In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically limited to a small number due to the computational cost of running the prediction model, which leads to a sampling error. Several methods, such as localization and inflation, exist to mitigate the sampling error, often requiring problem-dependent fine-tuning and design. This work introduces a nonintrusive sampling error mitigation method that modifies the ensemble to ensure a smooth turbulent spectrum. It turns out that the ensemble modification to satisfy the smooth spectrum leads to inhomogeneous localization and inflation, which apply spatially varying localization and inflation levels at different locations. The efficacy of the new idea is validated through a suite of stringent test regimes of the Lorenz 96 turbulent model.

翻译：在数据同化中，集合方法为非线性预测模型所描述的系统提供了一种传播概率密度的途径。尽管统计精度要求较大的集合规模，但由于运行预测模型的计算成本限制，集合规模通常被约束在较小数量，从而产生采样误差。现有多种方法（如局部化与膨胀）可用于缓解采样误差，但这些方法往往需要针对具体问题进行精细调参和设计。本研究提出一种非侵入式采样误差缓解方法，该方法通过修正集合以确保获得平滑的湍流能谱。研究表明，为满足平滑能谱条件而进行的集合修正会自然导出非均匀的局部化与膨胀策略，即在空间不同位置施加变化的自适应局部化与膨胀强度。通过采用Lorenz 96湍流模型的一系列严格测试体系，验证了这一新理念的有效性。