Abstract
Water pressure beneath glaciers influences ice velocity. Subglacial hydrology models are helpful for gaining insight into basal conditions, but models depend on unconstrained parameters, and ...a current challenge is reproducing elevated water pressures in winter. We eliminate terms related to englacial storage, opening by sliding, and melt due to changes in the pressure-melting-point temperature, to create a minimalist version of the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model, and apply this model to Helheim Glacier in east Greenland to explore the winter base state of the subglacial drainage system. Our results suggest that meltwater produced at the bed alone supports active winter drainage with large areas of elevated water pressure and preferential drainage pathways, using a continuum approach that allows for transitions between flow regimes. Transmissivity varies spatially over several orders of magnitude from 10
−4
to 10
3
m
2
s
−1
, with regions of weak transmissivity representing poorly connected regions of the system. Bed topography controls the location of primary drainage pathways, and high basal melt rates occur along the steep valley walls. Frictional heat from sliding is a dominant source of basal melt; different approaches for calculating basal shear stress produce significantly different basal melt rates and subglacial discharge.
Subglacial hydrology plays a key role in many glaciological processes, including ice dynamics via the modulation of basal sliding. Owing to the lack of an overarching theory, however, a variety of ...model approximations exist to represent the subglacial drainage system. The Subglacial Hydrology Model Intercomparison Project (SHMIP) provides a set of synthetic experiments to compare existing and future models. We present the results from 13 participating models with a focus on effective pressure and discharge. For many applications (e.g. steady states and annual variations, low input scenarios) a simple model, such as an inefficient-system-only model, a flowline or lumped model, or a porous-layer model provides results comparable to those of more complex models. However, when studying short term (e.g. diurnal) variations of the water pressure, the use of a two-dimensional model incorporating physical representations of both efficient and inefficient drainage systems yields results that are significantly different from those of simpler models and should be preferentially applied. The results also emphasise the role of water storage in the response of water pressure to transient recharge. Finally, we find that the localisation of moulins has a limited impact except in regions of sparse moulin density.
Subglacial hydrology has a strong influence on glacier and ice sheet dynamics, particularly through the dependence of sliding velocity on subglacial water pressure. Significant challenges are ...involved in modeling subglacial hydrology, as the drainage geometry and flow mechanics are constantly changing, with complex feedbacks that play out between water and ice. A clear tradition has been established in the subglacial hydrology modeling literature of distinguishing between channelized (efficient) and sheetlike (inefficient or distributed) drainage systems or components and using slightly different forms of the governing equations in each subsystem to represent the dominant physics. Specifically, many previous subglacial hydrology models disregard opening by melt in the sheetlike system or redistribute it to adjacent channel elements in order to avoid runaway growth that occurs when it is included in the sheetlike system. We present a new subglacial hydrology model, SHAKTI (Subglacial Hydrology and Kinetic, Transient Interactions), in which a single set of governing equations is used everywhere, including opening by melt in the entire domain. SHAKTI employs a generalized relationship between the subglacial water flux and the hydraulic gradient that allows for the representation of laminar, turbulent, and transitional regimes depending on the local Reynolds number. This formulation allows for the coexistence of these flow regimes in different regions, and the configuration and geometry of the subglacial system evolves naturally to represent sheetlike drainage as well as systematic channelized drainage under appropriate conditions. We present steady and transient example simulations to illustrate the features and capabilities of the model and to examine sensitivity to mesh size and time step size. The model is implemented as part of the Ice Sheet System Model (ISSM).
Results are presented and compared for the Community Earth System Model version 2 (CESM2) simulations of the middle Holocene (MH, 6 ka) and Last Interglacial (LIG, 127 ka). These simulations are ...designated as Tier 1 experiments (midHolocene and lig127k) for the Coupled Model Intercomparison Project phase 6 (CMIP6) and the Paleoclimate Modeling Intercomparison Project phase 4 (PMIP4). They use the low‐top, standard 1° version of CESM2 contributing to CMIP6 DECK, historical, and future projection simulations, and to other modeling intercomparison projects. The midHolocene and lig127k provide the opportunity to examine the responses in CESM2 to the orbitally induced changes in the seasonal and latitudinal distribution of insolation. The insolation anomalies result in summer warming over the Northern Hemisphere continents, reduced Arctic summer minimum sea ice, and increased areal extent of the North African monsoon. The Arctic remains warm throughout the year. These changes are greater in the lig127k than midHolocene simulation. Other notable changes are reduction of the Niño3.4 variability and Drake Passage transport and a small increase in the Atlantic Meridional Overturning Circulation from the piControl to midHolocene to lig127k simulation. Comparisons to paleo‐data and to simulations from previous model versions are discussed. Possible reasons for mismatches with the paleo‐observations are proposed, including missing processes in CESM2, simplifications in the CMIP6 protocols for these experiments, and dating and calibration uncertainties in the data reconstructions.
