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Geodynamics

EGU ECS

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.

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.

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.

GD Guide to EGU19

With this year’s EGU General Assembly (GA; #EGU19) looming in less than a week, it’s time for all attendees to finish (or start) their own scientific contributions, create their own personal programs as well as plan other activities during the conference. In this blog Nico Schliffke (GD ECS Rep) would like to share some useful advice how to successfully navigate through the conference and highlight relevant activities, both scientific and social, for Geodynamics Early Career Scientists (ECS).

The huge variety of scientific contributions (~18,000 at EGU18) might seem intimidating to begin with and makes it impossible for any individual to keep track of everything. To be well prepared for the conference, allow for a bit of time to create your own personal programme by logging in with your account details and search for relevant sessions, keywords, authors, friends or any other fields of interest. If you have found anything interesting, add it to your personal programme by ticking the ‘star’. After completing your personal programme you can print your own timetable or open it in the EGU 2019 app.

Besides all the (specific) scientific content of the GA, EGU19 offers a wide spread of exciting workshops and short courses to boost your personal and career skills, as well great debates, union wide events and division social events. Below you will find a list of highlight events, special ECS targeted events, social events and other things to keep in mind and to make the best of EGU19:

For first time attendees:

How to navigate the EGU: tips and tricks (Mon, 08:30 – 10:15, Room -2.16) – This workshop is led by several EGU ECS representatives and will give an overview of procedures during EGU as well as useful tips and tricks how to successfully navigate the GA.

GD workshops and short courses:

Geodynamics 101A: Numerical methods (Thur, 14:00-15:45, Room -2.62) Building on last year’s short course, we are happy to announce two short courses this year as a part of the ’Solid Earth 101’ series together with Seismology 101 and Geology 101. The first course deals with the basic concepts of numerical modelling, including discretisation of governing equations, building models, benchmarking (among others).

Geodynamics 101B: Large-scale dynamical processes (Fri, 14:00-15:45, Room -2.62)  The second short course will discuss the applications of geodynamical modelling. It will cover a state-of-art overview of main large-scale dynamics on Earth (mantle convection, continental breakup, subduction dynamics, crustal deformation..) but also discuss constraints coming from seismology (tomography) or the geological record.

Geology 101: The (hi)story of rocks (Tue, 14:00 – 15:45, Room -2.62)The complementary workshop in the 101 series: Find more about structural and petrological processes on Earth. It’s definitely worth knowing, otherwise why should we be doing many of these Geodynamical models?

Seismology 101 (Wed, 14:00 – 15:45, Room -2.62)The second complementary workshop in the 101 series. Many geodynamical models are based on observations using seismological methods. Find out more about earthquakes, beachballs and what semiologists are actually measuring – this is essential for any numerical or analogue geodynamical model!

GD related award ceremonies and lectures:

Arne Richter Award for Outstanding ECS Lecture by Mathew Domeier (Tue, 12:00-12:30 Room -2.21) – The Arne Richter award is an union-wide award for young scientists. We are happy to see that Mathew as a Geodynamicist has won the medal this year! Come along and listen to his current research.

Augustus Love Medal Lecture by Anne Davaille (Thur, 14:45-15:45, Room D1) – Listen to the exciting work of the first female winner of the Augustus Love Medal (the GD division award), Anne Davaille! She is specialised on experimental and analytical fluid dynamics which has given Geodynamics many new insights.

Arthur Holmes Medal Lecture by Jean Braun  (Tue, 12:45-13:45, Room E1) – This one of the most prestigious EGU award for solid Earth geosciences. Jean is a geodynamicist from Potsdam and works on integrating surface and lithospheric dynamics into numerical models.

GD division social activities:

ECS GD informal lunch  (Mon, 12:30-14:00) – Come and meet the ECS team behind these GD activities! Meet in front of the conference center (look for “GD” stickers), to head to the food court in Kagran (2 subway stops away from the conference center, opposite direction to city centre).

ECS GD dinner (Wed, 19:30-22:00) – Join us for a friendly dinner at a traditional Viennese ‘Heurigen’ with fellow ECS Geodynamicists at Gigerl – Rauhensteingasse 3, Wien 1. Bezirk!  If you would like to attend the ECS GD dinner on Wednesday, please fill out this form to keep track on the number of people: https://docs.google.com/forms/d/e/1FAIpQLScpi8gvDDMOOOjLbtq4BrElsoBtTv86Mud7qNQ5yl7qWP5cUA/viewform  Remember to bring some cash to pay for your own food and drinks!

