Closure of the Budget of Global Sea Level Rise Closure of the Budget of Global Sea Level Rise Over the GRACE Era: The Importance and Over the GRACE Era: The Importance and Magnitudes of the Corrections Required for Magnitudes of the Corrections Required for

Quaternary Ice-Age InfluenceQuaternary Ice-Age Influence

W.R. PeltierW.R. Peltier

Department of PhysicsDepartment of Physics

University of TorontoUniversity of Toronto

Continental Ice-Sheets and GlaciersContinental Ice-Sheets and Glaciersin the Modern Climate Systemin the Modern Climate System

Antarctica Greenland Alaska

Continental ice-sheets at the Last Maximum Continental ice-sheets at the Last Maximum of Glaciation at ~ 21 kaof Glaciation at ~ 21 ka

Based upon a fullcoupled atmosphere-ocean climate reconstruction ofLGM conditions usingthe NCAR CSM 1.4model (Peltier andSolheim QSR 2002).

The Gravity Recovery And Climate The Gravity Recovery And Climate Experiment--GRACEExperiment--GRACE

GRACE employs a K-band microwave GRACE employs a K-band microwave link to measure the distance between link to measure the distance between the COM’s of the two platforms (10 the COM’s of the two platforms (10 microns in distance accuracy)microns in distance accuracy)

It delivers a new gravity field for each It delivers a new gravity field for each month of operationmonth of operation

The time dependence of this global The time dependence of this global field is therefore measured directlyfield is therefore measured directly

This time dependence may be This time dependence may be interpreted in terms of the loss or gain interpreted in terms of the loss or gain of surface mass associated with both of surface mass associated with both past and ongoing changes in surface past and ongoing changes in surface ice coverice cover

Interpretation of modern rates of Interpretation of modern rates of change of surface ice cover require change of surface ice cover require correction for ice-age influence correction for ice-age influence

OrbitOrbit Altitude 485 kmAltitude 485 km Inclination 89 degreesInclination 89 degrees Eccentricity ~0.001Eccentricity ~0.001 non-repeat ground tracknon-repeat ground track earth pointed, three axis stableearth pointed, three axis stable bus separation ~220 kmbus separation ~220 km

The Sea Level Equation and rotational The Sea Level Equation and rotational feedbackfeedback

A primitiveversion of theSLE was firstformulated and solvedin papers byPeltier et aland Clark et alin 1978 basedupon the visco-elasticGreen functionsderived inPeltier 1974,1976

Models of Glaciation History---ICE-5GModels of Glaciation History---ICE-5G

NOTE: these figures are from the recent paper by Peltier and Fairbanks thatappeared in the December 2006 issue of QSR (25, 3322-3337). The new BarbadosRSL curve has also appeared in the Working Group 1 Report of the IPCC AR4

Holocene relative sea level historiesHolocene relative sea level histories

Three-dimensional displacement and the time-Three-dimensional displacement and the time-dependent gravitational fielddependent gravitational field

Solutions of the sea Level Equation: Solutions of the sea Level Equation: Present-day rate of change of sea levelPresent-day rate of change of sea level

Includingrotationalfeedback

Excludingrotationalfeedback

(a)-(b)(a) +dU/dt=dG/dt

This is the geodynamic background of Ice-Earth-Oceaninteractions within which GRACE is observing

The modern signals associated with massloss from the continents due to global warmingof the lower atmosphere are observed against this background

What GRACE Is Observing?What GRACE Is Observing?

GRACE

Hydrology GLDAS

GRACE-GLDAS

Global Land DataAssimilation System

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

Estimating mass loss and global sea level Estimating mass loss and global sea level rise: Alaska and Greenlandrise: Alaska and Greenland

Corrected forhydrology

Corrected for GIA

~.15 mm/yr in Global sea level rise

~.62 mm/yr inGlobal sea level rise

Estimating mass loss and global sea level rise: Estimating mass loss and global sea level rise: AntarcticaAntarctica

CSR GFZ

GIA

CSR-GIA GFZ-GIA

~.32 mm/yr inglobal sea levelrise

~.36 mm/yr inGlobal sea level rise

Rate of mass addition to the oceans-unfilteredRate of mass addition to the oceans-unfiltered

Global rate ofSLR due to theAddition of massTo the oceansBased upon rawGRACE data= -0.28 mm/yr+/- 0.21 mm/yr

Implying that the oceans are actually losingmass!!!

