Articles | Volume 14, issue 4
https://doi.org/10.5194/gmd-14-1899-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-14-1899-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Methods for assessment of models
| 
09 Apr 2021
Methods for assessment of models |
| 09 Apr 2021
| 09 Apr 2021
Analytical solutions for mantle flow in cylindrical and spherical shells
Stephan C. Kramer
CORRESPONDING AUTHOR
Department of Earth Science and Engineering, Imperial College London, London, UK
D. Rhodri Davies
Research School of Earth Sciences, The Australian National University, Canberra, Australia
Cian R. Wilson
Earth and Planets Laboratory, Carnegie Institution for Science, Washington, DC, USA
Related authors
Davor Dundovic, Joseph G. Wallwork, Stephan C. Kramer, Fabien Gillet-Chaulet, Regine Hock, and Matthew D. Piggott
EGUsphere, https://doi.org/10.5194/egusphere-2024-2649, https://doi.org/10.5194/egusphere-2024-2649, 2024
Short summary
Short summary
Accurate numerical studies of glaciers often require high-resolution simulations, which often prove too demanding even for modern computers. In this paper we develop a method that identifies whether different parts of a glacier require high or low resolution based on its physical features, such as its thickness and velocity. We show that by doing so we can achieve a more optimal simulation accuracy for the available computing resources compared to uniform resolution simulations.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Short summary
We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, and Angus Gibson
Geosci. Model Dev., 15, 5127–5166, https://doi.org/10.5194/gmd-15-5127-2022, https://doi.org/10.5194/gmd-15-5127-2022, 2022
Short summary
Short summary
Firedrake is a state-of-the-art system that automatically generates highly optimised code for simulating finite-element (FE) problems in geophysical fluid dynamics. It creates a separation of concerns between employing the FE method and implementing it. Here, we demonstrate the applicability and benefits of Firedrake for simulating geodynamical flows, with a focus on the slow creeping motion of Earth's mantle over geological timescales, which is ultimately the engine driving our dynamic Earth.
Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, and António M. Baptista
Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018, https://doi.org/10.5194/gmd-11-4359-2018, 2018
Short summary
Short summary
Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate representation of complex coastal topography. Unstructured mesh models are, however, often perceived as slow and inaccurate. We present a novel discontinuous Galerkin ocean model: Thetis. We demonstrate that the model is able to simulate baroclinic ocean flows with high accuracy on a triangular prismatic mesh. This work paves the way for highly accurate and efficient three-dimensional coastal ocean models.
Davor Dundovic, Joseph G. Wallwork, Stephan C. Kramer, Fabien Gillet-Chaulet, Regine Hock, and Matthew D. Piggott
EGUsphere, https://doi.org/10.5194/egusphere-2024-2649, https://doi.org/10.5194/egusphere-2024-2649, 2024
Short summary
Short summary
Accurate numerical studies of glaciers often require high-resolution simulations, which often prove too demanding even for modern computers. In this paper we develop a method that identifies whether different parts of a glacier require high or low resolution based on its physical features, such as its thickness and velocity. We show that by doing so we can achieve a more optimal simulation accuracy for the available computing resources compared to uniform resolution simulations.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Short summary
We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, and Angus Gibson
Geosci. Model Dev., 15, 5127–5166, https://doi.org/10.5194/gmd-15-5127-2022, https://doi.org/10.5194/gmd-15-5127-2022, 2022
Short summary
Short summary
Firedrake is a state-of-the-art system that automatically generates highly optimised code for simulating finite-element (FE) problems in geophysical fluid dynamics. It creates a separation of concerns between employing the FE method and implementing it. Here, we demonstrate the applicability and benefits of Firedrake for simulating geodynamical flows, with a focus on the slow creeping motion of Earth's mantle over geological timescales, which is ultimately the engine driving our dynamic Earth.
Lior Suchoy, Saskia Goes, Benjamin Maunder, Fanny Garel, and Rhodri Davies
Solid Earth, 12, 79–93, https://doi.org/10.5194/se-12-79-2021, https://doi.org/10.5194/se-12-79-2021, 2021
Short summary
Short summary
We use 2D numerical models to highlight the role of basal drag in subduction force balance. We show that basal drag can significantly affect velocities and evolution in our simulations and suggest an explanation as to why there are no trends in plate velocities with age in the Cenozoic subduction record (which we extracted from recent reconstruction using GPlates). The insights into the role of basal drag will help set up global models of plate dynamics or specific regional subduction models.
Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, and António M. Baptista
Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018, https://doi.org/10.5194/gmd-11-4359-2018, 2018
Short summary
Short summary
Unstructured meshes are attractive for coastal ocean modeling, as they allow more accurate representation of complex coastal topography. Unstructured mesh models are, however, often perceived as slow and inaccurate. We present a novel discontinuous Galerkin ocean model: Thetis. We demonstrate that the model is able to simulate baroclinic ocean flows with high accuracy on a triangular prismatic mesh. This work paves the way for highly accurate and efficient three-dimensional coastal ocean models.
Michael Rubey, Sascha Brune, Christian Heine, D. Rhodri Davies, Simon E. Williams, and R. Dietmar Müller
Solid Earth, 8, 899–919, https://doi.org/10.5194/se-8-899-2017, https://doi.org/10.5194/se-8-899-2017, 2017
Short summary
Short summary
Earth's surface is constantly warped up and down by the convecting mantle. Here we derive geodynamic rules for this so-called
dynamic topographyby employing high-resolution numerical models of global mantle convection. We define four types of dynamic topography history that are primarily controlled by the ever-changing pattern of Earth's subduction zones. Our models provide a predictive quantitative framework linking mantle convection with plate tectonics and sedimentary basin evolution.
