Evaluation of the Directional Derivative Approach for Timely and
Accurate Satellite-based Emission Estimation Using Chemical Transport
Model Simulation of Nitrogen Oxides
Abstract
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 NOx emissions using satellite-observed NO2
column amounts are proposed, leveraging external climatology of the
NOx:NO2 ratio and its directional derivative. These estimators are
evaluated within a WRF-CMAQ simulation of NOx by comparisons with the
model NOx 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
(RMSE). Lessons learned from this study using synthetic model data can
be readily applied to the usage of actual satellite observations for
emission estimation.