Behavior of the iterative ensemble-based variational method in nonlinear problems

Abstract

Abstract. The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

Echo state network model for analyzing solar-wind effects on the AU and AL indices

“…One plausible explanation is the effect of the solar-wind dynamic pressure, which is pro-portional to N sw V 2 sw . As some studies have suggested that field-aligned currents around the auroral latitudes are influenced by the solar-wind dynamic pressure (Iijima and Potemra, 1982;Wang et al, 2006;Nakano et al, 2009;Korth et al, 2010), it is possible that the enhancement of the field-aligned currents increases the auroral electrojets. Some studies suggested that the solar-wind dynamic pressure induces temporal effects on the ionospheric convection (Ober et al, 2007;Boudouridis et al, 2008).…”

“…However, since the feedback of y AU,k−1 and y AL,k−1 are contained, the optimal β cannot be obtained by linear regression. We thus obtained β using the ensemblebased optimization method (Nakano, 2021).…”

4DEnVar-based inversion system for ammonia emission estimation in China through assimilating IASI ammonia retrievals

“…These two issues might be partially addressed by using larger ensemble member and adding additional iteration loops, e.g. iteratively resampling ensemble of emission inventory and forming new linear approximations at the outer-loops as suggested by Nakano (2021). These however will severely increase the computational cost and thus challenge the inversion of long-term ammonia emission estimates over China.…”

Virtual sounding of solar-wind effects on the AU and AL indices based on an echo state network model

“…However, since the feedback of y AU,k−1 and y AL,k−1 are contained, the optimal β cannot be obtained by linear regression. We thus obtained β using the ensemble-based optimization method (Nakano, 2021).…”