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The Sassy Scientist – Analogue Modelling

The Sassy Scientist – Analogue Modelling

Every week, The Sassy Scientist answers a question on geodynamics, related topics, academic life, the universe or anything in between with a healthy dose of sarcasm. Do you have a question for The Sassy Scientist? Submit your question here.

David asks:


What do you think about analogue modelling?


Dear David,

Analogue modelling. Well, what’s not to like? Who doesn’t want to spend weeks or months finding the material that mimics behaviour we suspect to be relevant for Earth-like processes? And then, after finally finding the perfect material and sculpting a subduction zone, seeing it all sink to the bottom of the tank because the ‘lithosphere’ wasn’t placed perfectly on top of the ‘asthenosphere’?

Then again, the realm of analogue modelling isn’t all that grim… Even though you cannot blindly run many models to investigate the full parameter space, this is also a benefit. Analogue modelling requires you to make smart choices about the processes you seek to model. Then, the results are fairly close to the first-order response we consider appropriate for Earth. With numerical models we can simply add complexity on top of complexity on top of complexity, which makes it fairly difficult to constrain exactly what’s happening. Additionally, numerical models may produce exciting figures and results that seem to mimic what we interpret from our observations. In the end they simply numerically solve some equations. In analogue models on the other hand you actually see nature at work!

To conclude: analogue modelling is definitely worth the pain and effort (see João’s story). Unfortunately, research positions are limited, because it simply isn’t as sexy as numerical modelling. There are limited facilities worldwide, whereas for numerically modelling every university can provide you with a computer. So: get into it before the state of funding for analogue modelling becomes as comforting as the Dry Valleys of Antarctica!

Yours truly,

The Sassy Scientist

PS: This post was written after sitting through a disappointing analogue modelling session at EGU

The past is the key

The past is the key

Lorenzo Colli

“The present is the key to the past” is a oft-used phrase in the context of understanding our planet’s complex evolution. But this perspective can also be flipped, reflected, and reframed. In this Geodynamics 101 post, Lorenzo Colli, Research Assistant Professor at the University of Houston, USA, showcases some of the recent advances in modelling mantle convection.  

 

Mantle convection is the fundamental process that drives a large part of the geologic activity at the Earth’s surface. Indeed, mantle convection can be framed as a dynamical theory that complements and expands the kinematic theory of plate tectonics: on the one hand it aims to describe and quantify the forces that cause tectonic processes; on the other, it provides an explanation for features – such as hotspot volcanism, chains of seamounts, large igneous provinces and anomalous non-isostatic topography – that aren’t accounted for by plate tectonics.

Mantle convection is both very simple and very complicated. In its essence, it is simply thermal convection: hot (and lighter) material goes up, cold (and denser) material goes down. We can describe thermal convection using classical equations of fluid dynamics, which are based on well-founded physical principles: the continuity equation enforces conservation of mass; the Navier-Stokes equation deals with conservation of momentum; and the heat equation embodies conservation of energy. Moreover, given the extremely large viscosity of the Earth’s mantle and the low rates of deformation, inertia and turbulence are utterly negligible and the Navier-Stokes equation can be simplified accordingly. One incredible consequence is that the flow field only depends on an instantaneous force balance, not on its past states, and it is thus time reversible. And when I say incredible, I really mean it: it looks like a magic trick. Check it out yourself.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk

This is as simple as it gets, in the sense that from here onward every additional aspect of mantle convection results in a more complex system: 3D variations in rheology and composition; phase transitions, melting and, more generally, the thermodynamics of mantle minerals; the feedbacks between deep Earth dynamics and surface processes. Each of these additional aspects results in a system that is harder and costlier to solve numerically, so much so that numerical models need to compromise, including some but excluding others, or giving up dimensionality, domain size or the ability to advance in time. More importantly, most of these aspects are so-called subgrid-scale processes: they deal with the macroscopic effect of some microscopic process that cannot be modelled at the same scale as the macroscopic flow and is too costly to model at the appropriate scale. Consequently, it needs to be parametrized. To make matters worse, some of these microscopic processes are not understood sufficiently well to begin with: the parametrizations are not formally derived from first-principle physics but are long-range extrapolations of semi-empirical laws. The end result is that it is possible to generate more complex – thus, in this regard, more Earth-like – models of mantle convection at the cost of an increase in tunable parameters. But what parameters give a truly better model? How can we test it?

