1. Closure of the Budget of Global Sea Level Rise Over the GRACE Era: The Importance and Magnitudes of the Corrections Required for Quaternary Ice-Age Influence W.R. Peltier Department of Physics University of Toronto

2. Continental Ice-Sheets and Glaciers in the Modern Climate System AntarcticaGreenland Alaska

3. Continental ice-sheets at the Last Maximum of Glaciation at ~ 21 ka Based upon a full coupled atmosphere- ocean climate reconstruction of LGM conditions using the NCAR CSM 1.4 model (Peltier and Solheim QSR 2002).

4. The Gravity Recovery And Climate Experiment--GRACE GRACE employs a K-band microwave link to measure the distance between the COM’s of the two platforms (10 microns in distance accuracy) GRACE employs a K-band microwave link to measure the distance between the COM’s of the two platforms (10 microns in distance accuracy) It delivers a new gravity field for each month of operation It delivers a new gravity field for each month of operation The time dependence of this global field is therefore measured directly The time dependence of this global field is therefore measured directly This time dependence may be interpreted in terms of the loss or gain of surface mass associated with both past and ongoing changes in surface ice cover This time dependence may be interpreted in terms of the loss or gain of surface mass associated with both past and ongoing changes in surface ice cover Interpretation of modern rates of change of surface ice cover require correction for ice-age influence Interpretation of modern rates of change of surface ice cover require correction for ice-age influence Orbit Orbit Altitude 485 km Altitude 485 km Inclination 89 degrees Inclination 89 degrees Eccentricity ~0.001 Eccentricity ~0.001 non-repeat ground track non-repeat ground track earth pointed, three axis stable earth pointed, three axis stable bus separation ~220 km bus separation ~220 km

5. The Sea Level Equation and rotational feedback The Sea Level Equation and rotational feedback A primitive version of the SLE was first formulated and solved in papers by Peltier et al and Clark et al in 1978 based upon the visco-elastic Green functions derived in Peltier 1974, 1976

6. Models of Glaciation History---ICE-5G NOTE: these figures are from the recent paper by Peltier and Fairbanks that appeared in the December 2006 issue of QSR (25, 3322-3337). The new Barbados RSL curve has also appeared in the Working Group 1 Report of the IPCC AR4

7. Holocene relative sea level histories

8. Three-dimensional displacement and the time- dependent gravitational field

9. Solutions of the sea Level Equation: Present-day rate of change of sea level Including rotational feedback Excluding rotational feedback (a)-(b) (a) + dU/dt =dG/dt

10. This is the geodynamic background of Ice-Earth-Ocean interactions within which GRACE is observing The modern signals associated with mass loss from the continents due to global warming of the lower atmosphere are observed against this background

11. What GRACE Is Observing? GRACE HydrologyGLDAS GRACE- GLDAS Global Land Data Assimilation System

12. GIA Corrected GRACE Data over North America and Greenland: the New ICE-6G (VM5A) Model

13. Estimating mass loss and global sea level rise: Alaska and Greenland Corrected for hydrology Corrected for GIA ~.15 mm/yr in Global sea level rise ~.62 mm/yr in Global sea level rise

14. Estimating mass loss and global sea level rise: Antarctica CSR GFZ GIA CSR-GIA GFZ-GIA ~.32 mm/yr in global sea level rise ~.36 mm/yr in Global sea level rise

15. Rate of mass addition to the oceans-unfiltered Global rate of SLR due to the Addition of mass To the oceans Based upon raw GRACE data = -0.28 mm/yr +/- 0.21 mm/yr Implying that the oceans are actually losing mass!!!

16. However- the GIA correction for the rate of mass addition to the oceans is VERY large and negative Gaussianhalf-widthsCoefficientsexcluded Max. Degree and order Mass rate over the oceans- mm/yr dGeoid over Oceans- mm/yr No filter none120-1.80-0.30 400 Km none120-1.65-0.29 No filter (2,1) rot feedback120-1.32-0.26 400 Km (2,1)120-1.17-0.26

17. A Question of (Mass) Balance, 2002-2008 Mass loss from the continents Greenland+Alaska+Antarctica = ~1.05 mm/yr (Peltier, 2009, QSR) Small ice sheets and glaciers = ~0.95 mm/yr (Meier et al, 2007, Science) Continental drying = ~0.17 mm/yr (GLDAS) TOTAL = 2.17 mm/yr +/- 0.37 mm/yr Mass gain by the oceans (Peltier, 2009, QSR) Raw GRACE signal =~-0.28 mm/yr Correction due to spectral leakage =~-0.43 mm/yr Correction due to GIA (ICE-5G(VM2)) =~-1.80 mm/yr TOTAL = 1.95 mm/yr +/- 0.16 mm/yr It will be clear that mass balance is achieved only because of the magnitude of the GIA correction for the rate of gain of mass by the oceans

