Reﬁning an Inverse Dispersion method to Quantify Gas Sources on Rolling Terrain

In this thesis, an indirect methodology for estimating gas emission rate to the atmosphere from small surface point or area sources is investigated. More speciﬁcally, the thesis is a study of an “inverse dispersion” method which has become widely used for estimating ground-air gas ﬂuxes ( Q ) from agricultural sources. Like all inverse dispersion methods, the “bLS” (for “backward Lagrangian stochastic”) method hinges on the placement of concentration detectors upwind and downwind from the source, allowing to determine the rise (Δ c ) in mean gas concentration for which it is responsible. Also in common with the norm for “inverse dispersion”, a mathematical model of atmospheric dispersion is invoked so that the wanted source strength Q can be inferred from the measured concentration rise Δ c , which however must be supplemented with relevant meteorological information (such as mean wind direction and speed, and thermal stratiﬁca-tion). In the case of “‘bLS,” the dispersion model is a backward Lagrangian stochastic model, which computes ﬂuid element trajectories backwards in time and space from their arrival at the concentration detectors to their earlier point or points of contact with the source or sources. An assumption inherent to most implementations of inverse dispersion method is that wind statistics in the atmospheric surface layer are horizontally-homogeneous (i.e. wind statistics vary only with height). It is of interest to establish how robust the inverse dispersion approach may be, when applied to quantify sources on land surfaces that are patently not ﬂat and uniform – complications that result in horizontal variability of the wind statistics. In that context, this thesis analyses a trace gas dispersion experiment with multiple ﬁxed point sources arrayed on gently rolling terrain, to investigate the performance of inverse dispersion using a well-ii I Abstract It is common practice to estimate ground-air gas ﬂuxes ( Q ) from agricultural sources by inverse dispersion, placing detectors upwind and downwind from the source to determine mean gas concentration ( c ). Often however, topography compromises an assumption that is (normally) inherent to the inverse dispersion methodology, namely that wind statistics in the atmospheric surface layer are “undisturbed” (i.e. horizontally-homogeneous). We analysed a trace gas dispersion experiment with multiple ﬁxed point sources on gently rolling terrain, to investigate the performance of inverse dispersion using a dispersion model (WindTrax) that (strictly) is appropriate only for the case of horizontally-homogeneous ﬂow. Despite the fact that measured mean wind speeds revealed spatial variation of order ± 10% over the site, results of the inversion to estimate source strength indicate that the unwanted impact of this moderate terrain on the idealized c − Q relationship can be compensated by – in eﬀect – postulating an undisturbed Monin-Obukhov ﬂow in a terrain following height coordinate, such that (e.g.) light paths of the line-averaging concentration detectors are treated as curves having everywhere the true height above ground. This strategy permits easy extension of a well proven method to conditions that, `a priori, had been considered unsuitable. We also used the measurements to study the inﬂu-ence (on the accuracy of retrieved Q ) of discretionary elements of inverse dispersion procedure. These sensitivity studies addressed optimal placement of detectors relative to the source(s); data rejection criteria, such as threshold values for the friction velocity and the Obhukhov length; exclusion of mean wind directions that confound the “upwind/downwind” concentration diﬀerences; and the impact of alternative spatial representations of the source, supposing one had but partial information in that regard.