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Geothermal heat sources beneath glaciers and ice caps influence local ice-dynamics and mass balance but also control ice surface depression evolution as well as subglacial water reservoir dynamics. Resulting jökulhlaups (i.e., glacier lake outburst floods) impose danger to people and infrastructure, especially in Iceland, where they are closely monitored. Due to hundreds of meters of ice, direct measurements of heat source strength and extent are not possible. We present an indirect measurement method which utilizes ice flow simulations and glacier surface data, such as surface mass balance and surface depression evolution. Heat source locations can be inferred accurately to simulation grid scales; heat source strength and spatial distributions are also well quantified. Our methods are applied to the Mýrdalsjökull ice cap in Iceland, where we are able to refine previous heat source estimates. [ABSTRACT FROM AUTHOR]

Geothermal heat sources beneath glaciers and ice caps influence local ice-dynamics and mass balance, but also control ice surface depression evolution as well as subglacial water reservoir dynamics. Resulting jökulhlaups (i.e. glacier lake outburst floods) impose danger to people and infrastructure, especially in Iceland, where they are closely monitored. Due to hundreds of meters of ice, direct measurements of heat source strength and extent are not possible. We present an indirect measurement method which utilizes ice flow simulations and glacier surface data, such as surface mass balance and surface depression evolution. Heat source locations can be inferred accurately to simulation grid scales; heat source strength and spatial distributions are also well quantified. Our methods are applied to Mýrdalsjökull ice cap in Iceland, where we are able to refine previous heat source estimates. [ABSTRACT FROM AUTHOR]

In the European Alps, the Younger Dryas (YD) was characterised by the last major glacier advance, with equilibrium line altitudes being ∼ 220 to 290 m lower than during the Little Ice Age, and also by the development of rock glaciers. Dating of these geomorphic features, however, is associated with substantial uncertainties, leading to considerable ambiguities regarding the internal structure of this stadial, which is the most intensively studied one of the last glacial period. Here, we provide robust physical evidence based on 230 Th-dated cryogenic cave carbonates (CCCs) from a cave located at 2274 m a.s.l. in the Dolomites of northern Italy coupled with thermal modelling, indicating that early YD winters were only moderately cold in this part of the Alps. More precisely, we find that the mean annual air temperature dropped ≤ 3 ∘ C at the Allerød–YD transition. Our data suggest that autumns and early winters in the early part of the YD were relatively snow-rich, resulting in stable winter snow cover. The latter insulated the shallow subsurface in winter and allowed the cave interior to remain close to the freezing point (0 ∘ C) year-round, promoting CCC formation. The main phase of CCC precipitation at ∼ 12.2 ka coincided with the mid-YD transition recorded in other archives across Europe. Based on thermal modelling we propose that CCC formation at ∼ 12.2 ka was most likely associated with a slight warming of approximately + 1 ∘ C in conjunction with drier autumns and early winters in the second half of the YD. These changes triggered CCC formation in this Alpine cave as well as ice glacier retreat and rock glacier expansion across the Alps. [ABSTRACT FROM AUTHOR]

Non-surface mass balance is non-negligible for glaciers in Iceland. Several Icelandic glaciers are in the neo-volcanic zone where a combination of geothermal activity, volcanic eruptions and geothermal heat flux much higher than the global average lead to basal melting close to 150 mm w.e. a−1 for the Mýrdalsjökull ice cap and 75 mm w.e. a−1 for the largest ice cap, Vatnajökull. Energy dissipation in the flow of water and ice is also rather large for the high-precipitation, temperate glaciers of Iceland resulting in internal and basal melting of 20–150 mm w.e. a−1. The total non-surface melting of glaciers in Iceland in 1995–2019 was 45–375 mm w.e. a−1 on average for the main ice caps, and was largest for Mýrdalsjökull, the south side of Vatnajökull and Eyjafjallajökull. Geothermal melting, volcanic eruptions and the energy dissipation in the flow of water and ice, as well as calving, all contribute, and thus these components should be considered in mass-balance studies. For comparison, the average mass balance of glaciers in Iceland since 1995 is −500 to −1500 mm w.e. a−1. The non-surface mass balance corresponds to a total runoff contribution of 2.1 km3 a−1 of water from Iceland. [ABSTRACT FROM AUTHOR]

