This problem represents an interesting opportunity for scientists and statisticians to collaborate since the problem is too big for either community. The science is not well established, although fairly sophisticated ice flow models exist. They are even becoming relevant to explain some of the complexity seen in observational data. At the same time, the complex phenomena we see in observations may not be particularly relevant to assessing the risks of significant increases in sea level rise over the near future. The talk will review what we have learned about this problem through the PISCEES SciDAC project. This problem is rich with challenges and opportunities, particularly for realigning how our two communities engage each other. The talk will review the computational, scientific, and mathematical "reality checks" that might stop any reasonable person from considering this topic further. I then will point out how each of these challenges could be mitigated if these different perspectives were better integrated.

1. Ice Sheet Contribution to
Sea Level Rise
Charles Jackson
University of Texas – Austin
SAMSI Climate Opening Workshop August 21 – 25, 2017

2. SAMSI Climate Opening Workshop August 21 – 25, 2017
Support provided by
1. DOE SciDAC PISCEES (Predicting Ice Sheet and Climate
Evolution at Extreme Scales) grant DE-SC0008083 (Jackson,
Martin)
2. NASA ROSES grant 11AH89G (Jackson, Waibel)
3. NSF Polar Programs grant ANT-1142139 (Jackson, Hulbe)

3. SAMSI Climate Opening Workshop August 21 – 25, 2017
Outline
1. What are the science goals of UQ for
climate?
2. Problem of uncertainty in ice sheet initial
conditions.
3. Some defining characteristics of Marine Ice
Sheet Instability important to UQ.

4. What are the science goals
of UQ for climate?
Feynman gives a simple demonstration for a theory explaining
Challenger Shuttle disaster.

5. SAMSI Climate Opening Workshop August 21 – 25, 2017
Application of uncertainty
quantification to climate
There are significant computational, scientific,
and mathematical reality checks that confront
UQ approaches to climate. The challenges can
be mitigated by a better integration of efforts
from these different perspectives on UQ.

7. Likelihood test statistic
Bayesian expression for observational
constraints on parameter value selection
g(m) is climate model prediction of observations dobs.
C-1 is an inverse covariance matrix of modeling and
observational errors.

8. Computational costs
Atmosphere model
• 4-year integration of 1° CAM: $60
• 4-year integration of ¼° CAM: $20k
Ice sheet model
• 40,000 year integration of 1 km “higher order”
Antarctica: $600k

9. Projecting Ice Sheet and Climate Evolution
at Extreme Scales (PISCEES)
Stephen Price5 and Esmond Ng8
M. Eldred1, X. Asay-Davis*, K. Evans2, O. Ghattas6, M. Gunzburger3, P. Heimbach4,6, M. Hoffman*, C. Jackson6, J.
Jakeman1, L. Ju7, W. Lipscomb5, D. Martin8, M. Perego1, W. Sacks9, A . Salinger1, G. Stadler6, I. Tezaur1, R. Tuminaro1, M.
Vertenstein9, S. Williams8, P. Worley2
1Sandia National Laboratories, 2Oak Ridge National Laboratory,
3Florida State University, 4Massachusets Institute of Technology,
5Los Alamos National Laboratory, 6University of Texas at Austin,
7University of South Carolina, 8Lawrence Berkeley National Laboratory,
9National Center for Atmospheric Research
Supported by DOE Office of Science ASCR & BER through SciDAC
Additional Acknowledgements

11. (Dieng et al., 2017)

12. (IPCC AR5)

13. T. Isaac et al. / Journal of Computational Physics 296 (2015) 348–368

14. T. Isaac et al. / Journal of Computational Physics 296 (2015) 348–368

15. Eigenvectors of the Objective function Hessian
1st 2nd 100th
200th 500th 4000th

16. Eigenvalues of the Objective function Hessian
T. Isaac et al. / Journal of Computational Physics 296 (2015) 348–368

17. In a linear system with a scalar quantity of interest,
uncertainty is one dimensional. (Wilcox MIT)

18. Q: How do uncertainties in the basal traction parameter affect projections of sea level rise?
Uncertain parametersData
MAP
estimate
uncertainty
Surface velocity
Surface elevation
basal traction
Adjoint-based
Optimal Initialization
Inverse
UQ
Forward Propagation
of Uncertainties
Intrusive
Non-intrusive
Hessian
KLE expansion
+
Environmental forcing
Sea Level
Rise at
2200
surrogate
UQ Workflow
Bed topography
Active Subspaces M1

19. Marine Ice Sheet Instability
• Greatest potential for large (> 1 m) and rapid
increase in sea level.
• Ice bed topography is important and
uncertain. This was our initial focus.
• Turns out mass loss rate is very sensitive to
forcing across point of instability.

20. 90 Gigatons of ice is lost each year from Antarctica
NASA (http://svs.gsfc.nasa.gov/30492)

21. Thwaites and Pine Island basins

23. Marine Ice Sheet Instability
• Marine ice sheet instability is a 2D theory.
• Driving stresses proportional to thickness and
surface slope.
• Driving stresses increase as glacier retreats.
Profile of Thwaites from radar

24. Scott Waibel
Portland State University
Christina Hulbe
University of Otago, NZ
Dan Martin
Lawrence Berkeley Laboratory
SAMSI Climate Opening Workshop August 21 – 25, 2017
Additional Acknowledgements

25. Saving computational costs with BISICLES ice flow model
• Vertically averaged “L1L2” equations (Schoof and Hindmarsh 2010)
• Includes longitudinal coupling
• Good for fast sliding regimes
• 250 SUs / simulated year
S.L. Cornford, D.F. Martin, et al. "Adaptive
mesh, finite volume modeling of marine
ice sheets.", Journal of Computational
Physics, 232(1):529-549 (2013)

27. Experiment design
• Identify “trigger” forcing.
– Ramp up ocean melt slowly 1 m/year every 20
years
– Identify year at which dynamics contribute
significantly to mass loss. This is the point of
instability.
• At point of instability, turn off anomalous
forcing. Allow system to evolve freely.

32. 3D view of grounding line retreat
20x
VE

33. • Extra 10 years of forcing produced a 25% greater mass loss
rate that was sustained for entire 2000 years of retreat.
• Results are sensitive details of background melt profile and
number of pinning points.

36. G425
B260
B270

38. Once the instability was triggered, the rough bed resulted in a quicker deglaciation
B270 G425

39. G425 sustained a 30 - 235% greater mass loss rate
relative to B270 for 400 years
B270
Topography is not important to determining mass loss rates.
G425

40. B270G425
B260
Sealevelequivalent(mm)

41. SAMSI Climate Opening Workshop August 21 – 25, 2017
How rapidly ocean delivers heat to ice front in
the near future has a strong impact on rate of
sea level rise for next 1000 years.

42. SAMSI Climate Opening Workshop August 21 – 25, 2017
What I find most interesting and challenging
about the application of uncertainty
quantification to sea level rise is:
• The importance of learning from model
predictions to help determine the most
relevant experiment and observations.
• The extent to which we need to represent
uncertainties in boundary condition data.