The turbulent nature of the atmospheric boundary layer leads to wind-turbine power fluctuations and fatigue loading. The possibility to perform faster than real-time turbulent flow field simulations opens up applications in the forecasting and potentially actively controlling of turbulent structures. An important aspect of the forecasting, is the initialization of the simulation based on measurements, which will be the focus of this work. To this end, we use a 4D-Var approach, which is already being applied in numerical weather prediction applications. In this article, a fully developed pressure-driven atmospheric boundary layer is used as a case study. As a underlying model for the state estimation, we use a large eddy simulation (LES) code run on a relatively coarse grid, to decrease the model evaluation time. We take virtual measurements from a reference LES simulation, which is also used to benchmark the state estimation. For the 4D-Var optimization problem, we use a L-BFGS approach combined with an adjoint LES simulation for the gradient calculations.