Particle Filters for nonlinear data assimilation in high-dimensional systems

Leeuwen, Peter Jan van; Jan, Peter

doi:10.5802/afst.1560

Cited by 5 publications

(5 citation statements)

References 25 publications

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“…To overcome the Gaussian assumption of EnKF‐based methods, a more universal method, that is, PF, adopting Monte Carlo and importance sampling, has been successfully introduced in LDA to solve the non‐Gaussian/nonlinear assumption (Moradkhani, Hsu, et al., 2005; Van Leeuwen, 2017), which demonstrated that PF is superior to EnKF in several synthetic tests (DeChant & Moradkhani, 2012; Kivman, 2003). However, the MCMC resampling method subjectively determines the resampling step and acceptance probability of the candidate points, hence artificially enforcing the convergence of the sampled parameter values to a too narrow distribution.…”

Section: Theoretical and Methodological Innovations In Land Data Assi...mentioning

confidence: 99%

Land Data Assimilation: Harmonizing Theory and Data in Land Surface Process Studies

Li,

Liu,

et al. 2024

Reviews of Geophysics

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Data assimilation plays a dual role in advancing the “scientific” understanding and serving as an “engineering tool” for the Earth system sciences. Land data assimilation (LDA) has evolved into a distinct discipline within geophysics, facilitating the harmonization of theory and data and allowing land models and observations to complement and constrain each other. Over recent decades, substantial progress has been made in the theory, methodology, and application of LDA, necessitating a holistic and in‐depth exploration of its full spectrum. Here, we present a thorough review elucidating the theoretical and methodological developments in LDA and its distinctive features. This encompasses breakthroughs in addressing strong nonlinearities in land surface processes, exploring the potential of machine learning approaches in data assimilation, quantifying uncertainties arising from multiscale spatial correlation, and simultaneously estimating model states and parameters. LDA has proven successful in enhancing the understanding and prediction of various land surface processes (including soil moisture, snow, evapotranspiration, streamflow, groundwater, irrigation and land surface temperature), particularly within the realms of water and energy cycles. This review outlines the development of global, regional, and catchment‐scale LDA systems and software platforms, proposing grand challenges of generating land reanalysis and advancing coupled land‒atmosphere DA. We lastly highlight the opportunities to expand the applications of LDA from pure geophysical systems to coupled natural and human systems by ingesting a deluge of Earth observation and social sensing data. The paper synthesizes current LDA knowledge and provides a steppingstone for its future development, particularly in promoting dual driven theory‐data land processes studies.

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Section: Theoretical and Methodological Innovations In Land Data Assi...mentioning

confidence: 99%

Land Data Assimilation: Harmonizing Theory and Data in Land Surface Process Studies

Li,

Liu,

et al. 2024

Reviews of Geophysics

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“…After identifying the particular PF implementation best suited to the problem, an appropriate likelihood function needs to be defined to compute the conditional probability of the observations given the model state. When dealing with a large number of measurements, which might have correlated errors, the proposed likelihood distribution should ideally be the joint pdf of all these measurements (van Leeuwen, 2017). This implies that in SAR-based flood extent assimilation, where the pixel-wise flood inundation values constitute separate measurements and the images are often characterized by a multimodal histogram, a nonparametric approach to estimating the likelihood function must be chosen.…”

Section: Data Assimilation Frameworkmentioning

confidence: 99%

A Mutual Information‐Based Likelihood Function for Particle Filter Flood Extent Assimilation

Dasgupta

Hostache

Ramsankaran

et al. 2021

Water Resources Research

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Accurate flood inundation forecasts have the potential to minimize socioeconomic losses, but uncertainties in inflows propagated from the precipitation forecasts result in large prediction errors. Recent studies suggest that by assimilating independent flood observations, inherent uncertainty in hydraulic flood inundation modeling can be mitigated. Satellite observations from Synthetic Aperture Radar (SAR) sensors, with demonstrated flood monitoring capability, can thus be used to reduce flood forecast uncertainties through assimilation. However, researchers have struggled to develop an appropriate cost function to determine the innovation to be applied at each assimilation time step. Thus, a novel likelihood function based on mutual information (MI) is proposed here, for use with a particle filter‐based (PF) flood extent assimilation framework. Using identical twin experiments, synthetic SAR‐based probabilistic flood extents were assimilated into the hydraulic model LISFLOOD‐FP using the proposed PF‐MI algorithm. The 2011 flood event in the Clarence Catchment, Australia was used for this study. The impact of assimilating flood extents was evaluated in terms of subsequent flood extent evolution, floodplain water depths, flow velocities and channel water levels (WLs). Water depth and flow velocity simulations improved by ∼60% over the open loop on an average and persisted for up to 7 days, following the sequential assimilation of two post‐peak flood extent observations. Flood extents and channel WLs also showed mean improvements of ∼10% and ∼80% in accuracy, respectively, indicating that the proposed MI likelihood function can improve flood extent assimilation.

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“…Consider the problem of forecast, we want to get the estimation of x k given the measurements {y 1 , y 2 , ..., y k }. Under the Bayesian rule, we have [35]:…”

Section: Particle Filter a Basic Particle Filtermentioning

confidence: 99%

“…iv. Calculate the weights and normalize according to (33), ( 34) and (35). v. Obtain the analyzed state x a k and covariance P k of the states according to (36) and (37).…”

Section: Generate Initial Values With N Ensemble Membersmentioning

confidence: 99%

Sample Regenerating Particle Filter Combined With Unequal Weight Ensemble Kalman Filter for Nonlinear Systems

Cheng

Lin

2021

IEEE Access

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We present an approach which combines the sample regenerating particle filter (SRGPF) and unequal weight ensemble Kalman filter (UwEnKF) to obtain a more accurate forecast for nonlinear systems. Ensemble Kalman filter assumes that the model errors and observation errors are Gaussian distributed. Particle filter has demonstrated its ability in solving nonlinear and non-Gaussian problems. The main difficulty for the particle filter is the curse of dimensionality, a very large number of particles is needed. We adopt the idea of the unequal weight ensemble Kalman filter to define a proposal density for the particle filter. In order to keep the diversity of particles, we do not apply resampling as the traditional particle filter does, instead we regenerate new samples based on a posterior distribution. The performance of the combined sample regenerating particle filter and unequal weight ensemble Kalman filter algorithm is evaluated using the Lorenz 63 model, the results show that the presented approach obtains a more accurate forecast than the ensemble Kalman filter and weighted ensemble Kalman filter under Gaussian noise. Furthermore, for non-Gaussian noise, the performance of the approach is much better than the ensemble Kalman filter and more robust to noise with nonzero bias.

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Particle Filters for nonlinear data assimilation in high-dimensional systems

Cited by 5 publications

References 25 publications

Land Data Assimilation: Harmonizing Theory and Data in Land Surface Process Studies

Land Data Assimilation: Harmonizing Theory and Data in Land Surface Process Studies

A Mutual Information‐Based Likelihood Function for Particle Filter Flood Extent Assimilation

Sample Regenerating Particle Filter Combined With Unequal Weight Ensemble Kalman Filter for Nonlinear Systems

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