Despite their importance for sea-level rise, seasonal water availability, and as a source of geohazards, mountain glaciers are one of the few remaining subsystems of the global climate system for which no globally applicable, open source, community-driven model exists. Here we present the Open Global Glacier Model (OGGM), developed to provide a modular and open-source numerical model framework for simulating past and future change of any glacier in the world. The modeling chain comprises data downloading tools (glacier outlines, topography, climate, validation data), a preprocessing module, a mass-balance model, a distributed ice thickness estimation model, and an ice-flow model. The monthly mass balance is obtained from gridded climate data and a temperature index melt model. To our knowledge, OGGM is the first global model to explicitly simulate glacier dynamics: the model relies on the shallow-ice approximation to compute the depth-integrated flux of ice along multiple connected flow lines. In this paper, we describe and illustrate each processing step by applying the model to a selection of glaciers before running global simulations under idealized climate forcings. Even without an in-depth calibration, the model shows very realistic behavior. We are able to reproduce earlier estimates of global glacier volume by varying the ice dynamical parameters within a range of plausible values. At the same time, the increased complexity of OGGM compared to other prevalent global glacier models comes at a reasonable computational cost: several dozen glaciers can be simulated on a personal computer, whereas global simulations realized in a supercomputing environment take up to a few hours per century. Thanks to the modular framework, modules of various complexity can be added to the code base, which allows for new kinds of model intercomparison studies in a controlled environment. Future developments will add new physical processes to the model as well as automated calibration tools. Extensions or alternative parameterizations can be easily added by the community thanks to comprehensive documentation. OGGM spans a wide range of applications, from ice–climate interaction studies at millennial timescales to estimates of the contribution of glaciers to past and future sea-level change. It has the potential to become a self-sustained community-driven model for global and regional glacier evolution. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatiotemporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error-correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier. [ABSTRACT FROM AUTHOR]

Despite of their importance for sea-level rise, seasonal water availability, and as source of geohazards, mountain glaciers are one of the few remaining sub-systems of the global climate system for which no globally applicable, open source, community-driven model exists. Here we present the Open Global Glacier Model (OGGM, http://www.oggm.org), developed to provide a modular and open source numerical model framework for simulating past and future change of any glacier in the world. The modelling chain comprises data downloading tools (glacier outlines, topography, climate, validation data), a preprocessing module, a mass-balance model, a distributed ice thickness estimation model, and an ice flow model. The monthly mass-balance is obtained from gridded climate data and a temperature index melt model. To our knowledge, OGGM is the first global model explicitly simulating glacier dynamics: the model relies on the shallow ice approximation to compute the depth-integrated flux of ice along multiple connected flowlines. In this paper, we describe and illustrate each processing step by applying the model to a selection of glaciers before running global simulations under idealized climate forcings. Even without an in-depth calibration, the model shows a very realistic behaviour. We are able to reproduce earlier estimates of global glacier volume by varying the ice dynamical parameters within a range of plausible values. At the same time, the increased complexity of OGGM compared to other prevalent global glacier models comes at a reasonable computational cost: several dozens of glaciers can be simulated on a personal computer, while global simulations realized in a supercomputing environment take up to a few hours per century. Thanks to the modular framework, modules of various complexity can be added to the codebase, allowing to run new kinds of model intercomparisons in a controlled environment. Future developments will add new physical processes to the model as well as tools to calibrate the model in a more comprehensive way. OGGM spans a wide range of applications, from ice-climate interaction studies at millenial time scales to estimates of the contribution of glaciers to past and future sea-level change. It has the potential to become a self-sustained, community driven model for global and regional glacier evolution. [ABSTRACT FROM AUTHOR]

