Evaluation of the Directional Derivative Approach for Timely and Accurate Satellite-Based Emission Estimation Using Chemical Transport Model Simulation of Nitrogen Oxides

The directional derivative approach (DDA) has the potential to rapidly and accurately quantify emission distributions based on the directional derivative of satellite-observed column amounts with respect to the horizontal wind. From the first principles, this paper derives the DDA emission estimators with a range of complexity by vertically integrating the 3D continuity equation and simplifying the results under several assumptions and approximations. The connection and difference between the DDA and a widely used divergence method for emission estimation are highlighted. A key difference is that the DDA integrates from the surface to an intermediate altitude instead of to the top of the observed column. This leads to the inherent background removal of the DDA, in contrast to the explicit background removal necessitated by the divergence method theory. Linear fittings are used to account for the effects of topography, chemical reactions, and retrieval biases. Realistic estimators of ${NO}_x$ emissions using satellite-observed ${\text{NO}}_2$ column amounts are proposed, leveraging external climatology of the ${NO}_x$:${NO}_2$ ratio and its directional derivative. These estimators are evaluated within a WRF-CMAQ simulation of ${NO}_x$ by comparisons with the model ${NO}_x$ emissions. The DDA estimators consistently outperform the divergence method estimator, and the DDA estimator that considers both topography and chemistry features the lowest root mean square error. Lessons learned from this study using synthetic model data can be readily applied to the usage of actual satellite observations for emission estimation.