Articles | Volume 20, issue 3
Nonlin. Processes Geophys., 20, 329–341, 2013
Nonlin. Processes Geophys., 20, 329–341, 2013

Research article 23 May 2013

Research article | 23 May 2013

The impact of nonlinearity in Lagrangian data assimilation

A. Apte1 and C. K. R. T. Jones2 A. Apte and C. K. R. T. Jones
  • 1TIFR Centre for Applicable Mathematics, P. O. Bag 6503, Chikkabommasandra, Bangalore 560064, India
  • 2Department of Mathematics, University of North Carolina, Chapel Hill NC, 27599 USA

Abstract. The focus of this paper is on how two main manifestations of nonlinearity in low-dimensional systems – shear around a center fixed point (nonlinear center) and the differential divergence of trajectories passing by a saddle (nonlinear saddle) – strongly affect data assimilation. The impact is felt through their leading to non-Gaussian distribution functions. The major factors that control the strength of these effects is time between observations, and covariance of the prior relative to covariance of the observational noise. Both these factors – less frequent observations and larger prior covariance – allow the nonlinearity to take hold. To expose these nonlinear effects, we use the comparison between exact posterior distributions conditioned on observations and the ensemble Kalman filter (EnKF) approximation of these posteriors. We discuss the serious limitations of the EnKF in handling these effects.