Glaciers with extensive surface debris cover respond differently to climate forcing than those without supraglacial debris. In order to include debris-covered glaciers in projections of glaciogenic runoff and sea level rise and to understand the paleoclimate proxy recorded by such glaciers, it is necessary to understand the manner and timescales over which a supraglacial debris cover develops. Because debris is delivered to the glacier by processes that are heterogeneous in space and time, and these debris inclusions are altered during englacial transport through the glacier system, correctly determining where, when and how much debris is delivered to the glacier surface requires knowledge of englacial transport pathways and deformation. To achieve this, we present a model of englacial debris transport in which we couple an advection scheme to a full-Stokes ice flow model. The model performs well in numerical benchmark tests, and we present both 2-D and 3-D glacier test cases that, for a set of prescribed debris inputs, reproduce the englacial features, deformation thereof and patterns of surface emergence predicted by theory and observations of structural glaciology. In a future step, coupling this model to (i) a debris-aware surface mass balance scheme and (ii) a supraglacial debris transport scheme will enable the co-evolution of debris cover and glacier geometry to be modelled. [ABSTRACT FROM AUTHOR]

Monthly gravity field models from the GRACE satellite mission are widely used to determine ice mass changes of large ice sheets as well as smaller glaciers and ice caps. Here, we investigate in detail the ice mass changes of the Icelandic ice caps as derived from GRACE data. The small size of the Icelandic ice caps, their location close to other rapidly changing ice covered areas and the low viscosity of the mantle below Iceland make this especially challenging. The mass balance of the ice caps is well constrained by field mass balance measurements, making this area ideal for such investigations. We find that the ice mass changes of the Icelandic ice caps derived from GRACE gravity field models are influenced by both the large gravity change signal resulting from ice mass loss in southeast Greenland and the mass redistribution within the Earth mantle due to glacial isostatic adjustment since the Little Ice Age (~1890 AD). To minimize the signal that leaks towards Iceland from Greenland, we employ an independent mass change estimate of the Greenland Ice Sheet derived from satellite laser altimetry. We also estimate the effect of post Little Ice Age glacial isostatic adjustment, from knowledge of the ice history and GPS network constrained crustal deformation data. We find that both the leakage from Greenland and the post Little Ice Age glacial isostatic adjustment are important to take into account, in order to correctly determine Iceland ice mass changes from GRACE, and when applying these an average mass balance of the Icelandic ice caps of -11.4 ± 2.2 Gt yr-1 for the period 2003-2010 is found. This number corresponds well with available mass balance measurements. [ABSTRACT FROM AUTHOR]

We use daily surface velocities measured over several weeks in 2007 and 2008 on a slowly surging glacier in Yukon, Canada, to examine the ordinary melt-season dynamics in the context of the ongoing surge. Horizontal velocities within and just below the ~1.5 km-long zone of fastest flow, where the surge is occurring, are often correlated during intervals of low melt. This correlation breaks down during melt events, with the lower reaches of the fast-flow zone responding first. Velocity variability in this lower reach is most highly correlated with melt; velocities above and below appear to respond at least as strongly to the velocity variations of this reach as to local melt. GPS height records are suggestive of ice/bed separation occurring in the fast-flow zone but not below it, pointing to a hydrological cause for the short-term flow variability in the surging region. Independent velocity measurements over 6 years show a maximum July flow anomaly coincident with the location most responsive to melt. Results from a simple model of dashpots and frictional elements lend support to the hypothesis that this zone partly drives the dynamics of the ice above and below it. We speculate that the slow surge may enhance glacier sensitivity to melt-season processes, including short-term summer sliding events. [ABSTRACT FROM PUBLISHER]