Figure 1: The mantle convection model on the left runs in ten minutes on your laptop. It is not the Earth. The one on the right takes two days on a supercomputer. It is fancier, but it is still not the real Earth.

Meteorologists face similar issues with their models of atmospheric circulation. For example, processes related to turbulence, clouds and rainfall need to be parametrized. Early weather forecast models were… less than ideal. But meteorologists can compare every day their model predictions with what actually occurs, thus objectively and quantitatively assessing what works and what doesn’t. As a result, during the last 40 years weather predictions have improved steadily (Bauer et al., 2015). Current models are better at using available information (what is technically called data assimilation; more on this later) and have parametrizations that better represent the physics of the underlying processes.

If time travel is possible, where are the geophysicists from the future?

We could do the same, in theory. We can initialize a mantle convection model with some best estimate for the present-day state of the Earth’s mantle and let it run forward into the future, with the explicit aim of forecasting its future evolution. But mantle convection evolves over millions of years instead of days, thus making future predictions impractical. Another option would be to initialize a mantle convection model in the distant past and run it forward, thus making predictions-in-the-past. But in this case we really don’t know the state of the mantle in the past. And as mantle convection is a chaotic process, even a small error in the initial condition quickly grows into a completely different model trajectory (Bello et al., 2014). One can mitigate this chaotic divergence by using data assimilation and imposing surface velocities as reconstructed by a kinematic model of past plate motions (Bunge et al., 1998), which indeed tends to bring the modelled evolution closer to the true one (Colli et al., 2015). But it would take hundreds of millions of years of error-free plate motions to eliminate the influence of the unknown initial condition.

As I mentioned before, the flow field is time reversible, so one can try to start from the present-day state and integrate the governing equations backward in time. But while the flow field is time reversible, the temperature field is not. Heat diffusion is physically irreversible and mathematically unstable when solved back in time. Plainly said, the temperature field blows up. Heat diffusion needs to be turned off [1], thus keeping only heat advection. This approach, aptly called backward advection (Steinberger and O’Connell, 1997), is limited to only a few tens of millions of years in the past (Conrad and Gurnis, 2003; Moucha and Forte, 2011): the errors induced by neglecting heat diffusion add up and the recovered “initial condition”, when integrated forward in time (or should I say, back to the future), doesn’t land back at the desired present-day state, following instead a divergent trajectory.

Per aspera ad astra

As all the simple approaches turn out to be either unfeasible or unsatisfactory, we need to turn our attention to more sophisticated ones. One option is to be more clever about data assimilation, for example using a Kalman filter (Bocher et al., 2016; 2018). This methodology allow for the combining of the physics of the system, as embodied by the numerical model, with observational data, while at the same time taking into account their relative uncertainties. A different approach is given by posing a formal inverse problem aimed at finding the “optimal” initial condition that evolves into the known (best-estimate) present-day state of the mantle. This inverse problem can be solved using the adjoint method (Bunge et al., 2003; Liu and Gurnis, 2008), a rather elegant mathematical technique that exploits the physics of the system to compute the sensitivity of the final condition to variations in the initial condition. Both methodologies are computationally very expensive. Like, many millions of CPU-hours expensive. But they allow for explicit predictions of the past history of mantle flow (Spasojevic & Gurnis, 2012; Colli et al., 2018), which can then be compared with evidence of past flow states as preserved by the geologic record, for example in the form of regional- and continental-scale unconformities (Friedrich et al., 2018) and planation surfaces (Guillocheau et al., 2018). The past history of the Earth thus holds the key to significantly advance our understanding of mantle dynamics by allowing us to test and improve our models of mantle convection.

