1. Inferring Transients in Ice Flow, Ice-Sheet Thickness, and Accumulation Rate from Internal Layers (near the WAIS Divide ice-core site) Michelle Koutnik, Ed Waddington, Howard Conway University of Washington Tom Neumann NASA Steve Price Los Alamos National Laboratory

2. Radar profile from WAIS Divide (e.g. Neumann et al. 2008)

3. Radar profile from WAIS Divide (e.g. Neumann et al. 2008)

4. Radar profile from WAIS Divide ice core

5. Conway and Rasmussen (2009)Dixon et al. (2004) Modern surface velocity Modern accumulation rate

6. How do we infer histories of accumulation and ice dynamics from internal layers? How well can we infer histories of accumulation and ice dynamics from internal layers?

7. How do we infer histories of accumulation and ice flow from internal layers? Estimate unknowns (e.g. accumulation-rate history)

8. How do we infer histories of accumulation and ice flow from internal layers? Estimate unknowns (e.g. accumulation-rate history) Track particles through transient velocity field Generate internal layers

9. How do we infer histories of accumulation and ice flow from internal layers? Estimate unknowns (e.g. accumulation-rate history) Track particles through transient velocity field Generate internal layers Compare modeled observables to measured quantities; update parameters iterate.

10. DATA SET (known) Internal layers Layer ages Modern ice velocity (from GPS) Geometry Accumulation rates at any point and time

11. DATA SET (known) Internal layers Layer ages Modern ice velocity (from GPS) Geometry Accumulation rates at any point and time PARAMETER SET (unknown) Accumulation rate (x,t) External-flux forcing (x bounds,t) Ice thickness (x 0,t 0 ) Layer ages Ice flux into solution domain (x 0,t 0 ) Temperature-independent ice softness Geothermal flux

12. FORWARD ALGORITHM 2.5-D thermomechanical ice-flow model. Ice-surface evolution Ice-temperature evolution Ice-velocity field Track particles to map out an internal layer.

13. FORWARD ALGORITHM 2.5-D thermomechanical ice-flow model. Ice-surface evolution Ice-temperature evolution Ice-velocity field Track particles to map out an internal layer. INVERSE ALGORITHM Use a gradient inverse method. Regularized problem: Fit data within a tolerance Smooth accumulation profile Linearized problem Find updates to parameter estimates.

14. “There may be no model that exactly fits the data.” “If exact solutions exist, they may not be unique…” “The process of computing an inverse solution can be, and often is, extremely unstable in that a small change in measurement can lead to an enormous change in the estimated model.” (Aster et al. 2005, pg. 12)

15. Regularized problem Model size Model residuals

16. Linearized problem Model size Model residuals

17. How well can we infer histories of accumulation and ice flow from internal layers? Accumulation rate (x,t) External-flux forcing (x bounds,t) Ice thickness (x 0,t 0 ) Layer ages Ice flux into solution domain (x 0,t 0 ) Temperature-independent ice softness Geothermal flux

18. Two histories.

19. Ice divide Ice surface data = “data”

20. magenta = initial guess grey = actual (known) solution blue = inferred solution surface bed

21. magenta = initial guess grey = actual (known) solution blue = inferred solution

22. present day

23. What if accumulation rates are known through time?

24. magenta = initial guess grey = actual (known) solution blue = inferred solution black = inferred with accumulation rates through time

25. magenta = initial guess grey = actual (known) solution blue = inferred solution black = inferred with accumulation rates through time

27. … and with a different history…

30. “West Antarctica”

32. History of external flux?

34. Preliminary results: - Internal layers can be used to infer: accumulation-rate history ice-thickness (ice divide) history externally forced flux history - There may be some tradeoff between parameters, but accumulation rates through time may provide rate control - Requiring a spatially smooth accumulation history can sufficiently regularize this inverse problem Near WAIS Divide ice-core site: - Extend spatial and temporal histories beyond the Holocene - Use layers dated from the ice core

36. Regularized problem (see e.g. Eisen 2008)