Data assimilation systems (DAS) for numerical weather prediction (NWP) combine information from a numerical model of the atmospheric dynamics, observational data, and error statistics to analyze and predict the state of the atmosphere. Four-dimensional variational methods (4D-Var) produce an estimate (analysis) to the true state by solving a large-scale model-constrained optimization problem. The rapid growth in the data volume provided by satellite-based instruments has prompted research to assess and improve the forecast impact (''value'') of high-resolution observations.

This talk presents theoretical and practical aspects of hyperparameter sensitivity analysis in a 4D-Var DAS including evaluation of the forecast sensitivity to observations (FSO), prior state estimate, and parameterized error covariance models. An FSO-based optimization approach is formulated to identify deficiencies in the weight assigned to various observing system components and adaptively improve the use of observations.

The practical ability to implement this methodology is demonstrated in a computational environment that features all elements necessary for applications to NWP.