Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models.
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A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-‘96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-‘96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.
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- Award ID(s):
- 1821074
- NSF-PAR ID:
- 10297896
- Editor(s):
- Hoteit, Ibrahim
- Date Published:
- Journal Name:
- PLOS ONE
- Volume:
- 16
- Issue:
- 3
- ISSN:
- 1932-6203
- Page Range / eLocation ID:
- e0248266
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1371/journal.pone.0248266
