GRACE constraints on Earth rheology of the Barents Sea and Fennoscandia

Rovira-Navarro, Marc; van der Wal, Wouter; Barletta, Valentina R.; Root, Bart C.; Sandberg Sørensen, Louise

doi:https://doi.org/10.5194/se-11-379-2020

Articles | Volume 11, issue 2

https://doi.org/10.5194/se-11-379-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/se-11-379-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 11, issue 2

Research article

|

26 Mar 2020

Research article |

| 26 Mar 2020

GRACE constraints on Earth rheology of the Barents Sea and Fennoscandia

Marc Rovira-Navarro, Wouter van der Wal, Valentina R. Barletta, Bart C. Root, and Louise Sandberg Sørensen

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Final revised paper (published on 26 Mar 2020)
Preprint (discussion started on 13 Jun 2019)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Concerns over processing techniques', Anonymous Referee #1, 11 Jul 2019
- AC1: 'Response to Reviewer 1', Marc Rovira-Navarro, 03 Oct 2019
RC2: 'Review', Anonymous Referee #2, 28 Aug 2019
- AC2: 'Response to Reviewer 2', Marc Rovira-Navarro, 03 Oct 2019

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Marc Rovira-Navarro on behalf of the Authors (03 Oct 2019) Author's response Manuscript

ED: Publish as is (11 Oct 2019) by Nicolas Gillet

ED: Referee Nomination & Report Request started (26 Nov 2019) by Nicolas Gillet

RR by Anonymous Referee #1 (15 Jan 2020)

Suggestions for revision or reasons for rejection

The authors have responded to many of the criticisms raised and the manuscript reads much more clearly. In particular, I appreciate the expanded discussion surrounding the correlated uncertainties in the data used to process the GRACE observations. I also appreciate the attempt made to formally quantify the posterior uncertainties, though I think these estimates need to be made with care, as discussed below.

I am, however, unsatisfied by the argument for the bias toward long-wavelength and the added discussion of posterior uncertainty. As I see that the other reviewer has also raised these concerns, I believe it important to clarify these decisions before publication of the article.

The justification they give for cutting off the observations at l=60, is that higher order numbers contain negligible GIA signal. They support this assertion by showing the results of modeling GIA, using the ICE-5G model and an unspecified rheology. However, the paper is about fitting precisely these ice and rheological parameters to the GRACE observations. The authors have therefore pre-decided what the GIA signal should look like and which models should be considered valid. Processing the data so that it is consistent with this particular parameter set will aritificially improve the apparent goodness-of-fit by this and close parameter sets. Thus, only models with significant power in order numbers less than l=60 are actually considered, regardless of what smaller lengthscale GIA signals might exist and the degree to which these are not fit by the favoured models. In particular, this approach strongly penalizes the S04 model and drives the rheology conditioned on it to the end of it’s parameter range, perhaps artificially, causing me to remain skeptical of its fit.

The fits are biased toward long wavelengths by an additional methodological choice. The dataset the authors compile to fit maximum gravity disturbance rates is actually a single observation processed with filters of differing halfwidths - hardly a large set of unique information. It seems to me that the 200 km low-pass filter contains all the information of the 300 km low-pass filter, plus some smaller wavelength information. Thus, the lower frequency information (>300 km) is repeated in each data point, once again strongly biasing the fit to long-wavelength models, as with the decision to truncate.

I appreciate how the authors have tried to add formality to the rheological uncertainties by computing a confidence region, with reference to Numerical Recipes. I believe this formality requires a bit more to make it rigorous, and therefore credible. One of the problems with this formality is that it rests on the assumption of a dataset with independent observations or, at the very least, a measure of the covariance between the observations, which is not satisfied, as described above.

A statement of a confidence region, say 95%, indicates to the reader that the region 95% of the posterior probability of the parameters (e.g., upper mantle viscosity and lithospheric thickness) conditioned on the observations. The confidence regions given by the authors in figures 6 and 7 each extend to the boundary of the parameter ranges, suggesting that these are incomplete confidence regions - some of that posterior probability is off the figure. How much? I agree, in principle, that the lithosphere underlying the Barents Sea is unlikely to be much less than 40 km or much greater than 180 km. However, if their model requires it for goodness of fit, it suggests something is wrong with either the model, as with the S04 model, whose posterior lies at the extreme edge of the sampled parameters, or the confidence in the fitted data.

I don’t object to using the chi^2 as a shorthand for goodness of fit, as the authors did before this revision, and I still believe the manuscript presents important insights into the region’s viscous structure.

My suggestions can be summarized as follows:
1) Be very explicit about the decision to truncate at harmonic 60 and its possible consequences in this paper, not simply with reference to the Root supplemental material. Omitting that the decision is based on particular model runs is misleading at best.

2) Remove the formal claims of confidence regions, and describe the chi^2 values and the “data set” they are conditioned on as an appropriately approximate way to establish fit.

3) Include discussion include about the possibility of short-wavelength components of the GIA gravity signal admitting different ice and rheology models.

I have only two minor editorial changes:
pg1-l2: in-sight -> insight
pg6-l37 “less viscous upper mantle viscosity” -> “less viscous upper mantle”

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ED: Publish subject to minor revisions (review by editor) (16 Jan 2020) by Nicolas Gillet

AR by Marc Rovira-Navarro on behalf of the Authors (06 Feb 2020) Author's response Manuscript

ED: Publish as is (11 Feb 2020) by Nicolas Gillet

ED: Publish as is (17 Feb 2020) by Susanne Buiter (Executive editor)

AR by Marc Rovira-Navarro on behalf of the Authors (19 Feb 2020) Manuscript

Short summary

The Barents Sea and Fennoscandia were home to large ice sheets around 20 000 years ago. After the melting of these ice sheets, the land slowly rebounded. The rebound speed is determined by the viscosity of the deep Earth. The rebound is ongoing and causes small changes in the Earth’s gravity field, which can be measured by the GRACE satellite mission. We use these measurements to obtain the viscosity of the upper mantle and find that it is 2 times higher in Fennoscandia than in the Barents Sea.