A distributed glacier model for RASM Jeremy Fyke, Bill Lipscomb Los Alamos National Laboratory

Goal: Simulate the coupled evolution of Arctic glaciers and ice caps within RASM – Evolving land ice area Affects vegetation extent and albedo – Evolving land ice volume Affects global mean sea-level and Arctic Ocean freshwater fluxes

Why model glaciers and ice caps? Mass loss from glaciers and ice caps is raising global mean sea level by ~0.5–1.0 mm/yr (Meier et al. 2007, Jacob et al. 2012) This is comparable to the sea-level contribution from the Greenland and Antarctic ice sheets Over centuries of warming, ice sheets will dominate, but over upcoming decadal scales (e.g. RASM simulations), glaciers matter

The problem of scale, non-continuity and dependence on fine-scale topography

Dynamic modeling vs. scaling/statistics The evolution of the Greenland Ice Sheet (and large ice caps?) is best modeled with a dynamic ice sheet model (e.g., CISM). – Need bed topography, 3D SMB, and numerical techniques It is not practical to model ~100,000 Arctic ice caps/glaciers in the Arctic with explicit dynamics. – For most glaciers we have no bed/thickness data Small ice caps and glaciers are best modeled (either singly or as a distribution) with semi-empirical area/volume scaling laws. – No bed topography or thickness data needed – Just need elevation-dependent area (hypsometry) & surface mass balance, b(z), at grid-cell scale

Scaling laws Semi-empirical scaling laws (Bahr et al., 1997, 1998, 2009…) relate characteristic glacier area to characteristic volume, elevation range, accumulation area ratio (AAR) Can estimate exponents by physical reasoning (e.g., γ=1.37 for glaciers, 1.25 for ice caps) Devon Ice Cap, CanadaLyell Glacier, California Bahr et al., 1997 “not good for one glacier, but good for thousands…”

Scaling-law model requirements Initial location and hypsometry (area-elevation distribution) for every Arctic glacier – Impossible requirement until early 2012 release of Randolph Glacier Inventory: global-coverage database of 153,429 polygon glacier outlines – RGI + ASTER 30m-resolution imagery = individual glacier hypsometry Annual-average vertical profile of glacier SMB – Currently prescribed (standalone mode) – Coupling to climate model requires land surface calculations at multiple dynamic elevation levels for each land surface grid cell (implemented for CLM, UVic ESCM, in progress at GISS)

Basics of a distributed glacier model Data provide glacier area-elevation distribution (hypsometry) and number-size distribution Climate model provides b(z) for a given grid cell. DGM computes area-integrated glacier mass balance b > 0 implies glacier advance, b < 0 implies retreat Volume change: ΔV = b A Δt Area change: From area-volume scaling, V i = c A i γ Change in terminus elevation: From area-range scaling, R i = k A i η Change in area-elevation distribution: Assume similar shape of hypsometric profile over time? Repeat…

Prototype prognostic model Slight deviation from standard recipe: Prescribe vertical equilibrium line altitude change (from land surface SMB model) Generate new AAR Nudge area/volume towards characteristic equilibrium AAR Net loss (ablation) Net gain (accumulation)

Test-case Iceland: hypsometry

Test-case Iceland: forcing Model forced with an idealized 200 m rise in ELA (equivalent to 2°C temperature change, with no change in precip) Smoothed hypsometry extracted for 299 glacier outlines in Iceland inventory Each glacier run forward for 2000 years (a few serial minutes on a laptop for everything – trivial) Individual ice mass changes converted to integrated change in volume

NEED: volume evolution (SLR equiv) of Iceland Test simulation

General coupling of glaciers/ice sheets to RASM will require some model development thinking … Vertical profiles of annual-average SMB  multiple dynamic-elevation-dependent land surface calculations per grid cell – ‘virtual’ (zero-area) or ‘allocatable’ land columns Vegetation model should follow retreating ice margin… …or yield to dynamically advancing ice margin… …and global conservation of heat/moisture should be maintained during any ice margin migration How to integrate two land ice modules (‘scaling’ for many small glaciers and ‘dynamic’ for few large ice caps) into RASM?

…and science thinking What is the contribution of glaciers/ice caps to Arctic Ocean freshwater flux (compared to snow melt)? How important is glacial topography/albedo to regional/pan-Arctic climate on decadal scales? How does interannual variability affect Arctic SMB (how does RASM simulate interannual variability)?

Issues with individual-glacier approach Delineated ‘glacier’ polygons in RGI may be multiple dynamic glaciers Tidewater glaciers break ‘scaling law’ rules Glacier inception: scaling model cannot grow new glaciers in currently un-glaciated terrain – May not be an issue in a warming climate 10 5 glaciers may become a database/memory issue, especially in a parallel environment… continuous glacier number-size distribution n(a) (analogous to sea ice thickness distribution g(h))