Seeing the Northern Lights at the equator? Predicting the next reversal of Earth’s magnetic field.

Background

The geomagnetic field is a fundamental part of planet Earth, existing for at least 3.5 billion years. Yet far from being a constant, the field is very dynamic, exhibiting slow fluctuations and wandering magnetic poles which occasionally fully reverse in polarity. During a global magnetic field reversal, the usually strong dipolar field of the Earth fragments into multiple magnetic poles each of which drift across the planet’s surface. It is likely that around every one a local auroral oval forms allowing the ‘northern lights’ to appear anywhere a pole was close by – even at the equator.

The magnetic field wraps around our planet as an invisible force-field, providing  long-term protection to life on the surface and modern technological infrastructure from harmful solar radiation (Figure 1).

Figure 1: Observations of the Earth’s internal field recorded in space constrain the structure at the edge of the core (the source region). The future structure of the magnetic field is the focus of this project.

Although the current rate of reversals is about 2-3 times per million years, the last global reversal took place some 780,000 years ago, meaning that planet Earth is now well “overdue” a reversal. True or not, it is certainly the case that change is afoot: a patch of weak field in the south Atlantic (the south Atlantic anomaly) is spreading; the global field (expressed by the dipole strength) is weakening at a rate of 5% per century; and very recent measurements over the last few decades have shown that the magnetic North Pole has begun a sprint away from its historical position over northern Canada towards Siberia (Figure 2). Does this indicate that a period of significant change for the global field is upon us?

Figure 2: The path of the north magnetic dip pole (where the magnetic field is exactly vertical). Since the 1970s the pole has begun a sprint away from its historic position in northern Canada towards Siberia. Models predict that this trend will continue into the future. (Livermore et al., 2020).

 

Predicting the magnetic field is challenging, not the least because we do not yet have a complete representation that describes how the magnetic field changes. Although the basic physics is understood, the complexities and extreme conditions within the Earth’s core make it computationally difficult to model. The novel aspect of this project is to apply recent advances in Machine Learning or Deep Learning to the prediction of Earth’s magnetic field. The key idea behind the project is that a trained neural network may be able to spot patterns in the data that have so far either not been noticed or have been too complex to interpret; such networks may be able to supply accurate short-time forecasts of the internally generated magnetic field. One of the goals of the project is to assess the evidence for whether the geomagnetic field is likely to reverse and how fast it might do so.

Working with scientists at the British Geological Survey (BGS) in Edinburgh and DTU Space in Copenhagen, the project will begin with the investigation of the predictability of the magnetic field using a simple recurrent neural network. The project should appeal to those with geophysics, physics or a mathematical background interested in understanding the Earth’s mysterious magnetic field. As part of the project there is the opportunity to spend up to three months working with the BGS in Edinburgh and to visit DTU in Copenhagen. This project has an extra £7,000 (in addition to the usual research budget) to cover travel, accommodation and living expenses for this purpose.

Objectives

The objectives of the PhD project are as follows:

  1. Begin the investigation of the predictability of the magnetic field using a simple recurrent neural network such as an “echo state” neural network, which has been shown to model and predict complex dynamical systems with surprising accuracy. We will base our study on both the 400-yr observation-derived model (gufm1, Jackson et al. 2000), and more recent models based on satellite data over the last few decades. In both cases we will assess the ability to predict the last 10% (or so) of the time span of the model, and investigate what it may mean for the future evolution of the geomagnetic field. The predictions will be compared with forecasts produced from other models, for example numerical simulations of the dynamics of Earth’s core (Aubert, 2013).
  2. Considering the observations now as a movie with many hundreds of frames, we will apply techniques based on learning algorithms, such as auto-encoders (e.g. Vondrick et al. 2016) or other manifold learning and representation learning methods (such as Variational AutoEncoder or Generative Adversarial Networks) that can be used to guess the next few frames in the sequence and doing so predict the future structure. These methods essentially compress the images before prediction, thereby abstracting only the key components of the geomagnetic field that are changing. An additional benefit of these methods is that they can be used to detect anomalies in the movie, of particular interest being whether we can assess the predictability of features in the magnetic field such as geomagnetic jerks (e.g. Cox and Brown, 2013) which are currently regarded as “unpredictable”.
  3. Is the present state-of-the-art in numerical models of the geomagnetic field consistent with the real observations? This can be assessed by training a neural network on the output of a numerical simulation of Earth’s magnetic field: for example, the coupled Earth model of Aubert et al., 2013 or the database of simulated magnetic reversals at Leeds. Comparing a prediction from the trained network and the true evolution of the field will provide an important measure on whether or not the numerical models are a faithful representation of the Earth’s core.

