The geodetic mass balance of a glacier corresponds to glacier-wide volume changes, converted to mass changes using density assumptions. It is typically calculated by differencing multi-temporal digital elevation models. In this study, we show how the annual geodetic mass balance of a glacier can be derived from uncrewed aerial vehicle (UAV) data. The presented workflow is applied to two small- to medium-sized glaciers in the Kyrgyz Tien Shan (Central Asia): Bordu glacier and Sary-Tor glacier. The obtained geodetic mass balance is compared with the glaciological mass balance derived from a network of ablation stakes and snow pits. A previously calibrated mass-balance model is used to correct for the difference in acquisition dates. The results show that the determined geodetic mass balance matches closely with the glaciological mass balance. Besides, for both glaciers the geodetic mass balance does not seem to be particularly sensitive to the assumptions regarding volume-to-mass conversion. Therefore, our results demonstrate that UAVs can serve as a valuable instrument to quantify the annual geodetic mass balance and to validate the glaciological mass balance. The conventional glaciological mass-balance estimation often relies on interpolation and extrapolation methods, whereas UAVs offer the potential for direct data acquisition over the entire glacier surface.

We use the apparent horizontal shift of an englacial tephra layer outcrop to calculate local glacier mass balance on Sléttjökull, a lobe of Mýrdalsjökull in Southern Iceland. For this approach, the dipping angle of the englacial tephra layer in the glacier upstream of the outcrop and the flow velocity of the ice need to be known. An earlier investigation was expanded by the application of ground-penetrating radar, detecting the depth of the tephra along tracks with a total length of 10 km. Interpolation between the tracks enables us to derive the dipping angle of the layer along several flow lines. Together with glacier surface velocities, determined from feature tracking, we are able to estimate the local surface mass balance from the horizontal displacement of the tephra outcrop using freely available satellite imagery without additional fieldwork. The earlier local balance series was extended to the period 2014/15 to 2019/20. Although the results for the individual profiles differ slightly from each other, they show the same temporal pattern and clear variations from year to year. The results are compared to traditional mass-balance data from Hofsjökull. The two series show a good agreement in their interannual variability.

Decadal-scale, high-resolution geodetic measurements of glacier thinning have transformed our understanding of glacier response to climate change. Annual glacier mass balance can be estimated using remote-sensing proxies like snow-line altitude. These methods require field data for calibration, which are not available for most glaciers. Here we propose a method that combines multiple remotely-sensed proxies to obtain robust estimates of the annual glacier-wide balance using only remotely-sensed decadal-scale geodetic mass balance for calibration. The method is tested on Chhota Shigri, Argentière and Saint-Sorlin glaciers in the Himalaya and the Alps between 2001 and 2020, using four remotely-sensed proxies – the snow-line altitude, the minimum summer albedo over the glacier and two statistics of normalised difference snow index over the off-glacier area around the ablation zone. The reconstructed mass balance compares favourably with the corresponding glaciological field data (correlation coefficient 0.81 − 0.90, p < 0.001; root mean squared error 0.38 − 0.43 m w.e. a−1). The method presented may be useful to study interannual variability in mass balance on glaciers where no field data are available.

Despite their importance for regional water resource planning and as indicators of climate change, records of in situ glacier mass balance remain short and spatially sparse in the Himalaya. Here, we present an updated series of in situ mass-balance measurements from Rikha Samba Glacier, Nepal, between 2011 and 2021. The updated in situ mass balance is −0.39 ± 0.32 m w.e. for this period. We use an energy-mass balance model to extend the annual mass-balance series back to 1974. The model is forced using daily meteorological variables from ERA5-Land reanalysis data that is linearly bias-corrected using observations from an automatic weather station situated near the glacier terminus. The modeled mass balance is consistent with the in situ mass-balance series measured 2011–2021 and with previous glaciological and geodetic estimates. The model results indicate a mass balance of −0.56 ± 0.27 m w.e. a−1 over the reconstruction period of 1974–2021, which is comparable to the mass losses experienced by other Himalayan glaciers during this time. An assessment of the sensitivity of the glacier mass balance to meteorological forcing suggests that a change in temperature of ±1 K has a stronger effect on the calculated mass balance compared to a ±20% change in either precipitation, or relative humidity, or solar radiation.

