Using Improved Background-Error Covariances from an Ensemble Kalman Filter for Adaptive Observations

Abstract

A method for determining adaptive observation locations is demonstrated. This method is based on optimal estimation (Kalman filter) theory; it determines the observation location that will maximize the expected improvement, which can be measured in terms of the expected reduction in analysis or forecast variance. This technique requires an accurate model for background error statistics that vary both in space and in time. Here, these covariances are generated using an ensemble Kalman filter assimilation scheme. A variant is also developed that can estimate the analysis improvement in data assimilation schemes where background error statistics are less accurate. This approach is demonstrated using a quasigeostrophic channel model under perfect-model assumptions. The algorithm is applied here to find the supplemental rawinsonde location to add to a regular network of rawinsondes that will reduce analysis errors the most. The observation network is configured in this experiment so there is a data void in the western third of the domain. One-hundred-member ensembles from three data assimilation schemes are tested as input to the target selection procedure, two variants of the standard ensemble Kalman filter and a third perturbed observation (3DVAR) ensemble. The algorithm is shown to find large differences in the expected variance reduction depending on the observation location, the flow of the day, and the ensemble used in the adaptive observation algorithm. When using the two variants of the ensemble Kalman filter, the algorithm defined consistently similar adaptive locations to each other, and assimilation of the adaptive observation typically reduced analysis errors significantly. When the 3DVAR ensemble was used, the algorithm picked very different observation locations and the analyses were not improved as much. The amount of improvement from assimilating a supplemental adaptive observation instead of a fixed observation in the middle of the void depended on whether the observation was assimilated sporadically or during every analysis cycle. For sporadic assimilation, the adaptive observation provided a dramatic improvement relative to the supplemental fixed observation. When an adaptive observation was regularly assimilated every cycle, the improvement was smaller. For the sporadic assimilation of an adaptive observation, targeting based simply on the maximum spread in background forecasts provided similar target locations and similar analysis improvements to those generated with the full algorithm. The improvement from the regular assimilation of an adaptive observation based on the spread algorithm was no larger than when observations from a fixed target in the middle of the void were regularly assimilated.