However- the GIA correction for the rate of mass However- the GIA correction for the rate of mass addition to the oceans is VERY large and negativeaddition to the oceans is VERY large and negative

Gaussian Gaussian

half-widthshalf-widths

CoefficientsCoefficients

excludedexcluded

Max. Degree Max. Degree and orderand order

Mass rate Mass rate over the over the oceans-mm/yoceans-mm/yrr

dGeoid overdGeoid over

Oceans-Oceans-mm/yrmm/yr

No filterNo filter nonenone 120120 -1.80 -1.80 -0.30-0.30

400 Km400 Km nonenone 120120 -1.65-1.65 -0.29-0.29

No filterNo filter (2,1) rot(2,1) rot

feedbackfeedback

120120 -1.32-1.32 -0.26-0.26

400 Km400 Km (2,1)(2,1) 120120 -1.17-1.17 -0.26-0.26

A Question of (Mass) Balance, 2002-2008A 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/yrCorrection due to spectral leakage =~-0.43 mm/yrCorrection 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

SummarySummary

Inferences of the modern rates of mass loss from the Inferences of the modern rates of mass loss from the land and gain by the oceans using time dependent land and gain by the oceans using time dependent gravity data from GRACE are strongly contaminated by gravity data from GRACE are strongly contaminated by continuing ice-age influence.continuing ice-age influence.

The feedback onto sea level history due to the change in The feedback onto sea level history due to the change in Earth’s rotational state caused by the Late quaternary Earth’s rotational state caused by the Late quaternary ice-age cycle is profound and easily discernable in radio-ice-age cycle is profound and easily discernable in radio-carbon dated sea level histories from the Holocene carbon dated sea level histories from the Holocene interval of time.interval of time.

This feedback profoundly influences the correction that This feedback profoundly influences the correction that must be applied to GRACE data in estimating the rate at must be applied to GRACE data in estimating the rate at which the oceans are gaining mass due to the melting of which the oceans are gaining mass due to the melting of land ice. In the absence of the ice-age correction it would land ice. In the absence of the ice-age correction it would appear that the oceans were not gaining mass at all!appear that the oceans were not gaining mass at all!

When the appropriate ice-age corrections are computed When the appropriate ice-age corrections are computed using the ICE-5G (VM2) model of Earth-Ice-Ocean using the ICE-5G (VM2) model of Earth-Ice-Ocean interactions the sea level budget is closed. IN the interactions the sea level budget is closed. IN the absence of these corrections it is not. absence of these corrections it is not.

Sensitivity of Earth Rotation Predictions to Sensitivity of Earth Rotation Predictions to Mantle ViscosityMantle Viscosity

Frechet Kernels for the Mantle Viscosity Inverse Problem

FennoscandianRelaxation Times Relaxation Times

For Laurentide Rebound

Polar WanderSpeed and J2-dot

Mantle Viscosity Profiles Inferred by Formal Bayesian Inversion

Viscosity FixedBy Relaxation Time Data

ViscosityControlled byEarth Rotation

QUESTION: Given the newlyconstructed ICE-5G model ofglobal deglaciation, how well constrained is the viscosity in the lowermost mantle?

The Theory of Ice-Earth-Ocean Interactions

The goal of this research is to demonstratethat it is impossible to understand the degreeto which land ice is disappearing from the surface of the continents under modern climateconditions without fully understanding thecontinuing influence upon the gravitationalfield of the planet due to the most recentglacial cycle of the Late Quaternary Period.the main results in the presentation will befound in Peltier (2009, QSR, doi: 10.1016/j.quascirev.2009.04.004).

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

Back to the Problem of GRACEInterpretation and the Sea Level Budget Closure Problem

Verifying the quality of the model of ice-age influence

Sensitivity to gaussian filter halfwidthSensitivity to gaussian filter halfwidth

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

Comparison of GRACE with GIA: North Comparison of GRACE with GIA: North America and GreenlandAmerica and Greenland

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?

OutlineOutline Motivation: To establish (1) that the mass being lost from Motivation: To establish (1) that the mass being lost from

the land is balanced by the mass gained by the oceans the land is balanced by the mass gained by the oceans and (2) that when the sea level equivalent mass gained and (2) that when the sea level equivalent mass gained by the oceans is added to the steric contribution to sea by the oceans is added to the steric contribution to sea level one fits the Topex/Poseidon-Jason-1 observationslevel one fits the Topex/Poseidon-Jason-1 observations

GRACE data analyses of the rates of mass loss from GRACE data analyses of the rates of mass loss from Greenland, Alaska and Antarctica.Greenland, Alaska and Antarctica.

Contributions from small ice-sheets and glaciers and Contributions from small ice-sheets and glaciers and continental dessicationcontinental dessication

GRACE analysis of the sea level equivalent rate of gain GRACE analysis of the sea level equivalent rate of gain of mass by the oceans: the critical role of the GIA of mass by the oceans: the critical role of the GIA correctioncorrection

Sea level budget closure as a means of assessing the Sea level budget closure as a means of assessing the validity of the ICE-5G(VM2) predictions of the degree 2 validity of the ICE-5G(VM2) predictions of the degree 2 and order 1 Stokes coefficientsand order 1 Stokes coefficients

Summary Summary