C41A-1177 Can Subglacial Meltwater Films Carve into the Till Beneath? Insights from a Coupled Till-Water Model

1Institute of Computational and Mathematical Engineering Indraneel Kasmalkar1, Elisa Mantelli2, Jenny Suckale2 2 Department of Geophysics Notation -2 [email protected] [email protected] [email protected] [H] height scale. 10 m hi ice-water interface. [L] length scale. 10-2 m hs water-till interface. [D] grain diameter. 10-4 m t time. ice roof α incline angle. 10-3 rad What are subglacial meltwater systems? Model: Incompressible Laminar Flow + Bedload Transport [tp] time scale of phase p ν viscosity of 1.786x10-6 (ice, water, till) z Steady-state flow z water. m2s-1 Net Deposition. These are water systems found at the Inclined film of meltwater from z = hs to z = hi. U steady state x-velocity. x y coming out of the page y τc Shield's stress. 0.068 qs sediment flux. interface of the ice and the underlying Ice Upward Velocity x g gravity acc. 9.8 ms-2 The Navier Stokes equations govern water flow. ω Growth rate of Lw Latent heat of 3.36x105 sediment bed (till). z = hi Net Erosion. perturbation. The Exner Equation is a sediment transport fusion of water. J/kg This meltwater is generated due to Water λ defined as λ = [H]/[L]. -2 Downward QG Geothermal flux. 0.3 Wm equation that governs the evolution of till: z = hs γ1,γ2 x and y perturbation geothermal heating and shear friction from ρi Density of ice. 917 kgm-3 wavelength Velocity wavenumbers resp. Sediment (till) Sediment flux as a function of stress: G Ratio of grain to 2.6 the ice flow. γ γ = (γ12 + γ22)1/2 . water density. Empirically determined ψ stream-function in The meltwater starts out as a film only a few millimeters in Moving ripples in the till p0 till avg. porosity 0.2 exponent [2]. Fourier space. thickness, but it can later evolve into different systems:

Distributed network Time Evolution Net Sediment Sediment Bed Threshold Thin Film Single Channel Result: Instability for larger wavelengths - Channel initation of cavities of Till-Water Out-Flux Out-Flux Stress Stress Interface Ice on Top A simple yet powerful model: Linear Stability Analysis: how does the system behave for small perturbations? Water Growth rate vs Wavelength • No ice or till rheology. • No thermal processes. z ) Till ice roof Poiseuille ω Unstable • Hydrology by itself is causing channel initiation. z Flow x y Vertical advection is dominant x + Add a perturbation across the flow: Till and meltwater affect ice flow uniform Flow-advection destabilizes bedload transport Linearize the Subglacial meltwater weakens Find a steady system around 2. 3. Variable Steady Perturbation Growth basal resistance to ice flow by Weaker Till: state solution. the steady state. Upward Reduced stress State Rate advection increasing the pore pressure Faster Ice Flow Stable γ implies less erosion. of the sediment (till). The linearized Navier Stokes equations can be simplified using Given a perturbation, Horizontal diffusion blunts the stress Growth Rate (Real part Growth of Reinforces stream-function notation to get the Orr-Sommerfeld equation: solve the system for is dominant the growth rate ω. initial motion. 1. Channelization can Perturbation Wavelength localize till weakening Localized Till Weakening: (% of channel length) Perturbation and increase basal Slower Ice Flow Viscous Diffusion of Water Flow Advection of Water Flow induces upward resistance to ice flow. vertical velocity. Boundary Conditions: Flow-diffusion stabilizes (No Slip) nd 2. 3. We solve the Orr-Sommerfeld + Linearized Exner Equation with a 2 order finite difference scheme. Conclusions Speed of ice flow impacts sea level rise Water velocity Lateral stresses diffuses laterally. established. Ice loss in Antarctica and Greenland directly Result: Carving into the Till is Faster than Carving into the Ice The mechanisms of channel contribute to sea level rise. initiation arise purely from the Since till and subglacial hydrology influence What are the factors that govern the time scales of each phase Assume: channel height ~ 1 cm. hydrology of the system. ice flow, it is crucial to understand them. 1. 4. (ice, water, sediment) for responding to the perturbation? grain diameter ~ 0.1 mm. Sediment Since ice melting is very -3 incline angle ~ 10 rad. Perturbation migration. slow, a channel initiates ICE induces Question: How do channels initiate? channel Counters by eroding the till first. 7 upward geometry ~ 10 s initial motion. Previous studies such as Walder and Density Latent heat Geothermal vertical velocity. Ice evolves very slowly. References Fowler [3] address the evolution of of ice (ρi) (Lw) heat flux (QG) ? 1. Fisher et al (2015). High geothermal heat flux existing channels. But what forms channel geometry Carving into till is faster. WATER The path forward... measured below the West Antarctic Ice Sheet. channels in the first place? • height [H] Science Advances, E1500093. 2. Meyer-Peter, E; Müller, R. (1948). Formulas for bed- • length [L] ~ 10-2 s Is a meltwater film capable of carving out a load transport. Proceedings of the 2nd Meeting of Water Viscosity (ν) • incline (α) the International Association for Hydraulic channel for itself? What are the mechanisms Ax = b Structures Research. pp. 39–64. that help or hinder this process? TILL 3. Walder, J. and Fowler, A (1994). Channelized channel geometry subglacial drainage over a deformable bed. Journal ~ 10 s of Glaciology, 40:134. vs Grain to Other regimes: what Till deformation: Does a film carve into the till or the ice? Grain Better numerics: 4. Weertman, J (1972). General Theory of Water Flow water density if sediment is as grain-scale at the Base of a Glacier or Ice Sheet. Reviews of Which process is faster? diameter [D] Porosity (p0) spectral methods ratio (G) fast as hydrology? simulations Geophysics and Space Physics, 10:1.