Site is Loading, Please wait...

Author: Fabio Crameri

Geodynamic modelling kinematic descriptions

Kinematical descriptions for a compressed upper-mantle geodynamic numerical model setup.

Examples of two-dimensional domain and material discretisation. The domain discretisation in the left-hand side column Kinematical descriptions for a compressed upper-mantle model setup. The left column shows the undeformed, initial model setups and the right column shows the deformed model after a certain amount of model time has passed. In the Eulerian kinematical description the computational mesh is fixed and the generated positive topography is accommodated by implementing a layer of sticky air above the crust. When an Arbitrary Lagrangian-Eulerian approach is used, the domain width is often kept constant in geodynamic applications, such that the mesh only deforms vertically to accommodate the topography. In the Lagrangian formulation, the mesh deforms with the velocity computed on its nodes.

  • Creator: Fabio Crameri
  • This version: 12.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Dark version
  • Transparent background
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Geodynamic modelling problems

Common numerical problems in geodynamic modelling including drunken sailor instability, chequerboard patterns, and mesh dependency.

Common numerical problems in geodynamic modelling. (a) They include a Rayleigh-Taylor instability problem termed „drunken sailor“ instability, which arises from a numerical time step that is too large (e.g. Kaus et al., 2010; Rose et al., 2017) for the stress perturbations deriving from surface topography due to the typical crust-air density difference being much larger than density differences inside the Earth. The large time step size leads to a fast sloshing of the surface, as seen from the velocity vectors. Note that the vectors in the model without stabilisation are scaled down by one order of magnitude. The high velocities also lead to overshooting of the advected compositional field, i.e., values exceed 1. (b) The lid-driven cavity model (e.g. Erturk et al., 2005; Erturk, 2009; Thieulot, 2014) demonstrates the need for smoothing the pressure field when using Q1 x P0 elements in the finite element method. (c) Extension of a visco-plastic medium with shear bands forming at a viscous weak seed along the bottom (e.g. Lemiale et al., 2008; Kaus, 2010; Spiegelman et al., 2016; Glerum et al., 2018). The angle and thickness of the shear bands is dependent on the mesh resolution. Regularised plasticity implementations and sufficient resolution are required to achieve convergence with resolution (e.g. Duretz et al., 2020).

  • Creator: Fabio Crameri
  • This version: 12.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Transparent background
  • Dark background version
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Geodynamic modelling procedure

The procedure of a geodynamic modelling study.

The procedure of a geodynamic modelling study encompasses everything from the assemblage of both a physical and a numerical models based on a verified numerical code, to the design of a simplified model setup based on a certain modelling philosophy, the validation of the model through careful testing, the unbiased analysis of the produced model output, the oral, written, and graphical communication of the modelling approach and results, and the management of both software and data. Constant (re-)evaluation and potential subsequent adjustments of previous steps are key, and indeed necessary, throughout this process.

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Transparent background
  • Dark background version
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Numerical discretisation (domain & material)

Examples of numerical, two-dimensional domain and material discretisation.

Examples of two-dimensional domain and material discretisation. The domain discretisation in the left-hand side column illustrates different types of meshes. The top left mesh is built on a quadtree and also shown with several levels of mesh refinement (middle left) so as to better capture the circular interface. The bottom left panel shows an unstructured triangular mesh built so that element edges are aligned with the (quarter) circle perimeter. Note that non-rectangle quadrilateral elements can also be used to conform to an interface. The material discretisation is illustrated by different methods of material tracking in the right-hand side column based on either the particle-in-cell method (top right) or grid-based advection (bottom right) for the material contrasts indicated by the blueish colours.

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Dark version
  • Transparent background
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Governing equations

The governing equations of numerical modelling include conservation of mass, momentum, and energy with different types of rheology.

