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.

中文翻译：

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随机合奏平滑的高效算法

摘要

通过使用数据同化程序，使用数学模型和观察数据评估环境状态。目前，集成卡尔曼滤波器是最流行的数据同化算法之一。数据同化过程的重要组成部分不仅是评估预测值，而且还评估模型未描述的参数。来自集合卡尔曼滤波器中观测数据的单个校正过程可能无法提供所需的精度。在这方面，将来自特定时间间隔的数据用于估计给定时间的值的集成平滑算法变得越来越流行。本文考虑了先前提出的算法的推广，该算法是随机集成卡尔曼滤波器的一种版本。广义算法是整体平滑算法，其中对样本均值进行平滑，然后转换摄动整体。本文提出的变换矩阵用于估计预测值和参数。该算法的一个重要优点是它的局部性，这使得可以估计给定域中的参数。本文为该算法在整体平滑中的适用性提供了依据。使用被动污染物的传输和扩散的一维模型进行测试计算。该算法高效，可用于评估环境状态。本文提出的变换矩阵用于估计预测值和参数。该算法的一个重要优点是它的局部性，这使得可以估计给定域中的参数。本文为该算法在整体平滑中的适用性提供了依据。使用被动污染物的传输和扩散的一维模型进行测试计算。该算法高效，可用于评估环境状态。本文提出的变换矩阵用于估计预测值和参数。该算法的一个重要优点是它的局部性，这使得可以估计给定域中的参数。本文为该算法在整体平滑中的适用性提供了依据。使用被动污染物的传输和扩散的一维模型进行测试计算。该算法高效，可用于评估环境状态。使用被动污染物的传输和扩散的一维模型进行测试计算。该算法高效，可用于评估环境状态。使用被动污染物的传输和扩散的一维模型进行测试计算。该算法高效，可用于评估环境状态。