Backward-Time Lagrangian Stochastic Dispersion Models and Their Application to Estimate Gaseous Emissions

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  • a Division of Meteorology, Department of Geography, University of Alberta, Edmonton, Alberta, Canada
  • | b Defence Research Establishment Suffield, Medicine Hat, Alberta, Canada
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Abstract

“Backward” Lagrangian stochastic models calculate an ensemble of fluid element (particle) trajectories that are distinguished by each passing through an observation point. As shown, they can be faster and more flexible in calculating short-range turbulent dispersion from surface area sources than “forward” models, which simulate trajectories emanating from a source. Using a backward model, one may catalog a set of “touchdown” points (where trajectories reflect off the ground) and vertical touchdown velocities w0 of particles “on their way to” a sensor location. It is then trivial to deduce the average concentration resulting from a surface source using the touchdown catalog: by summing the reciprocal of w0 for touchdowns occurring within the source boundary. An advantage of this methodology is that while forward model trajectories are linked to a specific source, backward trajectories have no such dependence. In horizontally homogeneous flow, a “library” of touchdown catalogs (for representative surface roughnesses and atmospheric stabilities) would allow concentration (at a given height) to be rapidly calculated at any location from any uniform surface source.

A “well-mixed” backward model is exploited to calculate the touchdown points of particles passing over a small plot on their way to an observation tower and it is shown how to use those data to estimate the plot emission rate from a single measurement of average concentration, wind speed, and wind direction on the tower. The method was evaluated using 36 field experiments. Predicted emission rates using the backward method agreed well with mass balance estimates.

Abstract

“Backward” Lagrangian stochastic models calculate an ensemble of fluid element (particle) trajectories that are distinguished by each passing through an observation point. As shown, they can be faster and more flexible in calculating short-range turbulent dispersion from surface area sources than “forward” models, which simulate trajectories emanating from a source. Using a backward model, one may catalog a set of “touchdown” points (where trajectories reflect off the ground) and vertical touchdown velocities w0 of particles “on their way to” a sensor location. It is then trivial to deduce the average concentration resulting from a surface source using the touchdown catalog: by summing the reciprocal of w0 for touchdowns occurring within the source boundary. An advantage of this methodology is that while forward model trajectories are linked to a specific source, backward trajectories have no such dependence. In horizontally homogeneous flow, a “library” of touchdown catalogs (for representative surface roughnesses and atmospheric stabilities) would allow concentration (at a given height) to be rapidly calculated at any location from any uniform surface source.

A “well-mixed” backward model is exploited to calculate the touchdown points of particles passing over a small plot on their way to an observation tower and it is shown how to use those data to estimate the plot emission rate from a single measurement of average concentration, wind speed, and wind direction on the tower. The method was evaluated using 36 field experiments. Predicted emission rates using the backward method agreed well with mass balance estimates.

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