Here, u is the wind vector, K is a diagonal matrix whose elements are the diffusion coefficients, and s is a source term. This PDE models the atmospheric transport of the concentration of some contaminant c as a function of time and space. Solving this equation gives a concentration field that can be used in conjunction with CMS measurements to detect methane leaks. The traditional methods used to solve this PDE are grid-based CFD methods that couple (1) with the Navier-Stokes equations and, potentially, a turbulence model. These conventional methods pose two problems for this application. First, the inverse problem requires that the forward model is run many times with different parameters, and CFD models are too slow for the inversion to be performed as regularly as is needed for near real-time applications. Second, we are often only interested in simulating concentrations at specific points in space where sensors are located and any extra computation is wasted. Grid-based methods cannot accommodate this. Many inversions use the Gaussian plume atmospheric dispersion model e.g., ; ; ; , which is easy to implement and computationally inexpensive. The Gaussian plume model is an analytic solution to (1) under a number of simplifying assumptions (see Appendix A for details). One assumption made in the derivation of the plume model is that wind conditions remain constant long enough for the concentration field to reach a steady state. This assumption is frequently violated in practice and, when temporal averaging is applied to satisfy it, eliminates the high frequency elements of the signal that are seen in measurements and caused by variable wind conditions. Although the plume model sacrifices accuracy in comparison to a CFD model, it is computationally cheap and able to be easily run on a laptop.