Keywords:Ensemble data assimilation, Snow model, Snow precipitation, Single observation experiment
Coupled numerical models address interactions between processes in the atmosphere, ocean, land surface, biosphere, chemistry, cryosphere, and hydrology. Including the interactions between such processes can potentially extend the predictability and eventually help in reducing the uncertainty of the prediction. Coupled data assimilation is a branch of data assimilation that deals with coupled modeling systems. In this article the fundamentals of coupled data assimilation are first described through a mathematical example of a model including two coupled components. Then, through a series of single observation experiments, we analyze the forecast error covariance and correlation structures using the Maximum Likelihood Ensemble Filter (MLEF) data assimilation system with coupled atmosphere-land surface Weather Research and Forecasting (WRF) model . The atmospheric WRF component has been coupled with two land surface models: Noah and Noah-MP. Two observation locations with different precipitation regimes have been considered. Through this study, we found that error covariance and correlation were dependent on both location and land surface scheme. Snow precipitation likely caused more complex structures in error covariances and correlations compared to the precipitation-free site. The employment of a more realistic snow model was found to reduce the error covariance and error correlation between the atmosphere and the soil in the coupled system. We also have demonstrated, for the first time in a data assimilation study, that correlation structures can be useful in understanding the physical meaning of the forecast error covariance and as a basis for selecting the most important forecast error covariance components for the coupled data assimilation system. Overall, the complexity and structure of ensemble-based forecast error covariance appears to be meaningful, which is encouraging for the future applications of coupled atmosphere – land surface data assimilation.