GD/TS/SM drinks (Wed, after ECS GD dinner) – Don’t worry if you cannot make for the ECS GD dinner! After dinner we’ll have a 5 min walk to Bermuda Bräu – Rabensteig 6, 1010 Wien for some drinks together with ECS from Seismology (SM) and Tectonics/Structural (TS), so you can meet us there too!

GD Division meeting (Fri, 12:45-13:45 Room D2) – Elections and reports from the division president, ECS representative and other planning in GD related matters. Lunch provided!

Meet the division president of Geodynamics (Paul Tackley) and the ECS representative (Nico Schliffke) (Wed, 11:45-12:30, EGU Booth) – Come and discuss with the president and ECS rep about any GD related issues, suggestions or remarks.

Geodynamicists eating lunch at Kagran – it’s tradition by now.

EGU wide social activities:

Networking and ECS Zone (all week – red area)This area is dedicated to early career scientist all week and provides space to chillout, get your well deserved coffee or find out more about ECS related announcements.

Opening reception (Sun, 18:30 – 21:00, Foyer F) – Don’t miss out on many new faces and friends, as well as free food and drinks and the opening (ice-breaker) reception! There will also be a ECS corner to meet fellow young scientists, especially if it’s your first EGU.

EGU Award Ceremony (Wed, 17:30 – 20:00, Room E1) – All EGU medallists will receive their award at this ceremony.

ECS Forum (Wed, 12:45 – 13:45, Room L2)An open discussion on any ECS topic

ECS Networking and Careers Reception (by invitation only) (Tue, 19:00-20:30, Room F2)

Conveners’ reception (by invitation only) (Fri 19:30 – 0:00, Foyer F)

Credit: Kai Boggild (distributed via imaggeo.egu.eu)

Great debates

Science in policymaking: Who is responsible?  (Mon, 10:45 – 12:30, Room E1) – Actively take part in one of the presently most important and hot topic!

How can Early Career Scientists prioritise their mental wellbeing? (Tue, 19:00 – 20:30, Room E1) – Many ECS find it challenging to prioritise their mental wellbeing. Discuss with many other young scientist how to tackle this really important issue and maybe learn helpful tips how to improve your own wellbeing!

Other useful skills to polish your career/CV:

Help! I’m presenting at a scientific conference (Mon, 14:00 –15:45, Room -2.62) – Your first conference talk might be daunting. Find out best practices and tips how to create a concise and clear conference talk.

How to share your research with citizens and why it’s so important (Mon, 14:00-15:45, Room -2.16) – Do you share your research with the public? Can you explain in simple matters? An important topic for researchers currently!

How to make the most of your PhD or postdoc experience for getting your next job in academia (Tue, 16:15 – 18:00, Room -2.85) – It’s never too early to plan your next career step.

How to convene and chair a session at the General Assembly (Tue, 08:30-10:15, Room -2.85) – Find out what it needs to convene a session of short course at EGU. You may be surprised, but you could to it next year if you liked,

How to peer-review? (Mon, 16:15 -18:00, Room -2.85) – After the end of a PhD (or sometimes even earlier!) you may be asked to peer-review journal contributions, but hardly anyone knows the process beforehand.

How to find funding and write a research grant (Tue, 10:45-12:30, Room -2.16) – One of the major tasks when you finish your PhDs. It might even be useful when writing applications for travel support etc.

Funding opportunities: ERC grants (Tue, 12:45-13:45, Room 0.14) – Find out more about these generous grants and how to successfully apply for them

How to apply for the Marie Sklodowska-Curie grants (Wed, 12:45-13:45, Room 0.14)

Balancing work and personal life as a scientist (Wed, 16:15 – 18:00, Room -2.85) – Find out how not to lose sight of your hobbies and personal life in a increasingly competitive academic environment.

Other interesting events:

Academia is not the only route (Thu, 10:45-12:30, Room -2.16) – Are you finishing your degree and not overly excited by an academic future? Try this short course on exploring career alternatives both inside and outside academia

Games for Geoscience (Wed, 16:15-18:00 (Talks) in Room L8 and 14:00-15:45 (Posters), Hall X4) – Games are more fun than work! Learn more on how to use games for communication, outreach and much more.

Unconscious bias (Wed, 12:45-13:45, Room -2.32) – Become aware of the obstacles that some of your colleagues face every day, and that might prevent them from doing the best science

Promoting and supporting equality of opportunities in geosciences (Thu, 14:00-18:00, Room E1) – Any of us should promote an open, equal opportunity working environment and this session promises some very interesting talk on common issues, solutions and initiatives.

