Merging particle filter for sequential data assimilation

Nakano, S.; Ueno, G.; Higuchi, Tomoyuki

doi:10.5194/npg-14-395-2007

Cited by 113 publications

(84 citation statements)

References 24 publications

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“…This problem has been studied before by Nakano et al, (2007), and we use similar model parameters. They showed that tens of thousands of particles were needed with the standard particle filter with resampling for the result that we are able to achieve with 20 particles with the new method.…”

Section: Almost Equal Weightsmentioning

confidence: 99%

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Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Leeuwen

2010

Quart J Royal Meteoro Soc

331

309

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Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called 'curse of dimensionality'. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems.

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Section: Almost Equal Weightsmentioning

confidence: 99%

“…One tends to need a few hundred particles to solve this problem with the standard particle filter (Nakano et al, 2007).…”

Section: Application To the Lorenz-63 Modelmentioning

confidence: 99%

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Leeuwen

2010

Quart J Royal Meteoro Soc

331

309

View full text Add to dashboard Cite

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“…Recently there has been growing interest in particle filtering methods in particular, as these methods are better able to capture the nonlinearity inherent in many geophysical systems [e.g., the merging particle filter of Nakano et al (2007), the equivalent-weights filter of Ades and van Leeuwen (2013), and the implicit particle filter (Morzfeld et al 2012)]. At the same time, particle filters also tend to suffer from the ''curse of dimensionality'' where the required ensemble size grows very rapidly as the dimension increases.…”

Section: Introductionmentioning

confidence: 99%

Exploring Practical Estimates of the Ensemble Size Necessary for Particle Filters

Slivinski

Snyder

2016

Monthly Weather Review

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Particle filtering methods for data assimilation may suffer from the ''curse of dimensionality,'' where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of t 2 , a statistic that depends on observationspace quantities and that is related to the system dimension when the number of observations is large; for linear, Gaussian systems, the statistic t 2 can be computed from eigenvalues of an appropriately normalized covariance matrix. Tests with a low-dimensional system show that these asymptotic results remain useful when the system is nonlinear, with either the standard or optimal proposal implementation of the particle filter. This study explores approximations to the covariance matrices that facilitate computation in high-dimensional systems, as well as different methods to estimate the accumulated system noise covariance for the optimal proposal. Since t 2 may be approximated using an ensemble from a simpler data assimilation scheme, such as the ensemble Kalman filter, the asymptotic relations thus allow an estimate of the ensemble size required for a particle filter before its implementation. Finally, the improved performance of particle filters with the optimal proposal, relative to those using the standard proposal, in the same low-dimensional system is demonstrated.

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“…A challenging example for a particle filter is the 40-variable Lorenz 1995 model (Lorenz, 1995), which for the settings given below typically needs tens of thousands of particles (Nakano et al, 2007). The model equations are given by: The end point of that run was used as the initial condition for the data assimilation experiment.…”

Section: Application To the Lorenz-95 Modelmentioning

confidence: 99%

Efficient nonlinear data-assimilation in geophysical fluid dynamics

Leeuwen

2011

Computers & Fluids

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New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore

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Merging particle filter for sequential data assimilation

Cited by 113 publications

References 24 publications

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Exploring Practical Estimates of the Ensemble Size Necessary for Particle Filters

Efficient nonlinear data-assimilation in geophysical fluid dynamics

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