Four-dimensional variational data assimilation for mesoscale and storm-scale applications

The status and progress of the four-dimensional variational data assimilation (4DVAR) are briefly reviewed focusing on application to prediction of mesoscale/storm-scale atmospheric phenomena. Theoretical background is provided for each important component of the 4DVAR system - forecast and adjoint models, observations, background, cost function, preconditioning, and minimization. An overview of practical issues specific for mesoscale/storm-scale 4DVAR is then presented in terms of high-resolution observations, nonlinearity and discontinuity problem, model error, errors from lateral boundary condition, and precipitation assimilation. Practical strategies for efficient and simplified, 4DVAR are also introduced, e.g., incremental 4DVAR, poor man's 4DVAR, and inverse 3DVAR. A new concept on hybrid approach is proposed to combine an efficient 4DVAR scheme and the standard 4DVAR scheme aiming at reducing computational demand required by the standard 4DVAR while improving the accuracy of the simplified 4DVAR. Applications to both hydrostatic and nonhydrostatic models are illustrated and our vision on opportunities and directions for future research is provided.