Glacier Model Research Articles

Wind-tunnel measurements of sensible turbulent heat fluxes over melting ice

Accelerated glacier melt and the loss of perennial snowfields have been associated with increased warming in polar regions, at rates up to four times faster than the rest of the world, thereby reinforcing the critical need for improved models (and predictions) of glacier melt. An essential requirement for such models is an improved understanding of the sensible heat fluxes over glaciers. Since their complexity makes them difficult to model, and direct measurements of sensible turbulent heat fluxes over real glaciers are both rare and impractical, the present work involves simultaneous hot-wire anemometry and cold-wire thermometry measurements of two components of velocity and temperature above a melting glacier model in a series of wind-tunnel experiments. Both single- and multi-variable statistics were used to compare the turbulent velocity field measured over melting ice with that of a similar flow in the absence of ice. The results demonstrate that the ice's presence reduces the magnitude of the Reynolds stresses and vertical velocity variance, but also increases the streamwise velocity variance. The transient evolution of temperature statistics throughout the melt process was also investigated and found to be similar when suitably non-dimensionalized. The velocity and temperature fields were furthermore evaluated at an equivalent non-dimensional time during the melt process, in which statistics of the temperature field, and joint statistics of the vertical velocity and temperature, were studied. The present work lays the foundation for future laboratory-scale replications of the flow above melting glaciers, and provides additional insight into turbulent heat transfer over melting ice.

Late Holocene glacier and climate fluctuations in the Mackenzie and Selwyn mountain ranges, northwestern Canada

Abstract. Over the last century, northwestern Canada experienced some of the highest rates of tropospheric warming globally, which caused glaciers in the region to rapidly retreat. Our study seeks to extend the record of glacier fluctuations and assess climate drivers prior to the instrumental record in the Mackenzie and Selwyn mountains of northwestern Canada. We collected 27 10Be surface exposure ages across nine cirque and valley glacier moraines to constrain the timing of their emplacement. Cirque and valley glaciers in this region reached their greatest Holocene extents in the latter half of the Little Ice Age (1600–1850 CE). Four erratic boulders, 10–250 m distal from late Holocene moraines, yielded 10Be exposure ages of 10.9–11.6 ka, demonstrating that by ca. 11 ka, alpine glaciers were no more extensive than during the last several hundred years. Estimated temperature change obtained through reconstruction of equilibrium line altitudes shows that since ca. 1850 CE, mean annual temperatures have risen 0.2–2.3 ∘C. We use our glacier chronology and the Open Global Glacier Model (OGGM) to estimate that from 1000 CE, glaciers in this region reached a maximum total volume of 34–38 km3 between 1765 and 1855 CE and had lost nearly half their ice volume by 2019 CE. OGGM was unable to produce modeled glacier lengths that match the timing or magnitude of the maximum glacier extent indicated by the 10Be chronology. However, when applied to the entire Mackenzie and Selwyn mountain region, past millennium OGGM simulations using the Max Planck Institute Earth System Model (MPI-ESM) and the Community Climate System Model 4 (CCSM4) yield late Holocene glacier volume change temporally consistent with our moraine and remote sensing record, while the Meteorological Research Institute Earth System Model 2 (MRI-ESM2) and the Model for Interdisciplinary Research on Climate (MIROC) fail to produce modeled glacier change consistent with our glacier chronology. Finally, OGGM forced by future climate projections under varying greenhouse gas emission scenarios predicts 85 % to over 97 % glacier volume loss by the end of the 21st century. The loss of glaciers from this region will have profound impacts on local ecosystems and communities that rely on meltwater from glacierized catchments.