Related subject area
Solid Earth
Empirical modeling of tropospheric delays with uncertainty
CitcomSVE-3.0: a three-dimensional finite-element software package for modeling load-induced deformation and glacial isostatic adjustment for an Earth with a viscoelastic and compressible mantle
NSOAS24: a new global marine gravity model derived from multi-satellite sea surface slopes
GEOMAPLEARN 1.2: detecting structures from geological maps with machine learning – the case of geological folds
Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications
Reconciling surface deflections from simulations of global mantle convection
A Bayesian framework for inferring regional and global change from stratigraphic proxy records (StratMC v1.0)
Three-dimensional analytical solution of self-potential from regularly polarized bodies in a layered seafloor model
A fast surrogate model for 3D Earth glacial isostatic adjustment using Tensorflow (v2.8.0) artificial neural networks
ShellSet v1.1.0 parallel dynamic neotectonic modelling: a case study using Earth5-049
FastIsostasy v1.0 – a regional, accelerated 2D glacial isostatic adjustment (GIA) model accounting for the lateral variability of the solid Earth
Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time
Benchmarking the accuracy of higher-order particle methods in geodynamic models of transient flow
REHEATFUNQ (REgional HEAT-Flow Uncertainty and aNomaly Quantification) 2.0.1: a model for regional aggregate heat flow distributions and anomaly quantification
A new temperature–photoperiod coupled phenology module in LPJ-GUESS model v4.1: optimizing estimation of terrestrial carbon and water processes
High-precision 1′ × 1′ bathymetric model of Philippine Sea inversed from marine gravity anomalies
Deciphering past earthquakes from the probabilistic modeling of paleoseismic records – the Paleoseismic EArthquake CHronologies code (PEACH, version 1)
Modelling detrital cosmogenic nuclide concentrations during landscape evolution in Cidre v2.0
IMEX_SfloW2D v2: a depth-averaged numerical flow model for volcanic gas–particle flows over complex topographies and water
Simulation of a fully coupled 3D glacial isostatic adjustment – ice sheet model for the Antarctic ice sheet over a glacial cycle
AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling
PySubdiv 1.0: open-source geological modeling and reconstruction by non-manifold subdivision surfaces
Reconstructing tephra fall deposits via ensemble-based data assimilation techniques
ClinoformNet-1.0: stratigraphic forward modeling and deep learning for seismic clinoform delineation
Addressing challenges in uncertainty quantification: the case of geohazard assessments
DeepISMNet: three-dimensional implicit structural modeling with convolutional neural network
Towards automatic finite-element methods for geodynamics via Firedrake
MagmaFOAM-1.0: a modular framework for the simulation of magmatic systems
A global, spherical finite-element model for post-seismic deformation using Abaqus
SMAUG v1.0 – a user-friendly muon simulator for the imaging of geological objects in 3-D
CliffDelineaTool v1.2.0: an algorithm for identifying coastal cliff base and top positions
Capturing the interactions between ice sheets, sea level and the solid Earth on a range of timescales: a new “time window” algorithm
Structural, petrophysical, and geological constraints in potential field inversion using the Tomofast-x v1.0 open-source code
Spatial agents for geological surface modelling
RHEA v1.0: Enabling fully coupled simulations with hydro-geomechanical heterogeneity
Modelling of faults in LoopStructural 1.0
PALEOSTRIPv1.0 – a user-friendly 3D backtracking software to reconstruct paleo-bathymetries
LoopStructural 1.0: time-aware geological modelling
Sub3DNet1.0: a deep-learning model for regional-scale 3D subsurface structure mapping
Towards a model for structured mass movements: the OpenLISEM hazard model 2.0a
GO_3D_OBS: the multi-parameter benchmark geomodel for seismic imaging method assessment and next-generation 3D survey design (version 1.0)
PLUME-MoM-TSM 1.0.0: a volcanic column and umbrella cloud spreading model
HydrothermalFoam v1.0: a 3-D hydrothermal transport model for natural submarine hydrothermal systems
Synthetic seismicity distribution in Guerrero–Oaxaca subduction zone, Mexico, and its implications on the role of asperities in Gutenberg–Richter law
A new open-source viscoelastic solid earth deformation module implemented in Elmer (v8.4)
CobWeb 1.0: machine learning toolbox for tomographic imaging
pygeodyn 1.1.0: a Python package for geomagnetic data assimilation
IMEX_SfloW2D 1.0: a depth-averaged numerical flow model for pyroclastic avalanches
A multilayer approach and its application to model a local gravimetric quasi-geoid model over the North Sea: QGNSea V1.0
Development of an automatic delineation of cliff top and toe on very irregular planform coastlines (CliffMetrics v1.0)
Jungang Wang, Junping Chen, and Yize Zhang
Geosci. Model Dev., 18, 1487–1504, https://doi.org/10.5194/gmd-18-1487-2025, https://doi.org/10.5194/gmd-18-1487-2025, 2025
Short summary
Short summary
The Global Navigation Satellite System (GNSS) is widely used for real-time monitoring and early warning of geohazards. Accurate modeling of tropospheric delays is critical to achieving high-precision GNSS solutions, and using external delays can improve real-time GNSS convergence times. Current empirical delay models only provide delay but not uncertainty. We propose a global empirical delay model with uncertainty and demonstrate its benefits in accelerating GNSS positioning convergence.
Tao Yuan, Shijie Zhong, and Geruo A
Geosci. Model Dev., 18, 1445–1461, https://doi.org/10.5194/gmd-18-1445-2025, https://doi.org/10.5194/gmd-18-1445-2025, 2025
Short summary
Short summary
Earth and other planets deform under various forces. Numerical modeling is critical in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. We present benchmark results against a semi-analytical code. With its accuracy and efficiency, CitcomSVE-3.0 could advance research in planetary and climatic sciences.
Shengjun Zhang, Xu Chen, Runsheng Zhou, and Yongjun Jia
Geosci. Model Dev., 18, 1221–1239, https://doi.org/10.5194/gmd-18-1221-2025, https://doi.org/10.5194/gmd-18-1221-2025, 2025
Short summary
Short summary
NSOAS24, a new global marine gravity model derived from multi-satellite altimetry missions, represents a significant advancement over its predecessor, NSOAS22. Through optimized processing procedures, NSOAS24 resolves previous issues and demonstrates improved accuracy. Compared to NSOAS22, NSOAS24 shows a reduction of approximately 0.7 mGal in standard deviation when validated against recent shipborne data. Notably, its accuracy now rivals internationally recognized models DTU21 and V32.1.
David Oakley, Christelle Loiselet, Thierry Coowar, Vincent Labbe, and Jean-Paul Callot
Geosci. Model Dev., 18, 939–960, https://doi.org/10.5194/gmd-18-939-2025, https://doi.org/10.5194/gmd-18-939-2025, 2025
Short summary
Short summary
In this work, we develop two automated workflows for identifying fold structures on geological maps using machine learning. In one method, we identify map patterns suggestive of folding based on pre-defined rules and apply a clustering algorithm to group those from the same fold together. In the other, we train a convolutional neural network to identify folds based on a set of training examples. We apply both methods to a set of synthetic maps and to real-world maps from two locations in France.
Yury Alkhimenkov and Yury Y. Podladchikov
Geosci. Model Dev., 18, 563–583, https://doi.org/10.5194/gmd-18-563-2025, https://doi.org/10.5194/gmd-18-563-2025, 2025
Short summary
Short summary
The accelerated pseudo-transient (APT) method is an efficient way to solve partial differential equations, particularly well-suited for parallel computing. This paper explores the APT method's effectiveness in solving elastic, viscoelastic, and hydromechanical problems, focusing on quasi-static conditions in 1D, 2D, and 3D. The study examines the best numerical settings for fast and accurate solutions. The paper shows how the APT method can handle complex problems in high-resolution models.
Conor P. B. O'Malley, Gareth G. Roberts, James Panton, Fred D. Richards, J. Huw Davies, Victoria M. Fernandes, and Sia Ghelichkhan
Geosci. Model Dev., 17, 9023–9049, https://doi.org/10.5194/gmd-17-9023-2024, https://doi.org/10.5194/gmd-17-9023-2024, 2024
Short summary
Short summary
We wish to understand how the history of flowing rock within Earth's interior impacts deflection of its surface. Observations exist to address this problem, and mathematics and different computing tools can be used to predict histories of flow. We explore how modeling choices impact calculated vertical deflections. The sensitivity of vertical motions at Earth's surface to deep flow is assessed, demonstrating how surface observations can enlighten flow histories.
Stacey Edmonsond and Blake Dyer
EGUsphere, https://doi.org/10.5194/egusphere-2024-2579, https://doi.org/10.5194/egusphere-2024-2579, 2024
Short summary
Short summary
The chemistry of sedimentary rocks is used to reconstruct past changes in Earth’s climate and biogeochemical cycles. Reconstructing global change requires merging stratigraphic proxy records from many locations, each of which may be incomplete, time-uncertain, and influenced by both global and local processes. StratMC uses Bayesian modeling to see through this complexity, building more accurate and testable reconstructions of global change from stratigraphic data.
Pengfei Zhang, Yi-an Cui, Jing Xie, Youjun Guo, Jianxin Liu, and Jieran Liu
Geosci. Model Dev., 17, 8521–8533, https://doi.org/10.5194/gmd-17-8521-2024, https://doi.org/10.5194/gmd-17-8521-2024, 2024
Short summary
Short summary
Our study proposes a three-dimensional analytical solution for the self-potential (SP) method to detect seafloor massive sulfide deposits. Using the mirror image method, we derived formulas for the SP generated by polarized bodies in layered media. We conducted experiments with a simulated environment and compared the results with our theoretical predictions. The findings confirmed a high degree of accuracy, demonstrating the reliability of our approach for faster and precise SP modeling.
