Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation

Bocquet, Marc; Pires, Carlos A.; Lin Wu
August 2010
Monthly Weather Review;Aug2010, Vol. 138 Issue 8, p2997
Academic Journal
This review discusses recent advances in geophysical data assimilation beyond Gaussian statistical modeling, in the fields of meteorology, oceanography, as well as atmospheric chemistry. The non-Gaussian features are stressed rather than the nonlinearity of the dynamical models, although both aspects are entangled. Ideas recently proposed to deal with these non-Gaussian issues, in order to improve the state or parameter estimation, are emphasized. The general Bayesian solution to the estimation problem and the techniques to solve it are first presented, as well as the obstacles that hinder their use in high-dimensional and complex systems. Approximations to the Bayesian solution relying on Gaussian, or on second-order moment closure, have been wholly adopted in geophysical data assimilation (e.g., Kalman filters and quadratic variational solutions). Yet, nonlinear and non-Gaussian effects remain. They essentially originate in the nonlinear models and in the non-Gaussian priors. How these effects are handled within algorithms based on Gaussian assumptions is then described. Statistical tools that can diagnose them and measure deviations from Gaussianity are recalled. The following advanced techniques that seek to handle the estimation problem beyond Gaussianity are reviewed: maximum entropy filter, Gaussian anamorphosis, non-Gaussian priors, particle filter with an ensemble Kalman filter as a proposal distribution, maximum entropy on the mean, or strictly Bayesian inferences for large linear models, etc. Several ideas are illustrated with recent or original examples that possess some features of high-dimensional systems. Many of the new approaches are well understood only in special cases and have difficulties that remain to be circumvented. Some of the suggested approaches are quite promising, and sometimes already successful for moderately large though specific geophysical applications. Hints are given as to where progress might come from.


Related Articles

  • Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment. Simon, E.; Bertino, L. // Ocean Science;2009, Vol. 5 Issue 4, p495 

    We consider the application of the Ensemble Kalman Filter (EnKF) to a coupled ocean ecosystem model (HYCOM-NORWECOM). Such models, especially the ecosystem models, are characterized by strongly nonlinear interactions active in ocean blooms and present important difficulties for the use of data...

  • History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations. Emerick, Alexandre; Reynolds, Albert // Computational Geosciences;Jun2012, Vol. 16 Issue 3, p639 

    The ensemble Kalman filter (EnKF) has become a popular method for history matching production and seismic data in petroleum reservoir models. However, it is known that EnKF may fail to give acceptable data matches especially for highly nonlinear problems. In this paper, we introduce a procedure...

  • Linear and non-linear filtering in mathematical finance: a review. Date, P.; Ponomareva, K. // IMA Journal of Management Mathematics;Jul2011, Vol. 22 Issue 3, p195 

    This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to...

  • Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model. SUBRAMANIAN, ANEESH C.; HOTEIT, IBRAHIM; CORNUELLE, BRUCE; MILLER, ARTHUR J.; HAJOON SONG // Journal of the Atmospheric Sciences;Nov2012, Vol. 69 Issue 11, p3405 

    This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis...

  • An Intelligent Power Outlet System for the Smart Home of the Internet of Things. Fernández-Caramés, Tiago M. // International Journal of Distributed Sensor Networks;11/11/2015, p1 

    This paper presents an intelligent power outlet system that can be controlled wirelessly and that has been specifically designed to monitor electrical events in low-current loads. Each power outlet of the system embeds a microcontroller, a 2.4 GHz ZigBee interface, RFID (Radio Frequency...

  • Handling Nonlinearity in an Ensemble Kalman Filter: Experiments with the Three-Variable Lorenz Model. Yang, Shu-Chih; Kalnay, Eugenia; Hunt, Brian // Monthly Weather Review;Aug2012, Vol. 140 Issue 8, p2628 

    An ensemble Kalman filter (EnKF) is optimal only for linear models because it assumes Gaussian distributions. A new type of outer loop, different from the one used in 3D and 4D variational data assimilation (Var), is proposed for EnKF to improve its ability to handle nonlinear dynamics,...

  • A Threshold Model for Heron Productivity. Besbeas, Panagiotis; Morgan, Byron // Journal of Agricultural, Biological & Environmental Statistics (;Apr2012, Vol. 17 Issue 1, p128 

    We demonstrate the potential of conditionally Gaussian state-space models in integrated population modeling, when certain model parameters may be functions of previous observations. The approach is applied to a heron census, and the data are best described by a model with three population-size...

  • Out-of-Sequence Measurement Algorithm Based on Gaussian Particle Filter. Wei Wang; Xin-Han Huang; Min Wang // Information Technology Journal;2010, Vol. 9 Issue 5, p942 

    No abstract available.

  • Sequential Dynamic Classification Using Latent Variable Models. Lee, Seung Min; Roberts, Stephen J. // Computer Journal;Nov2010, Vol. 53 Issue 9, p1415 

    Adaptive classification is an important online problem in data analysis. The nonlinear and nonstationary nature of much data makes standard static approaches unsuitable. In this paper, we propose a set of sequential dynamic classification algorithms based on extension of nonlinear variants of...


Read the Article


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

Try another library?
Sign out of this library

Other Topics