Articles | Volume 25, issue 1
Nonlin. Processes Geophys., 25, 99–123, 2018
Nonlin. Processes Geophys., 25, 99–123, 2018

Research article 16 Feb 2018

Research article | 16 Feb 2018

Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation

Marie Bocher1,2, Alexandre Fournier3, and Nicolas Coltice2 Marie Bocher et al.
  • 1Computational Seismology, Institute of Geophysics, Department of Earth Sciences, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland
  • 2Laboratoire de Géologie de Lyon, Université Claude Bernard Lyon 1, Ecole Normale Supṕrieure de Lyon, Lyon, France
  • 3Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Diderot, CNRS (UMR 7154), Paris, France

Abstract. Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016). Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF) to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.

Short summary
We propose a new method to reconstruct the circulation in the Earth's mantle for the last 300 Myr. This method is based on the sequential assimilation of plate layouts obtained from plate tectonic reconstructions into mantle convection models. This method allows us to take into account uncertainties in plate tectonic reconstructions, and provides an estimation of the uncertainties in the final result. We test and validate this method in a controlled environment by using synthetic experiments.