there is an urgent need for a joint effort of the ice-sheet and glacier modeling community to develop standards for present-day ice masks for glacier and ice-sheet modeling, and protocols to avoid double-counting while also ensuring that glaciers in the ice-sheetś periphery are not omitted, and especially that their sensitivity to climate change is properly accounted for. While pertaining to both Greenland and Antarctica, these issues are most pressing in Antarctica, and ice masks and standards used in both communities should be revisited and reconciled.

Supplementary material

The Supplementary material for this article can be found at https://doi.org/10.1017/jog.2023.1.

Data

Data tables including glacier volumes recalculated from the ice thickness data set by Millan and others (2022a) and upscaled to the regional glacier area in the RGI 6.0 as well as code to generate the results and figures are available at https://doi.org/10.5281/zenodo.7492152 (Maussion and Hock, Reference Maussion and Hock2022).

Acknowledgments

R.H. was supported by NASA grant 80NSSC20K1296 and 80NSSC17K0566, and grant No. 324131 from the Research Council of Norway (RCN). F.M. was supported by the Austrian Science Fund FWF grant P30256. We thank Tad Pfeffer, David Bahr and an anonymous reviewer for valuable comments on the manuscript, and chief editor Hester Jiskoot for handling this paper. We also thank R. Millan for providing additional information for Table 1 and Figure 2 not available in their publication. Eric Petersen checked the language.

Author contributions

R.H. initiated the study, wrote the manuscript with edits from all co-authors and compiled Table 1 with input from F.M. F.M. and R.H. designed the figures, and F.M. generated them. F.M. computed the upscaled regional volume estimates. S.N. contributed with information and discussion of ice-sheet masks. All authors discussed the content and contributed to the clarity of the manuscript.

