Application of a Backwards Lagrangian Stochastic Model to Estimate Particulate Matter Emissions from Lidar Data

Advancements in elastic light detection and ranging (Lidar) data analysis have made possible the conversion of return signals due to scattering by aerosols to particulate matter (PM) concentrations. This has enabled the use of Lidar systems in PM emissions calculation. Bingham et al. (2009, J. Appl. Rem. Sens., 033510) describes the application of a mass balance technique to estimate emissions from a facility or operation. Additional techniques that utilize the PM calibrated Lidar data are being investigated for use in non-ideal measurement situations, such as limitations on scanning due to physical constraints and obstacles or U.S. Federal Aviation Authority restrictions. The authors are investigating the application of inverse modeling, which uses measured pollutant concentrations resulting from the activity (downwind minus upwind) and an atmospheric dispersion model to calculate the emission rate input into the model that results in the best fit between measured and modeled concentration impacts. Lagrangian stochastic (LS) models, or random flight models, have been shown to simulate atmospheric dispersion and transport fairly well in the surface layer of the atmosphere. A LS model simulates the motion of numerous particles (marked fluid elements or particles) in a fluid based on the fluid's transport and dispersion characteristics plus randomized variations. Several gaseous air pollutant emissions studies have used LS models in inverse modeling in agricultural settings over the past decade. Unlike most gases, particles may have significant settling and deposition due to gravitation forces depending on particle size and density. This may be an important factor, especially in plumes initially dominated by large particles (>~2 μm in diameter), such as in agriculture. Estimates of PM emissions, therefore, should account for particle deposition velocity (v_s). In this work we will convert a forward LS model given by Wang et al. (2008, Trans. ASABE, 1763-1774) that accounts for v_s into a backward LS (bLS) model for comparison against the WindTrax bLS model (www.thunderbeachscientific.com) that has proven effective at estimating emissions through inverse modeling but does not account for v_s. A forward LS model simulates particle motion forward in time from a source in small time steps dt, while a bLS model simulates motion backward in time from a measurement location toward the source as shown in Figure 1. Differences between estimated emissions from the two bLS models and the mass balance technique will be examined based on Lidar data previously collected from multiple agricultural PM sources. Figure 1. A lidar image showing a plume and an example backward trajectory for a single particle from a single pixel over two time steps.