On the use of adaptive ensemble Kalman filtering to mitigate error misspecifications in GRACE data assimilation

The ensemble Kalman filter (EnKF) has been proved as a useful algorithm to merge coarse-resolution Gravity Recovery and Climate Experiment (GRACE) data with hydrologic model results. However, in order for the EnKF to perform optimally, a correct forecast error covariance is needed. The EnKF estimates this error covariance through an ensemble of model simulations with perturbed forcing data. Consequently, a correct specification of perturbation magnitude is essential for the EnKF to work optimally. To this end, an adaptive EnKF (AEnKF), a variant of the EnKF with an additional component that dynamically detects and corrects error misspecifications during the filtering process, has been applied. Due to the low spatial and temporal resolutions of GRACE data, the efficiency of this method could be different than for other hydrologic applications. Therefore, instead of spatially or temporally averaging the internal diagnostic (normalized innovations) to detect the misspecifications, spatiotemporal averaging was used. First, sensitivity of the estimation accuracy to the degree of error in forcing perturbations was investigated. Second, efficiency of the AEnKF for GRACE assimilation was explored using two synthetic and one real data experiment. Results show that there is considerable benefit in using this method to estimate the forcing error magnitude and that the AEnKF can efficiently estimate this magnitude.