A benchmark study of numerical implementations of the sea-level equation in GIA modelling

Z. Martinec*, V. Klemann, W. van der Wal, R. E. M Riva, G. Spada, Y. Sun, D. Melini, S. B. Kachuck, V. Barletta, K. Simon, G. A, T. James

*Corresponding author for this work

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Abstract

The 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 amongst 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 ten numerical codes tested combine various temporal and spatial parameterizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parameterize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equi-angular grid, a Gauss-Legendre or an equi-area 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 three-dimensional 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.
Original languageEnglish
JournalGeophysical Journal International
Volume215
Issue number1
Pages (from-to)389-414
ISSN0956-540X
DOIs
Publication statusPublished - 2018

Bibliographical note

This article has been accepted for publication in Geophysical Journal International ©: 2018 The authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.The version of record is available online at: https://doi.org/10.1093/gji/ggy280

Cite this

Martinec, Z., Klemann, V., van der Wal, W., Riva, R. E. M., Spada, G., Sun, Y., ... James, T. (2018). A benchmark study of numerical implementations of the sea-level equation in GIA modelling. Geophysical Journal International, 215(1), 389-414. https://doi.org/10.1093/gji/ggy280
Martinec, Z. ; Klemann, V. ; van der Wal, W. ; Riva, R. E. M ; Spada, G. ; Sun, Y. ; Melini, D. ; Kachuck, S. B. ; Barletta, V. ; Simon, K. ; A, G. ; James, T. / A benchmark study of numerical implementations of the sea-level equation in GIA modelling. In: Geophysical Journal International. 2018 ; Vol. 215, No. 1. pp. 389-414.
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abstract = "The 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 amongst 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 ten numerical codes tested combine various temporal and spatial parameterizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parameterize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equi-angular grid, a Gauss-Legendre or an equi-area 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 three-dimensional 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.",
author = "Z. Martinec and V. Klemann and {van der Wal}, W. and Riva, {R. E. M} and G. Spada and Y. Sun and D. Melini and Kachuck, {S. B.} and V. Barletta and K. Simon and G. A and T. James",
note = "This article has been accepted for publication in Geophysical Journal International {\circledC}: 2018 The authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.The version of record is available online at: https://doi.org/10.1093/gji/ggy280",
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Martinec, Z, Klemann, V, van der Wal, W, Riva, REM, Spada, G, Sun, Y, Melini, D, Kachuck, SB, Barletta, V, Simon, K, A, G & James, T 2018, 'A benchmark study of numerical implementations of the sea-level equation in GIA modelling', Geophysical Journal International, vol. 215, no. 1, pp. 389-414. https://doi.org/10.1093/gji/ggy280

A benchmark study of numerical implementations of the sea-level equation in GIA modelling. / Martinec, Z.; Klemann, V.; van der Wal, W.; Riva, R. E. M; Spada, G.; Sun, Y.; Melini, D.; Kachuck, S. B.; Barletta, V.; Simon, K.; A, G.; James, T.

In: Geophysical Journal International, Vol. 215, No. 1, 2018, p. 389-414.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A benchmark study of numerical implementations of the sea-level equation in GIA modelling

AU - Martinec, Z.

AU - Klemann, V.

AU - van der Wal, W.

AU - Riva, R. E. M

AU - Spada, G.

AU - Sun, Y.

AU - Melini, D.

AU - Kachuck, S. B.

AU - Barletta, V.

AU - Simon, K.

AU - A, G.

AU - James, T.

N1 - This article has been accepted for publication in Geophysical Journal International ©: 2018 The authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.The version of record is available online at: https://doi.org/10.1093/gji/ggy280

PY - 2018

Y1 - 2018

N2 - The 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 amongst 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 ten numerical codes tested combine various temporal and spatial parameterizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parameterize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equi-angular grid, a Gauss-Legendre or an equi-area 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 three-dimensional 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.

AB - The 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 amongst 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 ten numerical codes tested combine various temporal and spatial parameterizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parameterize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equi-angular grid, a Gauss-Legendre or an equi-area 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 three-dimensional 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.

U2 - 10.1093/gji/ggy280

DO - 10.1093/gji/ggy280

M3 - Journal article

VL - 215

SP - 389

EP - 414

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 1

ER -