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TitleA benchmark study of numerical implementations of the sea level equation in GIA modelling
AuthorMartinec, Z; Klemann, V; van der Wal, W; Riva, R E M; Spada, G; Sun, Y; Melini, D; Kachuk, S B; Barletta, V; Simon, K; A, G; James, T SORCID logo
SourceGeophysical Journal International vol. 215, issue 1, 2018 p. 389-414, Open Access logo Open Access
Alt SeriesNatural Resources Canada, Contribution Series 20180013
PublisherOxford University Press (OUP)
Mediapaper; on-line; digital
File formatpdf; html
Subjectsgeophysics; mathematical and computational geology; tectonics; Nature and Environment; modelling; isostasy; glaciation; ice sheets; deglaciation; sea ice; sea level changes; crustal studies; deformation; displacement; topography; lithosphere; mantle; viscosity; earth rotation; gravity; tectonic environments; rheology; geodesy; Methodology; Oceans
Illustrationsmodels; tables; cross-sections; time series
ProgramClimate Change Geoscience Coastal Infrastructure
Released2018 07 13
AbstractThe ocean load in glacial isostatic adjustment (GIA) modelling is represented by the so-called sea level equation (SLE). The SLE describes the mass redistribution of water between ice sheets and oceans on a deforming Earth. Despite various teams independently investigating GIA, there has been no systematic intercomparison among the numerical solvers of the SLE through which the methods may be validated. The goal of this paper is to present a series of synthetic examples designed for testing and comparing the numerical implementations of the SLE in GIA modelling. The 10 numerical codes tested combine various temporal and spatial parametrizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parametrize the GIA-related field variables spatially. The surface ice-water load and solid Earth's topography are represented spatially either on an equiangular grid, a Gauss-Legendre or an equiarea grid with icosahedron-shaped spherical pixels. Comparisons are made in a series of five benchmark examples with an increasing degree of complexity. Due to the complexity of the SLE, there is no analytical solution to it. The accuracy of the numerical implementations is therefore assessed by the differences of the individual solutions with respect to a reference solution. While the benchmark study does not result in GIA predictions for a realistic loading scenario, we establish a set of agreed-upon results that can be extended in the future by including more complex case studies, such as solutions with realistic loading scenarios, the rotational feedback in the linear-momentum equation, and by considering a 3-D viscosity structure of the Earth's mantle. The test computations performed so far show very good agreement between the individual results and their ability to capture the main features of sea-surface variation and the surface vertical displacement. The differences found can often be attributed to the different approximations inherent in the various algorithms. This shows the accuracy that can be expected from different implementations of the SLE, which helps to assess differences noted in the literature between predictions for realistic loading cases.
Summary(Plain Language Summary, not published)
This paper compares the results of different computer models of the glacial isostatic adjustment (GIA) process in computing sea-level change. GIA is the surface-loading response of the Earth to past and present-day change to glaciers and ice sheets. GIA generates spatially variable sea-levels that change through time. The results of the comparison show good agreement between the different methods, with the differences generally thought to reflect the effect of various approximations. The good agreement indicates the generally mature state of the GIA modelling community and that previous results based on different implementations of the GIA process are robust and not in need of major revision.

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