References

Bahr, DB, Meier, MF and Peckham, SD (1997) The physical basis of glacier volume-area scaling. Journal of Geophysical Research: Solid Earth 102(B9), 20355–20362. doi: 10.1029/97JB01696CrossRefGoogle Scholar
Bahr, DB, Pfeffer, WT and Kaser, G (2015) A review of volume-area scaling of glaciers. Reviews of Geophysics 53(1), 95–140. doi: 10.1002/2014RG000470CrossRefGoogle ScholarPubMed
Bahr, DB and Radić, V (2012) Significant contribution to total mass from very small glaciers. The Cryosphere 6(4), 763–770. doi: 10.5194/tc-6-763-2012CrossRefGoogle Scholar
Bliss, A, Hock, R and Cogley, JG (2013) A new inventory of mountain glaciers and ice caps for the Antarctic periphery. Annals of Glaciology 54(63), 191–199. doi: 10.3189/2013AoG63A377CrossRefGoogle Scholar
Citterio, M and Ahlstrøm, AP (2013) Brief Communication: The aerophotogrammetric map of Greenland ice masses. The Cryosphere 7, 445–449. doi: 10.5194/tc-7-445-2013CrossRefGoogle Scholar
Cogley, JG (2012) Area of the ocean. Marine Geodesy 35(4), 379–388. doi: 10.1080/01490419.2012.709476CrossRefGoogle Scholar
Dyurgerov, MB (2003) Mountain and subpolar glaciers show an increase in sensitivity to climate warming and intensification of the water cycle. Journal of Hydrology 282(1–4), 164–176. doi: 10.1016/S0022-1694(03)00254-3CrossRefGoogle Scholar
Dyurgerov, MB and Meier, MF (2005) Glaciers and the Changing Earth System: A 2004 Snapshot (Vol. 58). Boulder: Institute of Arctic and Alpine Research, University of Colorado.Google Scholar
Farinotti, D and 6 others (2019) A consensus estimate for the ice thickness distribution of all glaciers on earth. Nature Geoscience 12(3), 168–173. doi: 10.1038/s41561-019-0300-3CrossRefGoogle Scholar
Fountain, AG, Basagic, HJ and Niebuhr, S (2016) Glaciers in equilibrium, McMurdo Dry Valleys, Antarctica. Journal of Glaciology 62(235), 976–989. doi: 10.1017/jog.2016.86CrossRefGoogle Scholar
Gardner, AS and 10 others (2013) A reconciled estimate of glacier contributions to sea level rise: 2003 to 2009. Science 340(6134), 852–857. doi: 10.1126/science.1234532CrossRefGoogle ScholarPubMed
Goelzer, H and 30 others (2018) Design and results of the ice sheet model initialisation experiments initMIP-Greenland: an ISMIP6 intercomparison. The Cryosphere 12(4), 1433–1460. doi: 10.5194/tc-12-1433-2018CrossRefGoogle Scholar
Goelzer, H and 41 others (2020) The future sea-level contribution of the Greenland ice sheet: a multi-model ensemble study of ISMIP6. The Cryosphere 14(9), 3071–3096. doi: 10.5194/tc-14-3071-2020CrossRefGoogle Scholar
Grinsted, A (2013) An estimate of global glacier volume. The Cryosphere 7(1), 141–151. doi: 10.5194/tc-7-141-2013CrossRefGoogle Scholar
Groh, A and 10 others (2019) Evaluating GRACE mass change time series for the Antarctic and Greenland ice sheet – methods and results. Geosciences 9(10), 415. doi: 10.3390/geosciences9100415CrossRefGoogle Scholar
Hanna, E and 10 others (2020) Mass balance of the ice sheets and glaciers – progress since AR5 and challenges. Earth-Science Reviews 201, 102976. doi: 10.1016/j.earscirev.2019.102976CrossRefGoogle Scholar
Hansen, N and 8 others (2022) Brief Communication: Impact of common ice mask in surface mass balance estimates over the Antarctic ice sheet. The Cryosphere 16, 711–718. doi: 10.5194/tc-16-711-2022CrossRefGoogle Scholar
Hock, R and 7 others (2019) GlacierMIP – a model intercomparison of global-scale glacier mass-balance models and projections. Journal of Glaciology 65(251), 453–467. doi: 10.1017/jog.2019.22CrossRefGoogle Scholar
Hock, R, De Woul, M, Radić, V and Dyurgerov, M (2009) Mountain glaciers and ice caps around Antarctica make a large sea-level rise contribution. Geophysical Research Letters 36(7). doi: 10.1029/2008GL037020CrossRefGoogle Scholar
Hock, R and Huss, M (2021) Glaciers and climate change. In Letcher, T (ed.), Climate Change: Observed Impacts on Planet Earth, 3rd edn, Chapter 8. Amsterdam: Elsevier, pp. 157–176, ISBN: 978-0-12-821575-3. doi: 10.1016/B978-0-12-821575-3.00009-8CrossRefGoogle Scholar
Horwath, M and 10 others (2022) Global sea-level budget and ocean-mass budget, with a focus on advanced data products and uncertainty characterisation. Earth System Science Data 14(2), 411–447. doi: 10.5194/essd-14-411-2022CrossRefGoogle Scholar
Howat, IM, Porter, C, Smith, BE, Noh, MJ and Morin, P (2019) The reference elevation model of Antarctica. The Cryosphere 13(2), 665–674. doi: 10.5194/tc-13-665-2019CrossRefGoogle Scholar
Huber, J, Cook, AJ, Paul, F and Zemp, M (2017) A complete glacier inventory of the Antarctic Peninsula based on Landsat 7 images from 2000 to 2002 and other preexisting data sets. Earth System Science Data 9(1), 115–131. doi: 10.5194/essd-9-115-2017CrossRefGoogle Scholar
Hugonnet, R and 10 others (2021) Accelerated global glacier mass loss in the early twenty-first century. Nature 592(7856), 726–731. doi: 10.1038/s41586-021-03436-zCrossRefGoogle ScholarPubMed
