A comparison of correlation-length estimation methods for the objective analysis of surface pollutants at Environment and Climate Change Canada

ABSTRACTAn objective analysis is one of the main components of data assimilation. By combining observations with the output of a predictive model we combine the best features of each source of information: the complete spatial and temporal coverage provided by models, with a close representation of the truth provided by observations. The process of combining observations with a model output is called an analysis. To produce an analysis requires the knowledge of observation and model errors, as well as its spatial correlation. This paper is devoted to the development of methods of estimation of these error variances and the characteristic length-scale of the model error correlation for its operational use in the Canadian objective analysis system. We first argue in favor of using compact support correlation functions, and then introduce three estimation methods: the Hollingsworth–Lonnberg (HL) method in local and global form, the maximum likelihood method (ML), and the diagnostic method. We perform one-dim...