A data assimilation algorithm for predicting rain

Convective-scale data assimilation uses high-resolution numerical weather prediction models and temporally and spatially dense observations of relevant atmospheric variables. In addition, it requires a data assimilation algorithm that is able to provide initial conditions for a state vector of large size with one third or more of its components containing prognostic hydrometeors variables whose non-negativity needs to be preserved. The algorithm also needs to be fast as the state vector requires a high updating frequency in order to catch fast-changing convection. A computationally efficient algorithm for quadratic optimization (QO, or formerly QP) is presented here, which preserves physical properties in order to represent features of the real atmosphere. Crucially for its performance, it exploits the fact that the resulting linear constraints may be disjoint. Numerical results on a simple model designed for testing convective-scale data assimilation show accurate results and promising computational cost. In particular, if constraints on physical quantities are disjoint and their rank is small, further reduction in computational costs can be achieved.