Tropical Data Assimilation and Analysis of Divergence

An important limitation of the ECMWF wind analyses has been the use of a nondivergent constraint on the analysis increments. We relax this constraint in the optimum interpolation analysis scheme and allow explicitly for divergent wind increments in the ECMWF analysis. We show that there is a strong response to divergent signals in the observations even when only a small portion of divergence is included in the statistical model of the wind forecast errors. As a result wind observations are analyzed more faithfully and tropical flow patterns appear more realistic with the divergent formulation. The previous nondivergent ECMWF analysis scheme provided divergent wind increments on larger scales, but on small scales the analysis increments of divergence were quite noisy. This effect disappears with the explicit inclusion of divergence in the correlation model and the divergent wind increments become smooth and coherent on all scales. Three different vertical correlation functions for the velocity potential have been tried, but none of them enhances tropical vertical velocities and convection to any significant degree when using single level data alone. Tests in data assimilations show that the divergent analyses fit wind data consistently better. Medium range forecasts from these assimilations are little affected by the improved analyses.