Huss, M and Farinotti, D (2012) Distributed ice thickness and volume of all glaciers around the globe. Journal of Geophysical Research: Earth Surface 117(F4). doi: 10.1029/2012JF002523CrossRefGoogle Scholar
The IMBIE Team (2018) Mass balance of the Antarctic ice sheet from 1992 to 2017. Nature 558(7709), 219–222. doi: 10.1038/s41586-018-0179-yCrossRefGoogle Scholar
IPCC (2013) Climate change 2013: The physical science basis. In Stocker, TF, Qin, D, Plattner, G-K, Tignor, M, Allen, SK, Boschung, J, Nauels, A, Xia, Y, Bex, V and Midgley, PM (eds), Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, UK and New York, NY, USA: Cambridge University Press, 1535pp.Google Scholar
IPCC (2019) IPCC special report on the ocean and cryosphere in a changing climate. In Pörtner, H-O, Roberts, DC, Masson-Delmotte, V, Zhai, P, Tignor, M, Poloczanska, E, Mintenbeck, K, Alegria, A, Nicolai, M, Okem, A, Petzold, J, Rama, B and Weyer, NM (eds). Cambridge, UK and New York, NY, USA: Cambridge University Press, 755pp. doi: 10.1017/9781009157964CrossRefGoogle Scholar
IPCC (2021) Climate change 2021: The physical science basis. In Masson-Delmotte, V, Zhai, P, Pirani, A, Connors, SL, Péan, C, Berger, S, Caud, N, Chen, Y, Goldfarb, L, Gomis, MI, Huang, M, Leitzell, K, Lonnoy, E, Matthews, JBR, Maycock, TK, Waterfield, T, Yelekçi, O, Yu, R and Zhou, B (eds), Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, UK and New York, NY, USA: Cambridge University Press, 2391pp. doi: 10.1017/9781009157896Google Scholar
Jouvet, G (2022) Inversion of a Stokes glacier flow model emulated by deep learning. Journal of Glaciology. doi: 10.1017/jog.2022.41Google Scholar
Li, F and 6 others (2022) Influence of glacier inventories on ice thickness estimates and future glacier change projections in the Tian Shan range, Central Asia. Journal of Glaciology. doi: 10.1017/jog.2022.60Google Scholar
Marzeion, B and 10 others (2020) Partitioning the uncertainty of ensemble projections of global glacier mass change. Earth's Future 8(7), e2019EF001470. doi: 10.1029/2019EF001470CrossRefGoogle Scholar
Marzeion, B, Jarosch, AH and Hofer, M (2012) Past and future sea-level change from the surface mass balance of glaciers. The Cryosphere 6(6), 1295–1322. doi: 10.5194/tc-6-1295-2012CrossRefGoogle Scholar
Maussion, F and Hock, R (2022). fmaussion/global_glacier_volume_paper: v1.1 (v1.1) [Data set]. Zenodo. doi: 10.5281/zenodo.7492152CrossRefGoogle Scholar
Meier, MF and Bahr, DB (1996) Counting glaciers: use of scaling methods to estimate the number and size distribution of the glaciers of the world. In Colbeck, SC (ed.). Glaciers, ice sheets and volcanoes: a tribute to Mark F. Meier. U.S. Army Corps of Engineers Cold Regions Research & Engineering Laboratory, Special Report, 96(27), 89–94.Google Scholar
Millan, R, Mouginot, J, Rabatel, A and Morlighem, M. (2022a) Ice velocity and thickness of the world's glaciers. Nature Geoscience 15(2), 124–129. doi: 10.1038/s41561-021-00885-zCrossRefGoogle Scholar
Millan, R, Mouginot, J, Rabatel, A and Morlighem, M (2022b) Author correction: Ice velocity and thickness of the world's glaciers. Nature Geoscience 15, 124–129. doi: 10.1038/s41561-022-01106-xCrossRefGoogle Scholar
Morlighem, M and 31 others (2017) BedMachine v3: complete bed topography and ocean bathymetry mapping of Greenland from multibeam echo sounding combined with mass conservation. Geophysical Research Letters 44, 11,051–11,061. doi: 10.1002/2017GL074954CrossRefGoogle ScholarPubMed
Morlighem, M and 37 others (2020) Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nature Geoscience 13, 132–137. doi: 10.1038/s41561-019-0510-8CrossRefGoogle Scholar
Mottram, R and 16 others (2021) What is the surface mass balance of Antarctica? An intercomparison of regional climate model estimates. The Cryosphere 15, 3751–3784. doi: 10.5194/tc-15-3751-2021CrossRefGoogle Scholar
Nowicki, S and 30 others (2013a) Insights into spatial sensitivities of ice mass response to environmental change from the SeaRISE ice sheet modeling project I: Antarctica. Journal of Geophysical Research: Earth Surface 118(2), 1002–1024. doi: 10.1002/jgrf.20081CrossRefGoogle Scholar
Nowicki, S and 31 others (2013b) Insights into spatial sensitivities of ice mass response to environmental change from the SeaRISE ice sheet modeling project II: Greenland. Journal of Geophysical Research: Earth Surface 118(2), 1025–1044. doi: 10.1002/jgrf.20081CrossRefGoogle Scholar
Nowicki, S and 8 others (2016) Ice sheet model intercomparison project (ISMIP6) contribution to CMIP6. Geoscientific Model Development 9(12), 4521–4545. doi: 10.5194/gmd-9-4521-2016CrossRefGoogle ScholarPubMed
Nowicki, S and 29 others (2020) Experimental protocol for sea level projections from ISMIP6 stand-alone ice sheet models. The Cryosphere 14(7), 2331–2368. doi: 10.5194/tc-14-2331-2020CrossRefGoogle Scholar
Oerlemans, J and Fortuin, JPF (1992) Sensitivity of glaciers and small ice caps to greenhouse warming. Science 258(5079), 115–117. doi: 10.1126/science.258.5079.115CrossRefGoogle ScholarPubMed
