Theoretical evaluation of a method for locating gaseous emission hot spots

This paper describes and theoretically evaluates a recently developed method that provides a unique methodology for mapping gaseous emissions from non-point pollutant sources. The horizontal radial plume mapping (HRPM) methodology uses an open-path, path-integrated optical remote sensing (PI-ORS) system in a horizontal plane to directly identify emission hot spots. The radial plume mapping methodology has been well developed, evaluated, and demonstrated. In this paper, the theoretical basis of the HRPM method is explained in the context of the method's reliability and robustness to reconstruct spatially resolved plume maps. Calculation of the condition number of the inversion's kernel matrix showed that this method has minimal error magnification (EM) when the beam geometry is optimized. Minimizing the condition number provides a tool for such optimization of the beam geometry because it indicates minimized EM. Using methane concentration data collected from a landfill with a tunable diode laser absorption spectroscopy (TDLAS) system, it is demonstrated that EM is minimal because the averaged plume map of many reconstructed plume maps is very similar to a plume map generated by the averaged concentration data. It is also shown in the analysis of this dataset that the reconstructions of plume maps are unique for the optimized HRPM beam geometry and independent of the actual algorithm applied.