Ryan Love, Glenn A. Milne, Parviz Ajourlou, Soran Parang, Lev Tarasov, and Konstantin Latychev
Geosci. Model Dev., 17, 8535–8551, https://doi.org/10.5194/gmd-17-8535-2024, https://doi.org/10.5194/gmd-17-8535-2024, 2024
Short summary
Short summary
A relatively recent advance in glacial isostatic adjustment modeling has been the development of models that include 3D Earth structure, as opposed to 1D structure. However, a major limitation is the computational expense. We have developed a method using artificial neural networks to emulate the influence of 3D Earth models to affordably constrain the viscosity parameter space. Our results indicate that the misfits are of a scale such that useful predictions of relative sea level can be made.
Jon B. May, Peter Bird, and Michele M. C. Carafa
Geosci. Model Dev., 17, 6153–6171, https://doi.org/10.5194/gmd-17-6153-2024, https://doi.org/10.5194/gmd-17-6153-2024, 2024
Short summary
Short summary
ShellSet is a combination of well-known geoscience software packages. It features a simple user interface and is optimised through the addition of a grid search input option (automatically searching for optimal models within a defined N-dimensional parameter space) and the ability to run multiple models in parallel. We show that for each number of models tested there is a performance benefit to parallel running, while two examples demonstrate a use case by improving an existing global model.
Jan Swierczek-Jereczek, Marisa Montoya, Konstantin Latychev, Alexander Robinson, Jorge Alvarez-Solas, and Jerry Mitrovica
Geosci. Model Dev., 17, 5263–5290, https://doi.org/10.5194/gmd-17-5263-2024, https://doi.org/10.5194/gmd-17-5263-2024, 2024
Short summary
Short summary
Ice sheets present a thickness of a few kilometres, leading to a vertical deformation of the crust of up to a kilometre. This process depends on properties of the solid Earth, which can be regionally very different. We propose a model that accounts for this often-ignored heterogeneity and run 100 000 simulation years in minutes. Thus, the evolution of ice sheets is modeled with better accuracy, which is critical for a good mitigation of climate change and, in particular, sea-level rise.
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024, https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Short summary
We introduce the Geoscientific ADjoint Optimisation PlaTform (G-ADOPT), designed for inverse modelling of Earth system processes, with an initial focus on mantle dynamics. G-ADOPT is built upon Firedrake, Dolfin-Adjoint and the Rapid Optimisation Library, which work together to optimise models using an adjoint method, aligning them with seismic and geologic datasets. We demonstrate G-ADOPT's ability to reconstruct mantle evolution and thus be a powerful tool in geosciences.
Rene Gassmöller, Juliane Dannberg, Wolfgang Bangerth, Elbridge Gerry Puckett, and Cedric Thieulot
Geosci. Model Dev., 17, 4115–4134, https://doi.org/10.5194/gmd-17-4115-2024, https://doi.org/10.5194/gmd-17-4115-2024, 2024
Short summary
Short summary
Numerical models that use simulated particles are a powerful tool for investigating flow in the interior of the Earth, but the accuracy of these models is not fully understood. Here we present two new benchmarks that allow measurement of model accuracy. We then document that better accuracy matters for applications like convection beneath an oceanic plate. Our benchmarks and methods are freely available to help the community develop better models.
Malte Jörn Ziebarth and Sebastian von Specht
Geosci. Model Dev., 17, 2783–2828, https://doi.org/10.5194/gmd-17-2783-2024, https://doi.org/10.5194/gmd-17-2783-2024, 2024
Short summary
Short summary
Thermal energy from Earth’s active interior constantly dissipates through Earth’s surface. This heat flow is not spatially uniform, and its exact pattern is hard to predict since it depends on crustal and mantle properties, both varying across scales. Our new model REHEATFUNQ addresses this difficulty by treating the fluctuations of heat flow within a region statistically. REHEATFUNQ estimates the regional distribution of heat flow and quantifies known structural signals therein.
Shouzhi Chen, Yongshuo H. Fu, Mingwei Li, Zitong Jia, Yishuo Cui, and Jing Tang
Geosci. Model Dev., 17, 2509–2523, https://doi.org/10.5194/gmd-17-2509-2024, https://doi.org/10.5194/gmd-17-2509-2024, 2024
Short summary
Short summary
It is still a challenge to achieve an accurate simulation of vegetation phenology in the dynamic global vegetation models (DGVMs). We implemented and coupled the spring and autumn phenology models into one of the DGVMs, LPJ-GUESS, and substantially improved the accuracy in capturing the start and end dates of growing seasons. Our study highlights the importance of getting accurate phenology estimations to reduce the uncertainties in plant distribution and terrestrial carbon and water cycling.
Dechao An, Jinyun Guo, Xiaotao Chang, Zhenming Wang, Yongjun Jia, Xin Liu, Valery Bondur, and Heping Sun
Geosci. Model Dev., 17, 2039–2052, https://doi.org/10.5194/gmd-17-2039-2024, https://doi.org/10.5194/gmd-17-2039-2024, 2024
Short summary
Short summary
Seafloor topography, as fundamental geoinformation in marine surveying and mapping, plays a crucial role in numerous scientific studies. In this paper, we focus on constructing a high-precision seafloor topography and bathymetry model for the Philippine Sea (5° N–35° N, 120° E–150° E), based on shipborne bathymetric data and marine gravity anomalies, and evaluate the reliability of the model's accuracy.
Octavi Gómez-Novell, Bruno Pace, Francesco Visini, Joanna Faure Walker, and Oona Scotti
Geosci. Model Dev., 16, 7339–7355, https://doi.org/10.5194/gmd-16-7339-2023, https://doi.org/10.5194/gmd-16-7339-2023, 2023
Short summary
Short summary
Knowing the rate at which earthquakes happen along active faults is crucial to characterize the hazard that they pose. We present an approach (Paleoseismic EArthquake CHronologies, PEACH) to correlate and compute seismic histories using paleoseismic data, a type of data that characterizes past seismic activity from the geological record. Our approach reduces the uncertainties of the seismic histories and overall can improve the knowledge on fault rupture behavior for the seismic hazard.
Sébastien Carretier, Vincent Regard, Youssouf Abdelhafiz, and Bastien Plazolles
Geosci. Model Dev., 16, 6741–6755, https://doi.org/10.5194/gmd-16-6741-2023, https://doi.org/10.5194/gmd-16-6741-2023, 2023
Short summary
Short summary
We present the development of a code to simulate simultaneously the dynamics of landscapes over geological time and the evolution of the concentration of cosmogenic isotopes in grains throughout their transport from the slopes to the river outlets. This new model makes it possible to study the relationship between the detrital signal of cosmogenic isotope concentration measured in sediment and the erosion--deposition processes in watersheds.
Mattia de' Michieli Vitturi, Tomaso Esposti Ongaro, and Samantha Engwell
Geosci. Model Dev., 16, 6309–6336, https://doi.org/10.5194/gmd-16-6309-2023, https://doi.org/10.5194/gmd-16-6309-2023, 2023
Short summary
Short summary
We present version 2 of the numerical code IMEX-SfloW2D. With this version it is possible to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). A simulation of the 1883 Krakatau eruption demonstrates the capability of the numerical model to face a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles.
Caroline J. van Calcar, Roderik S. W. van de Wal, Bas Blank, Bas de Boer, and Wouter van der Wal
Geosci. Model Dev., 16, 5473–5492, https://doi.org/10.5194/gmd-16-5473-2023, https://doi.org/10.5194/gmd-16-5473-2023, 2023
Short summary
Short summary
The waxing and waning of the Antarctic ice sheet caused the Earth’s surface to deform, which is stabilizing the ice sheet and mainly determined by the spatially variable viscosity of the mantle. Including this feedback in model simulations led to significant differences in ice sheet extent and ice thickness over the last glacial cycle. The results underline and quantify the importance of including this local feedback effect in ice sheet models when simulating the Antarctic ice sheet evolution.
