  In response to global concerns regarding air quality and the environmental
impact of greenhouse gas emissions, detecting and quantifying sources of
emissions has become critical. To understand this impact and target mitigations
effectively, methods for accurate quantification of greenhouse gas emissions
are required. In this paper, we focus on the inversion of concentration
measurements to estimate source location and emission rate. In practice, such
methods often rely on atmospheric stability class-based Gaussian plume
dispersion models. However, incorrectly identifying the atmospheric stability
class can lead to significant bias in estimates of source characteristics. We
present a robust approach that reduces this bias by jointly estimating the
horizontal and vertical dispersion parameters of the Gaussian plume model,
together with source location and emission rate, atmospheric background
concentration, and sensor measurement error variance. Uncertainty in parameter
estimation is quantified through probabilistic inversion using gradient-based
MCMC methods. A simulation study is performed to assess the inversion
methodology. We then focus on inference for the published Chilbolton dataset
which contains controlled methane releases and demonstrates the practical
benefits of estimating dispersion parameters in source inversion problems.
