A Statistical Evaluation of WRF-LES Trace Gas Dispersion

In recent years, new measurement systems have been deployed to monitor and quantify methane emissions from the natural gas sector. Large-eddy simulation (LES) has complemented measurement campaigns by serving as a controlled environment in which to study plume dynamics and sampling strategies. However, with few comparisons to controlled-release experiments, the accuracy of LES for modeling natural gas emissions is poorly characterized. In this paper, we evaluate LES from the Weather Research and Forecasting (WRF) model against measurements from the Project Prairie Grass campaign, surface layer similarity theory, and the Gaussian Plume Model. Using WRF-LES, we simulate continuous emissions from an ensemble of 30 near-surface trace gas sources in two stability regimes: strong and weak convection. We examine the impact of grid resolutions ranging from 6.25 m to 52 m in the horizontal dimension on model performance. We evaluate performance in a statistical framework, calculating fractional bias and conductingWelch’s C-tests. WRF-LES accurately simulates observed surface concentrations at 100m and beyond under strong convection; the magnitude of factional bias is less than 30% for the moderateand fineresolution simulations. However, in weakly convective conditions with strong winds, WRF-LES substantially overpredicts concentrations – the magnitude of fractional bias often exceeds 30%, and all but one C-test fails. Despite the good performance of dispersion in the strongly convective atmosphere, we find that both the strongly and weakly convective boundary layers disagree with empirical wind and temperature Monin-Obukhov similarity theory profiles that are often used to evaluate LES within the atmospheric surface layer. 14


Introduction
respectively. These forcings and the coarse grid resolution are consistent with Weil et al. (2012). 145 The WCBL is forced with constant 10 m s −1 geostrophic winds, 0.1 W K −1 m −1 surface heat flux,  conditions, we include a trace gas absorbing plane 500 m upwind of each source. 165 After a two-hour spin-up, we sample trace gas fields and winds every second during a 10-minute 166 period, matching the PPG measurement period. From these concentration fields, we calculate 167 crosswind integrated concentration (CWIC) at a given radius as: where is the concentration at a cell and Δ is the arclength between cells. To account for the 169 different release rates used in PPG, CWIC calculations throughout this study are normalized by 170 emission rate , and this quantity is referred to as "concentration" though strictly speaking it is 171 a "normalized crosswind integrated concentration". In order to compare the medium and coarse 172 simulations to the PPG horizontal array measurements collected at a height of 1.5 m, concentration 173 profiles are extrapolated using a 5th-order polynomial fit to concentrations in the lowest 100 m. We aim to compare as many observations to WRF-LES concentration simulations as possible.

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In principle, this comparison would best be achieved by running one simulation for each controlled  These classes are traditionally delineated using wind speeds and solar radiation, but they can be 210 alternatively delineated using a roughness length and Obukhov length (Golder 1972 where is the emission rate, is the plume centerline height, and is the wind speed at the 225 plume centerline. The values of and are numerically computed based on MOST, and downwind 226 distance is implicitly a function of these variables. SLS theory is strictly valid for releases at a 227 height of 0 m, but it agrees well with the observations in this study (Appendix). As such, we use 228 SLS theory as a proxy for hypothetical observations, with * and that match those of the LES.

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Although SLS theory cannot be used to directly study the sensitivity of dispersion to source where is the wind speed at the source, is the vertical plume spread, and ℎ is the emission is calculated as: where averages are taken over the set of measurements or simulations. NMSE is calculated as: where ℎ is the mean horizontal wind speed, is the average potential temperature, * is the 352 kinematic heat flux divided by friction velocity, and is the von Kármán constant, taken to be 0.4.

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We calculate directly from LES wind fields and compare it to empirical profiles based on the 354 LES values of * and using the Dyer (1974) equations (Figure 6 a,b). At all three resolutions, 355 the LES-based non-dimensional wind shear profiles in the SCBL agree well with one another.

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In this study, we assess the accuracy of WRF-LES for simulating trace gas dispersion in three 375 strongly convective and three weakly convective boundary layers where grid resolution is varied. 376 We compare 30 plumes within each simulation to horizontal and vertical measurements from