Retreat of mountain glaciers is a significant contributor to sea-level rise and a potential threat to human populations through impacts on water availability and regional hydrology. Like most of Earth's mountain glaciers, those in western North America are experiencing rapid mass loss. Projections of future large-scale mass change are based on surface mass balance models that are open to criticism, because they ignore or greatly simplify glacier physics. Here we use a high-resolution regional glaciation model, developed by coupling physics-based ice dynamics with a surface mass balance model, to project the fate of glaciers in western Canada. We use twenty-first-century climate scenarios from an ensemble of global climate models in our simulations; the results indicate that by 2100, the volume of glacier ice in western Canada will shrink by 70 ± 10% relative to 2005. According to our simulations, few glaciers will remain in the Interior and Rockies regions, but maritime glaciers, in particular those in northwestern British Columbia, will survive in a diminished state. We project the maximum rate of ice volume loss, corresponding to peak input of deglacial meltwater to streams and rivers, to occur around 2020-2040. Potential implications include impacts on aquatic ecosystems, agriculture, forestry, alpine tourism and water quality. [ABSTRACT FROM AUTHOR]

Simulating glacier surface evolution based on surface velocity and surface mass balance estimates is a common task in glaciology. Like any gravitationally driven flow that is not constrained at the upper surface, glaciers and ice sheets feature a free surface which becomes a free boundary problem within simulations. A kinematic boundary condition is often successfully utilized to represent the surface. However the naturally occurring constraint that the surface elevation (S) can not fall below the bed elevation (B), (S-B >= 0) in combination with a non zero mass balance complicates matter substantially.We present a numerical model to simulate the free surface evolution of glaciers that directly incorporates this natural constraint. It is based on the finite element software package FEniCS solving the Stokes equations for ice flow and a transport equation for the free surface evolution. The evolution of the free surface is treated as a variational inequality, constrained by the bedrock underlying the glacier or the topography of the surrounding ground. To solve this problem, the 'constrained' non–linear problem solving capabilities of PETSc's SNES interface are used. We partition the computational domain into regions where ice exists and its ice-free surroundings. For ice regions we solve the constrained kinematic boundary condition including mass balance and for the surroundings we only solve the constrained mass balance term. This approach is mass conserving as the constraint is considered in the solving process and thus does not require any ad-hoc post-processing steps to enforce mass conservation. The model will become freely available in the framework of the debadvect model (https://github.com/awirbel/debadvect), also providing additional functions for the generation of updated 3D domain models. [ABSTRACT FROM AUTHOR]

Drangajökull is a maritime ice cap located in northwest (Vestfirðir) Iceland. Drangajökull's evolution is therefore closely linked to atmospheric and ocean variability. In order to better constrain the Holocene climate and glacier history of Vestfirðir we model the past evolution of Drangajökull ice cap. Simulations from 10 ka to present are forced by general circulation model output, ice-core-based temperature reconstructions, and sea-surface temperature reconstructions. Based on these 10-thousand year simulations, Drangajökull did not persist through the Holocene. We estimate that air temperatures were 2.5–3.0 °C higher during the Holocene Thermal Maximum than the local 1960–1990 average. Simulations support Drangajökull's late Holocene inception between 2 and 1 ka, though intermittent ice likely occupied cirques as early as 2.6 ka. Drangajökull is primarily a Little Ice Age ice cap: it expanded between 1300 and 1750 CE, with the most rapid growth occurring between 1600 and 1750 CE. The maximum Holocene extent of Drangajökull occurred between 1700 and 1925 CE, despite the lowest late Holocene temperatures, occurring between 1650 and 1720 CE. Between 1700 and 1925 CE temperatures were likely 0.6–0.8 °C lower than the 1950–2015 reference temperature. The modern equilibrium line altitude (ELA) is bracketed by topographic thresholds: a 1 °C temperature increase from the modern ELA would eliminate the ice cap's accumulation area, while a reduction of 0.5 °C would lead to the rapid expansion of the ice cap across Vestfirðir. The proximity of Drangajökull to topographic thresholds may explain its late inception and rapid expansion during the Little Ice Age. [ABSTRACT FROM AUTHOR]