A variational assimilation technique in a hybrid isentropic-sigma coordinate

A three-dimensional variational (3dVAR) analysis set in a generalized vertical coordinate is described. This analysis technique has been applied to the Rapid Update Cycle (RUC), a mesoscale analysis/model system in the United States providing high-frequency, short-range forecasts. The RUC 3dVAR analysis is, in fact, set in a hybrid isentropic-sigma coordinate, but without loss of generality or applicability to other coordinate systems. The use of this coordinate provides an adaptive analysis space, with sloping of background error covariances in the proximity of baroclinic systems, and a stability-dependence for vertical error covariances. The basic characteristics of the RUC are described briefly, with special attention to its vertical coordinate. A detailed description of observation operators is provided. The WAR algorithm, including stream function and velocity potential as control variables for the multivariate aspect, is described in detail. A few examples of analysis results are provided. The RUC 3dVAR in hybrid-isentropic-sigma coordinates is being implemented at the National Centers for Environmental Prediction (NCEP) in 2001.