Assimilation of semi-qualitative observations with a stochastic ensemble Kalman filter

In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value. In such cases, most data assimilation schemes discard out-of-range values, treating them as not a number, with the loss of possibly useful qualitative information.

The current work focuses on the development of a data assimilation scheme that tackles observations with a detection limit. We present the Ensemble Kalman Filter Semi-Qualitative (EnKF-SQ) and test its performance against the Partial Deterministic Ensemble Kalman Filter (PDEnKF) of Borup et al.Both are designed to assimilate out-of-range observations explicitly: the out-of-range values are qualitative by nature (inequalities), but one can postulate a probability distribution for them and then update the ensemble members accordingly.