Comparison of retrospective optimal interpolation with four-dimensional variational assimilation

We propose a retrospective optimal interpolation (ROI) system that is derived from the quasi-static variational assimilation (QSVA) algorithm. Even when the four-dimensional variational assimilation (4D-Var) may fail to find the global minimum of a cost function because the function has multiple minima, ROI is shown to find this minimum. However, ROI’s ability to overcome the multiple minima problem depends on the observation time interval over the analysis window. Using the perturbation method, we can implement ROI without using an adjoint model, which is required by QSVA. For cost-effective implementation, we developed a reduced-rank formulation of ROI, based on the accuracy-saturation property.

From numerical experiments using the Lorenz three-variable model, we show that ROI finds the global minimum of the cost function even when the 4D-Var analysis is trapped in a local minimum. From experiments with the Lorenz 40-variable model, we confirm that the reduced-rank formulation becomes demonstrably cost-effective as the analysis window expands. Finally, we demonstrate a possible loss of efficiency of ROI with implications for future research.