Test models for filtering and prediction of moisture-coupled tropical waves

The filtering/data assimilation and prediction of moisture-coupled tropical waves is a contemporary topic with significant implications for extended-range forecasting. The development of efficient algorithms to capture such waves is limited by the unstable multiscale features of tropical convection which can organize large-scale circulations and the sparse observations of the moisture-coupled wave in both the horizontal and vertical. The approach proposed here is to address these difficult issues of data assimilation and prediction through a suite of analogue models which, despite their simplicity, capture key features of the observational record and physical processes in moisture-coupled tropical waves. The analogue models emphasized here involve the multicloud convective parametrization based on three cloud types (congestus, deep, and stratiform) above the boundary layer. Two test examples involving an MJO-like turbulent travelling wave and the initiation of a convectively coupled wave train are introduced to illustrate the approach. A suite of reduced filters with judicious model errors for data assimilation of sparse observations of tropical waves, based on linear stochastic models in a moisture-coupled eigenmode basis is developed here and applied to the two test problems. Both the reduced filter and 3D-Var with a full moist background covariance matrix can recover the unobserved troposphere humidity and precipitation rate; on the other hand, 3D-Var with a dry background covariance matrix fails to recover these unobserved variables. The skill of the reduced filtering methods in recovering the unobserved precipitation, congestus, and stratiform heating rates as well as the front-to-rear tilt of the convectively coupled waves exhibits a subtle dependence on the sparse observation network and the observation time.