The two geophysical processes believed to be most significantly contributing to secular
changes in the Earth's low degree zonal harmonics are briefly reviewed. While other
processes also contribute (e.g. Chao, 1993), they are generally secondary, have large
uncertainty, and are largely within the uncertainty estimates of these dominant effects. The
last ice age began 18,000 ybp and by 5,000 ybp the major ice sheets had nearly receded.
The Earth's crust, relieved of this loading, is in a state of gravitational non-equilibrium as
it rebounds through viscous flow in the mantle material to achieve equilibrium. The rate of
rebound is dictated by the viscosity of various layers within the underlying mantle [cf. Peltier,
(1985); Mitrovica and Peltier, (1993); Ivins et aI., (1993)] resulting in a slow increase in the
Earth's apparent oblateness. Hydrological mass redistribution associated with glacial and
ice sheet ablation is the second major process which contributes to the change in global sea
level and secular changes in the Earth's long wavelength geopotential. If the ice sheets and
glaciers are melting, mass transport is equatorwards into the ocean basins [see Trupin
(1993); Mitrovica and Peltier (1993) for a review of these effects.]
For the preliminary study described herein, we have used the relationships provided by
various published geophysical models to define the dependence of the secular rates on
model parameters. The adoption of specific forms of these models is the major shortcoming
of our approach, for as noted by these authors, there are a large number of mass
redistribution processes possible, and merely plausible candidates are described.
Furthermore, it is hard to quantify these shortcomings within an error analysis. Nevertheless,
global consistency, closure of models and geodetic observations, and the strength of an
inverse solution approach, can be demonstrated.
The contribution of the mass balance within the Antarctic and Greenland ice sheets to
both secular changes in the zonal harmonics and the Earth's spin axis was discussed by
Trupin (1993). Trupin used the contribution of mass change in the ice fields to the global
change in mean sea level as his dependent variables. He found that the "Steady-State" and
"Thinning Interior" mass change model for Antarctica produced similar secular effects. Both
models also agree well with our aggregate observations. The "Thickening Interior Model"
for Antarctica however, was distinct, and showed secular rate trends which were quite
dissimilar to those observed. For Greenland, both the "Outer Benson Line" and "Inner
Benson Line" models yielded similar secular trends. For our inverse solution, we adopted
Trupin's "Thinning Interior" Antarctic and "Inner Benson Line" Greenland models.
Mitrovica and Peltier (1993) (M&P) presented a study showing the predicted change in
the zonal harmonic secular rates as a function of the viscosity of the lower mantle. While
ready access to the upper mantle is obtained, the viscosity contrast within the mantle must
be inferred and it directly effects the rate at which the post-glacial crustal rebound occurs.
We have employed the M&P model. From Peltier (1988; Figure 7A) we have also obtained
the relationship between the secular polar motion and lower mantle viscosity.
Yearly mass balance in the mountain glacier systems has been studied by Trupin, Meier
and Wahr (1992) (TMW). From an assessment of mass balance in 85 glaciers accounting
for 74% of the mass volume change from these sources, these authors have produced
estimates of the contribution of the mountain glacier systems to the secular trend in the
Earth's zonal harmonics, secular polar motion, and contribution to global sea level changes.
Herein, we have adopted as known, these contributions.
We have used two different sets of pole rates to assess solution sensitivity. The first
solution uses the observed secular polar motion rate obtained by Gross (1994) in his
Space'93 analysis which likely well represents the long period average. The second solution
uses the rates obtained from the IERS pole series over the interval evaluated for this study
shown in Figures 1a through 1d. Both sets however, produce quite similar geophysical
parameter estimates. Table 6 summarizes these observations and other initial conditions for
the two least squares solution we have performed. Table 6 also gives the modeled
159
changes in the Earth's low degree zonal harmonics are briefly reviewed. While other
processes also contribute (e.g. Chao, 1993), they are generally secondary, have large
uncertainty, and are largely within the uncertainty estimates of these dominant effects. The
last ice age began 18,000 ybp and by 5,000 ybp the major ice sheets had nearly receded.
The Earth's crust, relieved of this loading, is in a state of gravitational non-equilibrium as
it rebounds through viscous flow in the mantle material to achieve equilibrium. The rate of
rebound is dictated by the viscosity of various layers within the underlying mantle [cf. Peltier,
(1985); Mitrovica and Peltier, (1993); Ivins et aI., (1993)] resulting in a slow increase in the
Earth's apparent oblateness. Hydrological mass redistribution associated with glacial and
ice sheet ablation is the second major process which contributes to the change in global sea
level and secular changes in the Earth's long wavelength geopotential. If the ice sheets and
glaciers are melting, mass transport is equatorwards into the ocean basins [see Trupin
(1993); Mitrovica and Peltier (1993) for a review of these effects.]
For the preliminary study described herein, we have used the relationships provided by
various published geophysical models to define the dependence of the secular rates on
model parameters. The adoption of specific forms of these models is the major shortcoming
of our approach, for as noted by these authors, there are a large number of mass
redistribution processes possible, and merely plausible candidates are described.
Furthermore, it is hard to quantify these shortcomings within an error analysis. Nevertheless,
global consistency, closure of models and geodetic observations, and the strength of an
inverse solution approach, can be demonstrated.
The contribution of the mass balance within the Antarctic and Greenland ice sheets to
both secular changes in the zonal harmonics and the Earth's spin axis was discussed by
Trupin (1993). Trupin used the contribution of mass change in the ice fields to the global
change in mean sea level as his dependent variables. He found that the "Steady-State" and
"Thinning Interior" mass change model for Antarctica produced similar secular effects. Both
models also agree well with our aggregate observations. The "Thickening Interior Model"
for Antarctica however, was distinct, and showed secular rate trends which were quite
dissimilar to those observed. For Greenland, both the "Outer Benson Line" and "Inner
Benson Line" models yielded similar secular trends. For our inverse solution, we adopted
Trupin's "Thinning Interior" Antarctic and "Inner Benson Line" Greenland models.
Mitrovica and Peltier (1993) (M&P) presented a study showing the predicted change in
the zonal harmonic secular rates as a function of the viscosity of the lower mantle. While
ready access to the upper mantle is obtained, the viscosity contrast within the mantle must
be inferred and it directly effects the rate at which the post-glacial crustal rebound occurs.
We have employed the M&P model. From Peltier (1988; Figure 7A) we have also obtained
the relationship between the secular polar motion and lower mantle viscosity.
Yearly mass balance in the mountain glacier systems has been studied by Trupin, Meier
and Wahr (1992) (TMW). From an assessment of mass balance in 85 glaciers accounting
for 74% of the mass volume change from these sources, these authors have produced
estimates of the contribution of the mountain glacier systems to the secular trend in the
Earth's zonal harmonics, secular polar motion, and contribution to global sea level changes.
Herein, we have adopted as known, these contributions.
We have used two different sets of pole rates to assess solution sensitivity. The first
solution uses the observed secular polar motion rate obtained by Gross (1994) in his
Space'93 analysis which likely well represents the long period average. The second solution
uses the rates obtained from the IERS pole series over the interval evaluated for this study
shown in Figures 1a through 1d. Both sets however, produce quite similar geophysical
parameter estimates. Table 6 summarizes these observations and other initial conditions for
the two least squares solution we have performed. Table 6 also gives the modeled
159