An efficient estimation of spatio-temporally distributed parameters in dynamic models by an ensemble Kalman filter

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 a synthetic experiment using a two-scale Lorenz96 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.