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An Information Criterion for Choosing Observation Locations in Data Assimilation and Prediction
SIAM/ASA Journal on Uncertainty Quantification ( IF 2.1 ) Pub Date : 2020-12-15 , DOI: 10.1137/19m1278235 Nan Chen
SIAM/ASA Journal on Uncertainty Quantification ( IF 2.1 ) Pub Date : 2020-12-15 , DOI: 10.1137/19m1278235 Nan Chen
SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 4, Page 1548-1573, January 2020.
An information criterion is proposed for determining the observation locations based on maximizing the information gain in the posterior distribution from data assimilation. It is applied to developing an off-line strategy using the long-term statistics from Eulerian observations and an online ensemble strategy for determining the initial locations of Lagrangian tracers. Decompose the total information gain into a signal and a dispersion part, accounting for the posterior mean and posterior uncertainty, respectively. Despite the information criterion being a nonlinear function of the posterior estimates and the intrinsic nonlinearity in the Lagrangian data assimilation, the total information gain can be solved via closed analytic formulae. The signal part is given by the solution of a set of Sylvester equations, and the dispersion part is associated with a Riccati equation. Numerical experiments based on a multiscale compressible rotating shallow water equation show that the information gain using the optimal strategy and that using the random assignment increase as a linear and a logarithm function of the number of the Eulerian observations $L$, respectively, until $L$ approaches the model degree of freedom, at which time the difference between the two information gains reaches the maximum. Afterwards, both the information gains are dominated by the dispersion part and increase as a function of $\ln{L}$. On the other hand, the optimal initial locations of the Lagrangian tracers resulting from the ensemble based strategy also succeed in improving the skill of recovering complex flow patterns and extreme events associated with single random realizations of the model.
中文翻译：
在数据同化和预测中选择观察位置的信息标准
SIAM / ASA不确定性量化期刊，第8卷，第4期，第1548-1573页，2020年1月。
提出了一种信息准则，用于基于最大化数据同化后验分布中的信息增益来确定观察位置。它用于使用欧拉观测的长期统计数据和用于确定拉格朗日示踪剂初始位置的在线总体策略来开发离线策略。将总信息增益分解为信号和分散部分，分别说明后验均值和后验不确定性。尽管信息准则是后验估计的非线性函数，并且在拉格朗日数据同化中具有固有非线性，但是总信息增益可以通过封闭解析公式求解。信号部分由一组Sylvester方程的解给出，色散部分与Riccati方程相关联。基于多尺度可压缩浅水旋转方程的数值实验表明，使用最优策略的信息增益和使用随机分配的信息增益分别增加为欧拉观测值$ L $的线性和对数函数，直到$ L $接近模型的自由度，这时两个信息增益之间的差异达到最大。之后，这两个信息增益都由色散部分支配，并作为$ \ ln {L} $的函数而增加。另一方面，
更新日期：2020-12-15
An information criterion is proposed for determining the observation locations based on maximizing the information gain in the posterior distribution from data assimilation. It is applied to developing an off-line strategy using the long-term statistics from Eulerian observations and an online ensemble strategy for determining the initial locations of Lagrangian tracers. Decompose the total information gain into a signal and a dispersion part, accounting for the posterior mean and posterior uncertainty, respectively. Despite the information criterion being a nonlinear function of the posterior estimates and the intrinsic nonlinearity in the Lagrangian data assimilation, the total information gain can be solved via closed analytic formulae. The signal part is given by the solution of a set of Sylvester equations, and the dispersion part is associated with a Riccati equation. Numerical experiments based on a multiscale compressible rotating shallow water equation show that the information gain using the optimal strategy and that using the random assignment increase as a linear and a logarithm function of the number of the Eulerian observations $L$, respectively, until $L$ approaches the model degree of freedom, at which time the difference between the two information gains reaches the maximum. Afterwards, both the information gains are dominated by the dispersion part and increase as a function of $\ln{L}$. On the other hand, the optimal initial locations of the Lagrangian tracers resulting from the ensemble based strategy also succeed in improving the skill of recovering complex flow patterns and extreme events associated with single random realizations of the model.
中文翻译：
在数据同化和预测中选择观察位置的信息标准
SIAM / ASA不确定性量化期刊，第8卷，第4期，第1548-1573页，2020年1月。
提出了一种信息准则，用于基于最大化数据同化后验分布中的信息增益来确定观察位置。它用于使用欧拉观测的长期统计数据和用于确定拉格朗日示踪剂初始位置的在线总体策略来开发离线策略。将总信息增益分解为信号和分散部分，分别说明后验均值和后验不确定性。尽管信息准则是后验估计的非线性函数，并且在拉格朗日数据同化中具有固有非线性，但是总信息增益可以通过封闭解析公式求解。信号部分由一组Sylvester方程的解给出，色散部分与Riccati方程相关联。基于多尺度可压缩浅水旋转方程的数值实验表明，使用最优策略的信息增益和使用随机分配的信息增益分别增加为欧拉观测值$ L $的线性和对数函数，直到$ L $接近模型的自由度，这时两个信息增益之间的差异达到最大。之后，这两个信息增益都由色散部分支配，并作为$ \ ln {L} $的函数而增加。另一方面，
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