To get a better overview of atmosphere-driven mass changes at the 79N Glacier (Nioghalvfjerdsfjorden Glacier), the largest outlet glacier of the northeast Greenland ice stream, the surface mass balance (SMB) is modeled by linking the COupled Snowpack and Ice surface energy and mass-balance model in PYthon (COSIPY) with the output of a regional atmospheric model (Polar WRF) for the years 2014–2018. After a manual model optimization, the model produces reliable results when compared to observations in the region and to values from the literature. High spatial resolution (1 km) simulations reveal strong interannual variability of the SMB. Stronger surface melting increased the ablation and runoff in years with high mass loss (2016 and 2017) whereas in other years (2015 and 2018) melting and refreezing inside the snowpack dominated the mass balance (MB). A cooler regional climate with higher snowfall-driven accumulation, higher albedo and reduced surface melt in the ablation period of 2018 resulted in a positive SMB in 2018, however, the annual total MB remained negative. The results suggest a promising new dataset for gaining more insights into mass-balance processes and their contribution to the acceleration of glacier retreat in northeast Greenland.

Glacier mass-balance observations at seasonal resolution have been performed since 1914 at two sites on Claridenfirn, Switzerland. The measurements are the longest uninterrupted records of glacier mass balance worldwide. Here, we provide a complete re-analysis of the 106-year series (1914–2020), focusing on both point and glacier-wide mass balance. The approaches to evaluate and homogenize the direct observations are described in detail. Based on conservative assumptions, average uncertainties of $\pm$0.25 m w.e. are estimated for glacier-wide mass balances at the annual scale. It is demonstrated that long-term variations in mass balance are clearly driven by melting, whereas decadal changes in accumulation are uncorrelated with mass balance and can only be relevant in short periods. Mass change of Claridenfirn is impacted by dry calving at a frontal ice cliff. Considerations of ice volume flux at a cross-profile reveal long-term variations in frontal ice loss accounting for $\sim$9% of total annual ablation on average. The effect of changes in frontal ablation mostly explains $\lt$10% of the mass-balance difference relative to the period 1960–1990, but accounts for $\sim$20% in 2010–2020. Glacier mass changes are discussed in the context of observations throughout the European Alps indicating that Claridenfirn is regionally representative.

Photogrammetric reconstructions of the Aldegondabreen glacier on Svalbard from 17 archival terrestrial oblique photographs taken in 1910 and 1911 reveal a past volume of 1373.7 ± 78.2 · 106 m3; almost five times greater than its volume in 2016. Comparisons to elevation data obtained from aerial and satellite imagery indicate a relatively unchanging volume loss rate of − 10.1 ± 1.6 · 106 m3 a−1 over the entire study period, while the rate of elevation change is increasing. At this rate of volume loss, the glacier may be almost non-existent within 30 years. If the changes of Aldegondabreen are regionally representative, it suggests that there was considerable ice loss over the entire 1900s for the low elevation glaciers of western Svalbard. The 1910/11 reconstruction was made from a few of the tens of thousands of archival terrestrial photographs from the early 1900s that cover most of Svalbard. Further analysis of this material would give insight into the recent history and future prospects of the archipelago's glaciers. Photogrammetric reconstructions of this kind of material require extensive manual processing to produce good results; for more extensive use of these archival imagery, a better processing workflow would be required.

The widespread occurrence of snow-ice formation on the pack ice plays a critical role in the mass balance of Antarctic sea ice. The stable isotope composition, ice texture and salinity of eight ice cores, obtained from the Amundsen Sea during the Oden Southern Ocean 2010/11 expedition from late December 2010 to January 2011, were investigated to illustrate the snow-ice growth process and its contribution to sea-ice development. Most previous research has utilized δ18O as an index tracer to determine the percentages of core length that contain meteoric water, i.e. snow ice. However, this standard practice of snow-ice identification might be biased due to normally low-resolution isotopic measurements and mixing/diffusion processes between the snow ice and underlying ice layers. Snow-ice contributions in these ice cores based instead on an updated isotope mixing model are also presented. Depth profiles of ice texture and salinity are described to serve as representations of the structures of these ice cores. Our isotope mixing model produced an average of 15.9% snow-ice contribution for pack ice in the Amundsen Sea, and meteoric water occupying 40% of snow-ice mass for all ice stations. These results are compared to previous investigations of snow-ice occurrence around Antarctica.

