Modeling of Subaqueous Melting of

Greenland Tidewater glaciers

Yun Xu1, Eric Rignot1,2, Dimitris Menemenlis2, Ian Fenty2, Mar Flexas2, François Primeau1

1 Earth System Science, University of California Irvine, Irvine, CA, United States2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, United States

Subaqueous Melting

– Melting occurs on the vertical calving face of tidewater glaciers

– large subaqueous melt rate [m/day]

– a potential trigger of calving

– causes glacier un-grounding and retreat, trigger glacier acceleration

Warm water

Subglacial runoff (fresh, cold)

(Motyka, 2003; Rignot et al., 2010)

Modeling of subaqueous melting with MITgcm

Melt water

subglacial runoffx

z

ΓT, ΓT follow Jenkins et al. (2010)

γT0, γS0 follow Losch (2008)

γT / γS Heat /salinity transfer coefficientW Vertical velocity

TB/SB Temperature/salinity at the BoundaryT / S Temperature/salinity of ocean water

2-D Sensitivity Experiments Results1. Melt rate (q) vs subglacial flux (Qsg)

q depends on Qsg: q is very small when there is no Qsg, and increases sub-linearly with Qsg. q is not sensitive to channel height q ~ m/d

2. Melt rate (q) vs thermal forcing (TF) TF = ocean temperature – freezing point

q increases linearly with TF

2-D Sensitivity Experiments – 20 m(h) x 5 m(v) resolution

Subglacial plume is not resolved

— 3D high-resolution

3-D Experiments

5 km

500 m

Resolution (ΔX × ΔY × ΔZ) : 2m × 2m × 1-2m

Domain size (L × W × H) : 1000m × 300m × 500m

Subglacial discharge* : ~30 m3/s

* Subglacial freshwater discharge in summer is ~500 m3/s (RACMO data), assumed to enter the ocean through discrete subglacial channels over 5-km ice front.

Simplifi

ed

Store Glacier

Subglacial Channel SizeAssume one channel in the middle of the domain.

Store glacier is close to hydrostatic equilibrium or afloat at the

terminus. The channel could be very big.

Tank experiments: In big channels,

fresh water could flow only through the top of the channel to ensure Fr > 1.

Fr = inertia / buoyancy =

10 m

3 m1 m/s

In this designed channel,

Fr = 1.13,

Re = 5000, (108 in

reality)

3-D Model ConfigurationFree surface, non-hydrostatic regime

Domain Size (L × W × H) 1000m × 300m × 500m

Resolution (ΔX × ΔY × ΔZ) 2 m × 2 m × 1-2 m

Ocean Forcing T, S from field observation

Subglacial channel size (W × H) 10 × 3 m

plume speed 1.0 m/s

viscA4 0.1

diffusivity 0

Results - Salinity

Distance to the ice(m)

Dep

th (m

)

Distance to the plume(m)

View from side View from ice

Temperature

Distance to the ice

(m)

Dep

th (m

)

Distance to the plume

(m)

View from side View from ice

Melt Rete

Dep

th (m

)

Distance to the plume(m)

View from ice

Average melt rate=

1.7 m/d

Melt Rate Derived FromObservations

Based on mass, heat and salinity conservation,

melt rate = 1.6 ± 1 m/dErrors mainly from1. velocity measurement, 2. omission of top 10m,3. constant current velocity assumption

where there is no measurement, and 4. tidal currents

Conclusions• The MITgcm shows that subglacial runoff is dependent on the

subglacial runoff and the ocean thermal forcing in 2-D sensitivity experiments.

• The growth of turbulent plume is resolved in the 3-D 2 m-resolution experiment. This upwelling plume brings heat from ocean bottom to the ice face to melt the ice.

• The summer melt rate of Store Glacier is about 1.7 m/d in the model, close to the observation derived melt rate of 1.6 ± 1 m/d.

• Several aspects of the model require more work, e.g. – sensitivity on subglacial runoff configuration;

– apply to larger domain.

Thank You!