Preprints
https://doi.org/10.5194/npg-2021-28
https://doi.org/10.5194/npg-2021-28

  07 Sep 2021

07 Sep 2021

Review status: this preprint is currently under review for the journal NPG.

Ensemble Riemannian Data Assimilation: Towards High-dimensional Implementation

Sagar Kumar Tamang1, Ardeshir Ebtehaj1, Peter Jan van Leeuwen2, Gilad Lerman3, and Efi Foufoula-Georgiou4 Sagar Kumar Tamang et al.
  • 1Department of Civil, Environmental and Geo-Engineering and Saint Anthony Falls Laboratory, University of Minnesota-Twin Cities, Twin Cities, Minnesota, USA
  • 2Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, USA
  • 3School of Mathematics, University of Minnesota-Twin Cities, Twin Cities, Minnesota, USA
  • 4Department of Civil and Environmental Engineering and Department of Earth System Science, University of California Irvine, Irvine, California, USA

Abstract. This paper presents the results of the Ensemble Riemannian Data Assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in Lorenz-96 (QG) model.

Sagar Kumar Tamang et al.

Status: open (until 02 Nov 2021)

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Sagar Kumar Tamang et al.

Sagar Kumar Tamang et al.

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Short summary
The outputs from Earth System models are optimally combined with satellite observations to produce accurate forecasts through a process called data assimilation. Many existing data assimilation methodologies have some assumptions regarding the shape of the probability distributions of model output and observations which results in forecast inaccuracies. In this paper, we test the effectiveness of a newly proposed methodology that relaxes such assumptions on high-dimensional models.