A percentile-based inverse modelling approach for enhanced source quantification using high-frequency concentration measurements

Atmospheric inverse modelling for source estimation typically relies on hourly-averaged concentration measurements, overlooking the rich information contained in real-world high-frequency data, largely due to the absence of suitable modelling frameworks. We present a novel inverse modelling approach that leverages this information by representing the full concentration probability distribution function (PDF) through concentration percentiles derived from a left-shifted clipped-gamma parameterisation, requiring only the mean and variance of concentration, with intermittency parameterised empirically. Mean and variance are modelled using Lagrangian and Eulerian approaches, respectively, within a backward dispersion framework to efficiently compute percentiles for integration within a Bayesian inversion. Applied to a controlled methane release field experiment at a geological carbon capture and storage site, higher-order percentiles improve emission rate estimates and reduce source location uncertainty compared to mean-based inversions, though location accuracy declines slightly; lower-order percentiles worsen performance, likely due to background methane variability. Percentiles inherently encapsulate mean concentration, so combining both offers no added benefit. The primary limitation lies in variance prediction, which is more uncertain and sensitive to turbulence than mean modelling. Exploiting high-frequency data beyond means, this percentile-based inverse modelling (PBIM) approach offers a practical path to improved source estimation, warranting further validation with longer-term, spatially extensive datasets or tracer releases with minimal background interference. • A novel inverse modelling approach for source quantification is introduced that represents the full concentration probability density function using percentiles • The approach exploits the full information content of high-frequency concentration measurements • Application to a methane emission source demonstrates that higher-order concentration percentiles yield more accurate emission estimates and reduced directional uncertainty, outperforming traditional mean-based inversions • This approach offers a practical route to improved source estimation, assuming the concentration variance is represented adequately