Articles | Volume 19, issue 18
https://doi.org/10.5194/gmd-19-8877-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/gmd-19-8877-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Lagrangian tracking methods applied to free surface boundaries in numerical geodynamic models
Timothy S. Gray
CORRESPONDING AUTHOR
Institute of Geophysics, Department of Earth and Planetary Sciences, ETH Zürich, Sonneggstrasse 5, 8092 Zurich, Switzerland
Paul J. Tackley
Institute of Geophysics, Department of Earth and Planetary Sciences, ETH Zürich, Sonneggstrasse 5, 8092 Zurich, Switzerland
Taras V. Gerya
Institute of Geophysics, Department of Earth and Planetary Sciences, ETH Zürich, Sonneggstrasse 5, 8092 Zurich, Switzerland
Related authors
Timothy S. Gray, Paul J. Tackley, and Taras V. Gerya
Geosci. Model Dev., 19, 8839–8854, https://doi.org/10.5194/gmd-19-8839-2026, https://doi.org/10.5194/gmd-19-8839-2026, 2026
Short summary
Short summary
We developed a new way to model how planetary surfaces rise and sink as the deep interior slowly flows. Existing approaches are either costly or unstable. Our method represents the surface smoothly within a fixed grid, which avoids artificial air layers and numerical problems. Tests show it matches established results while running faster and working in more realistic settings, such as loaded surfaces and global models. This makes simulations of surface evolution more reliable and accessible.
Timothy Stephen Gray, Paul James Tackley, and Taras Gerya
EGUsphere, https://doi.org/10.5194/egusphere-2025-6547, https://doi.org/10.5194/egusphere-2025-6547, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
This study introduces a new way to track Earth’s surface and other boundaries in computer models of the planet’s interior. It replaces noisy, tracer-based methods with a technique that cleanly follows surfaces while conserving volume. The approach produces smoother, more accurate results in both 2D and 3D, reduces dependence on large numbers of tracers, and supports future links between deep Earth processes, oceans, and surface environments.
Timothy S. Gray, Paul J. Tackley, and Taras V. Gerya
Geosci. Model Dev., 19, 8839–8854, https://doi.org/10.5194/gmd-19-8839-2026, https://doi.org/10.5194/gmd-19-8839-2026, 2026
Short summary
Short summary
We developed a new way to model how planetary surfaces rise and sink as the deep interior slowly flows. Existing approaches are either costly or unstable. Our method represents the surface smoothly within a fixed grid, which avoids artificial air layers and numerical problems. Tests show it matches established results while running faster and working in more realistic settings, such as loaded surfaces and global models. This makes simulations of surface evolution more reliable and accessible.
Julian Rogger, Khushboo Gurung, Emanuel B. Kopp, William J. Matthaeus, Benjamin J. W. Mills, Benjamin D. Stocker, Taras V. Gerya, and Loïc Pellissier
Geosci. Model Dev., 19, 4931–4960, https://doi.org/10.5194/gmd-19-4931-2026, https://doi.org/10.5194/gmd-19-4931-2026, 2026
Short summary
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Vegetation plays a fundamental role in regulating Earth’s climate on time scales ranging from seconds to millions of years. Here, we develop and test a new vegetation model that uses evolutionary principles to predict vegetation structure, functioning, and diversity under environmental conditions fundamentally different from the present. Using the model in combination with fossil data from Earth's past may help to better understand the response of vegetation systems to environmental change.
Timothy Stephen Gray, Paul James Tackley, and Taras Gerya
EGUsphere, https://doi.org/10.5194/egusphere-2025-6547, https://doi.org/10.5194/egusphere-2025-6547, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
This study introduces a new way to track Earth’s surface and other boundaries in computer models of the planet’s interior. It replaces noisy, tracer-based methods with a technique that cleanly follows surfaces while conserving volume. The approach produces smoother, more accurate results in both 2D and 3D, reduces dependence on large numbers of tracers, and supports future links between deep Earth processes, oceans, and surface environments.
Paul James Tackley
Geosci. Model Dev., 18, 8651–8662, https://doi.org/10.5194/gmd-18-8651-2025, https://doi.org/10.5194/gmd-18-8651-2025, 2025
Short summary
Short summary
Tracers are commonly used in geodynamical models to track various quantities as material moves around. However, methods used to advect them typically do not respect the mass conservation equation, resulting in gaps and bunches in the tracer distribution. Here a method to correct this, based on nudging tracer positions in order to respect mass conservation, is presented. Tests show that it is effective and has a low computational cost.
Paul James Tackley
Geosci. Model Dev., 18, 7389–7397, https://doi.org/10.5194/gmd-18-7389-2025, https://doi.org/10.5194/gmd-18-7389-2025, 2025
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Large density jumps in numerical simulations of solid Earth dynamics can cause numerical oscillations. An effective method to prevent these at a free surface already exists. Here this is tested for compositional layers deeper in the mantle. The stabilisation method works effectively if density gradients due purely to compositional gradients are used but produces severe artefacts if total density is used.
Joshua Martin Guerrero, Frédéric Deschamps, Yang Li, Wen-Pin Hsieh, and Paul James Tackley
Solid Earth, 14, 119–135, https://doi.org/10.5194/se-14-119-2023, https://doi.org/10.5194/se-14-119-2023, 2023
Short summary
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The mantle thermal conductivity's dependencies on temperature, pressure, and composition are often suppressed in numerical models. We examine the effect of these dependencies on the long-term evolution of lower-mantle thermochemical structure. We propose that depth-dependent conductivities derived from mantle minerals, along with moderate temperature and compositional correction, emulate the Earth's mean lowermost-mantle conductivity values and produce a stable two-pile configuration.
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Short summary
This study presents a new way to model how Earth’s surface changes over time as the deep interior moves. The method tracks the surface directly, allowing clearer and more detailed results worldwide while using less computing power. It improves accuracy compared to existing approaches and makes it easier to connect deep Earth processes with oceans, climate, landscapes, and life through time.
This study presents a new way to model how Earth’s surface changes over time as the deep...
Special issue