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Improved Variational Methods in Statistical Data Assimilation : Volume 22, Issue 2 (07/04/2015)

By Ye, J.

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Book Id: WPLBN0004017210
Format Type: PDF Article :
File Size: Pages 9
Reproduction Date: 2015

Title: Improved Variational Methods in Statistical Data Assimilation : Volume 22, Issue 2 (07/04/2015)  
Author: Ye, J.
Volume: Vol. 22, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Kadakia, N., Rozdeba, P. J., I. Abarbane, H. D., Quinn, J. C., & Ye, J. (2015). Improved Variational Methods in Statistical Data Assimilation : Volume 22, Issue 2 (07/04/2015). Retrieved from

Description: Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA. Data assimilation transfers information from an observed system to a physically based model system with state variables x(t). The observations are typically noisy, the model has errors, and the initial state x(t0) is uncertain: the data assimilation is statistical. One can ask about expected values of functions ⟨G(X)⟩ on the path X = {x(t0), ..., x(tm)} of the model state through the observation window tn = {t0, ..., tm}. The conditional (on the measurements) probability distribution P(X) = exp[−A0(X)] determines these expected values. Variational methods using saddle points of the action A0(X), known as 4DVar (Talagrand and Courtier, 1987; Evensen, 2009), are utilized for estimating ⟨G(X)⟩. In a path integral formulation of statistical data assimilation, we consider variational approximations in a realization of the action where measurement errors and model errors are Gaussian. We (a) discuss an annealing method for locating the path X0 giving a consistent minimum of the action A0(X0), (b) consider the explicit role of the number of measurements at each tn in determining A0(X0), and (c) identify a parameter regime for the scale of model errors, which allows X0 to give a precise estimate of ⟨G(X0)⟩ with computable, small higher-order corrections.

Improved variational methods in statistical data assimilation

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