Nudging Methods: A Critical Overview - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 26

Chapter 2
Nudging Methods: A Critical Overview
S. Lakshmivarahan and John M. Lewis
Abstract 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 apriori 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.