The accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change spatio-temporally, shows promise in quantifying and mitigating systematic model errors, the estimation of the spatio-temporally distributed model parameters has been practically challenging. Here we present an efficient and practical method to estimate time-varying parameters in high-dimensional spaces. In our proposed method, Hybrid Offline and Online Parameter Estimation with ensemble Kalman filtering (HOOPE-EnKF), model parameters estimated by EnKF are constrained by results of offline batch optimization, in which the posterior distribution of model parameters is obtained by comparing simulated and observed climatological variables. HOOPE-EnKF outperforms the original EnKF in synthetic experiments using a two-scale Lorenz96 model and a simple global general circulation model. One advantage of HOOPE-EnKF over traditional EnKFs is that its performance is not greatly affected by inflation factors for model parameters, thus eliminating the need for extensive tuning of inflation factors. We thoroughly discuss the potential of HOOPE-EnKF as a practical method for improving parameterizations of process-based models and prediction in real-world applications such as numerical weather prediction.

翻译：地球系统模型的准确性受到未知和/或未解析动力学的损害，因此对模型系统误差的量化至关重要。尽管允许参数时空变化的模型参数估计在量化和缓解系统模型误差方面显示出前景，但时空分布模型参数的估计在实践中一直具有挑战性。本文提出了一种在高维空间中估计时变参数的高效实用方法。在我们提出的混合离线与在线参数估计结合集合卡尔曼滤波（HOOPE-EnKF）方法中，由EnKF估计的模型参数受到离线批量优化结果的约束，该优化通过比较模拟和观测的气候变量获得模型参数的后验分布。在使用双尺度Lorenz96模型和简单全球大气环流模型的合成实验中，HOOPE-EnKF优于原始EnKF。HOOPE-EnKF相对于传统EnKF的一个优势是，其性能受模型参数膨胀因子的影响较小，从而无需对膨胀因子进行大量调优。我们深入讨论了HOOPE-EnKF作为实用方法在改进过程模型参数化及实际应用（如数值天气预报）中预测的潜力。