Baoyi Zhang, Linze Du, Umair Khan, Yongqiang Tong, Lifang Wang, and Hao Deng
Geosci. Model Dev., 16, 3651–3674, https://doi.org/10.5194/gmd-16-3651-2023, https://doi.org/10.5194/gmd-16-3651-2023, 2023
Short summary
Short summary
We propose a Hermite–Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D stratigraphic potential field (SPF) modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolants constrained by the scattered on-contact attribute points and off-contact attitude points of a set of strata in 3D space, we add a novel optimization term to iteratively obtain the true gradient magnitude.
Mohammad Moulaeifard, Simon Bernard, and Florian Wellmann
Geosci. Model Dev., 16, 3565–3579, https://doi.org/10.5194/gmd-16-3565-2023, https://doi.org/10.5194/gmd-16-3565-2023, 2023
Short summary
Short summary
In this work, we propose a flexible framework to generate and interact with geological models using explicit surface representations. The essence of the work lies in the determination of the flexible control mesh, topologically similar to the main geological structure, watertight and controllable with few control points, to manage the geological structures. We exploited the subdivision surface method in our work, which is commonly used in the animation and gaming industry.
Leonardo Mingari, Antonio Costa, Giovanni Macedonio, and Arnau Folch
Geosci. Model Dev., 16, 3459–3478, https://doi.org/10.5194/gmd-16-3459-2023, https://doi.org/10.5194/gmd-16-3459-2023, 2023
Short summary
Short summary
Two novel techniques for ensemble-based data assimilation, suitable for semi-positive-definite variables with highly skewed uncertainty distributions such as tephra deposit mass loading, are applied to reconstruct the tephra fallout deposit resulting from the 2015 Calbuco eruption in Chile. The deposit spatial distribution and the ashfall volume according to the analyses are in good agreement with estimations based on field measurements and isopach maps reported in previous studies.
Hui Gao, Xinming Wu, Jinyu Zhang, Xiaoming Sun, and Zhengfa Bi
Geosci. Model Dev., 16, 2495–2513, https://doi.org/10.5194/gmd-16-2495-2023, https://doi.org/10.5194/gmd-16-2495-2023, 2023
Short summary
Short summary
We propose a workflow to automatically generate synthetic seismic data and corresponding stratigraphic labels (e.g., clinoform facies, relative geologic time, and synchronous horizons) by geological and geophysical forward modeling. Trained with only synthetic datasets, our network works well to accurately and efficiently predict clinoform facies in 2D and 3D field seismic data. Such a workflow can be easily extended for other geological and geophysical scenarios in the future.
Ibsen Chivata Cardenas, Terje Aven, and Roger Flage
Geosci. Model Dev., 16, 1601–1615, https://doi.org/10.5194/gmd-16-1601-2023, https://doi.org/10.5194/gmd-16-1601-2023, 2023
Short summary
Short summary
We discuss challenges in uncertainty quantification for geohazard assessments. The challenges arise from limited data and the one-off nature of geohazard features. The challenges include the credibility of predictions, input uncertainty, and assumptions’ impact. Considerations to increase credibility of the quantification are provided. Crucial tasks in the quantification are the exhaustive scrutiny of the background knowledge coupled with the assessment of deviations of assumptions made.
Zhengfa Bi, Xinming Wu, Zhaoliang Li, Dekuan Chang, and Xueshan Yong
Geosci. Model Dev., 15, 6841–6861, https://doi.org/10.5194/gmd-15-6841-2022, https://doi.org/10.5194/gmd-15-6841-2022, 2022
Short summary
Short summary
We present an implicit modeling method based on deep learning to produce a geologically valid and structurally compatible model from unevenly sampled structural data. Trained with automatically generated synthetic data with realistic features, our network can efficiently model geological structures without the need to solve large systems of mathematical equations, opening new opportunities for further leveraging deep learning to improve modeling capacity in many Earth science applications.
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, and Angus Gibson
Geosci. Model Dev., 15, 5127–5166, https://doi.org/10.5194/gmd-15-5127-2022, https://doi.org/10.5194/gmd-15-5127-2022, 2022
Short summary
Short summary
Firedrake is a state-of-the-art system that automatically generates highly optimised code for simulating finite-element (FE) problems in geophysical fluid dynamics. It creates a separation of concerns between employing the FE method and implementing it. Here, we demonstrate the applicability and benefits of Firedrake for simulating geodynamical flows, with a focus on the slow creeping motion of Earth's mantle over geological timescales, which is ultimately the engine driving our dynamic Earth.
Federico Brogi, Simone Colucci, Jacopo Matrone, Chiara Paola Montagna, Mattia De' Michieli Vitturi, and Paolo Papale
Geosci. Model Dev., 15, 3773–3796, https://doi.org/10.5194/gmd-15-3773-2022, https://doi.org/10.5194/gmd-15-3773-2022, 2022
Short summary
Short summary
Computer simulations play a fundamental role in understanding volcanic phenomena. The growing complexity of these simulations requires the development of flexible computational tools that can easily switch between sub-models and solution techniques as well as optimizations. MagmaFOAM is a newly developed library that allows for maximum flexibility for solving multiphase volcanic flows and promotes collaborative work for in-house and community model development, testing, and comparison.
Grace A. Nield, Matt A. King, Rebekka Steffen, and Bas Blank
Geosci. Model Dev., 15, 2489–2503, https://doi.org/10.5194/gmd-15-2489-2022, https://doi.org/10.5194/gmd-15-2489-2022, 2022
Short summary
Short summary
We present a finite-element model of post-seismic solid Earth deformation built in the software package Abaqus for the purpose of calculating post-seismic deformation in the far field of major earthquakes. The model is benchmarked against an existing open-source post-seismic model demonstrating good agreement. The advantage over existing models is the potential for simple modification to include 3-D Earth structure, non-linear rheologies and alternative or multiple sources of stress change.
Alessandro Lechmann, David Mair, Akitaka Ariga, Tomoko Ariga, Antonio Ereditato, Ryuichi Nishiyama, Ciro Pistillo, Paola Scampoli, Mykhailo Vladymyrov, and Fritz Schlunegger
Geosci. Model Dev., 15, 2441–2473, https://doi.org/10.5194/gmd-15-2441-2022, https://doi.org/10.5194/gmd-15-2441-2022, 2022
Short summary
Short summary
Muon tomography is a technology that is used often in geoscientific research. The know-how of data analysis is, however, still possessed by physicists who developed this technology. This article aims at providing geoscientists with the necessary tools to perform their own analyses. We hope that a lower threshold to enter the field of muon tomography will allow more geoscientists to engage with muon tomography. SMAUG is set up in a modular way to allow for its own modules to work in between.
Zuzanna M. Swirad and Adam P. Young
Geosci. Model Dev., 15, 1499–1512, https://doi.org/10.5194/gmd-15-1499-2022, https://doi.org/10.5194/gmd-15-1499-2022, 2022
Short summary
Short summary
Cliff base and top lines that delimit coastal cliff faces are usually manually digitized based on maps, aerial photographs, terrain models, etc. However, manual mapping is time consuming and depends on the mapper's decisions and skills. To increase the objectivity and efficiency of cliff mapping, we developed CliffDelineaTool, an algorithm that identifies cliff base and top positions along cross-shore transects using elevation and slope characteristics.
