THE EFFECT OF LINEARIZATION ERRORS ON 4DVAR DATA ASSIMILATION

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 convecti ve parameterization is largest. These errors are much smaller for ''sm ooth convective'' points in the integration domain and for the nonconv ective regions. Decreasing of the amplitude of initial perturbations d oes 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 regim e changes (i;e., due to use of standard method). The authors then show that the quality of local four-dimensional variational (4DVAR) data a ssimilation results is correlated with the linearization errors: Slowe r convergence is associated with large errors. Consequently, the 4DVAR assimilation results are different for different convective points in the integration domain. The negative effect of linearization errors i s not, however, significant for the cases that are studied. Erroneous points slightly degrade 4DVAR results in the remaining points. This de gradation is reflected in decreased monotonicity of the cost function gradient reduction with iterations. These results suggest that there i s a probability for locally bad 4DVAR assimilation results when using standard adjoints of discontinuous parameterizations. In practice, whe n using for example observations, this is unlikely to cause errors tha t are larger than errors associated with other approximations and unce rtainties in the data assimilation integrations such as the linear app roximation errors and the uncertainties associated with the background and model errors statistics. This conclusion is similar to the conclu sions of prior 4DVAR assimilation studies that use the standard adjoin ts but unlike in these studies the results in the current study show t hat 1) the linearization errors are nonnegligible for small-amplitude initial perturbations and 2) the assimilation results are locally and even globally affected by these errors.