Data assimilation is the application of Bayes' theorem to condition the states of a dynamical systems model on observations. Any real-world application of Bayes' theorem is approximate, and therefore we cannot expect that data assimilation will preserve all of the information available from models and observations. We outline a framework for measuring information in models, observations, and evaluation data in a way that allows us to quantify information loss during (necessarily imperfect) data assimilation. This facilitates quantitative analysis of tradeoffs between improving (usually expensive) remote sensing observing systems vs. improving data assimilation design and implementation. We demonstrate this methodology on a previously published application of the Ensemble Kalman Filter used to assimilate remote sensing soil moisture retrievals from AMSR-E into the Noah land surface model.
Keywords: Bayesian Efficiency; Data Assimilation; Information Theory; Soil Moisture.