Thomas K. Flesch

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

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 ...

Deducing Ground-to-Air Emissions from Observed Trace Gas Concentrations: A Field Trial

The gas emission rate Q from an artificial 36-m2 surface area source was inferred from line-average concentration CL measured by an open-path laser situated up to 100 m downwind. Using a backward Lagrangian stochastic (bLS) model, a theoretical CL/Q relationship was established for each experimental trial by simulating an ensemble of fluid-element paths arriving in the laser beam under the prevailing micrometeorological conditions. The diagnosed emission rates (QbLS) were satisfactory for trials done when Monin‐Obukhov similarity theory gave a good description of the surface layer, but were poor during periods of extreme atmospheric stability ( | L | # 2 m) and transition periods in stratification. With such periods eliminated, the average value of the 15-min ratios QbLS/Q over n 5 77 fifteen-minute trials spanning 6 days was 1.02. Individual 15-min estimates, however, exhibited sizable variability about the true rate, with the standard deviation in QbLS/Q being sQ/Q 5 0.36. This variability is lessened (sQ/Q 5 0.22, n 5 46) if one excludes cases in which the detecting laser path lay above or immediately downwind from the source—a circumstance in which the laser path lies at the edge of the gas plume.

A two-dimensional trajectory-simulation model for non-Gaussian, inhomogeneous turbulence within plant canopies

We report a two-dimensional (alongwind u, vertical w) trajectory-simulation model, consistent with Thomsons (1987) well-mixed criteria, that allows for the non-Gaussian turbulence typical of flow within a plant canopy. The effect of non-Gaussian turbulence was examined by formulating a non-Gaussian u, w joint probability density function (PDF) as the sum of two Gaussian joint-PDFs. The resultant PDF reproduced the desired means, variances, skewnesses, and kurtoses, and the correct covariance. In prediction of the location of maximum concentration downwind of a line source in homogeneous, slightly non-Gaussian turbulence, it proved advantageous to incorporate skewness and kurtosis. However, in the case of inhomogeneous, highly non-Gaussian turbulence, the addition of skewness and kurtosis in the model resulted in substantially worse agreement with measurements than the results of the model using Gaussian PDFs. This may be due to inaccuracy in our PDF formulation. Dispersion predictions from the model with Gaussian PDFs were generally not statistically different from measurements. These results indicate that a two-dimensional Gaussian trajectory-simulation approach is adequate to predict mean concentrations and fluxes resulting from sources within plant canopies.

Estimating Spore Release Rates Using a Lagrangian Stochastic Simulation Model

Abstract Practical problems in predicting the spread of plant diseases within and between fields require knowledge of the rate of release Q of pathogenic spores into the air. Many plant pathogenic fungus spores are released into the air from plant surfaces inside plant canopies, where they are produced, or from diseased plant debris on the ground below plant canopies, where they have survived from one growing season to the next. There is no direct way to specify Q for naturally released microscopic fungus spores. It is relatively easy to measure average concentrations of spores above a source, however. A two-dimensional Lagrangian stochastic (LS) simulation model for the motion of spores driven by atmospheric turbulence in and above a plant canopy is presented. The model was compared 1) with measured concentration profiles of Lycopodium spores released from line sources at two heights inside a wheat canopy and 2) with concentration profiles of V. inaequalis ascospores measured above ground-level area sour...

Flow Boundaries in Random-Flight Dispersion Models: Enforcing the Well-Mixed Condition

Abstract Lagrangian stochastic (LS) dispersion models often use trajectory reflection to limit the domain accessible to a particle. It is shown how the well-mixed condition (Thomson) can he expressed in the Chapman-Kolmogorov equation for a discrete-time LS model to provide a test for the validity of a reflection algorithm. By that means it is shown that the usual algorithm (perfect reflection) is exactly consistent with the wmc when used to bound Gaussian homogeneous turbulence, but that no reflection scheme can satisfy the wmc when applied at a location where the probability distribution for the normal velocity is asymmetric, or locally inhomogeneous. Thus, there is no well-mixed reflection scheme for inhomogeneous or skew turbulence.

Turbulent Schmidt number from a tracer experiment

Measurements of pesticide emission from a bare soil were used to calculate the turbulent Schmidt number (Sc): the ratio of eddy diffusivity for momentum (eddy viscosity) to the diffusivity for tracer mass. The value of Sc has implications for the measurement of trace gas emissions, and there is a broad range of reported values for the atmospheric surface layer. During our experiment Sc averaged 0.6, with large variability between observation periods. The standard deviation in Sc was 0.31, with no obvious correlation to atmospheric conditions. Some of this variability is due to measurement uncertainty, but we believe it also reflects true variability in Sc. We show that flux-gradient formula, which assume higher values of Sc, underestimate the true tracer emission rate Q. We also show that a dispersion model with Sc = 0.6, does better at inferring Q than a model with Sc = 0.45. Published by Elsevier Science B.V.

