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Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter
A practical method for data assimilation in large, spatiotemporally chaotic systems, a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. Expand
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. Expand
Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
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 theExpand
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach.
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 fromExpand
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. Expand
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. Expand
Four-dimensional ensemble Kalman filtering
Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible anExpand
Optimal orbits of hyperbolic systems
Given a dynamical system and a function f from the state space to the real numbers, an optimal orbit for f is an orbit over which the time average of f is maximal. In this paper we consider someExpand
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-distanceExpand
A Guide to MATLAB®: For Beginners and Experienced Users
This book explains everything you need to know to begin using MATLAB, a comprehensive software system for mathematics and technical computing that should be useful to both beginning and experienced users. Expand