Holly Kyeore Han, Natalya Gomez, and Jeannette Xiu Wen Wan
Geosci. Model Dev., 15, 1355–1373, https://doi.org/10.5194/gmd-15-1355-2022, https://doi.org/10.5194/gmd-15-1355-2022, 2022
Short summary
Short summary
Interactions between ice sheets, sea level and the solid Earth occur over a range of timescales from years to tens of thousands of years. This requires coupled ice-sheet–sea-level models to exchange information frequently, leading to a quadratic increase in computation time with the number of model timesteps. We present a new sea-level model algorithm that allows coupled models to improve the computational feasibility and precisely capture short-term interactions within longer simulations.
Jérémie Giraud, Vitaliy Ogarko, Roland Martin, Mark Jessell, and Mark Lindsay
Geosci. Model Dev., 14, 6681–6709, https://doi.org/10.5194/gmd-14-6681-2021, https://doi.org/10.5194/gmd-14-6681-2021, 2021
Short summary
Short summary
We review different techniques to model the Earth's subsurface from geophysical data (gravity field anomaly, magnetic field anomaly) using geological models and measurements of the rocks' properties. We show examples of application using idealised examples reproducing realistic features and provide theoretical details of the open-source algorithm we use.
Eric A. de Kemp
Geosci. Model Dev., 14, 6661–6680, https://doi.org/10.5194/gmd-14-6661-2021, https://doi.org/10.5194/gmd-14-6661-2021, 2021
Short summary
Short summary
This is a proof of concept and review paper of spatial agents, with initial research focusing on geomodelling. The results may be of interest to others working on complex regional geological modelling with sparse data. Structural agent-based swarming behaviour is key to advancing this field. The study provides groundwork for research in structural geology 3D modelling with spatial agents. This work was done with NetLogo, a free agent modelling platform used mostly for teaching complex systems.
José M. Bastías Espejo, Andy Wilkins, Gabriel C. Rau, and Philipp Blum
Geosci. Model Dev., 14, 6257–6272, https://doi.org/10.5194/gmd-14-6257-2021, https://doi.org/10.5194/gmd-14-6257-2021, 2021
Short summary
Short summary
The hydraulic and mechanical properties of the subsurface are inherently heterogeneous. RHEA is a simulator that can perform couple hydro-geomechanical processes in heterogeneous porous media with steep gradients. RHEA is able to fully integrate spatial heterogeneity, allowing allocation of distributed hydraulic and geomechanical properties at mesh element level. RHEA is a valuable tool that can simulate problems considering realistic heterogeneity inherent to geologic formations.
Lachlan Grose, Laurent Ailleres, Gautier Laurent, Guillaume Caumon, Mark Jessell, and Robin Armit
Geosci. Model Dev., 14, 6197–6213, https://doi.org/10.5194/gmd-14-6197-2021, https://doi.org/10.5194/gmd-14-6197-2021, 2021
Short summary
Short summary
Fault discontinuities in rock packages represent the plane where two blocks of rock have moved. They are challenging to incorporate into geological models because the geometry of the faulted rock units are defined by not only the location of the discontinuity but also the kinematics of the fault. In this paper, we outline a structural geology framework for incorporating faults into geological models by directly incorporating kinematics into the mathematical framework of the model.
Florence Colleoni, Laura De Santis, Enrico Pochini, Edy Forlin, Riccardo Geletti, Giuseppe Brancatelli, Magdala Tesauro, Martina Busetti, and Carla Braitenberg
Geosci. Model Dev., 14, 5285–5305, https://doi.org/10.5194/gmd-14-5285-2021, https://doi.org/10.5194/gmd-14-5285-2021, 2021
Short summary
Short summary
PALEOSTRIP has been developed in the framework of past Antarctic ice sheet reconstructions for periods when bathymetry around Antarctica differed substantially from today. It has been designed for users with no knowledge of numerical modelling and allows users to switch on and off the processes involved in backtracking and backstripping. Applications are broad, and it can be used to restore any continental margin bathymetry or sediment thickness and to perform basin analysis.
Lachlan Grose, Laurent Ailleres, Gautier Laurent, and Mark Jessell
Geosci. Model Dev., 14, 3915–3937, https://doi.org/10.5194/gmd-14-3915-2021, https://doi.org/10.5194/gmd-14-3915-2021, 2021
Short summary
Short summary
LoopStructural is an open-source 3D geological modelling library with a model design allowing for multiple different algorithms to be used for comparison for the same geology. Geological structures are modelled using structural geology concepts and techniques, allowing for complex structures such as overprinted folds and faults to be modelled. In the paper, we demonstrate automatically generating a 3-D model from map2loop-processed geological survey data of the Flinders Ranges, South Australia.
Zhenjiao Jiang, Dirk Mallants, Lei Gao, Tim Munday, Gregoire Mariethoz, and Luk Peeters
Geosci. Model Dev., 14, 3421–3435, https://doi.org/10.5194/gmd-14-3421-2021, https://doi.org/10.5194/gmd-14-3421-2021, 2021
Short summary
Short summary
Fast and reliable tools are required to extract hidden information from big geophysical and remote sensing data. A deep-learning model in 3D image construction from 2D image(s) is here developed for paleovalley mapping from globally available digital elevation data. The outstanding performance for 3D subsurface imaging gives confidence that this generic novel tool will make better use of existing geophysical and remote sensing data for improved management of limited earth resources.
Bastian van den Bout, Theo van Asch, Wei Hu, Chenxiao X. Tang, Olga Mavrouli, Victor G. Jetten, and Cees J. van Westen
Geosci. Model Dev., 14, 1841–1864, https://doi.org/10.5194/gmd-14-1841-2021, https://doi.org/10.5194/gmd-14-1841-2021, 2021
Short summary
Short summary
Landslides, debris flows and other types of dense gravity-driven flows threaten livelihoods around the globe. Understanding the mechanics of these flows can be crucial for predicting their behaviour and reducing disaster risk. Numerical models assume that the solids and fluids of the flow are unstructured. The newly presented model captures the internal structure during movement. This important step can lead to more accurate predictions of landslide movement.
Andrzej Górszczyk and Stéphane Operto
Geosci. Model Dev., 14, 1773–1799, https://doi.org/10.5194/gmd-14-1773-2021, https://doi.org/10.5194/gmd-14-1773-2021, 2021
Short summary
Short summary
We present the 3D multi-parameter synthetic geomodel of the subduction zone, as well as the workflow designed to implement all of its components. The model contains different geological structures of various scales and complexities. It is intended to serve as a tool for the geophysical community to validate imaging approaches, design acquisition techniques, estimate uncertainties, benchmark computing approaches, etc.
Mattia de' Michieli Vitturi and Federica Pardini
Geosci. Model Dev., 14, 1345–1377, https://doi.org/10.5194/gmd-14-1345-2021, https://doi.org/10.5194/gmd-14-1345-2021, 2021
Short summary
Short summary
Here, we present PLUME-MoM-TSM, a volcanic plume model that allows us to quantify the formation of aggregates during the rise of the plume, model the phase change of water, and include the possibility to simulate the initial spreading of the tephra umbrella cloud intruding from the volcanic column into the atmosphere. The model is first applied to the 2015 Calbuco eruption (Chile) and provides an analytical relationship between the upwind spreading and some characteristic of the volcanic column.
Zhikui Guo, Lars Rüpke, and Chunhui Tao
Geosci. Model Dev., 13, 6547–6565, https://doi.org/10.5194/gmd-13-6547-2020, https://doi.org/10.5194/gmd-13-6547-2020, 2020
Short summary
Short summary
We present the 3-D hydro-thermo-transport model HydrothermalFoam v1.0, which we designed to provide the marine geosciences community with an easy-to-use and state-of-the-art tool for simulating mass and energy transport in submarine hydrothermal systems. HydrothermalFoam is based on the popular open-source platform OpenFOAM, comes with a number of tutorials, and is published under the GNU General Public License v3.0.