Micro-meteorological methods for estimating surface exchange with a disturbed windflow

This paper examines the accuracy with which trace gas fluxes, from a source that disturbs the local wind and microclimate, may be estimated from measured concentrations, above or downwind from the source. The familiar flux‐gradient methods, even if carefully applied within the near-surface constant-flux-layer, nevertheless posit horizontally-uniform wind and stability. Errors result if the windflow is actually advective (i.e. disturbed), so that its state is evolving in the alongwind direction. We take as an illustration the case of a gas evaporating uniformly .Q; kg m 2 s 1 / from a small lagoon. We modify the Rao‐Wyngaard‐Cote local advection model, verify it against existing observations of disturbed flows, then calculate the fields of windspeed, temperature and tracer concentration over land and lake. From these “data” we calculate several estimates of the (known) source strength Q. Results by integration of the horizontal flux .Q IHF / prove the most satisfactory, followed by those using a source‐receptor relationship based on a backward Lagrangian stochastic method .Q bLS /. Flux‐gradient estimates Q FG can be very seriously in error, and should only be used with caution in disturbed flow. These findings have generality beyond the specific case of a lagoon flow.

Deducing ground-to-air emissions from observed trace gas concentrations: A field trial with wind disturbance

Inverse-dispersion techniques allow inference of a gas emission rate Q from measured air concentration. In “ideal surface layer problems,” where Monin–Obukhov similarity theory (MOST) describes the winds transporting the gas, the application of the technique can be straightforward. This study examines the accuracy of an ideal MOST-based inference, but in a nonideal setting. From a6m 6 m synthetic area source surrounded by a 20 m 20 m square border of a windbreak fence (1.25 m tall), Q is estimated. Open-path lasers gave line-averaged concentration CL at positions downwind of the source, and an idealized backward Lagrangian stochastic (bLS) dispersion model was used to infer QbLS. Despite the disturbance of the mean wind and turbulence caused by the fence, the QbLS estimates were accurate when ambient winds (measured upwind of the plot) were assumed in the bLS model. In the worst cases, with CL measured adjacent to a plot fence, QbLS overestimated Q by an average of 50%. However, if these near-fence locations are eliminated, QbLS averaged within 2% of the true Q over 61 fifteen-minute observations (with a standard deviation Q/Q 0.20). Poorer accuracy occurred when in-plot wind measurements were used in the bLS model. The results show that when an inverse-dispersion technique is applied to disturbed flows without accounting for the disturbance, the outcome may still be of acceptable accuracy if judgment is applied in the placement of the concentration detector.

Methane and ammonia emissions from a beef feedlot in western Canada for a twelve-day period in the fall

Commercial feedlot operations are becoming a mainstay in the Canadian beef industry. These large operations that typically raise thousands of animals at a time represent a large localized source of methane (CH4) and of atmospheric pollutants such as ammonia (NH3) and particulate matter. An inverse dispersion model was utilized to calculate CH4 and NH3 emissions from a commercial cattle feedlot and an adjacent runoff retention pond. The feedlot measurements were collected within the interior of the feedlot enabling a near continuous emissions record over the 12 d of the study period. Average daily emission estimates of CH4 and NH3 were 323 and 318 g animal-1 d-1, respectively. The CH4 emissions represent 4% of the gross energy intake (GEI) and NH3 emissions represent 72% of the total N intake. Emissions from the runoff retention pond associated directly with the feedlot operation were approximately 2.7 and 2% of the daily average feedlot emissions of CH4 and NH3, respectively. Key words: Methane, ammonia, ...

Inverse-Dispersion Calculation of Ammonia Emissions from Wisconsin Dairy Farms

Ammonia (NH3) emissions were determined from three commercial dairy farms in the north-central U.S. The dairies employed similar management, having naturally ventilated free-stall barns where barn waste is scraped and transferred to outdoor lagoons. Three potential emission sources were distinguished at each farm: barns, lagoons, and sand separators. A backward Lagrangian stochastic (bLS) inverse-dispersion technique was used to measure emissions. Total farm emission varied from 15 to 330 kg NH3 d-1 depending on the farm and season. Inter-farm variability was largely explained by farm size (animal population). Emissions showed variability on seasonal and daily scales: summer rates were roughly ten times those of the winter, and mid-day rates were approximately three times those at night. The lagoons emitted 37% to 63% of the farm total during summer and fall, but they were frozen in winter and their emissions were immeasurably small. The yearly per-animal emissions from the three dairies were estimated at 20, 19, and 20 kg NH3 animal-1 year-1. Regarding the measurement technique, bLS proved well-suited to our study. With modest resources we were able to measure emissions from the variety of sources at each farm and quickly move between farms. Overall agreement in measured emissions at the three farms, together with a general harmony of our measurements with those from previous studies, provides a measure of confidence in the measurement strategy.