An Efficient Estimation of Time-Varying Parameters of Dynamic Models by Combining Offline Batch Optimization and Online Data Assimilation

Abstract

It is crucially important to estimate unknown parameters in process-based models by integrating observation and numerical simulation. For many applications in earth system sciences, a parameter estimation method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate 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 (SIRPF) is improved using a non-parametric posterior probabilistic distribution of time-invariant parameters obtained by comparing simulated and observed climatology. HOOPE-PF outperforms the original SIRPF in synthetic experiments with toy models and a real-data experiment with a conceptual hydrological model when an 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 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 models in earth system sciences such as land, ecosystem, hydrology, and paleoclimate reconstruction, HOOPE-PF can be applied to improve the simulation of these process-based models by considering time-varying model parameters.