Marisol Monterrubio-Velasco, F. Ramón Zúñiga, Quetzalcoatl Rodríguez-Pérez, Otilio Rojas, Armando Aguilar-Meléndez, and Josep de la Puente
Geosci. Model Dev., 13, 6361–6381, https://doi.org/10.5194/gmd-13-6361-2020, https://doi.org/10.5194/gmd-13-6361-2020, 2020
Short summary
Short summary
The Mexican subduction zone along the Pacific coast is one of the most active seismic zones in the world, where every year larger-magnitude earthquakes shake huge inland cities such as Mexico City. In this work, we use TREMOL (sThochastic Rupture Earthquake ModeL) to simulate the seismicity observed in this zone. Our numerical results reinforce the hypothesis that in some subduction regions single asperities are responsible for producing the observed seismicity.
Thomas Zwinger, Grace A. Nield, Juha Ruokolainen, and Matt A. King
Geosci. Model Dev., 13, 1155–1164, https://doi.org/10.5194/gmd-13-1155-2020, https://doi.org/10.5194/gmd-13-1155-2020, 2020
Short summary
Short summary
We present a newly developed flat-earth model, Elmer/Earth, for viscoelastic treatment of solid earth deformation under ice loads. Unlike many previous approaches with proprietary software, this model is based on the open-source FEM code Elmer, with the advantage for scientists to apply and alter the model without license constraints. The new-generation full-stress ice-sheet model Elmer/Ice shares the same code base, enabling future coupled ice-sheet–glacial-isostatic-adjustment simulations.
Swarup Chauhan, Kathleen Sell, Wolfram Rühaak, Thorsten Wille, and Ingo Sass
Geosci. Model Dev., 13, 315–334, https://doi.org/10.5194/gmd-13-315-2020, https://doi.org/10.5194/gmd-13-315-2020, 2020
Short summary
Short summary
We present CobWeb 1.0, a graphical user interface for analysing tomographic images of geomaterials. CobWeb offers different machine learning techniques for accurate multiphase image segmentation and visualizing material specific parameters such as pore size distribution, relative porosity and volume fraction. We demonstrate a novel approach of dual filtration and dual segmentation to eliminate edge enhancement artefact in synchrotron-tomographic datasets and provide the computational code.
Loïc Huder, Nicolas Gillet, and Franck Thollard
Geosci. Model Dev., 12, 3795–3803, https://doi.org/10.5194/gmd-12-3795-2019, https://doi.org/10.5194/gmd-12-3795-2019, 2019
Short summary
Short summary
The pygeodyn package is a geomagnetic data assimilation tool written in Python. It gives access to the Earth's core flow dynamics, controlled by geomagnetic observations, by means of a reduced numerical model anchored to geodynamo simulation statistics. It aims to provide the community with a user-friendly and tunable data assimilation algorithm. It can be used for education, geomagnetic model production or tests in conjunction with webgeodyn, a set of visualization tools for geomagnetic models.
Mattia de' Michieli Vitturi, Tomaso Esposti Ongaro, Giacomo Lari, and Alvaro Aravena
Geosci. Model Dev., 12, 581–595, https://doi.org/10.5194/gmd-12-581-2019, https://doi.org/10.5194/gmd-12-581-2019, 2019
Short summary
Short summary
Pyroclastic avalanches are a type of granular flow generated at active volcanoes by different mechanisms, including the collapse of steep pyroclastic deposits (e.g., scoria and ash cones) and fountaining during moderately explosive eruptions. We present IMEX_SfloW2D, a depth-averaged flow model describing the granular mixture as a single-phase granular fluid. Benchmark cases and preliminary application to the simulation of the 11 February pyroclastic avalanche at Mt. Etna (Italy) are shown.
Yihao Wu, Zhicai Luo, Bo Zhong, and Chuang Xu
Geosci. Model Dev., 11, 4797–4815, https://doi.org/10.5194/gmd-11-4797-2018, https://doi.org/10.5194/gmd-11-4797-2018, 2018
Short summary
Short summary
A multilayer approach is parameterized for model development, and the multiple layers are located at different depths beneath the Earth’s surface. This method may be beneficial for gravity/manget field modeling, which may outperform the traditional single-layer approach.
Andres Payo, Bismarck Jigena Antelo, Martin Hurst, Monica Palaseanu-Lovejoy, Chris Williams, Gareth Jenkins, Kathryn Lee, David Favis-Mortlock, Andrew Barkwith, and Michael A. Ellis
Geosci. Model Dev., 11, 4317–4337, https://doi.org/10.5194/gmd-11-4317-2018, https://doi.org/10.5194/gmd-11-4317-2018, 2018
Short summary
Short summary
We describe a new algorithm that automatically delineates the cliff top and toe of a cliffed coastline from a digital elevation model (DEM). The algorithm builds upon existing methods but is specifically designed to resolve very irregular planform coastlines with many bays and capes, such as parts of the coastline of Great Britain.
Cited articles
Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F.: Efficient
management of parallelism in object-oriented numerical software libraries,
in: Modern software tools for scientific computing, Birkhauser, Boston Inc., 163–202, 1997. a
Baumgardner, J. R.: Three-dimensional treatment of convective flow in the
Earth's mantle, J. Stat. Phys., 39, 501–511, https://doi.org/10.1007/BF01008348,
1985. a
Bernardi, C.: Optimal finite-element interpolation on curved domains, SIAM
J. Numer. Anal., 26, 1212–1240, 1989. a
Blankenbach, B., Busse, F., Christensen, U., Cserepes, L., Gunkel, D., Hansen, U., Harder, H., Jarvis, G., Koch, M., Marquart, G., Moore, D., Olson, P., Schmeling, H., and Schnaubelt, T.: A benchmark comparison for mantle
convection codes, Geophys. J. Int., 98, 23–38,
https://doi.org/10.1111/j.1365-246X.1989.tb05511.x, 1989. a
Buffa, A., De Falco, C., and Sangalli, G.: Isogeometric analysis: stable
elements for the 2D Stokes equation, Int. J. Numer. Meth. Fl., 65, 1407–1422, 2011. a
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: The effect of
depth–dependent viscosity on the planform of mantle convection, Nature, 279, 436–438, https://doi.org/10.1038/379436a0, 1996. a
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: A sensitivity study of
3-D-spherical mantle convection at 108 Rayleigh number: effects of
depth-dependent viscosity, heating mode and an endothermic phase change, J.
Geophys. Res., 102, 11991–12007, https://doi.org/10.1029/96JB03806, 1997. a
Busse, F. H., Christensen, U., Clever, R., Cserepes, L., Gable, C.,
Giannandrea, E., Guillou, L., Houseman, G., Nataf, H. C., Ogawa, M.,
Parmentier, M., Sotin, C., and Travis, B.: 3D convection at infinite
Prandtl number in Cartesian geometry – a benchmark comparison, Geophys.
Astrophys. Fluid Dyn., 75, 39–59, https://doi.org/10.1080/03091929408203646, 1994. a
Choblet, G., Cadek, O., Couturier, F., and Dumoulin, C.: OEDIPUS: a new tool to study the dynamics of planetary interiors, Geophys. J. Int., 170, 9–30, https://doi.org/10.1111/j.1365-246X.2007.03419.x, 2007. a, b
Dannberg, J. and Gassmoller, R.: Chemical trends in ocean islands explained by plume-slab interaction, P. Natl. Acad. Sci. USA, 115, 4351–4356,
https://doi.org/10.1073/pnas.1714125115, 2018. a
Davies, D. R. and Davies, J. H.: Thermally–driven mantle plumes reconcile
multiple hotspot observations, Earth Planet. Sc. Lett., 278, 50–54,
https://doi.org/10.1016/j.epsl.2008.11.027, 2009. a
Davies, D. R., Wilson, C. R., and Kramer, S. C.: Fluidity: a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics, Geochem. Geophy. Geosy., 120, Q06001, https://doi.org/10.1029/2011GC003551, 2011. a, b, c, d
Davies, D. R., Le Voci, G., Goes, S., Kramer, S. C., and Wilson, C. R.: The
mantle wedge's transient 3-D flow regime and thermal structure, Geochem.
