Energy balance of glacial isostatic adjustment: importance of the rotational feedback

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384762" target="_blank" >RIV/00216208:11320/18:10384762 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1093/gji/ggx469" target="_blank" >https://doi.org/10.1093/gji/ggx469</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/gji/ggx469" target="_blank" >10.1093/gji/ggx469</a>

Result language

angličtina

Original language name

Energy balance of glacial isostatic adjustment: importance of the rotational feedback

Original language description

Understanding the feedback between the glacial isostatic adjustment (GIA) and the Earth&apos;s rotation is important for an accurate prediction of sea level changes induced by climate and tectonic processes. Here we consider a simple, four-layer incompressible Earth model, recently used for a benchmark of GIA codes to estimate the accuracy of the linearized Liouville equation (LE) and to demonstrate that models with an incomplete or missing rotational feedback violate the principle of energy conservation. First, we compute GIA on a rotating Earth by solving the equation of motion coupled with LE in its full nonlinear form. By comparing the nonlinear LE solution with the traditional linearized one, we find that the radial component of the angular velocity vector is inaccurate in the latter case, with an error exceeding 10 per cent already after 1 kyr of evolution. To understand the cause of this discrepancy, we investigate the time evolution of different kinds of energy involved in the process. While the rotational, elastic and dissipative energies are straightforward to compute, the formula for the gravitational energy contains an integral that requires a careful, higher-order accurate evaluation of the gravitational potential perturbation. We circumvent this problem by transforming the integral into a different one, formulated in terms of displacement instead of potential. We find that the solution of the linearized LE equation does not conserve the energy, since, in the linearized case, the rate of change of the rotational energy is not equal to the power of the centrifugal force. We also compute the energy balance of GIA on a constantly rotating Earth, and demonstrate the importance of the rotational feedback in the equation of motion. The formalism derived in this study allows a detailed examination of the energy balance for a rotating, incompressible planetary body deformed by a surface load. As such, it may not only serve as a reliable tool for a posteriori testing of GIA numerical solutions but it can also be used in different planetary science applications.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10500 - Earth and related environmental sciences

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Geophysical Journal International

ISSN

0956-540X

e-ISSN

—

Volume of the periodical

212

Issue of the periodical within the volume

2

Country of publishing house

GB - UNITED KINGDOM

Number of pages

21

Pages from-to

955-975

UT code for WoS article

000418703900016

EID of the result in the Scopus database

2-s2.0-85042161866