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

Data assimilation (DA), the statistical combination of computer models with measurements, is applied in a variety of scientific fields involving forecasting of dynamical systems, most prominently in atmospheric and ocean sciences. The existence of misreported or unknown observation times (time error) poses a unique and interesting problem for DA. Mapping observations to incorrect times causes bias in the prior state and affects assimilation. Algorithms that can improve the performance of ensemble Kalman filter DA in the presence of observing time error are described. Algorithms that can estimate the distribution of time error are also developed. These algorithms are then combined to produce extensions to ensemble Kalman filters that can both estimate and correct for observation time errors. A low-order dynamical system is used to evaluate the performance of these methods for a range of magnitudes of observation time error. The most successful algorithms must explicitly account for the nonlinearity in the evolution of the prediction model.