  Accurate estimation of error covariances (both background and observation) is
crucial for efficient observation compression approaches in data assimilation
of large-scale dynamical problems. We propose a new combination of a covariance
tuning algorithm with existing PCA-type data compression approaches, either
observation- or information-based, with the aim of reducing the computational
cost of real-time updating at each assimilation step. Relying on a local
assumption of flow-independent error covariances, dynamical assimilation
residuals are used to adjust the covariance in each assimilation window. The
estimated covariances then contribute to better specify the principal
components of either the observation dynamics or the state-observation
sensitivity. The proposed approaches are first validated on a shallow water
twin experiment with correlated and non-homogeneous observation error. Proper
selection of flow-independent assimilation windows, together with sampling
density for background error estimation, and sensitivity of the approaches to
the observations error covariance knowledge, are also discussed and illustrated
with various numerical tests and results. The method is then applied to a more
challenging industrial hydrological model with real-world data and a non-linear
transformation operator provided by an operational precipitation-flow
simulation software.
