Comparison of Different Methods to Parameterize Errors in Inverse Modeling of Atmospheric Emissions

Abstract Inverse modeling has been used to complement and validate the inventory-based estimation of atmospheric emission, and provide crucial temporal information on emissions when an unknown source. It requires the environmental observations and the simulations by atmospheric dispersion models (ADMs) as the input, as well as the a priori emission information but is not mandatory. The parameterization of the errors in observation, ADM, and prior considers the corresponding uncertainty, which affects the performance of an inverse model with respect to the continuity and smoothness in the estimation. Three strategies were investigated for this task in this study, assuming the homologous errors, site-dependent errors, and spatiotemporal correlated site-dependent errors. The standard Tikhonov method and the joint estimation method were used to include these strategies and estimate the emission during a field experiment. The results demonstrate that assuming homologous errors brings a simple and effective parameterization, although the temporal oscillatory in estimation. The strategy of site-dependent errors improves the continuity of estimation with the cost of reduced fit to the observations. Further considering the spatiotemporal correlations among sites leads to a smoother temporal variation of emissions, which achieves the best agreement and correlation with observations based on the joint method.