TITLE

Implications of Stochastic and Deterministic Filters as Ensemble-Based Data Assimilation Methods in Varying Regimes of Error Growth

AUTHOR(S)
Lawson, W. Gregory; Hansen, James A.
PUB. DATE
August 2004
SOURCE
Monthly Weather Review;Aug2004, Vol. 132 Issue 8, p1966
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Accurate numerical prediction of fluid flows requires accurate initial conditions. Monte Carlo methods have become a popular and realizable approach to estimating the initial conditions necessary for forecasting, and have generally been divided into two classes: stochastic filters and deterministic filters. Both filters strive to achieve the error statistics predicted by optimal linear estimation, but accomplish their goal in different fashions, the former by way of random number realizations and the latter via explicit mathematical transformations. Inspection of the update process of each filter in a one-dimensional example and in a two-dimensional dynamical system offers a geometric interpretation of how their behavior changes as nonlinearity becomes appreciable. This interpretation is linked to three ensemble assessment diagnostics: rms analysis error, ensemble rank histograms, and measures of ensemble skewness and kurtosis. Similar expressions of these diagnostics exist in a hierarchy of models. The geometric interpretation and the ensemble diagnostics suggest that both filters perform as expected in a linear regime, but that stochastic filters can better withstand regimes with nonlinear error growth.
ACCESSION #
14084039

 

Related Articles

  • Monte Carlo Based Personalized PageRank on Dynamic Networks. Zhang Junchao; Chen Junjie; Jiancheng Song; Rong-Xiang Zhao // International Journal of Distributed Sensor Networks;2013, p1 

    In large-scale networks, the structure of the underlying network changes frequently, and thus the power iteration method for Personalized PageRank computation cannot deal with this kind of dynamic network efficiently In this paper, we design a Monte Carlo-based incremental method for...

  • On a Monte Carlo method for neutron transport criticality computations. Maire, Sylvain; Talay, Denis // IMA Journal of Numerical Analysis;Oct2006, Vol. 26 Issue 4, p657 

    We give a stochastic representation of the principal eigenvalue of some homogeneous neutron transport operators. Our construction is based upon the Feynman–Kac formula for integral transport equations, and uses probabilistic techniques only. We develop a Monte Carlo method for criticality...

  • UNIFORM APPROXIMATIONS OF DISCRETE-TIME FILTERS. HEINE, KARI; CRISAN, DAN // Advances in Applied Probability;Dec2008, Vol. 40 Issue 4, p979 

    Throughout recent years, various sequential Monte Carlo methods, i.e. particle filters, have been widely applied to various applications involving the evaluation of the generally intractable stochastic discrete-time filter. Although convergence results exist for finitetime intervals, a stronger...

  • Inference of statistical bounds for multistage stochastic programming problems. Shapiro, Alexander // Mathematical Methods of Operations Research;2003, Vol. 58 Issue 1, p57 

    We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower...

  • Iterative construction of the optimal Bermudan stopping time. Kolodko, Anastasia; Schoenmakers, John // Finance & Stochastics;2006, Vol. 10 Issue 1, p27 

    We present an iterative procedure for computing the optimal Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by...

  • CALCULATION OF THE INDOOR GAMMA DOSE RATE DISTRIBUTION DUE TO BUILDING MATERIALS IN THE NETHERLANDS. de Jong, P.; van Dijk, J. W. E. // Radiation Protection Dosimetry;2008, Vol. 132 Issue 4, p381 

    In this study, a model to determine the indoor absorbed dose rate in air due to building materials is applied to a representative set of 1336 Dutch dwellings of which the areas occupied by the various kinds of building material are well documented. Using a Monte Carlo method, the building...

  • THE MARKOV CHAIN MONTE CARLO REVOLUTION. Diaconis, Persi // Bulletin (New Series) of the American Mathematical Society;Apr2009, Vol. 46 Issue 2, p179 

    The use of simulation for high-dimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through micro-local analysis.

  • Additive Schwarz with aggregation-based coarsening for elliptic problems with highly variable coefficients. Scheichl, R.; Vainikko, E. // Computing;Sep2007, Vol. 80 Issue 4, p319 

    We develop a new coefficient-explicit theory for two-level overlapping domain decomposition preconditioners with non-standard coarse spaces in iterative solvers for finite element discretisations of second-order elliptic problems. We apply the theory to the case of smoothed aggregation coarse...

  • Direction choice for accelerated convergence in hit-and-run sampling. Kaufman, David E.; Smith, Robert L. // Operations Research;Jan/Feb98, Vol. 46 Issue 1, p84 

    Hit-and-Run algorithms are Monte Carlo procedures for generating points that are asymptotically distributed according to general absolutely continuous target distributions G over open bounded regions S. Applications include nonredundant constraint identification, global optimization, and Monte...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics