An Efficient Algorithm for Stochastic Ensemble Smoothing

Abstract

The state of the environment is assessed with a mathematical model and observational data by using a data assimilation procedure. At present the ensemble Kalman filter is one of the most popular data assimilation algorithms. An important component of the data assimilation procedure is assessment not only of the predicted values, but also of parameters that are not described by the model. A single correction procedure from observational data in the ensemble Kalman filter may not provide the required accuracy. In this regard, an ensemble smoothing algorithm in which data from a certain time interval are used to estimate values at a given time is becoming increasingly popular. This paper considers a generalization of a previously proposed algorithm which is a version of the stochastic ensemble Kalman filter. The generalized algorithm is an ensemble smoothing algorithm in which smoothing is performed for the sample mean, and then the ensemble of perturbations is transformed. The transformation matrix proposed in this paper is used to estimate both the predicted value and the parameter. An important advantage of the algorithm is its locality, which makes it possible to estimate the parameter in a given domain. The paper provides a justification of the applicability of this algorithm to ensemble smoothing. Test calculations are performed with a one-dimensional model of transport and diffusion of a passive pollutant. The algorithm is efficient and can be used to assess the state of the environment.