Ten Fifteen Years of Development on UMISM: Application to Advance and Retreat of the Siple Coast Region James L Fastook Jesse V Johnson Sean Birkel We thank the NSF, which has supported the development of this model over many years through several different grants.

INTRODUCTION: UMISM ● The University of Maine Ice Sheet Model has expanded from the original mass and momentum ICE DYNAMICS solver which forms its core, to include components for calculating: – THERMODYNAMICS for internal ice temperatures. – ISOSTASY for the response of the bed to changing ice load. – BASAL WATER for the distribution and movement of water produced by basal melting, used to predict regions where sliding occurs.

INTRODUCTION: (continued) – CLIMATE for the response of the net accumulation rates to changing climate and ice sheet configuration. – ICE SHELF/CALVING for the grounding line response to the changing ice sheet. – EMBEDDED model, for better resolution with reasonable run times. ● All of these are important improvements that increase the accuracy of the physics, as well as the realism and utility of the model.

ICE DYNAMICS ● Shallow Ice Approximation: – Numerically integrated momentum through the vertical. – Temperature-dependent ice hardness. – NO LONGITUDINAL STRESSES !!

ICE DYNAMICS: (continued) ● INPUT: – Mass balance (from CLIMATE). – Sliding distribution (from BASAL WATER). – Bed (from ISOSTASY). – Ice hardness (from THERMODYNAMICS). ● OUTPUT: – Ice thickness (for ISOSTASY and BASAL WATER). – Ice surface elevation (for CLIMATE). – Velocities (for THERMODYNAMICS).

THERMODYNAMICS ● Energy Conservation: – 1-D temperature profiles. – Vertical diffusion and advection. – NO horizontal diffusion (OK). – NO horizontal advection (maybe NOT OK). ● Surface Boundary conditions: Temperature (from CLIMATE). ● Basal Boundary conditions: Geothermal heat flux OR Presence of water (from BASAL WATER). ● Other heat sources: Internal shear and/or Basal sliding (both from ICE DYNAMICS).

THERMODYNAMICS (continued) ● INPUT: – Surface temperature and mass balance (from CLIMATE). – Geothermal heat flux. – Internal heat sources (from ICE DYNAMICS). – Presence of water (from BASAL WATER). ● OUTPUT: – Internal temperatures (for ICE DYNAMICS). – Basal temperature and melt/freeze rates (for BASAL WATER).

ISOSTASY ● Several models: – Pseudo-elastic, hydrostatically-supported plate (SLOW). – Viscous point loading (FAST). – Visco-elastic plate (COMING SOON). ● INPUT: – Ice thickness (from ICE DYNAMICS). ● OUTPUT: – Bed elevation (for ICE DYNAMICS and CLIMATE).

BASAL WATER ● Conservation of water: – Basal melt/freeze rates as source. – Movement down hydrostatic gradient. – Diffusive, Advective, Loss to aquifer terms. ● INPUT: – Ice thickness (from ICE DYNAMICS). – Bed (from ISOSTASY). – Melt/freeze rates (from THERMODYNAMICS). ● OUTPUT: – Basal water amount (for ICE DYNAMICS to define sliding area and magnitude).

CLIMATE (several) ● Simple lapse rate: – Surface temperature from latitude and elevation lapse rates. – Accumulation proportional to temperature. ● (warm: LOTS, cold: LITTLE) – Positive Degree Days from latitude-dependent imposed seasonal amplitude. – Ablation proportional to PDD. – Net Mass Balance = Accumulation – Ablation.

CLIMATE (continued) ● INPUT: – Ice Elevation (from ICE DYNAMICS). – Bed (from ISOSTASY). – Latitude. ● OUTPUT: – Surface temperature (for THERMODYNAMICS). – Net Mass Balance (for ICE DYNAMICS and THERMODYNAMICS).

CLIMATE (better) ● NCEP2 data-based: From re-analysis gridded monthly-mean temperature and monthly total precipitation. – Partition precipitation into SNOW or RAIN depending on monthly mean temperature adjusted for “climate knob”and lapse rate-based elevation change. ● Accumulation = SNOW. – Count PDD from monthly mean temperatures adjusted for “climate knob” and lapse rate-based elevation change. ● Ablation proportional to PDD. – Net Mass Balance = Accumulation – Ablation. ● INPUT/OUTPUT: the same.

