Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors

This paper seeks to represent the tropical short-range forecast error covariances of the European Centre for Medium-Range Weather Forecasts (ECMWF) model in terms of equatorial waves. The motivation for undertaking this investigation is increasing observational evidence indicating that a substantial fraction of the tropical large-scale variability can be explained by equatorially trapped wave solutions known from shallow-water theory. Short-range forecast differences from a data-assimilation ensemble were taken to serve as a proxy for background errors. It was found that the equatorial waves coupled to convection can explain on average 60-70% of the error variance in the tropical free atmosphere. The largest part of this explained variance is represented by the equatorial Rossby (ER) modes, and a significant percentage pertains to the equatorial inertio-gravity (EIG) modes. Eastward-propagating FIG modes have maximum variance in the stratosphere, where the short-wave variance in westward-moving waves is particularly small. This feature is most likely related to the phase of the quasi-biennial oscillation during the study period, suggesting that significant temporal variations could be present in longer-term time series of such statistics. The vertical correlations for ER modes display characteristics similar to those of their extratropical counterparts: correlations narrow towards shorter scales and in the stratosphere. However, the present statistics do not display the significant increase with altitude of the horizontal correlation scale for the height field which is typical for global, quasi-geostrophic statistics commonly used in current data-assimilation schemes. Furthermore, tropospheric ER correlations are vertically asymmetric and deeper for the n = I mode than for higher modes. Most likely, deep convection, acting as a generator of equatorial wave motion, is the dominant mechanism underlying these results. In spite of its relatively small contribution to the tropospheric variance, the Kelvin-wave coupling plays a decisive role for determining the characteristics of the horizontal correlation near the equator. EIG modes also play an important role for the tropical mass-wind coupling; these waves have a major impact by reducing the meridional correlation scales and the magnitudes of the balanced height-field increments.