AbstractData 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 trade‐offs between improving (usually expensive) remote sensing observing systems versus 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 Advanced Microwave Scattering Radiometer for Earth (AMSR‐E) into the Noah land surface model.