TITLE

A Variance-Minimizing Filter for Large-Scale Applications

AUTHOR(S)
van Leeuwen, P. J.
PUB. DATE
September 2003
SOURCE
Monthly Weather Review;Sep2003, Vol. 131 Issue 9, p2071
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A truly variance-minimizing filter is introduced and its performance is demonstrated with the Korteweg–DeVries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four-dimensional variational data assimilation (4DVAR)-like methods relying on perfect model dynamics have difficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When observations are available, the so-called importance resampling algorithm is applied. From Bayes's theorem it follows that each ensemble member receives a new weight dependent on its “distance” to the observations. Because the weights are strongly varying, a resampling of the ensemble is necessary. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be formulated that way. Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However, in the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, governed by strongly nonlinear dynamics, shows that the method is working satisfactorily. The strong and weak points of the method are discussed and possible improvements are proposed.
ACCESSION #
10659922

 

Related Articles

  • Multifractal and statistical analyses of heat release fluctuations in a spark ignition engine. Sen, Asok K.; Litak, Grzegorz; Kaminski, Tomasz; Wendeker, Mirosław // Chaos;Sep2008, Vol. 18 Issue 3, p033115 

    Using multifractal and statistical analyses, we have investigated the complex dynamics of cycle-to-cycle heat release variations in a spark ignition engine. Three different values of the spark advance angle (Δβ) are examined. The multifractal complexity is characterized by the singularity...

  • Un Groupe Hyperbolique Est Déterminé Par Son Bord. Paulin, Frédéric // Journal of the London Mathematical Society;1996, Vol. 54 Issue 1, p50 

    We construct on the boundary of a hyperbolic group (in Gromov's sense) a natural visual measure and a natural crossratio. We prove that the I-quasiconformal homeomorphisms (in Pansu's sense) between the boundaries of hyperbolic groups are the quasimöbius maps (that is, the bijections that...

  • Get Physical. Kim, Scott // Discover;Oct2003, Vol. 24 Issue 10, p83 

    Presents several puzzles on motion and mechanics. Assumption of the weight of blocks in a tumbling diagram; Reason that two spherical balls of equal size but with different weights would hit the ground at different times if dropped simultaneously.

  • Shell transitions between metastable states of Yukawa balls. Käding, S.; Block, D.; Melzer, A.; Piel, A.; Kählert, H.; Ludwig, P.; Bonitz, M. // Physics of Plasmas;Jul2008, Vol. 15 Issue 7, p073710 

    Spherical dust clusters composed of several concentric shells are experimentally investigated with particular interest on transitions between different configurations and transitions of particles between different shells. Transitions between different ground and metastable configurations are...

  • From Inference to Physics. Caticha, Ariel // AIP Conference Proceedings;11/7/2008, Vol. 1073 Issue 1, p23 

    Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further. We calculate the probability for an arbitrary path followed by a system as it moves from given initial to final states. For an...

  • A flexible approach to location problems. Rodríguez-Chía, Antonio M.; Nickel, Stefan; Puerto, Justo; Fernández, Francisco R. // Mathematical Methods of Operations Research;2000, Vol. 51 Issue 1, p69 

    Abstract. When dealing with location problems we are usually given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the...

  • Posttest Probability Calculation by Weights. Rembold, Christopher M.; Watson, Denny // Annals of Internal Medicine;Jan88, Vol. 108 Issue 1, p115 

    Presents an article which reintroduced a different form of Bayes' theorem that allows calculation of posttest probabilities by adding quantities known as weights in the interpretation of diagnostic tests. Function of a weight; Factor in which clinicians rely on in interpreting the results of a...

  • The Weighted Hardy Inequality: New Proofs and the Case p = 1. Sinnamon, Gord; Stepanov, Vladimir D. // Journal of the London Mathematical Society;1996, Vol. 54 Issue 1, p89 

    An elementary proof is given of the weight characterisation for the Hardy inequality (∫0∞(∫0∞f)qυ(x)dx)1/q ≤C (∫0∞fpu)1/p for f≥0, (1.1) in the case 0 < q < p, 1 < p < ∞. It is also shown that certain weighted inequalities with monotone kernels...

  • ANTHROPOMETRIC CHARACTERISTICS AND VO2 MAX OF URBAN TRIBALAND NON-TRIBAL BOYS OF TRIPURA. SINHA, UMA; NAG, S. K. // Indian Journal of Scientific Research;Dec2012, Vol. 3 Issue 2, p111 

    Anthropometry is the single most portable, systemized technique, universally applicable, inexpensive, and noninvasive method available to assess the proportions, size, and composition of the human body. Maximum oxygen uptake (VO2 max) is internationally accepted parameter to evaluate the...

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