Subglacial Hydrology Model Research Articles

SHMIP The subglacial hydrology model intercomparison Project

ABSTRACTSubglacial 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.

MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids

Abstract. We introduce MPAS-Albany Land Ice (MALI) v6.0, a new variable-resolution land ice model that uses unstructured Voronoi grids on a plane or sphere. MALI is built using the Model for Prediction Across Scales (MPAS) framework for developing variable-resolution Earth system model components and the Albany multi-physics code base for the solution of coupled systems of partial differential equations, which itself makes use of Trilinos solver libraries. MALI includes a three-dimensional first-order momentum balance solver (Blatter–Pattyn) by linking to the Albany-LI ice sheet velocity solver and an explicit shallow ice velocity solver. The evolution of ice geometry and tracers is handled through an explicit first-order horizontal advection scheme with vertical remapping. The evolution of ice temperature is treated using operator splitting of vertical diffusion and horizontal advection and can be configured to use either a temperature or enthalpy formulation. MALI includes a mass-conserving subglacial hydrology model that supports distributed and/or channelized drainage and can optionally be coupled to ice dynamics. Options for calving include “eigencalving”, which assumes that the calving rate is proportional to extensional strain rates. MALI is evaluated against commonly used exact solutions and community benchmark experiments and shows the expected accuracy. Results for the MISMIP3d benchmark experiments with MALI's Blatter–Pattyn solver fall between published results from Stokes and L1L2 models as expected. We use the model to simulate a semi-realistic Antarctic ice sheet problem following the initMIP protocol and using 2 km resolution in marine ice sheet regions. MALI is the glacier component of the Energy Exascale Earth System Model (E3SM) version 1, and we describe current and planned coupling to other E3SM components.

Relationship Between Greenland Ice Sheet Surface Speed and Modeled Effective Pressure

AbstractWe use a numerical subglacial hydrology model and remotely sensed observations of Greenland Ice Sheet surface motion to test whether the inverse relationship between effective pressure and regional melt season surface speeds observed at individual sites holds on a regional scale. The model is forced with daily surface runoff estimates for 2009 and 2010 across an ~8,000‐km2 region on the western margin. The overall subglacial drainage system morphology develops similarly in both years, with subglacial channel networks growing inland from the ice sheet margin and robust subglacial pathways forming over bedrock ridges. Modeled effective pressures are compared to contemporaneous regional surface speeds derived from TerraSAR‐X imagery to investigate spatial relationships. Our results show an inverse spatial relationship between effective pressure and ice speed in the mid‐melt season, when surface speeds are elevated, indicating that effective pressure is the dominant control on surface velocities in the mid‐melt season. By contrast, in the early and late melt seasons, when surface speeds are slower, effective pressure and surface speed have a positive relationship. Our results suggest that outside of the mid‐melt season, the influence of effective pressures on sliding speeds may be secondary to the influence of driving stress and spatially variable bed roughness.

BrAHMs V1.0: a fast, physically based subglacial hydrology model for continental-scale application

Abstract. We present BrAHMs (BAsal Hydrology Model): a physically based basal hydrology model which represents water flow using Darcian flow in the distributed drainage regime and a fast down-gradient solver in the channelized regime. Switching from distributed to channelized drainage occurs when appropriate flow conditions are met. The model is designed for long-term integrations of continental ice sheets. The Darcian flow is simulated with a robust combination of the Heun and leapfrog–trapezoidal predictor–corrector schemes. These numerical schemes are applied to a set of flux-conserving equations cast over a staggered grid with water thickness at the centres and fluxes defined at the interface. Basal conditions (e.g., till thickness, hydraulic conductivity) are parameterized so the model is adaptable to a variety of ice sheets. Given the intended scales, basal water pressure is limited to ice overburden pressure, and dynamic time stepping is used to ensure that the Courant–Friedrichs–Lewy (CFL) condition is met for numerical stability. The model is validated with a synthetic ice sheet geometry and different bed topographies to test basic water flow properties and mass conservation. Synthetic ice sheet tests show that the model behaves as expected with water flowing down gradient, forming lakes in a potential well or reaching a terminus and exiting the ice sheet. Channel formation occurs periodically over different sections of the ice sheet and, when extensive, displays the arborescent configuration expected of Röthlisberger channels. The model is also shown to be stable under high-frequency oscillatory meltwater inputs.

SHAKTI: Subglacial Hydrology and Kinetic, Transient Interactions v1.0

Abstract. 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).

Dynamics of active subglacial lakes in Recovery Ice Stream.

Recovery Ice Stream has a substantial number of active subglacial lakes that are observed, with satellite altimetry, to grow and drain over multiple years. These lakes store and release water that could be important for controlling the velocity of the ice stream. We apply a subglacial hydrology model to analyze lake growth and drainage characteristics together with the simultaneous development of the ice stream hydrological network. Our outputs produce a good match between modeled lake location and those identified using satellite altimetry for many of the lakes. The modeled subglacial system demonstrates development of pressure waves that initiate at the ice stream neck and transit to within 100 km of the terminus. These waves alter the hydraulic potential of the ice stream and encourage growth and drainage of the subglacial lakes. Lake drainage can cause large R-channels to develop between basal overdeepenings that persist for multiple years. The pressure waves, along with lake growth and drainage rates, do not identically repeat over multiple years, due to basal network development. This suggests that the subglacial hydrology of Recovery Ice Stream is influenced by regional drainage development on the scale of hundreds of kilometers rather than local conditions over tens of kilometers.

Limited Impact of Subglacial Supercooling Freeze‐on for Greenland Ice Sheet Stratigraphy

AbstractLarge units of disrupted radiostratigraphy (UDR) are visible in many radio‐echo sounding data sets from the Greenland Ice Sheet. This study investigates whether supercooling freeze‐on rates at the bed can cause the observed UDR. We use a subglacial hydrology model to calculate both freezing and melting rates at the base of the ice sheet in a distributed sheet and within basal channels. We find that while supercooling freeze‐on is a phenomenon that occurs in many areas of the ice sheet, there is no discernible correlation with the occurrence of UDR. The supercooling freeze‐on rates are so low that it would require tens of thousands of years with minimal downstream ice motion to form the hundreds of meters of disrupted radiostratigraphy. Overall, the melt rates at the base of the ice sheet greatly overwhelm the freeze‐on rates, which has implications for mass balance calculations of Greenland ice.

Incorporating modelled subglacial hydrology into inversions for basal drag

Abstract. A key challenge in modelling coupled ice-flow–subglacial hydrology is initializing the state and parameters of the system. We address this problem by presenting a workflow for initializing these values at the start of a summer melt season. The workflow depends on running a subglacial hydrology model for the winter season, when the system is not forced by meltwater inputs, and ice velocities can be assumed constant. Key parameters of the winter run of the subglacial hydrology model are determined from an initial inversion for basal drag using a linear sliding law. The state of the subglacial hydrology model at the end of winter is incorporated into an inversion of basal drag using a non-linear sliding law which is a function of water pressure. We demonstrate this procedure in the Russell Glacier area and compare the output of the linear sliding law with two non-linear sliding laws. Additionally, we compare the modelled winter hydrological state to radar observations and find that it is in line with summer rather than winter observations.

Modeling Antarctic subglacial lake filling and drainage cycles

Abstract. The growth and drainage of active subglacial lakes in Antarctica has previously been inferred from analysis of ice surface altimetry data. We use a subglacial hydrology model applied to a synthetic Antarctic ice stream to examine internal controls on the filling and drainage of subglacial lakes. Our model outputs suggest that the highly constricted subglacial environment of our idealized ice stream, combined with relatively high rates of water flow funneled from a large catchment, can combine to create a system exhibiting slow-moving pressure waves. Over a period of years, the accumulation of water in the ice stream onset region results in a buildup of pressure creating temporary channels, which then evacuate the excess water. This increased flux of water beneath the ice stream drives lake growth. As the water body builds up, it steepens the hydraulic gradient out of the overdeepened lake basin and allows greater flux. Eventually this flux is large enough to melt channels that cause the lake to drain. Lake drainage also depends on the internal hydrological development in the wider system and therefore does not directly correspond to a particular water volume or depth. This creates a highly temporally and spatially variable system, which is of interest for assessing the importance of subglacial lakes in ice stream hydrology and dynamics.

Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model version 0.6

Abstract. We describe and test a two-horizontal-dimension subglacial hydrology model which combines till with a distributed system of water-filled, linked cavities which open through sliding and close through ice creep. The addition of this sub-model to the Parallel Ice Sheet Model (PISM) accomplishes three specific goals: (a) conservation of the mass of water, (b) simulation of spatially and temporally variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (c) convergence under grid refinement. The model is a common generalization of four others: (i) the undrained plastic bed model of Tulaczyk et al. (2000b), (ii) a standard "routing" model used for identifying locations of subglacial lakes, (iii) the lumped englacial–subglacial model of Bartholomaus et al. (2011), and (iv) the elliptic-pressure-equation model of Schoof et al. (2012). We preserve physical bounds on the pressure. In steady state a functional relationship between water amount and pressure emerges. We construct an exact solution of the coupled, steady equations and use it for verification of our explicit time stepping, parallel numerical implementation. We demonstrate the model at scale by 5 year simulations of the entire Greenland ice sheet at 2 km horizontal resolution, with one million nodes in the hydrology grid.