Figure 2: A schematic illustration of a reconstruction of past mantle flow obtained via the adjoint method. Symbols represent model states at discrete times. They are connected by lines representing model evolution over time. The procedure starts from a first guess of the state of the mantle in the distant past (orange circle). When evolved in time (red triangles) it will not reproduce the present-day state of the real Earth (purple cross). The adjoint method tells you in which direction the initial condition needs to be shifted in order to move the modeled present-day state closer to the real Earth. By iteratively correcting the first guess an optimized evolution (green stars) can be obtained, which matches the present-day state of the Earth.

1.Or even to be reversed in sign, to make the time-reversed heat equation unconditionally stable.

Geodynamics in Planetary Science

Geodynamics in Planetary Science

It is a question that humankind has been asking for thousands of years:

Are we alone in the Universe or are there other worlds like our own?

As of today, it is unknown whether or not inhabited planets exist outside of our own solar system. With the discovery of the extrasolar planet 51 Peg b in 1992, it was confirmed that our sun is not the only star that hosts planets and therefore the search for extraterrestrial life has expanded beyond our own solar system.
However, before we look for an inhabited exoplanet, we must understand what makes a planet habitable.
Of course, the best example of an inhabited (and hence habitable) planet is our Earth and therefore it is a reasonable approach to first look for Earth-like planets. So, the question we should ask is

What makes Earth habitable?

  • The planet should be in the so-called habitable zone: the zone where the planet contains liquid water on its surface. One usually calculates this zone assuming an Earth-like atmosphere.  [e.g. Lammer et al., 2009]
  • The planet also needs to have an atmosphere that protects it from radiation but also keeps the planet warm with greenhouse gases. [e.g. Seager, 2013]
  • The planet should be made of rock and should have a molten core. A convective outer core gives rise to a magnetic field that protects the planet from solar winds and cosmic rays. [e.g. Shahar et al., 2019]

Interestingly, we can couple all three points: greenhouse gases in the atmosphere can heat a planet that is too far away from its host star and therefore make it habitable. On the other hand, they can also heat a planet too much such that it becomes inhabitable.
The third point (a planet made of rock with a molten core) brings geodynamics into play: plate tectonics and volcanic outgassing contribute to burial and recycling of atmospheric gases [Seager, 2013].
In our solar system, Earth is the only inhabited planet, and it is also the only planet we know of that exhibits plate tectonics (including exoplanets).
For example, Venus, our neighbouring sister planet, is very similar to Earth in terms of size, mass and composition. Some studies even suggest that Venus might have been the first habitable planet of our solar system [Way et al., 2016].
But present-day Venus is an inhospitable planet with a very thick carbon dioxide atmosphere (90 times denser than that of Earth) and an extremely hot surface temperature (up to 750K) which is mainly because of runaway greenhouse gases. But why did Earth become habitable and Venus did not?
To explain their different evolutionary paths, plate tectonics might play a major role. Through plate tectonics, Earth can efficiently recycle carbon back into its surface (deep carbon cycle) and this may help to prevent a runaway Greenhouse effect.

The importance of plate tectonics on the habitability of a planet is still being studied, and it is not yet fully understood how efficient this recycling is.

Plate tectonics also influences the generation of a magnetic field. Plate tectonics efficiently cools the mantle by subducting cold slabs into the deep interior, which leads to high heat flow out of the core. Therefore, the style of mantle convection controls the convection in the outer core. This then generates the magnetic field of a planet. The magnetic field acts as a protective shield from the solar winds, which otherwise might erode the planet’s atmosphere. As discussed above, the atmosphere controls the climate mainly through greenhouse gases. The resulting climate influences the tectonic regime: cool climates are favourable for plate tectonics because they facilitate the formation of weak shear-zones in the lithosphere [Foley et al., 2016].
This coupling between the climate, mantle and the core is called the “whole planet coupling” [Foley et al., 2016] and as a whole, it might explain why Earth and Venus have evolved so differently.

Whole planet coupling“: The atmosphere controls the climate which influences the tectonic regime. Subducting slabs cool the mantle which leads to high heat flow out the core. Therefore, the mantle convection controls the type of convection in the outer core which can generate a magnetic field. The magnetic field protects the atmosphere from solar winds and cosmic rays.