Glaciations and palaeoclimate of the last millennium in the Drongtso Lungpa Co Valley, southeastern Tibetan Plateau, based on cosmogenic 10Be exposure dating and glacier modelling

Glaciations and palaeoclimate of the last millennium in the Drongtso Lungpa Co Valley, southeastern Tibetan Plateau, based on cosmogenic 10Be exposure dating and glacier modelling

Ice-flow model emulator based on physics-informed deep learning

Abstract Convolutional neural networks (CNN) trained from high-order ice-flow model realisations have proven to be outstanding emulators in terms of fidelity and computational performance. However, the dependence on an ensemble of realisations of an instructor model renders this strategy difficult to generalise to a variety of ice-flow regimes found in the nature. To overcome this issue, we adopt the approach of physics-informed deep learning, which fuses traditional numerical solutions by finite differences/elements and deep-learning approaches. Here, we train a CNN to minimise the energy associated with high-order ice-flow equations within the time iterations of a glacier evolution model. As a result, our emulator is a promising alternative to traditional solvers thanks to its high computational efficiency (especially on GPU), its high fidelity to the original model, its simplified training (without requiring any data), its capability to handle a variety of ice-flow regimes and memorise previous solutions, and its relatively simple implementation. Embedded into the ‘Instructed Glacier Model’ (IGM) framework, the potential of the emulator is illustrated with three applications including a large-scale high-resolution (2400x4000) forward glacier evolution model, an inverse modelling case for data assimilation, and an ice shelf.

Examining the effect of ice dynamic changes on subglacial hydrology through modelling of a synthetic Antarctic glacier

Abstract Hydrologic pathways beneath ice sheets and glaciers play an important role in regulating ice flow. Antarctica has experienced, and will continue to experience, changes in ice dynamics and geometry, but the associated changes in subglacial hydrology have received less attention. Here, we use the GlaDS subglacial hydrology model to examine drainage evolution beneath an idealised Antarctic glacier in response to steepening ice surface slopes, accelerating ice velocities and subglacial lake drainages. Ice surface slope changes exerted a dominant influence, redirecting basal water to different outlet locations and substantially increasing channelised discharge crossing the grounding line. Faster ice velocities had comparatively negligible effects. Subglacial lake drainage results indicated that lake refilling times play a key role in drainage system evolution, with lake flux more readily accommodated following shorter refilling times. Our findings are significant for vulnerable Antarctic regions currently experiencing dynamic thinning since subglacial water re-routing could destabilise ice shelves through enhanced sub-shelf melting, potentially hastening irreversible retreat. These changes could also affect subglacial lake activity. We, therefore, emphasise that including a nuanced and complex representation of subglacial hydrology in ice-sheet models could provide critical information on the timing and magnitude of sea-level change contributions from Antarctica.

Reconciling ice dynamics and bed topography with a versatile and fast ice thickness inversion

Abstract. We present a novel thickness inversion approach that leverages satellite products and state-of-the-art ice flow models to produce distributed maps of sub-glacial topography consistent with the dynamic state of a given glacier. While the method can use any complexity of ice flow physics as represented in ice dynamical models, it is computationally cheap and does not require bed observations as input, enabling applications on both local and large scales. Using the mismatch between observed and modelled rates of surface elevation change (dh/dt) as the misfit functional, iterative point-wise updates to an initial guess of bed topography are made, while mismatches between observed and modelled velocities are used to simultaneously infer basal friction. The final product of the inversion is not only a map of ice thickness, but is also a fully spun-up glacier model that can be run forward without requiring any further model relaxation. Here we present the method and use an artificial ice cap built inside a numerical model to test it and conduct sensitivity experiments. Even under a range of perturbations, the method is stable and fast. We also apply the approach to the tidewater glacier Kronebreen on Svalbard and finally benchmark it on glaciers from the Ice Thickness Models Intercomparison eXperiment (ITMIX, Farinotti et al., 2017), where we find excellent performance. Ultimately, our method shown here represents a fast way of inferring ice thickness where the final output forms a consistent picture of model physics, input observations and bed topography.

Glacier projections sensitivity to temperature-index model choices and calibration strategies

Abstract The uncertainty of glacier change projections is largely influenced by glacier models. In this study, we focus on temperature-index mass-balance (MB) models and their calibration. Using the Open Global Glacier Model (OGGM), we examine the influence of different surface-type dependent degree-day factors, temporal climate resolutions (daily, monthly) and downscaling options (temperature lapse rates, temperature and precipitation corrections) for 88 glaciers with in-situ observations. Our findings indicate that higher spatial and temporal resolution observations enhance MB gradient representation due to an improved calibration. The addition of surface-type distinction in the model also improves MB gradients, but the lack of independent observations limits our ability to demonstrate the added value of increased model complexity. Some model choices have systematic effects, for example weaker temperature lapse rates result in smaller projected glaciers. However, we often find counter balancing effects, such as the sensitivity to different degree-day factors for snow, firn and ice, which depends on how the glacier accumulation area ratio changes in the future. Similarly, using daily versus monthly climate data can affect glaciers differently depending on the shifting balance between melt and solid precipitation thresholds. Our study highlights the importance of considering minor model design differences to predict future glacier volumes and runoff accurately.

