Abstract
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 the Lorenz-96 (QG) model.
Highlights
The science of data assimilation (DA) aims to optimally estimate the probability distribution of a state variable of interest in an Earth system model (ESM) given the information content of observations and previous time forecasts to improve their predictive abilities (Kalnay, 2003; Carrassi et al, 2018)
We demonstrated that data assimilation (DA) over the Wasserstein space through the ensemble Riemannian data assimilation (EnRDA) (Tamang et al, 2021) can be properly scaled and result in improved predictability of non-Gaussian geophysical dynamics at relatively high dimensions, under systematic errors
We applied the EnRDA to the 40-dimensional chaotic Lorenz-96 system and a two-layer quasi-geostrophic representation of atmospheric circulation and compared its results with the stochastic ensemble Kalman filter and the particle filter with comparable ensemble size
Summary
The science of data assimilation (DA) aims to optimally estimate the probability distribution of a state variable of interest in an Earth system model (ESM) given the information content of observations and previous time forecasts to improve their predictive abilities (Kalnay, 2003; Carrassi et al, 2018). Tamang et al (2020) proposed to use the Wasserstein distance to regularize a variational DA framework for treating systematic errors arising from the model forecast in chaotic systems. To reduce the computational cost, Tamang et al (2021) used entropic regularization of the OMT formulation (Cuturi, 2013) through a new framework, called ensemble Riemannian data assimilation (EnRDA), to cope with systematic errors and tested it on a three-dimensional Lorenz-63 model (Lorenz, 1963). The computational complexity of finding an optimal joint coupling between two m-dimensional probability distributions supported on d points in each dimension using the entropic regularization is O(d2m) This might impose a significant limitation on the direct use of EnRDA for highdimensional geophysical problems, where the problem dimension exceeds millions.
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