Milestones

Year 1: Familiarisation with geomagnetic observations, the theory of the dynamics of Earth’s core and models of the geodynamo. Hands-on experiments of basic machine learning with application to predicting the Earth’s magnetic field. Two weeks visit to BGS Edinburgh.

Year 2: Application of frame-prediction techniques to movies of the geomagnetic field derived from observations. Visit to DTU Space and one month in BGS Edinburgh.

Year 3: Application of machine learning algorithms applied to the output of numerical simulations of the Earth’s core; comparison to the real geomagnetic signal. Six weeks visit to Edinburgh.

Training

The student will learn techniques of machine learning using both Matlab and Python, with standard deep learning libraries such as Keras, Caffe, Pytorch and Tensorflow, and will have the opportunity to take relevant specific undergraduate or masters level courses. The student will also have access to a broad spectrum of training workshops at Leeds that include techniques in numerical modelling, through to managing your degree and preparing for your viva.  The student will be a part of the world-leading deep Earth research group, a vibrant part of the Institute of Geophysics and Tectonics, comprising about 12 staff members, 10 postdocs and 15 PhD students. The deep Earth group has a strong portfolio of international collaborators which the student will benefit from.

The project will be based primarily at Leeds. There are project partners in both Edinburgh and Copenhagen who the student will visit to see how geomagnetism has an impact on everyday life from smartphone navigation to space weather impacts on the power grid. There will also be opportunities to attend international conferences (UK, Europe, US and elsewhere), and other possible collaborative visits within Europe.

Requirements

We seek a highly motivated candidate with a strong background in mathematics, physics, computation, geophysics or another highly numerate discipline.  Knowledge of geomagnetism is not required, and training will be given in all aspects of the PhD.

For further information please contact Phil Livermore (p.w.livermore@leeds.ac.uk).

Websites

Movies showing the historical change in the geomagnetic field can be found at

https://sos.noaa.gov/datasets/earths-magnetic-declination/

https://www.youtube.com/watch?v=NHRMxH3M2po

Stern, D. A (2002) Millennium of Geomagnetism, online material: http://www.phy6.org/earthmag/mill_1.htm

 

References

Aubert, J., Finlay, C. C., & Fournier, A. (2013). Bottom-up control of geomagnetic secular variation by the Earth’s inner core. Nature, 502(7470), 219–223. http://doi.org/10.1038/nature12574

Cox, G A, and Brown, W J. 2013. Rapid dynamics of the Earth’s core Astronomy and Geophysics, 54(5) 5.32-5.37

Finlay, C. C., Olsen, N., Kotsiaros, S., Gillet, N., & Tøffner-Clausen, L. (2016). Recent geomagnetic secular variation from Swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model. Earth Planets and Space, 68(1), 1–18. http://doi.org/10.1186/s40623-016-0486-1

Jackson, A., Jonkers, A., & Walker, M. (2000). Four centuries of geomagnetic secular variation from historical records. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 358(1768), 957–990.

Livermore, P.W., Finlay, C.C. and Bayliff, M., 2020. Recent north magnetic pole acceleration towards Siberia caused by flux lobe elongation. Nature Geoscience, 13(5), pp.387-391.

Vondrick, C., Pirsiavash, H. & Torralba, A.  (2016) Generating Videos with Scene Dynamics, NIPS  https://arxiv.org/abs/1609.02612