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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
Historic
Publication Date:
2015
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 http://hawaiilibrary.net/


Description
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.

Summary
Improved variational methods in statistical data assimilation

Excerpt
Abarbanel, H. D.: Predicting the Future: Completing Models of Observed Complex Systems, Springer, New York, 2013.; Aguiar e Oliviera, H., Ingber, L., Petraglia, A., Petraglia, M. R., and Machado, M. A. S.: Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing, Vol. 35, Springer, New York, 2012.; Bennett, A. F.: Inverse Modeling of the Ocean and Atmosphere, Cambridge University Press, 2002.; Eibern, H. and Schmidt, H.: A four-dimensional variational chemistry data assimilation scheme for Eulerian chemistry transport modeling, J. Geophys. Res.-Atmos., 104, 18583–18598, 1999.; Evensen, G.: Data Assimilation: The Ensemble Kalman Filter, Springer, New York, 2009.; Zadeh, K. S.: Parameter estimation in flow through partially saturated porous materials, J. Comput. Phys., 227, 10243–10262, 2008.; Kostuk, M.: Synchronization and statistical methods for the data assimilation of HVc neuron models, PhD thesis in Physics, University of California, San Diego, available at: http://escholarship.org/uc/item/2fh4d086 (last access: 2 October 2014), 2012.; Kostuk, M., Toth, B., Meliza, C., Margoliash, D., and Abarbanel, H.: Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods, Biol. Cybern., 106, 155–167, 2012.; Laplace, P. S.: Memoir on the probability of causes of events, Mémoires de Mathématique et de Physique, Tome Sixième, 1774.; Lorenc, A. C. and Payne, T.: 4D-Var and the butterfly effect: statistical four-dimensional data assimilation for a wide range of scales, Q. J. Roy. Meteorol. Soc., 133, 607–614, 2007.; Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130–141, 1963.; Lorenz, E. N.: Predictability – a problem partly solved, in: Predictability of Weather and Climate, edited by: Palmer, T. and Hagedorn, R., Cambridge University Press, 40–58, 2006.; Mechhoud, S., Witrant, E., Dugard, L., and Moreau, D.: Combined distributed parameters and source estimation in tokamak plasma heat transport, in: 2013 European Control Conference (ECC), 17–19 July, Zurich, 47–52, 2013.; NIST/SEMATECH e-Handbook of Statistical Methods: http://www.itl.nist.gov/div898/handbook/ (last access: 12 January 2014), 2012.; Press, W. H., Teokulsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in C: the Art of Scientific Computing, Cambridge University Press, 2012.; Quinn, J. C.: A path integral approach to data assimilation in stochastic nonlinear systems, PhD thesis in Physics, University of California, San Diego, available at: http://escholarship.org/uc/item/0bm253qk (last access: 2 October 2014), 2010.; Rey, D., Eldridge, M., Kostuk, M., Abarbanel, H. D., Schumann-Bischoff, J., and Parlitz, U.: Accurate state and parameter estimation in nonlinear systems with sparse observations, Phys. Lett. A, 378, 869–873, 2014.; Talagrand, O. and Courtier, P.: Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation, I: Theory, Q. J. Roy. Meteorol. Soc., 113, 1311–1328, 1987.; Waëchter, A.: An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering, PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA, 2002.; Zinn-Justin, J.: Quantum Field Theory and Critical Phenomena, Oxford University Press, 2002.

 

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