A Quantile Conserving Ensemble Filter Framework. Part I: Updating an Observed Variable
A Quantile Conserving Ensemble Filter Framework. Part I: Updating an Observed Variable
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分位数守恒集成滤波器框架。
DOI：
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发表时间：
2022
影响因子：
3.2
通讯作者：
Jeffrey L. Anderson
中科院分区：
文献类型：
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作者：
Jeffrey L. Anderson
提出了确定性单变量集成滤波的一般框架。该框架将连续先验概率密度函数（PDF）拟合到先验集合。观测似然的函数表示与先验PDF相结合，以获得连续分析（后验）PDF。还需要先验和分析的累积分布函数。关键创新在于计算分析系综，以便每个系综成员的分位数与其先前的分位数相同。许多选择以前的PDF家庭和似然函数进行了说明。具有正态似然的正态先验的选择等价于集合平差卡尔曼滤波。先验的一些其他选择包括伽玛分布、反伽玛分布、贝塔分布、贝塔素数分布、对数正态分布和指数分布。先验分布和似然性都可以在一组区间上定义，这提供了额外的灵活性，可以用于实现Huber似然性等方法，用于偶尔出现离群值的观测。先验和似然也可以被定义为允许像二元法线或核滤波器这样的选择的分布之和。可以使用经验分布，例如对任意PDF和函数的分段线性近似。另一个经验选择导致秩直方图滤波器。这里的结果是单变量的，可用于计算观测变量的增量或任何变量的边际分布，以进行再分析。增量的线性回归可以用来更新串行滤波器中的状态变量，以建立综合的数据同化系统。第2部分将讨论将框架扩展到多元数据同化的其他方法。
A general framework for deterministic univariate ensemble filtering is presented. The framework fits a continuous prior probability density function (PDF) to the prior ensemble. A functional representation for the observation likelihood is combined with the prior PDF to get a continuous analysis (posterior) PDF. Cumulative distribution functions for the prior and analysis are also required. The key innovation is that an analysis ensemble is computed so that the quantile of each ensemble member is the same as its prior quantile. Many choices for the prior PDF family and the likelihood function are described. A choice of normal prior with normal likelihood is equivalent to the ensemble adjustment Kalman filter. Some other choices for the prior include gamma, inverse gamma, beta, beta prime, log-normal and exponential distributions. Both prior distributions and likelihoods can be defined over a set of intervals giving additional flexibility that can be used to implement methods like a Huber likelihood for observations with occasional outliers. Priors and likelihoods can also be defined as sums of distributions allowing choices like bivariate normals or kernel filters. Empirical distributions, for instance piecewise linear approximations to arbitrary PDFs and functions can be used. Another empirical choice leads to the rank histogram filter. Results here are univariate and can be used to compute increments for observed variables or marginal distributions for any variable for a reanalysis. Linear regression of increments can be used to update state variables in a serial filter to build a comprehensive data assimilation system. Part 2 will discuss other methods for extending the framework to multivariate data assimilation.
影响因子：
5.4
作者：
A. Schöniger;Wolfgang Nowak;H. Franssen
通讯作者：
A. Schöniger;Wolfgang Nowak;H. Franssen
影响因子：
3.2
作者：
Stroud, Jonathan R.;Katzfuss, Matthias;Wikle, Christopher K.
通讯作者：
Wikle, Christopher K.