CLIMATE (further...) ● GCM result-based: – LGM configuration provided as topography input to GCM (Bromwich). – Results: gridded monthly-mean temperature and monthly total precipitation. – Same treatment as NCEP2 data-based. – NCEP2 data-based: “Modern” climate. – GCM results-based: “Ice Age” climate. – Switch between the two by some proxy. ● (sea level ??? internally calculated). ● INPUT/OUTPUT: the same.

ICE SHELF/CALVING ● A parameterization of Weertman slab thinning is used to control advance and retreat of the grounding line through application of an ablation rate (i.e., thinning) in elements containing a grounding line. ● Improvements include a more complete treatment of the ice shelf that forms in front of the grounding line. This will require a more complete treatment of the longitudinal stresses (the Morland equations), currently absent from the model.

EMBEDDED MODELS ● High-resolution, limited domain – runs inside ● Low-resolution, larger domain model. ● Modeling the whole ice sheet allows margins to be internally generated. – No need to specify flux or ice thickness along a boundary transecting an ice sheet. ● Specification of appropriate Boundary Conditions for limited-domain model, based on spatial and temporal interpolations of larger-domain model.

APPLICATION TO SIPLE COAST: A GLACIAL CYCLE with 3 climate proxies. ● Temperature proxies for the “climate knob” are derived from deep cores, Vostok, Byrd, and Taylor. ● A glacial cycle beginning at 88 KBP is run to the present. ● “Climate knob,” areal extent, and flotation volume are shown.

Ice Surface Difference for Vostok Proxy, at 15 KBP, immediately before retreat occurs. Full-domain: nodes, 40 km spacing, 10 yr timesteps, 2 hr runtime. Limited-domain: 5600 nodes, 20 km spacing, 5 yr timesteps, 2.4 hr runtime.

Ice Surface and Bathymetry for Vostok Proxy, at 15 KBP, immediately before retreat occurs.

Velocity for Vostok Proxy, at 15 KBP, immediately before retreat occurs.

Velocity for Vostok Proxy, at present.

Velocity for Vostok Proxy, at 15 KBP and at present.

Ice Surface Difference at 69KBP, at time during growth where the Ross Ice Shelf is just grounded and thickening at Siple Dome is minimal.

FLOTATION VOLUMES ● Sea Level Equivalent at present: m.s.l. ● Sea Level Equivalent at -15,000: m.s.l. – m lower. ● Sea Level Equivalent at -69,000: m.s.l. – 0.89 m lower.

Velocity for Vostok Proxy, at 15 KBP, immediately before retreat occurs.

Velocity for Vostok Proxy, at 14 KBP.

Velocity for Vostok Proxy, at 13 KBP.

Velocity for Vostok Proxy, at 12.9 KBP.

Velocity for Vostok Proxy, at 12.8 KBP.

Velocity for Vostok Proxy, at 12.7 KBP.

Velocity for Vostok Proxy, at 12.6 KBP.

Velocity for Vostok Proxy, at 12.5 KBP.

Velocity for Vostok Proxy, at 12.4 KBP.

Velocity for Vostok Proxy, at 12.3 KBP.

Velocity for Vostok Proxy, at 12.2 KBP.

Velocity for Vostok Proxy, at 12.1 KBP.

Velocity for Vostok Proxy, at 12 KBP.

Velocity for Vostok Proxy, at 11.9 KBP.

Velocity for Vostok Proxy, at 11.8 KBP.

Velocity for Vostok Proxy, at 11.7 KBP.

Velocity for Vostok Proxy, at 11.6 KBP.

Velocity for Vostok Proxy, at 11.5 KBP.

Velocity for Vostok Proxy, at 11.4 KBP.

Velocity for Vostok Proxy, at 11.3 KBP.

Velocity for Vostok Proxy, at 11.2 KBP.

Velocity for Vostok Proxy, at 11.1 KBP.

Velocity for Vostok Proxy, at 11 KBP.

Velocity for Vostok Proxy, at 10 KBP.

Velocity for Vostok Proxy, at 9 KBP.

Velocity for Vostok Proxy, at 8 KBP.

Velocity for Vostok Proxy, at 7 KBP.

Velocity for Vostok Proxy, at 6 KBP.

Velocity for Vostok Proxy, at 5 KBP.

Velocity for Vostok Proxy, at 4 KBP.

Velocity for Vostok Proxy, at 3 KBP.

Velocity for Vostok Proxy, at 2 KBP.

Velocity for Vostok Proxy, at 1 KBP.

Velocity for Vostok Proxy, at present.