The value added by atmospheric measurements to the analyses and forecasts produced by data assimilation systems (DAS) is closely determined by the representation of the statistical properties of the errors in the prior forecast estimate (background) and observations. Four-dimensional variational data assimilation (4D-Var) aims to provide an optimal estimate to the initial state by solving a large-scale PDE model-constrained optimization problem. We present recent advances in the evaluation of the model forecast error sensitivity to observations, error covariance parameter specification, and impact estimation in a 4D-Var DAS. Mathematical aspects and practical issues are discussed together with the current status of implementation at numerical weather prediction centers. Special emphasis will be given to the diagnosis, forecast sensitivity, and impact estimation of correlated observational errors in high-resolution data from hyperspectral remote sensing instruments.