Extending Ensemble Kalman Filter Algorithms to Assimilate Observations with an Uncertain Observation Time

Abstract:

While most modern observations of the earth system include a precise time, this has not always been the case. For example, many older archived radiosonde observations do not include the time at which each individual observation was taken but instead include only the launch time, or in some cases only the allowable launch window. Historical ocean profiles may also not include the exact time of observations at each depth.

Ensemble Kalman filter algorithms can be extended to deal with uncertain observation times under certain conditions. In particular, we describe algorithms that are designed to deal with groups of observations that share an unknown observing time drawn from a known distribution. As an example, suppose the time of sonde observations of temperature, moisture and winds at a given level is unknown, but is constrained by a launch window. A set of algorithms of varying complexity and cost is developed to address this problem, estimating both the time offset and an improved estimate of the analysis state. The methods range from simple linear extrapolation of model time tendency to nonlinear approximations of the entire evolving model trajectory in a method related to incremental analysis update. The methods are tested with the Lorenz-96 40-variable model. These methods could be particularly relevant for the use of old observations like those used in century or longer reanalyses.