Ohmura, A (2004) Cryosphere during the twentieth century. In Sparling, JY and Hawkesworth, CJ (eds), The State of the Planet: Frontiers and Challenges in Geophysics. Washington, DC: American Geophysical Union, pp. 239–257. doi: 10.1029/150GM19CrossRefGoogle Scholar
Oppenheimer, M and 14 others (2019) Sea level rise and implications for low-lying islands, coasts and communities. In Pörtner, H-O, Roberts, Dc, Masson-Delmotte, V, Zhai, P, Tignor, M, Poloczanska, E, Mintenbeck, K, Alegría, A, Nicolai, M, Okem, A, Petzold, J, Rama, B and Weyer, NM (eds), IPCC Special Report on the Ocean and Cryosphere in a Changing Climate. Cambridge, UK and New York, NY, USA: Cambridge University Press, pp. 321–445. doi: 10.1017/9781009157964.006Google Scholar
Pelto, BM, Maussion, F, Menounos, B, Radić, V and Zeuner, M (2020) Bias-corrected estimates of glacier thickness in the Columbia River Basin, Canada. Journal of Glaciology 66(260), 1051–1063. doi: 10.1017/jog.2020.75CrossRefGoogle Scholar
Pfeffer, WT and 10 others (2014) The Randolph Glacier Inventory: a globally complete inventory of glaciers. Journal of Glaciology 60(221), 537–552. doi: 10.3189/2014JoG13J176CrossRefGoogle Scholar
Pritchard, HD and 5 others (2020) Towards Bedmap Himalayas: development of an airborne ice-sounding radar for glacier thickness surveys in High-Mountain Asia. Annals of Glaciology 61(81), 35–45. doi: 10.1017/aog.2020.29CrossRefGoogle Scholar
Radić, V and 5 others (2014) Regional and global projections of twenty-first century glacier mass changes in response to climate scenarios from global climate models. Climate Dynamics 42(1), 37–58. doi: 10.1007/s00382-013-1719-7CrossRefGoogle Scholar
Radić, V and Hock, R (2010) Regional and global volumes of glaciers derived from statistical upscaling of glacier inventory data. Journal of Geophysical Research: Earth Surface 115(F1). doi: 10.1029/2009JF001373CrossRefGoogle Scholar
Raper, SC and Braithwaite, RJ (2005) The potential for sea level rise: new estimates from glacier and ice cap area and volume distributions. Geophysical Research Letters 32(5). doi: 10.1029/2004GL021981Google Scholar
Rastner, P and 5 others (2012) The first complete inventory of the local glaciers and ice caps on Greenland. The Cryosphere 6(6), 1483–1495. doi: 10.5194/tc-6-1483-2012CrossRefGoogle Scholar
RGI Consortium (2017) Randolph Glacier Inventory – A Dataset of Global Glacier Outlines, Version 6. NSIDC: National Snow and Ice Data Center, Boulder, Colorado USA. doi: 10.7265/4m1f-gd79CrossRefGoogle Scholar
Rounce, DR and 10 others (2021) Distributed global debris thickness estimates reveal debris significantly impacts glacier mass balance. Geophysical Research Letters 48(8), e2020GL091311.CrossRefGoogle ScholarPubMed
Rounce, DR and 12 others (2023) Global glacier change in the 21st century: Every tenth of a degree temperature increase matters. Science 379(6627), 78–83. doi: 10.1126/science.abo.1324CrossRefGoogle Scholar
Schröder, L and 5 others (2019) Four decades of Antarctic surface elevation changes from multi-mission satellite altimetry. The Cryosphere 13(2), 427–449.CrossRefGoogle Scholar
Seroussi, H and 38 others (2019) initMIP-Antarctica: an ice sheet model initialization experiment of ISMIP6. The Cryosphere 13(5), 1441–1471. doi: 10.5194/tc-13-1441-2019CrossRefGoogle Scholar
Seroussi, H and 45 others (2020) ISMIP6 Antarctica: a multi-model ensemble of the Antarctic ice sheet evolution over the 21st century. The Cryosphere 14(9), 3033–3070. doi: 10.5194/tc-14-3033-2020CrossRefGoogle Scholar
Shepherd, A and 88 others (2020) Mass balance of the Greenland ice sheet from 1992 to 2018. Nature 579(7798), 233–239. doi: 10.1038/s41586-019-1855-2Google Scholar
Simonsen, SB, Barletta, VR, Colgan, WT and Sørensen, LS (2021) Greenland ice sheet mass balance (1992–2020) from calibrated radar altimetry. Geophysical Research Letters 48(3), e2020GL091216. doi: 10.1029/2020GL091216CrossRefGoogle Scholar
Van Wyk de Vries, M, Carchipulla-Morales, D, Wickert, AD and Minaya, V (2022) Glacier thickness and ice volume of the Northern Andes. Scientific Data 9, 342. doi: 10.1038/s41597-022-01446-8CrossRefGoogle Scholar
Velicogna, I and 9 others (2020) Continuity of ice sheet mass loss in Greenland and Antarctica from the GRACE and GRACE follow-on missions. Geophysical Research Letters 47(8), e2020GL087291. doi: 10.1029/2020GL087291CrossRefGoogle Scholar
Watson, CS and 5 others (2020) Mass loss from calving in Himalayan proglacial lakes. Frontiers in Earth Science 7, 342. doi: 10.3389/feart.2019.00342CrossRefGoogle Scholar
Welty, E and 13 others (2020) Worldwide version-controlled database of glacier thickness observations, Earth System Scientific Data 12, 3039–3055. doi: 10.5194/essd-12-3039-2020CrossRefGoogle Scholar
Werder, MA, Huss, M, Paul, F, Dehecq, A and Farinotti, D (2020) A Bayesian ice thickness estimation model for large-scale applications. Journal of Glaciology 66(255), 137–152. doi: 10.1017/jog.2019.93CrossRefGoogle Scholar
Figure 0