Glacial extent and mass balance are sensitive climate proxies providing solid information on past climatic conditions. However, series of annual mass-balance measurements of more than 60 years are scarce. To our knowledge, this is the first time the latewood density data (MXD) of the Swiss stone pine (Pinus cembra L.) have been used to reconstruct the summer mass balance (Bs) of an Alpine glacier. The MXD-based Bs well correlates with a Bs reconstruction based on the May to September temperature. Winter precipitation has been used as an independent proxy to infer the winter mass balance and to obtain an annual mass-balance (Bn) estimate dating back to the glaciological year 1811/12. The reconstructed MXD/precipitation-based Bn well correlates with the data both of the Careser and of other Alpine glaciers measured by the glaciological method. A number of critical issues should be considered in both proxies, including non-linear response of glacial mass balance to temperature, bedrock topography, ice thinning and fragmentation, MXD acquisition and standardization methods, and finally the ‘divergence problem’ responsible for the recently reduced sensitivity of the dendrochronological data. Nevertheless, our results highlight the possibility of performing MXD-based dendroglaciological reconstructions using this stable and reliable proxy.

Direct measurements of spatially distributed vertical strain within ice masses are scientifically valuable but challenging to acquire. We use manual marker tracking and automatic cross correlation between two repeat optical televiewer (OPTV) images of an ~100 m-long borehole at Derwael Ice Rise (DIR), Antarctica, to reconstruct discretised, vertical strain rate and velocity at millimetre resolution. The resulting profiles decay with depth, from −0.07 a−1 at the surface to ~−0.002 a−1 towards the base in strain and from −1.3 m a−1 at the surface to ~−0.5 m a−1 towards the base in velocity. Both profiles also show substantial local variability. Three coffee-can markers installed at different depths into adjacent boreholes record consistent strain rates and velocities, although averaged over longer depth ranges and subject to greater uncertainty. Measured strain-rate profiles generally compare closely with output from a 2-D ice-flow model, while the former additionally reveal substantial high-resolution variability. We conclude that repeat OPTV borehole logging represents an effective means of measuring distributed vertical strain at millimetre scale, revealing high-resolution variability along the uppermost ~100 m of DIR, Antarctica.

The quantification of snow transport, both in wind tunnels and the field, apply particle counting methods limited to punctual sampling of relatively small volumes. Particle counting can only capture horizontal mass fluxes, failing to measure snow erosion or deposition. Herein, we present a novel low-cost sensor tool, based on a Microsoft Kinect, adapted to capture snow surface changes during snow drifting at unprecedented spatial and temporal resolutions. In the wind tunnel setting of these experiments we observe a balance between erosion and deposition at low wind speeds, while erosion is dominant at higher wind speeds. Significant differences in power spectral densities of surface mass flux and horizontal particle mass flux are observed. We show that for the saltation-length-scale parameter λ = 1, the integrated particle flux can be used to estimate the total surface mass flux in the wind tunnel. This provides an important basis to interpret mass flux measurements in the field.

With the conclusion of the Last Glacial Maximum (LGM), about 20 000 years ago, ended the most recent long-lasting cold phase in Earth history. This last glacial advance left a strong observable imprint on the landscape, such as moraines, trimlines and other glacial geomorphic features. These features reflect the extent of former glaciers and ice caps, which in turn provides information on past temperature and precipitation conditions. Here we present an inverse approach to reconstruct the equilibrium line altitudes (E) from observed ice extents. The ice-flow model is developed solving the mass conservation equation using the shallow ice approximation and implemented using Graphical Processing Units (GPUs). We present the theoretical basis of the inversion method, which relies on a Tikhonov regularization, and demonstrate its ability to constrain spatial variations in mass balance with idealized and real glaciers.

Haxilegen Glacier No.51 (43.731°N, 84.391°E; CN5Y741C0051) is located in the Kuytun river basin, Erenharbirga range, eastern Tien Shan. This study presents the annual mass balance of Haxilegen Glacier No.51 for 7 hydrological years and uses a temperature-index and an accumulation model to reconstruct the annual mass balance from 1999 to 2015. The model is calibrated against annual altitudinal mass-balance measurements and then applied to the period with no measurements. We find an accumulated mass balance of −6.06 ± 0.88 m w.e.a−1 over the period of 16 hydrological years, with an average annual value of −0.32 ± 0.22 m w.e.a−1. The mean glacier-wide annual, summer and winter balances for 1999 to 2015 are −0.37, −0.54 and 0.16 ± 0.22 m w.e.a−1, respectively, with a high correlation coefficient (r = 0.95, p < 0.001) between annual balance and summer balance. The calculated mass-balance sensitivity of the glacier to temperature is −0.51 m w.e.a−1 °C−1 and to precipitation is 0.08 m w.e.a−1 for a 10% increase. The sensitivity of seasonal mass balance indicates that temperature during the melt season (May–August) and annual precipitation are the major contributors to mass-balance fluctuation.

