Data assimilation (DA) combines numerical model simulations with observed data to obtain the best possible description of a dynamical system and its uncertainty. Incorrect modeling assumptions can lead to filter divergence, making model identification an important issue in the field of DA. Variations in dynamic model structures can result in differences in parameter dimensions, complicating the resampling step in PFs. To meet this challenge, the Sequential Hierarchical Bayesian Model (SHBM) is proposed in this paper, which integrates the evolution model along with observation model from the DA scheme, and the hierarchical parameter model. A two-step resampling method are also proposed to estimate the SHBM: the first step uses the resampling scheme in the bootstrap filter to resample new particles based on weights, which may produce some duplicate particles; the second step utilizes the Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods to draw new particles from the target distribution. This approach ensures particle diversity, with the first step aiming at avoiding particle degeneracy, and the second step intends to prevent the sample impoverishment. The performance in the Advection Equation example and Lorenz 96 example demonstrates the effectiveness of the proposed method.

Air quality warning and forecasting systems are usually based on numerical chemical transport models (CTMs). Those dynamic models perform predictions by simulating the life cycles of the atmospheric components, including emission, transport and removal. However, the accuracy of these CTMs are still limited because of many imperfections, e.g., uncertainties in the input sources such as emission inventories, wind fields, boundary conditions, as well as insufficient knowledge about the atmospheric dynamics themselves. All these will mislead the CTM prediction constantly, or in a systematic way. In this paper, an approach based on machine learning is applied to predict model bias in the CTM. It is then combined with the CTM for formulating a hybrid forecast system. To our knowledge, it is the first time that machine learning methods are used in this way. The hybrid system is tested on the fine particular matter (PM_2.5) prediction in Shanghai, China. The results showed that machine learning can be an effective tool to improve the accuracy of CTM prediction. In case of short term PM_2.5 forecast (forecast length less than 12 h), statistical metrics of the root mean square error, mean absolute error, mean absolute percentage error as well as the air quality rank predicted accuracy all show the forecast skill is remarkably improved; while for long term prediction, improvement is not ensured.