Research ArticleOCEANOGRAPHY

Reconciling past changes in Earth’s rotation with 20th century global sea-level rise: Resolving Munk’s enigma

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Science Advances  11 Dec 2015:
Vol. 1, no. 11, e1500679
DOI: 10.1126/sciadv.1500679
  • Fig. 1 Munk’s enigma of global sea-level rise (1).

    (A) Clock error from 500 B.C.E. to 1600 C.E. inferred from untimed partial solar eclipses (magenta; arrows reflect allowable bounds) and untimed total and annular solar eclipses (blue lines) listed in Appendix B of Stephenson (4) [see also Stephenson and Morrison (3)]. The green line represents the clock error associated with the slowing of Earth’s rotation due to tidal dissipation (TD) (3, 6). The red line represents the clock error computed by adding to the green line the signal due to GIA, as predicted using the VM1 viscosity profile (13, 14) and the ICE-5G ice history (15). (Inset) Change in the rotation period associated with the red and green lines in the main frame, also plotted relative to the value for 1820 C.E. (B) Rate of change of the J2 harmonic from 1976 to 1990. The shaded region represents the satellite-derived (79) observational constraint on the secular rate of change in the J2 harmonic from 1976 to 1990. The red dot represents the predicted J2 rate due to ongoing GIA computed using the VM1 viscosity model (13, 14) and the ICE-5G ice history (15). The blue bar represents the correction to the GIA prediction associated with the melting of glaciers (including those at the periphery of the Greenland Ice Sheet) tabulated by Vaughan et al. (18). The vertical range of the blue bar reflects the uncertainty in this melt contribution (0.7 ± 0.1 mm/year). The right ordinate scale maps the J2 rate into an associated acceleration of Earth’s axial rate of rotation (11). (C) TPW rate over the 20th century. The black arrow with error ellipse represents the secular rate of TPW relative to mantle reference frames as inferred from astronomic and geodetic data (12). (The black arrow at the bottom left of the map shows the amplitude scale for the TPW vector.) The dashed red line and the solid red line represent the TPW vector associated with ongoing GIA computed using the viscosity model VM1 and either the standard (11) or the revised ice age rotational stability theory (21), respectively. The blue line represents the TPW signal driven by the melting of glaciers (18). The fact that the GIA predictions based on the VM1 viscosity model (and, in the case of the TPW datum, the old rotation theory) fit all three rotation observables and do not allow for any excess signal associated with modern ice mass flux. Frame (B) defines Munk’s enigma.

  • Fig. 2 Mantle viscosity profiles adopted in this study.

    The dashed gray line and the solid black line represent the VM1 (13, 14) and MF (26) radial profiles of viscosity from the base of the lithosphere to the CMB. The former has a viscosity jump of a factor of 2 at the 670-km boundary between the upper mantle and the lower mantle. The latter (a 23-layer model) is characterized by an increase in viscosity of greater than two orders of magnitude from the base of the lithosphere to the deep mantle and is consistent with inferences based on observations related to both GIA (2426) and mantle convection (2731).

  • Fig. 3 Revised analysis of Munk’s enigma (1).

    (A) Integrated clock error (as in Fig. 1A) inferred from ancient eclipse observations. The green line represents the clock error associated with the slowing of Earth’s rotation due to tidal dissipation (TD) (3, 6). The solid red line represents the clock error computed by adding to the green line a signal due to ongoing GIA predicted using the MF viscosity profile (26) and the global ice history of Fleming and Lambeck (32). The shaded region bounds three predictions of the total clock error computed by adding to the solid red line the three time series of clock error in Fig. 4 associated with angular momentum exchange between the fluid outer core and the mantle (CMC) (33). (Inset) Change in the rotation period associated with the red and green lines in the main frame relative to the value for 1820 C.E. (B) Rate of change of the J2 harmonic from 1976 to 1990. As in Fig. 1B, the shaded region represents the satellite-derived (79) observational constraint on the secular rate of change in the J2 harmonic from 1976 to 1990. The red dot represents the predicted J2 rate due to ongoing GIA computed using the MF model (26). The blue bar represents the correction to the GIA prediction associated with the melting of glaciers (including those at the periphery of the Greenland Ice Sheet) tabulated by Vaughan et al. (18) (0.7 ± 0.1 mm/year). (C) TPW rate over the 20th century. The black arrow with error ellipse represents the secular rate of the TPW relative to mantle reference frames as inferred from astronomic and geodetic data (12). The solid red line represents the TPW signal associated with ongoing GIA computed using the viscosity model MF (26) and the rotational stability theory described by Mitrovica et al. (21). The blue line represents the TPW signal driven by the melting of glaciers (18).

  • Fig. 4 Impact of core-mantle coupling on Earth’s rotation.

    (Inset) Change in rotation period due to angular momentum exchange between the fluid outer core and the mantle, as computed by Dumberry and Bloxham (33) (solid line), relative to the value for 1820 C.E. Dashed and dotted lines represent the best-fitting linear trend through the solid line and the mean pre–1820 C.E. value of the solid line, respectively. (Main frame) Clock error computed by integrating the three time series in the inset.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Munk’s enigma of global sea-level rise (1): the VM2 model.
    • Fig. S2. Sensitivity of GIA predictions of the J2 rate to variations in mantle viscosity.

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