arXiv subjects

Geir Evensen

Publications and source records attributed to Geir Evensen.

4 recordsLinked to original sources

arXiv2020

A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.

stat.ME↗

arXiv2019

Revising the stochastic iterative ensemble smoother

Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm, without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity, and (b) that the ensemble does not lose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz-96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).

physics.data-an↗

arXiv2018

Accounting for model errors in iterative ensemble smoothers

In the strong-constraint formulation of the history-matching problem, we assume that all the model errors relate to a selection of uncertain model input parameters. One does not account for additional model errors that could result from, e.g., excluded uncertain parameters, neglected physics in the model formulation, the use of an approximate model forcing, or discretization errors resulting from numerical approximations. If parameters with significant uncertainties are unaccounted for, there is a risk for an unphysical update, of some uncertain parameters, that compensates for errors in the omitted parameters. This paper gives the theoretical foundation for introducing model errors in ensemble methods for history matching. In particular, we explain procedures for practically including model errors in iterative ensemble smoothers like ESMDA and IES. Also, we demonstrate the impact of adding (or neglecting) model errors in the parameter-estimation problem.

physics.data-an↗

arXiv2017

Data Assimilation in the Geosciences - An overview on methods, issues and perspectives

We commonly refer to state-estimation theory in geosciences as data assimilation. This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical information (such as a dynamical evolution model), provides an estimate of its state. Data assimilation is standard practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean and environment modeling; in all circumstances where one intends to estimate the state of a large dynamical system based on limited information. While the complexity of data assimilation, and of the methods thereof, stands on its interdisciplinary nature across statistics, dynamical systems and numerical optimization, when applied to geosciences an additional difficulty arises by the continually increasing sophistication of the environmental models. Thus, in spite of data assimilation being nowadays ubiquitous in geosciences, it has so far remained a topic mostly reserved to experts. We aim this overview article at geoscientists with a background in mathematical and physical modeling, who are interested in the rapid development of data assimilation and its growing domains of application in environmental science, but so far have not delved into its conceptual and methodological complexities.

physics.ao-ph↗