Plain Language Summary
The modeling of past climates, using physically based tools and comparing to paleo‐observations, is increasingly seen as a strong test of the models that are used for the projection of future climate changes. We report on simulations by one of the latest large‐scale climate models, the Community Earth System Model version 2 (CESM2), for the two most recent warm epochs: the current interglacial—the Holocene, which began 11,650 years ago ‐ and the previous interglacial—the Last Interglacial, which extended from 129,000 to 116,000 years ago. The simulations find summer warming over the Northern Hemisphere continents, reduced Arctic summer sea ice, and increased areal extent of the North African monsoon. Cryospheric and oceanic feedbacks drive year‐round Arctic warmth. The CESM2 middle Holocene and Last Interglacial simulations are an important resource for the community participating in the Coupled Model Intercomparison Project phase 6 (CMIP6).
Key Points
Orbital configurations for 6 ka and 127 ka force enhanced Northern Hemisphere summer insolation versus the preindustrial, with greater anomalies at 127 ka
This forcing in CESM2 yields summer warming over Northern Hemisphere continents, reduced Arctic minimum sea ice, and increased extent of the North African monsoon
The middle Holocene and Last Interglacial simulations provide out‐of‐sample tests of CESM2
During the Last Interglacial, approximately 129 to 116 ka (thousand years ago), the Arctic summer climate was warmer than the present, and the Greenland Ice Sheet retreated to a smaller extent than ...its current state. Previous model‐derived and geological reconstruction estimates of the sea‐level contribution of the Greenland Ice Sheet during the Last Interglacial vary widely. Here, we conduct a transient climate simulation from 127 to 119 ka using the Community Earth System Model (CESM2), which includes a dynamic ice sheet component (the Community Ice Sheet Model, CISM2) that is interactively coupled to the atmosphere, land, ocean, and sea ice components. Vegetation distribution is updated every 500 years based on biomes simulated using a monthly climatology to force the BIOME4 equilibrium vegetation model. Results show a substantial retreat of the Greenland Ice Sheet, reaching a minimum extent at 121.9 ka, equivalent to a 3.0 m rise in sea level relative to the present day, followed by gradual regrowth. In contrast, a companion simulation employing static vegetation based on pre‐industrial conditions shows a much smaller ice‐sheet retreat, highlighting the importance of the changes in high‐latitude vegetation distribution for amplifying the ice‐sheet response.
Plain Language Summary
Arctic summer climates during the Last Interglacial period (approximately 129‐116 thousand years ago) were warmer than the present, and part of the Greenland Ice Sheet likely melted, contributing substantially to global sea‐level rise. Estimates of how much the ice sheet melted range widely. We use a coupled climate model that represents different parts of the Earth system (atmosphere, ocean, sea ice, land) with an evolving Greenland Ice Sheet model to simulate the period from 127‐119 thousand years ago. Our results show that the Greenland Ice Sheet reached its minimum size 121.9 thousand years ago, losing an equivalent of 3.0 m of sea level compared to the present day. We also show that changes in Arctic vegetation distribution during the Last Interglacial have a strong influence on the climate, and therefore how much the Greenland Ice Sheet retreats.
Key Points
A simulation from 127 to 119 ka with CESM2‐CISM2 reveals retreat and incipient regrowth of the Greenland Ice Sheet for the Last Interglacial
The Greenland Ice Sheet reaches a minimum extent at 121.9 ka with a contribution of 3.0 m sea‐level equivalent relative to present day
Simulated forest and tundra expansion in Canada and Greenland leads to greater warming and ice loss than with a pre‐industrial land cover
Water flow within and beneath glaciers and ice sheets influences ice dynamics and is relevant for practical applications such as modeling outburst floods from mountain glaciers. The most general ...models for glacial hydrologic conduits include an energy equation, wherein a heat transfer coefficient controls the rate at which heat generated by mechanical energy dissipation is transferred to conduit walls, producing melt. Previous models employ heat transfer coefficients derived for engineering heat transfer problems, where heat is transferred between the walls of a conduit and a flowing fluid that enters the conduit at a temperature different from the wall temperature. These heat transfer coefficients may not be appropriate for glacial hydrologic conduits in temperate ice, where the water and conduit walls (ice) are at almost the same temperature. We revisit the energy transport equations that provide a basis for the derivation of heat transfer coefficients and highlight the distinctions between the heated walls and dissipated energy heat transfer cases. We present computational results for both cases across a wide range of Reynolds numbers in circular conduit and sheet geometries. We show that the heat transfer coefficients for transfer of heat generated by mechanical energy dissipation to circular conduit walls are smaller than calculated using the Dittus‐Boelter correlation by approximately a factor of 2. However, heat transfer coefficients are higher for flow through a wide sheet at
Re=106, highlighting the influence of noncircular geometries on heat transfer in englacial conduits and subglacial drainage systems.
