Numerical discretization causing error variance loss and the need for inflation
Numerical discretization causing error variance loss and the need for inflation
复制标题
数值离散化导致误差方差损失和通货膨胀的需要
DOI：
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发表时间：
2021
影响因子：
8.9
通讯作者：
O. Pannekoucke
中科院分区：
文献类型：
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作者：
R. Ménard;S. Skachko;O. Pannekoucke
模型离散化误差对误差协方差传播的影响比对状态变量的影响具有更复杂的性质。对流传输方程进行了分析，其中相关误差协方差函数的连续（在空间和时间上）传播可以被写入，求解并与应用于协方差矩阵的离散模型进行比较。该问题的数值分析是用一维问题进行的，但也用用于化学数据同化的三维化学传输模式（CTM）进行了说明。结果表明，方差损失（连续传播的解决方案相比）取决于协方差函数本身以及数值离散化方案。方差损失对相关长度特别敏感。在一个简单的一阶离散化中，得到了一个解析表达式，并用于推导通货膨胀的解析表达式。例如，实验表明，在密集的观测网络（具有空间不相关的误差）上进行分析后，在传播步骤中会发生显著的方差损失。使用（方差）膨胀方案，我们能够在整个积分过程中恢复每个网格点和每个时间步的方差损失。应用于EnKF的方差膨胀方案可以被公式化以改变系综的方差扩展或直接作用于状态。
The effects of model discretization errors on the propagation of error covariance have a more complex nature than the effect on the state variable. The analysis is carried out for the advection transport equation, where the continuous (in space and time) propagation of the related error covariance function can be written, solved and compared with the discrete model applied to the covariance matrix. The numerical analysis of the problem is carried out with a 1D‐problem, but is also illustrated with a 3D chemical transport model (CTM) used for chemical data assimilation. It is shown that variance loss (compared to the continuous propagation solution) depends on the covariance function itself as well as the numerical discretization scheme. The variance loss is particularly sensitive to the correlation length. In a simple first‐order discretization, an analytical expression is obtained and is used to derive an analytical expression for inflation. Experiments show, for example, that following an analysis over a dense network of observations (with spatially uncorrelated errors) a significant variance loss occurs in the propagation step. With the (variance) inflation scheme, we are able to restore the variance lost at each grid point, and at each timestep, during the entire integration. The variance inflation scheme applied to an EnKF can be formulated to change the variance spread of the ensemble or to act directly on the state.