Table 1. Summary of published estimates of area and ice volume, and associated sea-level equivalent (SLE) of all glaciers on Earth excluding the ice sheets. Estimates including and excluding the glaciers in the periphery of the Greenland and Antarctica ice sheet are given. Where reported, ocean area (Asea, 106 km2), ice density (ρice, kg m−3) and ocean water density (ρw, kg m−3) used to convert ice volumes to SLE are given. Unless specified otherwise, SLE estimates do not account for the effect of ice below sea level already displacing ocean water. Three estimates (Huss and others, 2012; Farinotti and others, 2019; Millan and others, 2022a) are based on thickness inversion using process-based models, while all other estimates are based on scaling methods.

Figure 1

Fig. 1. Location of glaciers in the periphery of the (a) Greenland (RGI region 5) and (b) Antarctic ice sheet (RGI region 19) as defined by the RGI 6.0 (RGI Consortium, 2017). All outlines displayed in (b) are obtained from Bliss and others (2013). In Greenland only RGI glaciers with connectivity levels 0 and 1 (89 717 km2) have been considered in previous RGI-based ice volume estimates. In Antarctica the glaciers in the RGI that were excluded in Millan and others (2022a, M22) are shown in yellow. Subantarctic island glaciers outside the plotted domain cover 3476 km2 (2.6% of total area of 132 867 km2 in RGI 6.0 region 19).

Figure 2

Fig. 2. Published estimates of glacier ice volume. (a) Regional estimates for the primary regions of the RGI 6.0 (RGI Consortium, 2017) sorted by the total glacier area. High Mountain Asia includes RGI regions 13–15. RGI regions 1 (Alaska) and 2 (Western Canada and USA) are combined following Millan and others (2022a). Estimates of sea-level equivalent (SLE) for (b) all glaciers globally and (c) all glaciers excluding the Antarctic and Greenland periphery (Table 1). Studies are sorted by publication year. (d) Global glacier volume as a function of the inventoried or estimated glacier area for the studies shown in (b), abbreviated by first letter of first author and year. The global volume and area estimate by Millan and others (2022a)* excludes 80.3% of the area in the Antarctic periphery as defined by the RGI 6.0 (region 19, Fig. 1) and thus is considerably lower than their estimates when this area is included (Table 1). Note that their numbers include the corrections reported in Millan and others (2022b). Uncertainties are shown where reported.

Supplementary material: PDF

Hock et al. supplementary material

Hock et al. supplementary material

Download Hock et al. supplementary material(PDF)
PDF 140.8 KB