A partial ensemble Kalman filtering approach to enable use of range limited observations

The ensemble Kalman filter (EnKF) relies on the assumption that an observed quantity can be regarded as a stochastic variable that is Gaussian distributed with mean and variance that equals the measurement and the measurement noise, respectively. When a gauge has a minimum and/or maximum detection limit and the observed quantity is outside this range, the signal from the gauge can, however, not be related to the observed quantity in this way. The current study proposes a method for utilizing this kind of out-of-range observations with the EnKF by explicitly treating the out-of-range observations. By doing this it is possible to update the ensemble members that are within the observable range of the gauge towards the observation limit and thereby reduce the ensemble spread. The method is tested using both a linear and a non-linear simple forcing-driven model in perfect model experiments where the same model and noise descriptions are used for the truth simulation and for the EnKF. The results show that the positive impact of the method in case of range-limited observations can exceed that of increasing the ensemble size from 10 to 100 and that the method makes it possible to improve model forecasts using observations that would otherwise have been non-informative.