Four-dimensional data assimilation with optimized viscosity using High Resolution Doppler Lidar observations

We present a four-dimensional variational data assimilation (4D-Var) technique with optimized eddy viscosity for the retrieval of the detailed atmospheric boundary-layer structures from High-Resolution Doppler Lidar (HRDL) radial velocity observations. The 4D-Var is based on the calculus of variations and optimal control theory to recover complete and dynamically consistent data set by minimizing the difference between limited observations and corresponding model predictions. To reflect the nature of the atmospheric boundary layer under various stability conditions, eddy viscosity is treated as part of control variables to be optimized in the 4D-Var model. The mathematical formulation for optimizing eddy viscosity is presented. The model is validated by conducting numerical experiments that utilize synthetic observations. We then apply the 4D-Var to the HRDL data measured under convective and stable conditions.