The governing equations of geodynamic numerical modelling include conservation of mass, momentum, and energy with different types of rheology. ρ is the density, t is time, v the velocity vector, σ the stress tensor, g the gravitational acceleration vector, Cp the heat capacity, T the temperature, k the thermal conductivity, H a volumetric heat production term (e.g., due to radioactive decay) and the term S = S + S2 + S3 accounts for friction heating, adiabatic heating, and the release or consumption of latent heat (e.g., associated with phase changes), respectively. Note that the plastic rheology depicted here is the geodynamic approximation of brittle failure.

  • Creator: Fabio Crameri
  • This version: 19.01.2022
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Transparent background
  • Dark background version
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Computing

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain.

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain shown on the left. For sequential programming, the code performs two tasks A and B in a sequential manner, on a single thread which has access to all of the computer’s memory. When the same code is executed in parallel relying on OpenMP, each processor of the computer concurrently carries out a part of tasks A and B so that the compute wall clock time is shorter. If relying on MPI-based parallelisation, the domain is usually broken up so that each thread ‘knows’ only a part of the domain. Tasks A and B are also executed in parallel by all the CPUs, but now, there is a distributed architecture of processors and memory interlinked by a dedicated network. The Scientific colour map ‘batlow‘ is used to represent individual domain parts to all readers.

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Transparent background
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Numerical discretisation (space & time)

One-dimensional discretisation in space and time based on discrete temporal and spatial steps.

One-dimensional discretisation used in geodynamic numerical models in space (horizontal axis) and time (vertical axis) based on discrete steps in space (h) and time (Δt).

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-ink.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
  • Dark version
  • Transparent background
  • Vector format
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Atmospheric CO2 concentration

Globally averaged concentration of carbon dioxide (CO2) in the atmosphere for the time period 803’719 BCE – 2018.

Globally averaged concentration of carbon dioxide (CO2) in the atmosphere for the time period 803’719 BCE – 2018. Shown is data from Bereiter et al. (2015) and the concentration is measured in parts per million (ppm). The long-term global average atmospheric concentrations of CO2 have been combined using several sources, all available at the NOAA/ESRL Global Monitoring Division. Not only the level of CO2 in the atmosphere matters, but also the rate at which it has changed. It took us a matter of decades to achieve larger changes than previous ones, which occurred over centuries or even thousands of years. This gives species, planetary systems, and ecosystems much less time to adapt. The Scientific colour map ‘bilbao‘ is used to represent data accurately and to all readers.

  • Creator: Fabio Crameri
  • This version: 02.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri based on data compiled by Bereiter et al. (2015) is available via the open-access s-ink.org repository.
  • Related reference: Bereiter, B., Eggleston, S., Schmitt, J., Nehrbass‐Ahles, C., Stocker, T. F., Fischer, H., … & Chappellaz, J. (2015). Revision of the EPICA Dome C CO2 record from 800 to 600 kyr before present. Geophysical Research Letters, 42(2), 542-549.
  • Alternative graph aspect ratio
  • Alternative colour maps
  • Transparent background
  • Light & dark background versions
  • Perceptually uniform colour map
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

World countries CO2 emissions

The World’s countries’ CO2 emissions per capita and year, for the year 2018.

The World’s countries’ carbon dioxide (CO2) emissions per capita and year, for the year 2018, driving climate change. Shown is the CAIT data, which is available on climatewatchdata.org/ghg-emissions. The Scientific colour map ‘bilbao‘ is used to represent data accurately and to all readers.

  • Creator: Fabio Crameri
  • This version: 01.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri based on CAIT data (Climate Watch, 2020) is available via the open-access s-Ink repository.
  • Related reference: Climate Watch, 2020, GHG Emissions, Washington, DC: World Resources Institute
  • Alternative map projections
  • Transparent background
  • Light & dark background versions
  • Perceptually uniform colour map
  • Colour-vision deficiency friendly
  • Readable in black&white
Download

Faulty or missing link? – Please report them via a reply below!

Exit mobile version
%%footer%%