The positive degree-day (PDD) model provides a particularly simple approach to estimate surface melt from land ice based solely on air temperature. Here, we use a climate and snow pack simulation of the Greenland ice sheet (Modèle Atmosphérique Régional, MAR) as a reference, to analyze this scheme in three realizations that incorporate the sub-monthly temperature variability differently: (i) by local values, (ii) by local values that systematically overestimate the dampened variability associated with intense melting or (iii) by one constant value. Local calibrations reveal that incorporating local temperature variability, particularly resolving the dampened variability of melt areas, renders model parameters more temperature-dependent. This indicates that the negative feedback between surface melt and temperature variability introduces a non-linearity into the temperature – melt relation. To assess the skill of the individual realizations, we hindcast melt rates from MAR temperatures for each realization. For this purpose, we globally calibrate Greenland-wide, constant parameters. Realization (i) exhibits shortcomings in the spatial representation of surface melt unless temperature-dependent instead of constant parameters are calibrated. The other realizations perform comparatively well with constant parametrizations. The skill of the PDD model primarily depends, however, on the consistent calibration rather than on the specific representation of variability.

The mass-balance of Muztag Ata No. 15 (MZ15) glacier in the eastern Pamir is reconstructed between 1980 and 2012 using an energy-based mass-balance model. The results show that this glacier has been characterized by obvious interannual mass-balance changes during 1980–2012 with a slightly positive mass balance during 1998–2012. Precipitation in the ablation season is a primary driver of these mass-balance fluctuations. Distinct changes in the mass-balance of MZ15 glacier between 1980–1997 and 1998–2012 are thought to be associated with changes in the regionally averaged meridional wind speed and corresponding precipitation in the ablation season. The negative and positive mass-balance phases during 1980–1997 and 1998–2012, respectively, were associated with northerly and southerly wind anomalies in the eastern Pamir and their corresponding decreasing and increasing precipitation. These changes in circulation appear to be linked to the mid-latitude climate. Finally, contrary to the variation of most glaciers on the Tibetan Plateau, glaciers in the Karakoram-western Kunlun-eastern Pamir appear to have retreated more slowly over the past 10 years than during the 1970s-2000. This contrasting trend may be caused by different changes in snowfall and different topography factors in different regions under warming and increased precipitation.

We present the glacier-wide summer surface mass balances determined by a detailed hydrological balance (sSMBhydro) and the quantification of the uncertainties of the calculations on the Argentière and Mer de Glace-Leschaux drainage basins, located in the upper Arve watershed (French Alps), over the period 1996–2004. The spatial distribution of precipitation within the study area was adjusted using in situ winter mass-balance measurements. The sSMBhydro performance was assessed via a comparison with the summer surface mass balances based on in situ glaciological observations (sSMBglacio). Our results show that the sSMBhydro has an uncertainty of ± 0.67 m w.e. a−1 at Argentière and ± 0.66 m w.e. a−1 at Mer de Glace-Leschaux. Estimates of the Argentière sSMBhydro values are in good agreement with the sSMBglacio values. These time series show almost the same interannual variability. From the marked difference between the sSMBhydro and sSMBglacio values for the Mer de Glace-Leschaux glacier, we suspect a significant role of groundwater fluxes in the hydrological balance. This study underlines the importance of taking into account the groundwater transfers to represent and predict the hydro-glaciological behaviour of a catchment.

