A Comparison of Analysis and Forecast Correction Techniques:Impact of Negative Dissipation

Abstract

The impact of negative dissipation on posttime analysis and forecast correction techniques is examined in a simplified context. The experiments are conducted using a three-level quasigeostrophic model (with a nonsingular tangent propagator matrix) under a perfect-model assumption. Corrections to the initial analysis errors are obtained by operating on the forecast error with (i) the full inverse of the forward tangent propagator, (ii) an inverse composed of a subset of the first leading singular vectors (pseudoinverse), and (iii) the tangent equations with a negative time step (backward integration). When the forecast error is known exactly, using negative dissipation during the full-inverse or backward-integration calculation results in an analysis-error estimate that projects too weakly onto the leading singular vectors and too strongly onto the decaying singular vectors. These discrepancies are small for weak dissipation but increase as the dissipation strength is increased. When the forecast error is known inexactly, negative dissipation provides a beneficial damping of the backward-in-time growth of uncertainties present in the forecast error. This damping effect is found to be due to a fairly uniform change in the singular values, not changes in the singular vectors. However, even for very strong negative dissipation, the uncertainty in the forecast error still grows during the full inverse or backward integration. Therefore, the analysis error estimate will still be dominated by the trailing singular vectors, which represent the decaying part of the initial error. This is in contrast to the pseudoinverse technique, which, like the adjoint sensitivity, is dominated by the fastest growing part of the initial error, and is therefore relatively insensitive to the analysis uncertainty contained within the forecast error. Thus, while full-inverse and backward-integration calculations may provide an analysis perturbation that results in a significantly improved forecast, the analysis error estimate is accurate only when the forecast error is known exactly (i.e., perfect model experiments), regardless of the sign of the dissipation. These results hold for both global and regional forecast errors.