Geophy. Geosy., 17, 78–100, https://doi.org/10.1002/2015GC006125, 2016. a
Davies, D. R., Valentine, A. P., Kramer, S. C., Rawlinson, N., Hoggard, M. J., Eakin, C., and Wilson, C.: Earth's multi-scale topographic response to global mantle flow, Nat. Geosci., 12, 845–850, https://doi.org/10.1038/s41561-019-0441-4, 2019. a
Davies, G. F.: Dynamic Earth: plates, plumes and mantle convection, Cambridge University Press, Cambridge, 1999. a
Davies, J. H. and Stevenson, D. J.: Physical Model of Source Region of
Subduction Zone Volcanics, J. Geophys. Res., 97, 2037–2070,
https://doi.org/10.1029/91JB02571, 1992. a
Garel, F., Goes, S., Davies, D. R., Davies, J. H., Kramer, S. C., and Wilson,
C. R.: Interaction of subducted slabs with the mantle transition-zone: A
regime diagram from 2-D thermo-mechanical models with a mobile trench and
an overriding plate, Geochem. Geophy. Geosy., 15, 1739–1765,
https://doi.org/10.1002/2014GC005257, 2014. a
Girault, V. and Raviart, P.-A.: Finite element methods for Navier-Stokes
equations: theory and algorithms, vol. 5, Springer Science & Business Media, Berlin, Heidelberg,
2012. a
Gurnis, M.: Phanerozoic marine inundation of continents driven by dynamic
topography above subducting slabs, Nature, 364, 589–593,
https://doi.org/10.1038/364589a0, 1993. a
Gurnis, M. and Davies, G. F.: Mixing in numerical-models of mantle convection
incorporating plate kinematics, J. Geophys. Res., 91, 6375–6395,
https://doi.org/10.1029/JB091iB06p06375, 1986. a
Hager, B. H. and Richards, A. M.: Long–wavelength variations in Earth's
geoid: Physical models and dynamical implications, Philos. T. R. Soc.
London, 328, 309–327, 1989. a
Heister, T., Dannberg, J., Gassmoller, R., and Bangerth, W.: High accuracy
mantle convection simulation through modern numerical methods: II: realistic models and problems, Geophys. J. Int., 210, 833–851,
https://doi.org/10.1093/gji/ggx195, 2017. a, b
Hernlund, J. W. and Tackley, P. J.: Modeling mantle convection inside the
spherical annulus, Phys. Earth Planet. Int., 171, 48–54,
https://doi.org/10.1016/j.pepi.2008.07.037, 2008. a
Hoang, T., Verhoosel, C. V., Auricchio, F., van Brummelen, E. H., and Reali,
A.: Mixed isogeometric finite cell methods for the stokes problem, Comput.
Meth. Appl. M., 316, 400–423, 2017. a
Hunt, S. A., Davies, D. R., Walker, A. M., McCormack, R. J., Wills, A. S.,
Dobson, D. P., and Li, L.: On the increase in thermal diffusivity caused by
the perovskite to post-perovskite phase transition and its implications for
mantle dynamics, Earth Planet. Sc. Lett., 319, 96–103,
https://doi.org/10.1016/j.epsl.2011.12.009, 2012. a
Jarvis, G. T.: Effects of curvature on two–dimensional models of mantle
convection: cylindrical polar coordinates, J. Geophys. Res., 98, 4477–4485, 1993. a
Jones, T. D., Davies, D. R., Campbell, I. H., Wilson, C. R., and Kramer, S. C.:
Do mantle plumes preserve the heterogeneous structure of their deep-mantle
source?, Earth Planet. Sc. Lett., 434, 10–17,
https://doi.org/10.1016/j.epsl.2015.11.016, 2016. a
Jones, T. D., Davies, D. R., and Sossi, P. A.: Tungsten isotopes in mantle
plumes: Heads it's positive, tails it's negative, Earth Planet. Sc. Lett.,
506, 255–267, https://doi.org/10.1016/j.epsl.2018.11.008, 2019. a
King, S. D., Lee, C., van Keken, P. E., Leng, W., Zhong, S., Tan, E., Tosi,
N., and Kameyama, M. C.: A community benchmark for 2-D Cartesian
compressible convection in Earth's mantle, Geophys. J. Int., 179, 1–11,
2009. a
Kloecking, M., White, N. J., Maclennan, J., McKenzie, D., and Fitton, J. G.:
Quantitative Relationships Between Basalt Geochemistry, Shear Wave Velocity, and Asthenospheric Temperature Beneath Western North America, Geochem. Geophy. Geosy., 19, 3376–3404, https://doi.org/10.1029/2018GC007559, 2019. a
Kramer, S. C.: Assess (v1.0), Analytical Solutions for the Stokes Equations in Spherical Shells in python, Zenodo, https://doi.org/10.5281/zenodo.3891545, 2020. a, b, c
Kramer, S. C., Wilson, C. R., and Davies, D. R.: An implicit free-surface
algorithm for geodynamical simulations, Phys. Earth Planet. Int., 194,
25–37, https://doi.org/10.1016/j.pepi.2012.01.001, 2012. a, b, c, d
Kramer, S. C., Wilson, C. R., Davies, D. R., et al.: FluidityProject/fluidity: New test cases Analytical solutions for mantle flow in cylindrical and spherical shells (Version 4.1.17), Zenodo, https://doi.org/10.5281/zenodo.3988620, 2020. a
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods, Geophys. J. Int., 191, 12–29, https://doi.org/10.1111/j.1365-246X.2012.05609.x, 2012. a, b
Logg, A., Mardal, K.-A., and Wells, G.: Automated Solution of Differential
Equations by the Finite Element Method: The FEniCS Book, Lecture Notes in
Computational Science and Engineering, Springer, Berlin,
84, https://doi.org/10.1007/978-3-642-23099-8, 2012. a
McKenzie, D. P., Roberts, J. M., and Weiss, N. O.: Convection in the
Earth's mantle: towards a numerical simulation, J. Fluid Mech., 62,
465–538, https://doi.org/10.1017/S0022112074000784, 1974. a
McNamara, A. K. and Zhong, S.: Thermo–chemical structures beneath Africa
and the Pacific Ocean, Nature, 437, 1136–1139, https://doi.org/10.1038/nature04066, 2005. a
Meurer, A., Smith, C. P., Paprocki, M., Čertík, O., Kirpichev, S. B.,
Rocklin, M., Kumar, A., Ivanov, S., Moore, J. K., Singh, S., Rathnayake, T.,
Vig, S., Granger, B. E., Muller, R. P., Bonazzi, F., Gupta, H., Vats, S.,
Johansson, F., Pedregosa, F., Curry, M. J., Terrel, A. R., Roučka, v.,
Saboo, A., Fernando, I., Kulal, S., Cimrman, R., and Scopatz, A.: SymPy:
symbolic computing in Python, PeerJ, 3, e103,
https://doi.org/10.7717/peerj-cs.103, 2017. a
Mitrovica, J. X., Beaumont, C., and Jarvis, G. T.: Tilting of continental
interiors by the dynamical effects of subduction, Tectonics, 8, 1079–1094,
https://doi.org/10.1029/TC008i005p01079, 1989. a
Moresi, L. N. and Solomatov, V. S.: Numerical investigations of 2D convection with extremely large viscosity variations, Phys. Fluid, 7, 2154–2162, https://doi.org/10.1063/1.868465, 1995. a
Morgan, W. J.: Deep mantle convection plumes and plate motions, Am. Assoc.
