Quantifying the Representativeness Errors Caused by Scale Transformation of Remote Sensing Data in Stochastic Ensemble Data Assimilation

Representativeness error caused by scale transformation (REST) is an intrinsic property of data assimilation, as assimilating new observations likely involves the fusion of multisource and multiscale data. Earlier studies focused on specific cases and failed to obtain a general concept. This study attempts to achieve a further understanding of REST in both theory and practice. Based on scale-related definitions and formulations, the statistical RESTs of observation errors and analysis errors are deduced in stochastic ensemble data assimilation. Experiments based on ensemble Kalman filter are conducted to validate the interpretability of the proposed formulations. A synthetic experiment uses the stochastic Lorenz model as the forecasting operator, and a real-world experiment employs a simple biosphere model as the forecasting operator and uses a series of mixed ground-based and remote sensing soil moisture observations. The results confirm that REST should be proportional to the scale difference when assimilating direct observations and both system states and observations are homogeneous processes. Due to the nonlinearity in modeling, assimilation, and scale transformation, increasing RESTs are found if the scale of the observation is much larger than that of the state space, or multiscale observations are added into the assimilation system. Quantifying REST improves the understanding of uncertainty in data assimilation, but further studies on REST are required in both theory and practice, for example, REST correlates with other errors in forcing, parameters, and models, and introduces an observation operator to assimilate indirect observations.