Evaluating the impact of enhanced horizontal resolution over the Antarctic domain using a variable-resolution Earth system model

Abstract. Earth system models are essential tools for understanding the impacts of a warming world, particularly on the contribution of polar ice sheets to sea level change. However, current models lack full coupling of the ice sheets to the ocean and are typically run at a coarse resolution (1∘ grid spacing or coarser). Coarse spatial resolution is particularly a problem over Antarctica, where sub-grid-scale orography is well-known to influence precipitation fields, and glacier models require high-resolution atmospheric inputs. This resolution limitation has been partially addressed by regional climate models (RCMs), which must be forced at their lateral and ocean surface boundaries by (usually coarser) global atmospheric datasets, However, RCMs fail to capture the two-way coupling between the regional domain and the global climate system. Conversely, running high-spatial-resolution models globally is computationally expensive and can produce vast amounts of data. Alternatively, variable-resolution grids can retain the benefits of high resolution over a specified domain without the computational costs of running at a high resolution globally. Here we evaluate a historical simulation of the Community Earth System Model version 2 (CESM2) implementing the spectral element (SE) numerical dynamical core (VR-CESM2) with an enhanced-horizontal-resolution (0.25∘) grid over the Antarctic Ice Sheet and the surrounding Southern Ocean; the rest of the global domain is on the standard 1∘ grid. We compare it to 1∘ model runs of CESM2 using both the SE dynamical core and the standard finite-volume (FV) dynamical core, both with identical physics and forcing, including prescribed sea surface temperatures (SSTs) and sea ice concentrations from observations. Our evaluation reveals both improvements and degradations in VR-CESM2 performance relative to the 1∘ CESM2. Surface mass balance estimates are slightly higher but within 1 standard deviation of the ensemble mean, except for over the Antarctic Peninsula, which is impacted by better-resolved surface topography. Temperature and wind estimates are improved over both the near surface and aloft, although the overall correction of a cold bias (within the 1∘ CESM2 runs) has resulted in temperatures which are too high over the interior of the ice sheet. The major degradations include the enhancement of surface melt as well as excessive cloud liquid water over the ocean, with resultant impacts on the surface radiation budget. Despite these changes, VR-CESM2 is a valuable tool for the analysis of precipitation and surface mass balance and thus constraining estimates of sea level rise associated with the Antarctic Ice Sheet.

Exploring the ability of the variable-resolution Community Earth System Model to simulate cryospheric–hydrological variables in High Mountain Asia

Abstract. Earth system models (ESMs) can help to improve the understanding of climate-induced cryospheric–hydrological impacts in complex mountain regions, such as High Mountain Asia (HMA). Coarse ESM grids, however, have difficulties in representing cryospheric–hydrological processes that vary over short distances in complex mountainous environments. Variable-resolution (VR) ESMs can help to overcome these limitations through targeted grid refinement. This study investigates the ability of the VR Community Earth System Model (VR-CESM) to simulate cryospheric–hydrological variables such as the glacier surface mass balance (SMB) over HMA. To this end, a new VR grid is generated, with a regional grid refinement up to 7 km over HMA. Two coupled atmosphere–land simulations are run for the period 1979–1998. The second simulation is performed with an updated glacier cover dataset and includes snow and glacier model modifications. Comparisons are made to gridded outputs derived from a globally uniform 1∘ CESM grid, observation-, reanalysis-, and satellite-based datasets, and a glacier model forced by a regional climate model (RCM). Climatological biases are generally reduced compared to the coarse-resolution CESM grid, but the glacier SMB is too negative relative to observation-based glaciological and geodetic mass balances, as well as the RCM-forced glacier model output. In the second simulation, the SMB is improved but is still underestimated due to cloud cover and temperature biases, missing model physics, and incomplete land–atmosphere coupling. The outcomes suggest that VR-CESM could be a useful tool to simulate cryospheric–hydrological variables and to study climate change in mountainous environments, but further developments are needed to better simulate the SMB of mountain glaciers.

