Nudging Methods: A Critical Overview

  • S. Lakshmivarahan
  • John M. Lewis


A review of the various methods used to implement the “nudging” form of data assimilation has been presented with the intension of identifying both the pragmatic and theoretical aspects of the methodology. Its appeal rests on the intuitive belief that forecast corrections can be made on the basis of feedback control where forecast error from earlier times is incorporated into the dynamics. Further, the methodology is easy to implement. However, its early-period implementation with a nudging coefficient based on pure empiricism with slight consideration of the time scales of motion lacked a firm theoretical foundation. This empirical approach is reviewed but then placed in the context of advances that have attempted to optimally choose the nudging coefficient based on a functional that fits model to data as well as fitting the coefficient to an a priori estimate of the coefficient. Original research in this review makes it clear that these “optimal” methods have unintentionally neglected the inherent presence of serially correlated error in the nudged model. And in the absence of account for this error, the results are non-optimal. Finally, the theories of observer-based nudging and forward-backward nudging are presented as promising avenues of research for the nudging process of dynamic data assimilation.


Kalman Filter Data Assimilation Forecast Error Numerical Weather Prediction Covariance Matrix Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Our thanks are due to an anonymous reviewer for his detailed comments that improved the quality and the readability of this chapter. We wish to thank Mr. Dung Phan for his timely help in typesetting this chapter. S. Lakshmivarahan’s efforts are supported in part by NSF EPSCOR RII Track 2 Grant 105-155900 and by NSF Grant 105-15400.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of OklahomaNormanUSA
  2. 2.National Severe Storms LaboratoryNormanUSA
  3. 3.Desert Research InstituteRenoUSA

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