Extending ensemble Kalman filter algorithms to assimilate observations with an unknown time offset

Data assimilation (DA), the statistical combination ofcomputer models with measurements, is applied in a variety of scientificfields involving forecasting of dynamical systems, most prominently inatmospheric and ocean sciences. The existence of misreported or unknownobservation times (time error) poses a unique and interesting problem forDA. Mapping observations to incorrect times causes bias in the prior stateand affects assimilation. Algorithms that can improve the performance ofensemble Kalman filter DA in the presence of observing time error aredescribed. Algorithms that can estimate the distribution of time error arealso developed. These algorithms are then combined to produce extensions toensemble Kalman filters that can both estimate and correct for observationtime errors. A low-order dynamical system is used to evaluate theperformance of these methods for a range of magnitudes of observation timeerror. The most successful algorithms must explicitly account for thenonlinearity in the evolution of the prediction model.