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

Abstract

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.

Tectonic predictions with mantle convection models

“…We suggest here that using inversions of dynamical evolution using surface velocities as data constraints rather than inputs should lead to improved rheologies and resulting mantle flow. Methods like sequential data assimilation (Bocher et al 2016(Bocher et al , 2017 and adjoint-based inversions (Li et al 2017) are under development for that very purpose.…”

“…We parameters. Such methods based on adjoint codes (Li et al 2017) and bayesian approaches (Bocher et al 2016(Bocher et al , 2017 are under development.…”

101 Geodynamic modelling: How to design, interpret, and communicate numerical studies of the solid Earth

“…The possibility of incorporating data and estimating the model uncertainties in inverse models has recently led to an increasing amount of efforts combining both inverse and forward methods in geodynamic modelling. For example, adjoint methods (Reuber et al, 2018b(Reuber et al, , 2020, pattern recognition Atkins et al (2016), and sequential data assimilation (Bocher et al, 2016(Bocher et al, , 2018 have been incorporated in lithosphere and mantle dynamics models. One of the most common ways of solving the inverse problem in geodynamics is to run many forward models and subsequently test which one fits the observations best (Baumann and Kaus, 2015).…”

Sequential Monte Carlo Methods in the nimble and nimbleSMC R Packages

“…Users are welcome to modify this basic EnKF if a different version is desired -see Section 7 for an overview of creating and modifying particle filters in nimble. Recently, the EnKF has been used extensively for atmospheric data modeling (Houtekamer and Zhang 2016), as well as for problems in petroleum modeling (Heidari, Gervais, Ravalec, and Wackernagel 2013) and geophysics (Bocher, Fournier, and Coltice 2018).…”