标题： 弱约束数据同化中的模型误差协方差估计 显示英文标题

标题： Model Error Covariance Estimation for Weak Constraint Data Assimilation

摘要： 受弱约束四维变分数据同化中的状态估计可以显著取决于数据和模型误差协方差。 因此，这些估计的准确性严重依赖于正确指定模型和观测数据误差协方差。 在这项工作中，我们假设数据误差已知，并集中于通过将弱约束四维变分问题构建成正则逆问题来估计模型误差协方差，在这里逆模型误差协方差作为正则化矩阵。 我们考虑了模型误差协方差的各向同性和非各向同性形式。 使用代表元方法，我们将四维变分问题从状态空间转换到数据空间，从而能够有效地应用正则化参数选择技术。 代表元方法还提供了最优状态估计的解析表达式，使我们可以推导出三种正则化参数选择方法的矩阵表达式，即L曲线法、广义交叉验证(GCV)法和卡方法。 我们通过将模拟数据同化到一维传输方程中（该方程用于模拟各种观测噪声和前向模型扰动下的野火烟雾传输）来验证我们的方法。 在这些实验中，目标是识别能够准确捕捉观测数据与模型预测对同化状态估计影响的模型误差协方差。 正则化参数选择方法成功地估计了反映先验模型预测比观测数据更可靠还是更不可靠的各向同性和非各向同性模型误差协方差的超参数。 结果进一步表明，当先验模型更准确时，各向同性方差就足够了；而当观测数据更可靠时，则优选非各向同性协方差。 显示英文摘要

摘要： State estimates from weak constraint 4D-Var data assimilation can vary significantly depending on the data and model error covariances. As a result, the accuracy of these estimates heavily depends on the correct specification of both model and observational data error covariances. In this work, we assume that the data error is known and and focus on estimating the model error covariance by framing weak constraint 4D-Var as a regularized inverse problem, where the inverse model error covariance serves as the regularization matrix. We consider both isotropic and non-isotropic forms of the model error covariance. Using the representer method, we reduce the 4D-Var problem from state space to data space, enabling the efficient application of regularization parameter selection techniques. The Representer method also provides an analytic expression for the optimal state estimate, allowing us to derive matrix expressions for the three regularization parameter selection methods i.e. the L-curve, generalized cross-validation (GCV), and the Chi-square method. We validate our approach by assimilating simulated data into a 1D transport equation modeling wildfire smoke transport under various observational noise and forward model perturbations. In these experiments the goal is to identify the model error covariances that accurately capture the influence of observational data versus model predictions on assimilated state estimates. The regularization parameter selection methods successfully estimate hyperparameters for both isotropic and non-isotropic model error covariances, that reflect whether the first guess model predictions are more or less reliable than the observational data. The results further indicate that isotropic variances are sufficient when the first guess is more accurate than the data whereas non-isotropic covariances are preferred when the observational data is more reliable.