Plain Language Summary
Most models of glacial hydrology that solve for the temperature of water and ice depend on heat transfer coefficients that are based on experiments of flow through pipes with heated walls. In and below glaciers, however, the ice walls are not heated but are almost the same temperature as the flowing water, and the commonly used correlations may not be appropriate. In this case, the flow itself produces heat through dissipation. We revisit the equations that heat transfer coefficients are based upon and highlight distinctions between these two situations. We present computational results of heat transfer coefficients for both cases. We find that heat transfer coefficients for the dissipation case are smaller than for the heated wall case for circular conduits, but higher for sheet flow, with implications for how current modeling assumptions may misrepresent processes related to glacier dynamics.
Key Points
Theoretical framework clarifies differences between heat transfer of dissipated mechanical energy and classical wall heat transfer
New heat transfer coefficients are derived for transfer of dissipated mechanical energy as heat to walls of glacial conduits and sheets
New coefficients are lower for circular conduits than previously used, but higher for sheet flow, highlighting the importance of geometry
Each summer, large volumes of surface meltwater drain off the Greenland ice sheet (GrIS) surface through moulins to the bed, impacting subglacial hydrology and ice flow dynamics. Supraglacial surface ...routing delays may propagate to englacial and subglacial hydrologic systems, requiring accurate assessment to correctly estimate subglacial effective pressures. We compare hourly supraglacial moulin discharge simulations from three surface meltwater routing models – the synthetic unit hydrograph (SUH), the bare-ice component of surface routing and lake filling (SRLF), and the rescaled width function (RWF) – for four internally drained catchments on the southwestern Greenland ice sheet surface. The routing models are forced identically using surface runoff from the Modèle Atmosphérique Régionale regional climate model (RCM). For each catchment, simulated moulin hydrographs are input to the SHAKTI subglacial hydrologic model to simulate diurnally varying subglacial effective-pressure variations in the vicinity of a single moulin. Overall, all three routing models produce more realistic moulin discharges than simply using RCM runoff outputs without surface routing but produce significant differences in peak moulin discharge and time to peak. In particular, the RWF yields later, smaller peak moulin discharges than the SUH or SRLF due to its representation of slow interfluve flow between supraglacial meltwater channels, and it can readily accommodate the seasonal evolution of supraglacial stream and river networks. Differences among the three routing models are reflected in a series of simple idealized subglacial hydrology simulations that yield different diurnal effective-pressure amplitudes; however, the supraglacial hydrologic system acts as short-term storage for surface meltwater, and the temporal mean effective pressure is relatively consistent across routing models.
We explore potential changes in Greenland ice sheet form and flow associated with increasing ice temperatures and relaxing effective ice viscosities. We define “thermal‐viscous collapse” as a ...transition from the polythermal ice sheet temperature distribution characteristic of the Holocene to temperate ice at the pressure melting point and associated lower viscosities. The conceptual model of thermal‐viscous collapse we present is dependent on: (1) sufficient energy available in future meltwater runoff, (2) routing of meltwater to the bed of the ice sheet interior, and (3) efficient energy transfer from meltwater to the ice. Although we do not attempt to constrain the probability of thermal‐viscous collapse, it appears thermodynamically plausible to warm the deepest 15% of the ice sheet, where the majority of deformational shear occurs, to the pressure melting point within four centuries. First‐order numerical modeling of an end‐member scenario, in which prescribed ice temperatures are warmed at an imposed rate of 0.05 K/a, infers a decrease in ice sheet volume of 5 ± 2% within five centuries of initiating collapse. This is equivalent to a cumulative sea‐level rise contribution of 33 ± 18 cm. The vast majority of the sea‐level rise contribution associated with thermal‐viscous collapse, however, would likely be realized over subsequent millennia.
Key Points
Meltwater may warm deepest 15% of the ice sheet to melting point in 400 years
This would substantially reduce ice viscosity where the majority of shear occurs
This would yield ∼5% ice sheet volume loss, ∼33 cm sea level rise, over 500 years
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