A benchmark study for glacial isostatic adjustment codes

Abstract

The study of glacial isostatic adjustment (GIA) is gaining an increasingly important role within the geophysical community. Understanding the response of the Earth to loading is crucial in various contexts, ranging from the interpretation of modern satellite geodetic measurements (e.g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modelling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of agreed numerical results through which the methods may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. This has taken place within a collaboration facilitated through European Cooperation in Science and Technology (COST) Action ES0701. The approaches benchmarked are based on significantly different codes and different techniques. The test computations are based on models with spherical symmetry and Maxwell rheology and include inputs from different methods and solution techniques: viscoelastic normal modes, spectral-finite elements and finite elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants

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

“…The other viscous amplitudes denoted by A i in Spada et al (2011) are shown to vanish identically. For Heaviside loading (f(s) = 1/s), the inverse Laplace transform of eq.…”

“…Under assumption (91), Vermeersen et al (1994), Sabadini & Vermeersen (2004) and Spada et al (2011) showed that the time relaxation of the polar motion m(t) is characterized only by the rotational frequencies a i . This fact is expressed by eq.…”

“…is the Laplace-transformed polar-motion transfer function representing the displacement of the rotation axis of the instantaneous configuration κ(t) with respect to the co-rotating frame O(x 1 , x 2 , x 3 ) for a unit surface-mass loading excitation (Spada et al 2011). The objective of this section is to compare the polar-motion function m(t) calculated by the LD method with that resulting from the TD method (presented in Section 5).…”

“…(88) can be arranged as (e.g. Wu & Peltier 1984;Vermeersen et al 1997;Sabadini & Vermeersen 2004;Spada et al 2011) …”

“…That is why we will not consider the rotational feedback on the sea level equation, but our surface load model will be defined by a simple spherical cap used by Spada et al (2011) for a benchmark study of the numerical performance of GIA computational codes. This provides the rotational amplitudes and the rotational relaxation times of the M3L70V01 model (Spada et al 2011) for the case where the rotational-feedback mechanism is included, which may then serve as a benchmark for other GIA computational codes. A full exploitation of the rotational-feedback effect on the complete suite of GIA-related observables, including the rotational feedback on the sea level equation, is the next step for future study.…”