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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…
In this paper, we present a UKF-PF based hybrid nonlinear filter for space object tracking. Estimating the state and its associated uncertainty, also known as filtering is paramount to the tracking process. The periodicity of the Keplerian…
Global maps of the solar photospheric magnetic flux are fundamental drivers for simulations of the corona and solar wind and therefore are important predictors of geoeffective events. However, observations of the solar photosphere are only…
In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of…
Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…
Every day, weather forecasting centres around the world make use of noisy, incomplete observations of the atmosphere to update their weather forecasts. This process is known as data assimilation, data fusion or state estimation and is best…
Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…
Data assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields,…
This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint…
Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter…
This paper presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters,…
Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated…
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…
Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this…
Recent studies have demonstrated that it is possible to combine machine learning with data assimilation to reconstruct the dynamics of a physical model partially and imperfectly observed. Data assimilation is used to estimate the system…
To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…