Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter
A local ensemble Kalman filter for atmospheric data assimilation
A new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region.
Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
- B. Hunt
- 1 October 1992
We present a measure-theoretic condition for a property to hold «almost everywhere» on an infinite-dimensional vector space, with particularemphasis on function spaces such as C k and L p . Like the…
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.
- Jaideep Pathak, B. Hunt, M. Girvan, Zhixin Lu, E. Ott
- Computer SciencePhysical Review Letters
- 12 January 2018
We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from…
Balance and Ensemble Kalman Filter Localization Techniques
Abstract In ensemble Kalman filter (EnKF) data assimilation, localization modifies the error covariance matrices to suppress the influence of distant observations, removing spurious long-distance…
Reservoir observers: Model-free inference of unmeasured variables in chaotic systems.
It is shown that the reservoir observer can be a very effective and versatile tool for robustly reconstructing unmeasured dynamical system variables.
Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model
A general method is proposed that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme, and is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.
Four-dimensional ensemble Kalman filtering
Ensemble Kalman filteringwas developed as away to assimilate observed data to track the current state in a computational model. In this paper we showthat the ensemble approach makes possible an…
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data.
This work uses recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process to form a modified autonomous reservoir.
Local low dimensionality of atmospheric dynamics.
It is shown that the Earth's atmosphere often has low BV dimension, and the implications for improving weather forecasting are discussed.