The rotational feedback on linear-momentum balance in glacial isostatic adjustment

Abstract

S U M M A R YThe influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number.The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance.We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.Key words: Sea level change; Geopotential theory; Earth rotation variations. I N T RO D U C T I O NThe redistribution of ice and water over the Earth's surface during glaciation and deglaciation cycles due to changes in climate induces 3-D crustal motion, gravity-field variations and changes in sea level, which is known collectively as glacial isostatic adjustment (GIA). The surface-m...

Glacial Isostatic Adjustment modelling: historical perspectives, recent advances, and future directions

“…Over both timescales these mechanisms result in a change in the distribution of water across the ocean and this will excite additional solid Earth deformation, thus further altering the rotational state of the Earth. These feedbacks were first implemented within the sealevel equation by Milne and Mitrovica (1998), and a number of important updates to the theory have been made in recent 265 years Mitrovica and Wahr, 2011;Martinec and Hagedoorn, 2014).…”

Using GRACE to Explain Variations in the Earth's Oblateness

“…Based on the ICE-6G ice history model (Peltier et al, 2015), we create three regional GIA fingerprints for the Laurentide ice sheet and two fingerprints for the Fennoscandian ice sheet ( Figure S5), in order to allow for the possible presence of regional biases in the input GIA model. Further more, we include two fingerprints representing the C 21 and S 21 coefficients to account for any possible errors in modeling the Earth's rotational feedback (e.g., Martinec & Hagedoorn, 2014;Mitrovica & Wahr, 2011). It is based on the IJ05 ice history (Ivins & James, 2005), which has been shown to provide the closest agreement to a data-driven GIA solution (Riva et al, 2009).…”

“…More information about preparing regional GIA models can be found in supporting information (Text S2). Further more, we include two fingerprints representing the C 21 and S 21 coefficients to account for any possible errors in modeling the Earth's rotational feedback (e.g., Martinec & Hagedoorn, 2014;Mitrovica & Wahr, 2011). Altogether, we are using 163 fingerprints (Data Set S1).…”

Short Comment in response to Reviewer’s comments

“…These feedbacks were first implemented within the sea-level equation by Milne and Mitrovica (1998), and a number of important updates to the theory have been made in recent years (Mitrovica et al, 2005;Mitrovica and Wahr, 2011;Martinec and Hagedoorn, 2014).…”