Glaciers spanning large altitudinal ranges often experience different climatic regimes with elevation, creating challenges in acquiring mass-balance and climate observations that represent the entire glacier. We use mixed methods to reconstruct the 1991–2014 mass balance of the Kahiltna Glacier in Alaska, a large (503 km2) glacier with one of the greatest elevation ranges globally (264–6108 m a.s.l.). We calibrate an enhanced temperature index model to glacier-wide mass balances from repeat laser altimetry and point observations, finding a mean net mass-balance rate of −0.74 mw.e. a−1( ± σ = 0.04, std dev. of the best-performing model simulations). Results are validated against mass changes from NASA's Gravity Recovery and Climate Experiment (GRACE) satellites, a novel approach at the individual glacier scale. Correlation is strong between the detrended model- and GRACE-derived mass change time series (R2 = 0.58 and p ≪ 0.001), and between summer (R2 = 0.69 and p = 0.003) and annual (R2 = 0.63 and p = 0.006) balances, lending greater confidence to our modeling results. We find poor correlation, however, between modeled glacier-wide balances and recent single-stake monitoring. Finally, we make recommendations for monitoring glaciers with extreme altitudinal ranges, including characterizing precipitation via snow radar profiling.

Quantifying historic changes in glacier size and mass balance is important for understanding how the cryosphere responds to climate variability and change. Airborne photogrammetry enables glacier extent and equilibrium line altitudes (ELAs) to be monitored for more glaciers at lower cost than traditional mass-balance programs and other remote-sensing techniques. Since 1977, end-of-summer-snowlines, which are a proxy for annual ELAs, have been recorded for 50 glaciers in the Southern Alps of New Zealand using oblique aerial photographs. In this study, we use structure from motion photogrammetry to estimate the camera parameters, including position, for historic photographs, which we then use to measure glacier change. We apply this method to a small maritime New Zealand glacier (Brewster Glacier, 1670–2400 m a.s.l.) to derive annual ELA and length records between 1981 and 2017, and quantify the uncertainties associated with the method. Our length reconstruction shows largely continuous terminus retreat of 365 ± 12 m for Brewster Glacier since 1981. The ELA record, which compares well with glaciological mass-balance data measured between 2005 and 2015, shows pronounced interannual variability. Mean ELAs range from 1707 ± 6 to 2303 ± 5 m a.s.l., with the highest ELAs occurring in the last decade.

Abramov glacier, located in the Pamir Alay, Kyrgyzstan, is a reference glacier within the Global Terrestrial Network for Glaciers. Long-term glaciological measurements exist from 1968 to 1998 and a mass-balance monitoring programme was re-established in 2011. In this study we re-analyse existing mass-balance data and use a spatially distributed mass-balance model to provide continuous seasonal time series of glacier mass balance covering the period 1968–2014. The model is calibrated to seasonal mass-balance surveys and then applied to the period with no measurements. Validation and recalibration is carried out using snowline observations derived from satellite imagery and, after 2011, also from automatic terrestrial camera images. We combine direct measurements, remote observations and modelling. The results are compared to geodetic glacier volume change over the past decade and to a ground-penetrating radar survey in the accumulation zone resolving several layers of accumulation. Previously published geodetic mass budget estimates for Abramov glacier suggest a close-to-zero mass balance for the past decade, which contradicts our results. We find a low plausibility for equilibrium conditions over the past 15 years. Instead, we suggest that the glacier’s sensitivity to increased summer air temperature is decisive for the substantial mass loss during the past decade.

Glacier mass balance and runoff are simulated from 1955 to 2014 for the catchment (46% glacier cover) containing Chhota Shigri Glacier (Western Himalaya) using gridded data from three regional climate models: (1) the Rossby Centre regional atmospheric climate model v.4 (RCA4); (2) the REgional atmosphere MOdel (REMO); and (3) the Weather Research and Forecasting Model (WRF). The input data are downscaled to the simulation grid (300 m) and calibrated with point measurements of temperature and precipitation. Additional input is daily potential global radiation calculated using a DEM at a resolution of 30 m. The mass-balance model calculates daily snow accumulation, melt and runoff. The model parameters are calibrated with available mass-balance measurements and results are validated with geodetic measurements, other mass-balance model results and run-off measurements. Simulated annual mass balances slightly decreased from −0.3 m w.e. a−1 (1955–99) to −0.6 m w.e. a−1 for 2000–14. For the same periods, mean runoff increased from 2.0 m3 s−1 (1955–99) to 2.4 m3 s−1 (2000–14) with glacier melt contributing about one-third to the runoff. Monthly runoff increases are greatest in July, due to both increased snow and glacier melt, whereas slightly decreased snowmelt in August and September was more than compensated by increased glacier melt.