Petr. Geol. B., 56, 203–213, 1972. a
Nakagawa, T. and Tackley, P. J.: The interaction between the post-perovskite
phase change and a thermo-chemical boundary layer near the core-mantle
boundary, Earth Planet. Sc. Lett., 238, 204–216, 2005. a
Oldham, D. N. and Davies, J. H.: Numerical investigation of layered convection in a three-dimensional shell with application to planetary mantles, Geochem. Geophy. Geosy., 5, Q12C04, https://doi.org/10.1029/2003GC000603, 2004. a
Olson, P., Deguen, R., Hinnov, L. A., and Zhong, S. J.: Controls on geomagnetic reversals and core evolution by mantle convection in the Phanerozoic, Phys. Earth Planet. Int., 214, 87–103, https://doi.org/10.1016/j.pepi.2012.10.003, 2013. a
Popov, I. Yu., Lobanov, I. S., Popov, S. I., Popov, A. I., and Gerya, T. V.: Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity, Solid Earth, 5, 461–476, https://doi.org/10.5194/se-5-461-2014, 2014. a
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A.
T. T., Bercea, G.-T., Markall, G. R., and Kelly, P. H. J.: Firedrake:
Automating the Finite Element Method by Composing Abstractions, ACT T.
Math. Softw., 43, 1–24, https://doi.org/10.1145/2998441, 2016. a
Roache, P. J.: Code Verification by the Method of Manufactured Solutions,
J. Fluid. Eng.-T. ASME, 124, 4–10, https://doi.org/10.1115/1.1436090, 2002. a
Solheim, L. P. and Peltier, W. R.: Avalanche effects in phase transition
modulated convection – a model of Earth's mantle, J. Geophys. Res., 99,
6997–7018, 1994. a
Stadler, G., Gurnis, M., Burstedde, C., Wilcox, L. C., Alisic, L., and Ghattas, O.: The dynamics of plate tectonics and mantle flow: from local to global scales, Science, 329, 1033–1038, https://doi.org/10.1126/science.1191223, 2010. a
Stotz, I. L., Iaffaldano, G., and Davies, D. R.: Pressure-Driven Poiseuille
Flow: A Major Component of the Torque-Balance Governing Pacific Plate Motion, Geophys. Res. Lett., 45, 117–125, https://doi.org/10.1002/2017GL075697, 2018. a
Tackley, P. J.: Modelling compressible mantle convection with large viscosity
contrasts in a three-dimensional spherical shell using the Yin-Yang grid,
Phys. Earth Planet. Int., 171, 7–18, https://doi.org/10.1016/j.pepi.2008.08.005, 2008. a
Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle, Nature, 361, 699–704,
https://doi.org/10.1038/361699a0, 1993. a
Tan, E., Leng, W., Zhong, S., and Gurins, M.: On the location of plumes and
mobility of thermo–chemical structures with high bulk modulus in the 3-D
compressible mantle, Geochem. Geophy. Geosy., 12, Q07005,
https://doi.org/10.1029/2011GC003665, 2011. a
The Sage Developers: SageMath, the Sage Mathematics Software System (Version 8.6), available at: https://www.sagemath.org (last access: 1 June 2020), 2019. a
Thieulot, C.: Analytical solution for viscous incompressible Stokes flow in a spherical shell, Solid Earth, 8, 1181–1191, https://doi.org/10.5194/se-8-1181-2017, 2017. a, b
Tosi, N., Stein, C., Noack, L., Hüttig, C., Maierová, P., Samuel, H.,
Davies, D. R., Wilson, C. R., Kramer, S. C., Thieulot, C., Glerum, A.,
Fraters, M., Spakman, W., Rozel, A., and Tackley, P. J.: A community
benchmark for viscoplastic thermal convection in a 2-D square box,
Geochem. Geophy. Geosy., 16, 2175–2196,
https://doi.org/10.1002/2015GC005807, 2015. a
Travis, B. J., Anderson, C., Baumgardner, J. R., Gable, C. W., Hager, B. H.,
O'Connell, R. J., Olson, P., Raefsky, A., and Schubert, G.: A benchmark
comparison of numerical methods for infinite Prandtl number thermal
convection in two–dimensional Cartesian geometry, Geophys. Astrophys.
Fluid Dyn., 55, 137–160, 1990. a
van Keken, P. E.: Cylindrical scaling for dynamical cooling models of the
Earth, Phys. Earth. Planet. Int., 124, 119–130, 2001. a
van Keken, P. E. and Ballentine, C. J.: Whole–mantle versus layered mantle
convection and the role of a high–viscosity lower mantle in terrestrial
volatile evolution, Earth Planet. Sc. Lett., 156, 19–32, 1998. a
van Keken, P. E. and Ballentine, C. J.: Dynamical models of mantle volatile
evolution and the role of phase transitions and temperature–dependent
rheology, J. Geophys. Res., 104, 7137–7151, 1999. a
van Keken, P. E. and Yuen, D. A.: Dynamical influences of high viscosity in
the lower mantle induced by the steep melting curve of perovskite: effects of curvature and time–dependence, J. Geophys. Res., 100, 15233–15248,
1995. a
van Keken, P. E., King, S. D., Schmeling, H., Christensen, U. R., Neumeister, D. and Doin, M. P.: A comparison of methods for the modeling of
thermo–chemical convection, J. Geophys. Res., 102, 22477–22495, 1997. a
van Keken, P. E., Kiefer, B., and Peacock, S.: High resolution models of
subduction zones: Implications for mineral dehydration reactions and the
transport of water into the deep mantle, Geochem. Geophy. Geosy., 3, 1056, https://doi.org/10.1029/2001GC000256, 2002. a
van Keken, P. E., Currie, C., King, S. D., Behn, M. D., Cagnioncle, A., He,
J., Katz, R. F., Lin, S., Parmentier, E. M., Spiegelman, M., and Wang, K.: A community benchmark for subduction zone modeling, Phys. Earth Planet. Int., 171, 187–197, https://doi.org/10.1016/j.pepi.2008.04.015, 2008. a
Wilson, C. R., Spiegelman, M., and van Keken, P. E.: TerraFERMA: The
Transparent Finite Element Rapid Model Assembler for multiphysics problems in Earth sciences, Geochem. Geophy. Geosy., 18, 769–810,
https://doi.org/10.1002/2016GC006702, 2017. a
Wolstencroft, M., Davies, J. H., and Davies, D. R.: Nusselt-Rayleigh number
scaling for spherical shell Earth mantle simulation up to a Rayleigh
number of 109, Phys. Earth Planet. Int., 176, 132–141,
https://doi.org/10.1016/j.pepi.2009.05.002, 2009. a
Zhong, S., Gurnis, M., and Hulbert, G.: Accurate determination of
surface normal stress in viscous flow from a consistent boundary flux
method, Phys. Earth Planet. Int., 78, 1–8,
https://doi.org/10.1016/0031-9201(93)90078-N, 1993. a, b
Zhong, S., Zuber, M. T., Moresi, L., and Gurnis, M.: Role of
temperature-dependent viscosity and surface plates in spherical shell models of mantle convection, J. Geophys. Res., 105, 11063–11082,
https://doi.org/10.1029/2000JB900003, 2000.
a, b
Short summary
Computational models of Earth's mantle require rigorous verification and validation. Analytical solutions of the underlying Stokes equations provide a method to verify that these equations are accurately solved for. However, their derivation in spherical and cylindrical shell domains with physically relevant boundary conditions is involved. This paper provides a number of solutions. They are provided in a Python package (Assess) and their use is demonstrated in a convergence study with Fluidity.
Computational models of Earth's mantle require rigorous verification and validation. Analytical...
