The Effect of Linearization Errors on 4DVAR Data Assimilation

Abstract

Abstract The authors show that the linear approximation errors in the presence of a discontinuous convective parameterization operator are large for a small number of grid points where the noise produced by the convective parameterization is largest. These errors are much smaller for “smooth convective” points in the integration domain and for the nonconvective regions. Decreasing of the amplitude of initial perturbations does not reduce the errors in noisy points. This result indicates that the tangent linear model solution is erroneous in these points due to the linearization that does not include the linear variations of regime changes (i.e., due to use of standard method). The authors then show that the quality of local four-dimensional variational (4DVAR) data assimilation results is correlated with the linearization errors: Slower convergence is associated with large errors. Consequently, the 4DVAR assimilation results are different for different convective points in the integration domain. The nega...