Historical and projected evolutions of glaciers in response to climate change in High Mountain Asia

Glacier changes are regarded as the conspicuous icon of climate change in High Mountain Asia (HMA) alpine environments. Multi-temporal glacier coverage is essential for mass balance estimations and understanding glacial changes in response to climate variability. However, consistent multi-temporal glacier area datasets across the HMA are limited due to challenges posed by seasonal snow and cloud cover in remote sensing satellite images. In this study, a new method is proposed to estimate glacier and nonseasonal snow (GNS) areas by combining the normalized difference snow index (NDSI) and bright temperature bands from Landsat remote sensing images in 1990s, 2000s, 2010s and 2020s. Meanwhile, the integrated ice dynamic Open Global Glacier Model (OGGM) is applied to simulate nine typical glaciers and project their changes using 15 general circulation models (GCMs) under four shared socioeconomic pathways (SSPs). The results showed that total GNS areas in HMA were estimated at 71.26 × 103 km2 in the 1990s, and decreased to 53.17 × 103 km2 in the 2020s. Massive proportions of GNS were mainly distributed in the southeast and northwest region. Tipping points of GNS indicating a transition from mass balance gain to loss during four periods were detected in the Upper Tarim basin, Inner Tibetan Plateau, Upper Yangtze river basin, Upper Brahmaputra river basin, and Upper Salween river basin. The reduction of total GNS area was attributed to significantly rising temperature and decreasing solid precipitation. The projections indicate that glacier shrinkages will be the dominant trend in the future, and most typical glaciers will experience a mass loss of 60% under SSP245 (SSP2-RCP4.5) and over 90% under SSP585 (SSP5-RCP8.5) by the end of the century. The response of glaciers to climate change is also found to be influenced by factors including local topography and elevation ranges. The findings of this study provides a better understanding of glacial dynamics in response to climate change and highlights the importance of making water resources management strategies to mitigate the influence of glacier retreat.

Projecting the Impact of Climate Change on Runoff in the Tarim River Simulated by the Soil and Water Assessment Tool Glacier Model

Analyzing the future changes in runoff is crucial for efficient water resources management and planning in arid regions with large river systems. This paper investigates the future runoffs of the headwaters of the Tarim River Basin under different emission scenarios by forcing the hydrological model SWAT-Glacier using six regional climate models from the Coordinated Regional Downscaling Experiment (CORDEX) project. Results indicate that compared to the period of 1976~2005, temperatures are projected to increase by 1.22 ± 0.72 °C during 2036~2065 under RCP8.5 scenarios, with a larger increment in the south Tianshan mountains and a lower increment in the north Kunlun Mountains. Precipitation is expected to increase by 3.81 ± 14.72 mm and 20.53 ± 27.65 mm during 2036–2065 and 2066–2095, respectively, under the RCP8.5 scenario. The mountainous runoffs of the four headwaters that directly recharge the mainstream of the Tarim River demonstrate an overall increasing trend in the 21st century. Under the RCP4.5 and RCP8.5 scenarios, the runoff is projected to increase by 3.2% and 3.9% (amounting to 7.84 × 108 m3 and 9.56 × 108 m3) in 2006–2035. Among them, the runoff of the Kaidu River, which is dominated by rainfall and snowmelt, is projected to present slightly decreasing trends of 3~8% under RCP4.5 and RCP8.5 scenarios. For catchments located in the north Kunlun Mountains (e.g., the Yarkant and Hotan Rivers which are mix-recharged by glacier melt, snowmelt, and rainfall), the runoff will increase significantly, especially in summer due to increased glacier melt and precipitation. Seasonally, the Kaidu River shows a forward shift in peak flow. The summer streamflow in the Yarkant and Hotan rivers is expected to increase significantly, which poses challenges in flood risk management.

