Basal Shear Stress of the Ross Ice Streams from Control Method

Inversions Ian Joughin

Jet Propulsion Lab, California Institute of TechnologySlawek Tulaczyk

University of California, Santa CruzDouglas R. MacAyeal

Dept. of Geophysical Sciences, University of Chicago

Merce

rWhillansKambBindschad

lerMacAyeal

A

BC

D

E

Ice Stream Motion Over a Till Bed

Ice ~1000 m

Till ~6 m

Dep

th

Velocity

Dep

th

Velocity

Viscous Deforming Bed(Alley,Blankenship et al)

Weak Plastic Bed (Kamb,Tulaczyk,Engelhardt et

al)

A weak bed implies inability to support high driving stress

Ice Stream Equations

022 2

x

zgHu

x

v

y

uH

yy

v

x

uH

xs

Viscous

0ˆ22 2

x

zgH

x

v

y

uH

yy

v

x

uH

xs

Plastic

Control-method techniques can be used to invert equations for basal shear stress (MacAyeal, 1992).

•Similar solutions for both plastic and viscous models (force balance).

•Inversions are robust with respect to errors in velocity and bed topography.

•Inversions are sensitive to surface elevation noise

Inversion Result

Forward Model

NoiseInversion Procedure

Inversion Simulations

Bed Elevation - BEDMAP

Data Sets

Surface Elevation – RAMP/SOAR

B – Temperature Model

E=1 E=3

b (kPa) b (kPa)

Ice Stream Box d

(kPa) Viscous Plastic db Viscous Plastic db

BT 40.7 8.4 12.6 26% 17.0 24.4 51% B1 20.7 1.2 1.8 7% 4.3 5.8 24% B2 15.4 2.8 2.8 18% 5.5 5.3 35% MB 20.5 6.2 6.0 30% 8.6 9.0 43%

Ice Stream B

DB 7.9 0.6 0.5 7% 2.5 2.3 31%

Ice Streams A&B

Ice Stream C

E=1 E=3

b (kPa) b (kPa)

Ice Stream Box d

(kPa) Viscous Plastic db Viscous Plastic db

CT1 58.5 36.4 36.5 62% 43.0 42.9 73% CT2 90.0 77.8 81.3 88% 81.0 84.5 92% CO 44.7 9.6 11.0 23% 18.8 19.3 43% CA 18.5 8.5 8.6 46% 10.7 10.7 58%

Ice Stream C

CS 23.1 18.8 18.0 80% 19.5 18.6 82%

E=1 E=3

b (kPa) b (kPa)

Ice Stream Box d

(kPa) Viscous Plastic db Viscous Plastic db

DT 45.3 38.8 39.4 86% 40.1 42.0 91% DO 29.7 7.7 9.2 28% 13.6 13.8 46% UD 23.2 0.8 1.2 4% 6.7 7.2 30%

Ice Stream D

DS 11.8 3.9 4.2 34% 5.5 5.8 48%

Ice Stream E ES 21.4 14.8 14.9 69% 16.1 15.9 75%

Ice Streams D&E

Weak Margins ?

Summary

Fairly uniform weak (few kPa) bed beneath ice streams (E has significant sticky spots).

Tributaries a mixture of strong and weak bedded regions.

Some ambiguity in basal shear stress because flow law not well constrained.

Neither model nor data appear to support weak margins.