What I’ve learned from teaching geosciences in prisons – (Thu, 14:00-15:45, Hall X4 – Poster) by GD ECS Phil Heron.

Rhyme Your Research (Tue, 14:00 – 15:45, Room -2.16) – Reveal the poet in you and explain your research in an interesting and unusual way!

This is just a small list of possible activities during EGU19, and I’m sure to have missed out many more. So keep your eyes and ears open for additional events and spread the word if you know anything of particular interest. Also make sure you follow the GD Blog, our social media (EGU GD Facebook page) and EGU Twitter, to keep updated with any more information during the week! The official hashtag is #EGU19. All the best for EGU and I am looking forward to meeting many of you there!

Reproducible Computational Science

Krister with his bat-signal shirt for reproducibility.

We’ve all been there – you’re reading through a great new paper, keen to get to the Data Availability only to find nothing listed, or the uninspiring “data provided on request”. This week Krister Karlsen, PhD student from the Centre for Earth Evolution and Dynamics (CEED), University of Oslo shares some context and tips for increasing the reproducibility of your research from a computational science perspective. Spread the good word and reach for the “Gold Standard”!

Historically, computational methods and modelling have been considered the third avenue of the sciences, but they are now some of the most important, paralleling experimental and theoretical approaches. Thanks to the rapid development of electronics and theoretical advances in numerical methods, mathematical models combined with strong computing power provide an excellent tool to study what is not available for us to observe or sample (Fig. 1). In addition to being able to simulate complex physical phenomena on computer clusters, these advances have drastically improved our ability to gather and examine high-dimensional data. For these reasons, computational science is in fact the leading tool in many branches of physics, chemistry, biology, and geodynamics.

Figure 1: Time–depth diagram presenting availability of geodynamic data. Modified from (Gerya, 2014).

A side effect of the improvement of methods for simulation and data gathering is the availability of a vast variety of different software packages and huge data sets. This poses a challenge in terms of sufficient documentation that will allow the study to be reproduced. With great computing power, comes great responsibility.

“Non-reproducible single occurrences are of no significance to science.” – Popper (1959)

Reproducibility is the cornerstone of cumulative science; the ultimate standard by which scientific claims are judged. With replication, independent researchers address a scientific hypothesis and build up evidence for, or against, it. This methodology represents the self-correcting path that science should take to ensure robust discoveries; separating science from pseudoscience. Reports indicate increasing pressure to publish manuscripts whilst applying for competitive grants and positions (Baker, 2016). Furthermore, a growing burden of bureaucracy takes away precious time designing experiments and doing research. As the time available for actual research is decreasing, the number of articles that mention a “reproducibility crisis?” are rising towards the present day peak (Fig. 2). Does this mean we have become sloppy in terms of proper documentation?

Figure 2: Number of titles, abstracts, or keywords that contain one of the following phrases: “reproducibility crisis,” “scientific crisis,” “science in crisis,” “crisis in science,” “replication crisis,” “replicability crisis”, found in the Web of Science records. Modified from (Fanelli, 2018).

Are we facing a reproducibility crisis?

A survey conducted by Nature asked 1,576 researchers this exact question, and reported 52% responded with “Yes, a significant crisis,” and 38% with “Yes, a slight crisis” (Baker, 2016). Perhaps more alarming is that 70% report they have unsuccessfully tried to reproduce another scientist’s findings, and more than half have failed to reproduce their own results. To what degree these statistics apply to our own field of geodynamics is not clear, but it is nonetheless a timely remainder that reproducibility must remain at the forefront of our dissemination. Multiple journals have implemented policies on data and software sharing upon publication to ensure the replication and reproduction of computational science is maintained. But how well are they working? A recent empirical analysis of journal policy effectiveness for computational reproducibility sheds light on this issue (Stodden et al., 2018). The study randomly selected 204 papers published in Science after the implementation of their code and data sharing policy. Of these articles, 24 contained sufficient information, whereas for the remaining 180 publications the authors had to be contacted directly. Only 131 authors replied to the request, of these 36% provided some of the requested material and 7% simply refused to share code and data. Apparently the implementation of policies was not enough, and there is still a lot of confusion among researchers when it comes to obligations related to data and code sharing. Some of the anonymized responses highlighted by Stodden et al. (2018) underline the confusion regarding the data and code sharing policy:

Putting aside for the moment that you are, in many cases, obliged to share your code and data to enhance reproducibility; are there any additional motivating factors in making your computational research reproducible? Freire et al. (2012) lists a few simple benefits of reproducible research:

1. Reproducible research is well cited. A study (Vandewalle et al., 2009) found that published articles that reported reproducible results have higher impact and visibility.

