An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering
An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering
复制标题
DOI：
10.1016/j.advwatres.2011.04.014
复制
发表时间：
2011-07
影响因子：
4.7
通讯作者：
Haiyan Zhou;J. Jaime Gómez-Hernández;Harrie‐Jan Hendricks Franssen;Liangping Li
中科院分区：
文献类型：
--
作者：
Haiyan Zhou;J. Jaime Gómez-Hernández;Harrie‐Jan Hendricks Franssen;Liangping Li
集合卡尔曼滤波(EnKF)是各学科常用的实时数据同化算法。这里，在水文地质背景下，EnKF被应用于根据对数电导率和瞬变测压水头数据来实现对数电导率。在这种情况下，状态向量由离散含水层区域上的对数电导率和测压水头组成，预测模型是地下水流数值模型，并顺序同化瞬时测压水头数据以更新状态向量。众所周知，对于线性预测模型和多高斯分布的状态向量，所有卡尔曼滤波的性能都是最优的。在不同的卡尔曼滤波器中，EnKF提供了一种稳健的解决方案来解决非线性问题；然而，它不能很好地处理非高斯状态向量分布。在标准的EnKF中，随着时间的推移和更多的状态观测被同化，分布变得更接近高斯，即使最初的分布显然是非高斯的。提出了一种新的方法，将原始状态向量变换为新的一元高斯型向量。对滤波后的向量进行反向变换，可确保状态向量分量的初始非高斯单变量分布始终保持不变。该方法基于对所有位置和所有时间步长的每个变量进行正态得分变换。在一个类似河流沉积的合成双峰含水层中进行了验证，并与标准的EnKF方法进行了比较。该方法在分析的各个方面(对数电导率表征以及流动和输运预测)都优于标准的EnKF方法。
The ensemble Kalman filter (EnKF) is a commonly used real-time data assimilation algorithm in various disciplines. Here, the EnKF is applied, in a hydrogeological context, to condition log-conductivity realizations on log-conductivity and transient piezometric head data. In this case, the state vector is made up of log-conductivities and piezometric heads over a discretized aquifer domain, the forecast model is a groundwater flow numerical model, and the transient piezometric head data are sequentially assimilated to update the state vector. It is well known that all Kalman filters perform optimally for linear forecast models and a multiGaussian-distributed state vector. Of the different Kalman filters, the EnKF provides a robust solution to address non–linearities; however, it does not handle well non-Gaussian state-vector distributions. In the standard EnKF, as time passes and more state observations are assimilated, the distributions become closer to Gaussian, even if the initial ones are clearly non-Gaussian. A new method is proposed that transforms the original state vector into a new vector that is univariate Gaussian at all times. Back transforming the vector after the filtering ensures that the initial non-Gaussian univariate distributions of the state-vector components are preserved throughout. The proposed method is based in normal-score transforming each variable for all locations and all time steps. This new method, termed the normal-score ensemble Kalman filter (NS-EnKF), is demonstrated in a synthetic bimodal aquifer resembling a fluvial deposit, and it is compared to the standard EnKF. The proposed method performs better than the standard EnKF in all aspects analyzed (log-conductivity characterization and flow and transport predictions).