To understand the habitability of exoplanets, we therefore need to investigate all the components of the whole planet coupling. Most interestingly for geodynamicists, it is the interior dynamics of a planet’s mantle that couples all these different components!

In the past years, astronomers have discovered many exoplanets, and we expect many more to join this list. For some of them, astronomers and astrophysicists can measure its size, mass, and sometimes even the atmospheric composition and/or surface temperature.
This is very different from studying the Earth, where we can gather a lot of information about the interior through, for example, seismology. Geophysicists, Astronomers, Astrophysicists and many other research disciplines have to collaborate such that they can understand an exoplanet’s whole planet coupling and potential habitability. For geodynamicists the challenge will be to infer the exoplanet’s interior dynamics from a limited amount of data only.

References:
Foley, B. J. and Driscoll, P. E.: Whole planet coupling between climate, mantle, and core: Implications for the evolution of rocky planets, Geochemistry, Geophysics, Geosystems, Vol. 17, 2016.
Lammer, H., et al.: What makes a planet habitable?, The Astronomy and Astrophysics Review, Vol. 17, 2009.
Seager, S.: Exoplanet Habitability. Science, Vol. 340, 2013.
Shahar, A., Driscoll, P., Weinberger, A. and Cody, G.: What makes a planet habitable?, Science, Vol. 364, 2019.
Way, M. J., et al.: Was Venus the first habitable world of our solar system?, Geophysical Research Letters, Vol. 43, 2016.

Introducing the blog team!

Introducing the blog team!

It’s time for another proper introduction of the blog team! As you will probably know, things have been a bit silent on the blog front lately. This is because all the blog editors were very busy and also: it’s hard to upload 52 times a year. You come up with some great blog ideas! (if you do: e-mail us, please!). Luckily, we used the EGU General Assembly to find some fresh blood for the blog team. Together with the seasoned blog team members and a new blog strategy, we are buzzing to give you regular content once again. Expect the usual blog posts on Wednesday at 9:00 am and in the future, maybe expect a little extra on Fridays… But who are these great people providing you with your weekly dose of geodynamics news?

The Blog Team

Iris van Zelst
I am a PhD student in the Seismology and Wave Physics group at ETH Zürich, Switzerland. I am right at the seismology border of geodynamic research, as I am combining geodynamic modelling with dynamic rupture modelling to look at earthquakes in subduction zones on the entire timescale relevant to the process. I also occasionally look at some data, because you should always keep it real. I am in the final year of my PhD (oh help!), so my aim as Editor-in-Chief is to make sure everyone else is organised and uploading regularly, while I will be mostly pulling the strings behind the scenes and writing an occasional blog post. Such as this one! In my spare time, I love to read lots of books in all kinds of genres, go to the theatre, and play a little bit of theatre myself. I recently enrolled in an improv class and it is so much fun! All the world’s a stage. You can reach my via e-mail.

Luca Dal Zilio
I am a postdoctoral researcher in Mechanical Engineering and Geophysics at the California Institute of Technology (Caltech). My research is primarily aimed at understanding the relationship between crustal deformation and earthquakes in mountain belts, such as the Alps and Himalaya. By combining theoretical, computational, and observational approaches, I attempt to understand the interplay between geodynamic space–time scales of millions of years of slow and broadly distributed regional deformation with seismic space–time scales of rapid and localised earthquake processes. My passion lies in democratising science communication via innovative and accessible tools in order to spread scientific research and discovery. And yes, I like coffee. Espresso. You can reach me via e-mail.

Anne Glerum
I am a postdoctoral researcher at GFZ Potsdam, Germany. With numerical models, I investigate the link between local stress and strain observations and far-field forcing in the East African Rift System. Other modelling interests include magma-tectonic feedback and surface evolution during continental extension. Outside of research, I love to go on walks with my dog, to explore my new home Berlin and to read books on all possible topics. I’m excited to show you the variety of geodynamics and its overlap with other disciplines as an editor of the GD blog team. You can reach me via e-mail.