The Glacier‐Climate Interaction Over the Tibetan Plateau and Its Surroundings During the Last Glacial Maximum

AbstractGlacier growth affects the local climate, and in turn, can either promote or prohibit its own growth. Such feedback has not been considered in modeling the glaciers of the Tibetan Plateau and its surroundings (TPS) during the Last Glacial Maximum (LGM; ∼28–23 ka). We find that the volume/area of the glaciers simulated by a coupled glacier‐climate model is 20%/10% less than that by a standalone glacier model forced with fixed climate fields; glaciers advance toward their western rims and yet decrease in the interior of TPS. Such changes in spatial patterns improve model‐data comparison. Moreover, the expansion of glaciers warms the winter surface temperature of the eastern TPS and decreases precipitation almost everywhere. These effects are primarily due to the added surface elevation, which blocks the water vapor brought by westerlies and south‐westerlies, reducing precipitation and increasing surface temperatures to the east and northeast of the newly grown glaciers.

Consistency in the fingerprints of projected sea level change 2015–2100CE

SUMMARY A large ensemble of ice sheet projections to the end of the 21st century have been compiled within community-based initiatives. These ensembles allow for assessment of uncertainties in projections associated with climate forcing and a wide range of parameters governing ice sheet and shelf dynamics, including ice-ocean interactions. Herein, we compute geographically variable sea level ‘fingerprints’ associated with ∼320 simulations of polar ice sheet projections included in the Ice Sheet Model Intercomparison Project for CMIP6 and ∼180 projections of glacier mass changes from the Glacier Model Intercomparison Project. We find a strong correlation (coefficient > 0.97) between all fingerprints of Greenland Ice Sheet projections when considering a global region outside the near field of the ice sheet. Consistency in the fingerprints for the Antarctic Ice Sheet (AIS) projections is much weaker, though correlation coefficients > 0.80 were found for all projections with global mean sea level (GMSL) greater than 10 cm. The far-field variability in the fingerprints associated with the AIS is due in large part to the sea level change driven by Earth rotation changes. The size and position of the AIS on the south pole makes the rotational component of the sea level fingerprint highly sensitive to the geometry of the ice mass flux, a geometry that becomes more consistent as the GMSL associated with the ice sheet projection increases. Finally, the fingerprints of glacier mass flux show an intermediate level of consistency, with contributions from Antarctic glaciers being the primary driver of decorrelation.

Research progress on simulation of high-altitude glaciers and permafrost on the qinghai-tibet plateau based on hydrological models

The Qinghai-Tibet Plateau's uniqueness: The Qinghai-Tibet Plateau is located in a high-altitude region, with a much higher average elevation than the surrounding areas at the same latitude. It is home to the majority of the world's glaciers and permafrost in the middle and lower latitudes. Glaciers are extremely sensitive to climate change, and the unique glaciers and permafrost on the Qinghai-Tibet Plateau are especially vulnerable. The predecessors simulated and predicted glaciers using the distributed hydrological model and the glacier system model, and frozen soil using the accumulated temperature statistical model and the freezing number model. Simultaneously, these models have gone through a development process from low-end to high-end, which improves the accuracy and fit of the Qinghai-Tibet Plateau study. This paper will compare the advantages and disadvantages of these distributed hydrological models and glacier system models using a literature review method. We discovered that the glacier model's distributed hydrological model can simulate and analyze glacier runoff, and the Glacer's system model can better classify the glacier. The freezing mumer model has made significant contributions to the dynamic change simulation of frozen soil and the estimation of its maximum thawing depth.

Robust reconstruction of glacier beds using transient 2D assimilation with Stokes

AbstractInitialising model glaciers such that they match well with their real counterparts and are thus able to make more accurate predictions is an ongoing challenge in glacier modelling. We set out a data-assimilation approach using an ensemble Kalman filter in a 2D flowline example that provides one possible solution to this problem. We show that our approach is valid across a range of parameters and scenarios, including deliberately data-deficient or inaccurate ones, and leads to robust retrieval of the glacier bed. We also provide some suggestions for how best to use data assimilation within a mountain-glacier context.