18. Summary Inferences of the modern rates of mass loss from the land and gain by the oceans using time dependent gravity data from GRACE are strongly contaminated by continuing ice-age influence. Inferences of the modern rates of mass loss from the land and gain by the oceans using time dependent gravity data from GRACE are strongly contaminated by continuing ice-age influence. The feedback onto sea level history due to the change in Earth’s rotational state caused by the Late quaternary ice-age cycle is profound and easily discernable in radio- carbon dated sea level histories from the Holocene interval of time. The feedback onto sea level history due to the change in Earth’s rotational state caused by the Late quaternary ice-age cycle is profound and easily discernable in radio- carbon dated sea level histories from the Holocene interval of time. This feedback profoundly influences the correction that must be applied to GRACE data in estimating the rate at which the oceans are gaining mass due to the melting of land ice. In the absence of the ice-age correction it would appear that the oceans were not gaining mass at all! This feedback profoundly influences the correction that must be applied to GRACE data in estimating the rate at which the oceans are gaining mass due to the melting of land ice. In the absence of the ice-age correction it would appear that the oceans were not gaining mass at all! When the appropriate ice-age corrections are computed using the ICE-5G (VM2) model of Earth-Ice-Ocean interactions the sea level budget is closed. IN the absence of these corrections it is not. When the appropriate ice-age corrections are computed using the ICE-5G (VM2) model of Earth-Ice-Ocean interactions the sea level budget is closed. IN the absence of these corrections it is not.

19. Sensitivity of Earth Rotation Predictions to Mantle Viscosity Frechet Kernels for the Mantle Viscosity Inverse Problem Fennoscandian Relaxation Times For Laurentide Rebound Polar Wander Speed and J2-dot Mantle Viscosity Profiles Inferred by Formal Bayesian Inversion Viscosity Fixed By Relaxation Time Data Viscosity Controlled by Earth Rotation QUESTION: Given the newly constructed ICE-5G model of global deglaciation, how well constrained is the viscosity in the lowermost mantle?

20. The Theory of Ice-Earth-Ocean Interactions The goal of this research is to demonstrate that it is impossible to understand the degree to which land ice is disappearing from the surface of the continents under modern climate conditions without fully understanding the continuing influence upon the gravitational field of the planet due to the most recent glacial cycle of the Late Quaternary Period. the main results in the presentation will be found in Peltier (2009, QSR, doi: 10.1016/j.quascirev.2009.04.004).

21. A Second Aside on Global Glaciation History In order to make accurate predictions of ice-age related influence the space-time distribution of continental ice must be accurately specified

22. Back to the Problem of GRACE Interpretation and the Sea Level Budget Closure Problem Verifying the quality of the model of ice-age influence

23. Sensitivity to gaussian filter halfwidth

24. Sensitivity to number of terms in the fit and to filter half-width: North America and Greenland

25. Comparison of GRACE with GIA: North America and Greenland

26. The Sea Level Budget Closure Problem: Is the rate at which mass is being added to the oceans equal to the rate of mass loss from the land?

27. Outline Motivation: To establish (1) that the mass being lost from the land is balanced by the mass gained by the oceans and (2) that when the sea level equivalent mass gained by the oceans is added to the steric contribution to sea level one fits the Topex/Poseidon-Jason-1 observations Motivation: To establish (1) that the mass being lost from the land is balanced by the mass gained by the oceans and (2) that when the sea level equivalent mass gained by the oceans is added to the steric contribution to sea level one fits the Topex/Poseidon-Jason-1 observations GRACE data analyses of the rates of mass loss from Greenland, Alaska and Antarctica. GRACE data analyses of the rates of mass loss from Greenland, Alaska and Antarctica. Contributions from small ice-sheets and glaciers and continental dessication Contributions from small ice-sheets and glaciers and continental dessication GRACE analysis of the sea level equivalent rate of gain of mass by the oceans: the critical role of the GIA correction GRACE analysis of the sea level equivalent rate of gain of mass by the oceans: the critical role of the GIA correction Sea level budget closure as a means of assessing the validity of the ICE-5G(VM2) predictions of the degree 2 and order 1 Stokes coefficients Sea level budget closure as a means of assessing the validity of the ICE-5G(VM2) predictions of the degree 2 and order 1 Stokes coefficients Summary Summary