Anna Gülcher
I am a PhD student at the Geophysical Fluid Dynamics group at ETH Zürich, Switzerland. With the use of numerical modelling, I study the interior dynamics of the Earth and other planets. For my research, I am trying the put geophysical, geological, and geochemical observations in a geodynamically coherent framework (with an emphasis on trying). I found a passion for windsurfing early on while still living in my flat home country (the Netherlands). Yet, since moving to mountainous Switzerland, I have traded in my windsurfing equipment for hiking boots or snowboarding gear and try to spend my free time in the Alps to seek some adrenaline. I’ve very recently started to learn how to play the guitar, and am very proud to say that I can now play my very first complete song. I am excited to be part of the GD team as an Editor! You can reach me via e-mail.

Diogo Lourenço
I am a postdoctoral researcher at the Department of Earth and Planetary Sciences at the University of California Davis, USA. My research aims at understanding the evolution and interior dynamics of the Earth and other rocky planets, primarily through the use of numerical models. When I am not working on theoretical geodynamics, I like to keep things theoretical. I like reading and playing music. Sometimes I also exercise by walking around museums and looking at things. With my work as an editor in this blog, I hope to bring geodynamics to the reader in a friendly and exciting way. I also hope to help building a more involved and integrative geodynamics community. You can reach me via e-mail.

Tobias Meier
I am currently a PhD student at the Center for Space and Habitability (CSH) at the University of Bern. My research focuses on understanding the interior dynamics of rocky exoplanets, particularly planets that are partly molten. At the CSH, Earth and planetary scientists and astrophysicists work side-by-side to understand the formation and evolution of solar system bodies and exoplanets. As an editor of the GD blog I will nurture the link between geodynamics and terrestrial planet evolution and foster interactions between related disciplines.
As an undergraduate I worked in the field of cosmology, so it was necessary for me to downsize from thinking about the vast scales of the universe to zooming in on individual planets when I transitioned to my PhD work. At the time of writing, there has not been a confirmation of an inhabited exoplanet where we could possibly travel to. So, on our own wonderful planet, I enjoy hiking in the beautiful Swiss mountains and I also (almost) never say no to a game of table tennis. You can reach me (also for table tennis!) via e-mail.

Antoine Rozel
I am a senior researcher in ETH Zürich. After studying physics (nobody is perfect), I have been working on numerical simulations of mantle convection involving absurd rheologies for quite a while now, I am getting old. I am also interested in crust and craton production in all solar system planets. To make life even more beautiful, I have also finished the conservatory in classical piano and I organised some painting exhibitions in the last years (you can find my gallery here). I have also found recently that -when I do not play pinball or videogames- I can save time by doing both music and sport at the same time by playing Japanese drums (taiko)! You can reach me via e-mail.

Grace Shephard
I am a Researcher at the Centre for Earth Evolution and Dynamics (CEED) at the University of Oslo, Norway. My research links plate tectonics,​ palaeogeography, and deep mantle structure and dynamics. I spend much of my time hunting for evidence to constrain the opening and closure of ocean basins, particularly around the Arctic, Atlantic and the Pacific. I think GPlates is an excellent Tardis with which to time travel. Geodynamics offers a lot of interdisciplinary and creative avenues to explore – and why not follow up your idea with a blog post! You can reach me via e-mail or find a sporadic tweet at @ShepGracie.

The Sassy Scientist
I am currently employed at a first tier research institute where I am continuously working with the greatest minds to further our understanding of the solid Earth system. Whether it is mantle or lithosphere structure and dynamics, solid Earth rheology parameters, earthquake processes, integrating observations with model predictions or inversions: you have read a paper of mine. Even if you are working on a topic I haven’t mentioned here, I still know everything about it. Do you have any problems in your research career? I have already experienced them. Do you struggle with your work-life balance? Been there, done that. Nowadays, I have only one hobby: helping you out by answering the most poignant questions in geodynamics, research, and life. I am waiting for you right here. Get inspired.