2. Code and software comparisons. Well documented computational research allows software developed for similar purposes to be compared in terms of performance (e.g. efficiency and accuracy). This can potentially reveal interesting and publishable differences between seemingly identical programs.

3. Efficient communication of science between researchers. New-comers to a field of research can more efficiently understand how to modify and extend an existing program, allowing them to more easily build upon recently published discoveries (this is simply the positive counterpart to the argument made against software sharing earlier).

“Replicability is not reproducibility: nor is it good science.” – Drummond (2009)

I have discussed reproducibility over quite a few paragraphs already, without yet giving it a proper definition. What precisely is reproducibility? Drummond (2009) proposes a distinction between reproducibility and replicability. He argues that reproducibility requires, at the minimum, minor changes in experiment or model setup, while replication is an identical setup. In other words, reproducibility refers to a phenomenon that can be predicted to recur with slightly different experimental conditions, while replicability describes the ability to obtain an identical result when an experiment is performed under precisely the same conditions. I think this distinction makes the utmost sense in computational science, because if all software, data, post-processing scripts, random number seeds and so on, are shared and reported properly, the results should indeed be identical. However, replicability does not ensure the validity of the scientific discovery. A robust discovery made using computational methods should be reproducible with a different software (made for similar purposes, of course) and small perturbations to the input data such as initial conditions, physical parameters, etc. This is critical because we rarely, if ever, know the model inputs with zero error bars. A way for authors to address such issues is to include a sensitivity analysis of different parameters, initial conditions and boundary conditions in the publication or the supplementary material section.

Figure 3: Illustration of the “spectrum of reproducibility”, ranging from not reproducible to the gold standard that includes code, data and executable files that can directly replicate the reported results. Modified from (Peng, 2011).

However, the gold standard of reproducibility in computation-involved science, like geodynamics, is often described as what Drummond would classify as replication (Fig. 3). That is, making all data and code available to others to easily execute. Even though this does not ensure reproducibility (only replicability), it provides other researchers a level of detail regarding the work-flow and analysis that is beyond what can usually be achieved by using common language. And this deeper understanding can be crucial when trying to reproduce (and not replicate) the original results. Thus replication is a natural step towards reproduction. Open-source community codes for geodynamics, like eg. ASPECT (Heister et al., 2017), and more general FEM libraries like FEniCS (Logg et al., 2012), allows for friction-free replication of results. An input-file describing the model setup provides a 1-to-1 relation to the actual results1 (which in many cases is reasonable because the data are too large to be easily shared). Thus, sharing the post-processing scripts accompanied by the input file on eg. GitHub, will allow for complete replication of the results, at low cost in terms of data storage.

Light at the end of the tunnel?

In order to improve practices for reproducibility, contributions will need to come from multiple directions. The community needs to develop, encourage and maintain a culture of reproducibility. Journals and funding agencies can play an important role here. The American Geosciences Union (AGU) has shared a list of best practices regarding research data2 associated with a publication:

• Deposit the data in support of your publication in a leading domain repository that handles such data.

• If a domain repository is not available for some of all of your data, deposit your data in a general repository such as Zenodo, Dryad, or Figshare. All of these repositories can assign a DOI to deposited data, or use your institution’s archive.

• Data should not be listed as “available from authors.”

• Make sure that the data are available publicly at the time of publication and available to reviewers at submission—if you are unable to upload to a public repository before submission, you may provide access through an embargoed version in a repository or in datasets or tables uploaded with your submission (Zenodo, Dryad, Figshare, and some domain repositories provide embargoed access.) Questions about this should be sent to journal staff.

• Cite data or code sets used in your study as part of the reference list. Citations should follow the Joint Declaration of Data Citation Principles.

• Develop and deposit software in GitHub which can be cited, or include simple scripts in a supplement. Code in Github can be archived separately and assigned a DOI through Zenodo for submission.

In addition to best practice guidelines, wonderful initiatives from other communities include a research prize. The European College of Neuropsychopharmacology offers a (11,800 USD) award for negative results, more specifically for careful experiments that do not confirm an accepted hypothesis or previous result. Another example is the International Organization for Human Brain Mapping who awards 2,000 USD for the best replication study − successful or not. Whilst not a prize per se, at recent EGU General Assemblies in Vienna the GD community have held sessions around the theme of failed models. Hopefully, similar initiatives will lead by example so that others in the community will follow.

1To the exact same results, information about the software version, compilers, operating system etc. would also typically be needed.

2 AGU’s definition of data includes all code, software, data, methods and protocols used to produce the results here.

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