The impact of rheological uncertainty on dynamic topography predictions

Much effort is being made to extract the dynamic components of the Earth’s topography driven by density heterogeneities in the mantle. Seismically mapped density anomalies have been used as an input into mantle convection models to predict the present-day mantle flow and stresses applied on the Earth’s surface, resulting in dynamic topography. However, mantle convection models give dynamic topography amplitudes generally larger by a factor of ∼ 2, depending on the flow wavelength, compared to dynamic topography amplitudes obtained by removing the isostatically compensated topography from the Earth’s topography. In this paper, we use 3-D numerical experiments to evaluate the extent to which the dynamic topography depends on mantle rheology. We calculate the amplitude of instantaneous dynamic topography induced by the motion of a small spherical density anomaly (∼ 100 km radius) embedded into the mantle. Our experiments show that, at relatively short wavelengths (< 1000 km), the amplitude of dynamic topography, in the case of non-Newtonian mantle rheology, is reduced by a factor of ∼ 2 compared to isoviscous rheology. This is explained by the formation of a low-viscosity channel beneath the lithosphere and a decrease in thickness of the mechanical lithosphere due to induced local reduction in viscosity. The latter is often neglected in global mantle convection models. Although our results are strictly valid for flow wavelengths less than 1000 km, we note that in non-Newtonian rheology all wavelengths are coupled, and the dynamic topography at long wavelengths will be influenced.


Main comment:
Discrepancy between observed and predicted dynamic topography: As you explain in Lines 41-55 there is a mismatch between the amplitude of observed residual topography and dynamic topography predicted from simulations. Over the last few years, there has been a general focus on the long-wavelength (degree 2) components, where the driving density anomalies have comparable lateral scales to the depth of the mantle. Instantaneous flow kernals (with no lateral viscosity variations) show that the effect of features such as a low viscosity asthenosphere are less pronounced at the lower degrees than at higher degrees (shorter wavelengths). Thus, I think that the experimental set up that you are using is more suited to comparison with shorter wavelength density anomalies, and the results on long-wavelength dynamic topography predictions could turn out to be less dramatic.
Nevertheless, I think that there is also potentially an issue with amplitudes at short wavelengths. Studies that attempt to include the shallow mantle tend to predict larger dynamic topography than we observe in residual topography (e.g. Steinberger, 2016;Steinberger et al., 2019;Davies et al., 2019). My suspicion is that the conversion between seismic velocity and density structure is largely to blame, but your results show that the rheological assumptions may also be a significant factor. I therefore think that the motivation in your study should probably be more nuanced than it is currently written.
Additional comments: L15-17 (in abstract): In this sentence, it is unclear that you have shown that using a power law rheology reduces dynamic topography and so potentially helps to explain this discrepancy. Please clarify, particularly the final sub-clause.
L34: "...created by plate tectonic processes." I think this should be expanded further to improve clarity. Essentially, it is dominated by isostatic topography associated with variations in the thickness and density of sediments, crust and lithospheric mantle.
L34-39: I think that this section is a little misleading. There are two separate types of observation: i) the absolute amplitude of dynamic topography at the present-day and ii) the rate at which it is changing. Measurements of residual topography constrain the former, as you explain in the next paragraph. The couple of sentences here on sedimentary basins are more to do with the rates of change, and in that sense are a little out of context with the rest of the manuscript. I'd suggest either clarifying this issue or removing these sentences.
L43: "...isostatic components..." is a little vague. Specifically we want to remove isostatic topography arising from sediments, crustal structure and the lithospheric mantle if we want to investigate signals arising from deeper mantle convection.
L47: Rather than the accuracy of the measurements, it is more whether the measurements are truly a proxy for deeper mantle contributions that depends upon the factors you highlight here. L85: Replace ρ with ∆ρ and explain the difference between air and water-loaded dynamic topography.
L95-96: This is a little hard to read and would benefit from clearer grammar. L108: Replace "...normal total stress..." with "...total normal stress...".  ii) make all streamlines the same colour (either white or black), iii) place the key entries in their true depth order (lith, channel, asthen). I also think it could be clearer that the relative viscosity jumps between layers are what is important, rather than absolute values, but it is fine as is.