An efficient estimation of time-varying parameters of dynamic models by combining offline batch optimization and online data assimilation

It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate the time-varying parameters of relatively low dimensional models is presented. In the newly proposed method, called Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF), an inflation method to maintain the spread of ensemble members in a sampling-importance-resampling particle filter is improved using a non-parametric posterior probabilistic distribution of time-invariant parameters obtained by comparing simulated and observed climatology. The HOOPE-PF outperforms the original sampling-importance-resampling particle filter in synthetic experiments with toy models and a real-data experiment with a conceptual hydrological model especially when the ensemble size is small. The advantage of HOOPE-PF is that its performance is not greatly affected by the size of perturbation to be added to ensemble members to maintain their spread while it is critically important to get the optimal performance in the original particle filter. Since HOOPE-PF is the extension of the existing particle filter which has been extensively applied to many earth system models such as land, ecosystem, hydrology, and paleoclimate reconstruction, the HOOPE-PF can be applied to improve the simulation of these earth system models by considering time-varying model parameters.