A penalized four-dimensional variational data assimilation method for reducing forecast error related to adaptive observations

Four-dimensional variational (4D-Var) data assimilation method is used to find the optimal initial conditions by minimizing a cost function in which background information and observations are provided as the input of the cost function. The optimized initial conditions based on background error covariance matrix and observations improve the forecast. The targeted observations determined by using methods such as adjoint sensitivity, observation sensitivity, or singular vectors may further improve the forecast. In this paper, we are proposing a new technique-consisting of a penalized 4D-Var data assimilation method that is able to reduce the forecast error significantly. This technique consists in penalizing the cost function by a forecast aspect defined over the verification domain at the verification time. The results obtained using the penalized 4D-Var method show that the initial condition is optimally estimated, thus resulting in a better forecast by significantly reducing the forecast error over the verification domain at verification time.