Computational Modeling of Ice Sheets and Glaciers

Computational Modeling of Ice Sheets and Glaciers

Compatible Finite Elements for Glacier Modeling

Compatible Finite Elements for Glacier Modeling

Modeling the form, distribution and paleoclimatic implications of former glaciers in the Teke Peninsula (Eastern Mediterranean, Turkey)

The Western Taurus Mountains on the Teke Peninsula, Southwestern Turkey, saw substantial glaciation in the late Quaternary period. Accurate reconstructions of former glacier extent in this relatively marginal area of glaciation are important for establishing the paleoclimate in the Eastern Mediterranean Basin. From west to east, the mountains of Sandıras, Karadağ, Akdağ (Kaş), and Beydağları preserve clear evidence of cirques and moraines, representing glacial valley land systems. This study used calculation tools for Glacier Reconstruction, (GlaRe) and Equilibrium Line Altitude (ELA), with glacier outlines based on the geomorphological evidence and Digital Elevation Models (DEMs), to determine the distribution and ELAs of former glaciers and to estimate paleotemperature and paleo-precipitation during the maximum ice extent. The results are analyzed at three scales: for each glacier, between glaciers and between mountain ranges. While the glaciation was at its peak, we estimate that glaciers covered a total area of 26.4 km2 (1.28 ± 0.08 km2 on Sandıras Mountain, 3.86 ± 0.23 km2 on Karadağ, 16.17 ± 0.970 km2 on Akdağ (Kaş), and 5.09 ± 0.30 km2 in Beydağları): the longest glacier was in Akdağ (Kaş) with a length of 5787 m. Average paleo-ELA (pELA) was calculated as 2077 m a.s.l in Sandıras, 2097 m a.s.l in Karadağ, 2565 m a.s.l in Akdağ (Kaş), and 2468 m a.s.l in Beydağları. Glacier modeling estimated that the maximum ice thickness in Akdağ was 240 m ± 14, and the average thickness 75 ± 4 m. Among these mountains, Karadağ had the lowest elevation to which glaciers descended (1760 ± 16 m a.s.l). Topographic analyses revealed that glaciers formed in the four mountains mostly in the North-facing localities with highest slope values of 18 to 30°. During the maximum glaciation period air temperature depression has been estimated as 8 to 9° Celsius; That required a precipitation increase of some 40 to 60 % compared to present, to produce the former glaciers mapped in the Teke Peninsula.

Late glacial climate evolution in the Patagonian Andes (44–47° S) from alpine glacier modelling

Late glacial climate evolution in the Patagonian Andes (44–47° S) from alpine glacier modelling

Active temperate glacial landsystem evolution in association with outwash head/depositional overdeepenings

AbstractThe response of temperate glaciers to rapid climate warming is reflected in the geomorphology (landsystem) resulting from snout recession. This paper develops a locally diverse process‐form model of active temperate glaciers through mapping and quantification of historical landscape change on the Fjallsjökull‐Hrútárjökull foreland, SE Iceland. Quantification of volumetric and areal changes on the foreland are based on time series of archival aerial images for the period 1945–1998, high‐resolution satellite imagery for 2014 and digital elevation models of differences derived from time series of UAV imagery for the years 2014, 2016, 2018, 2019 and 2022. Landscape change and glacier snout behaviour since 1945 highlights the importance of azonal and potentially intrazonal signatures in temperate glacial landsystems, particularly: (1) the development and collapse of partially supraglacial outwash fans to produce outwash heads fronting depositional overdeepenings; and (2) the emergence of ice‐cored eskers that record the evolution of englacial drainage networks operating over overdeepenings. Such landform assemblages are manifested as substantial ice‐cored/hummocky terrains, a characteristic of deglaciating forelands that is likely to be widely replicated wherever ice‐contact glacifluvial assemblages create outwash heads that act as depositional overdeepenings. Due to its significantly greater supraglacial debris cover, complete de‐icing of the Hrútárjökull snout in response to post‐1945 warming was delayed until around 2014. This constitutes a prime example of incremental stagnation, which in a rapidly warming climate has resulted in significant landscape change (land surface elevation collapse of 0.8 m a−1) over the last 8 years.