Received 6 January 2016; accepted 13 February 2016; published 16 February 2016
Air pollutant emissions from concentrated animal feeding operations (CAFOs), such as large commercial cattle feedlots, are a major air quality concern because of their harmful effects on human health and the environment. Air pollutants emitted from cattle feedlots include ammonia (NH3)   , hydrogen sulfide (H2S)   , greenhouse gases (GHGs) such as nitrous oxide (N2O)  and methane (CH4)  , volatile organic compounds (VOCs)  , and particulate matter (PM)   . Assessing the potential impact of these air pollutants, individually or in combination, on downwind locations remains challenging because of several factors, including lack of accurate emission rate estimates and reliable emission estimation methods   . To address this, the US Environmental Protection Agency (EPA) initiated the National Air Emissions Monitoring Study (NAEMS) in 2005 as a 2-yr study to measure air pollutant emission rates at several participating CAFOs for development of new and improvement of existing emission estimation methods   . Beef cattle feedlots were not part of the NAEMS; in 2011, however, the EPA requested quality-assured PM and gaseous emission rates from CAFOs, which now included cattle feedlots, to supplement those collected through NAEMS  .
In large beef and dairy cattle feedlots, the animals are typically confined in open dirt lots. For these CAFOs, emission estimation is challenging because direct measurement of emission rates is often not feasible. Because the open dirt lots are exposed to and influenced by the outside environment, determining emission rates requires accounting for the temporal and spatial variability of emission rates, surface heterogeneity and local meteorology.
Several methods can be used to estimate pollutant emission rates from area sources, such as feedlots: these include micrometeorological techniques  , box models  , and inverse dispersion models  . The authors of the present study were involved in a large air quality project that included estimation of PM emission rates from a large commercial beef cattle feedlot in Kansas. The PM emission rates for the cattle feedlot studied were determined using several estimation methods, which included AERMOD, WindTrax and the flux-gradient technique, and estimates were already presented in published companion studies    . In Bonifacio et al.  , emission rates for total suspended particulates (TSP), PM with aerodynamic diameter ≤ 10 µm (PM10), and PM with aerodynamic diameter ≤ 2.5 µm (PM2.5) determined using the flux-gradient technique were presented. Compared to other previously published values for California and Texas feedlots, these determined emission rates were significantly lower than those reported by EPA  and Auvermann et al.  but were within range of others   .
The method applied in emission rate estimation is a critical factor that can contribute to differences among reported PM emission rates―others include feedlot management practices, PM sampling methods, and measurement designs (e.g., length of measurement period). In a companion study  , PM10 emission rates determined by AERMOD and WindTrax were already compared. Although it was found that AERMOD produced higher emission rates, a very high linearity (R2 ≥ 0.93) in calculated emission rates between AERMOD and WindTrax was observed, indicating the possibility of developing conversion factors  . In the present study, PM10 emission rates determined by WindTrax and the flux-gradient technique were compared using the same set of concentration and meteorological measurements employed in companion studies   . Effect of measurement heights used on emission estimation with each method was also verified. Similar to the previous study, the possibility of development of conversion factors between these two methods was explored.
2. Materials and Methods
The PM10 concentrations and meteorological conditions were measured at a commercial cattle feedlot in Kansas. From these field measurements, PM10 emission rates were calculated with WindTrax via inverse dispersion analysis, and with the flux-gradient technique using estimated vertical PM10 concentration profiles and approximated PM10 eddy diffusivities.
2.1. Feedlot Description
The feedlot studied is generally rectangular in shape and has approximate dimensions of 0.5 and 1.7 km in east- west and north-south directions, respectively (Figure 1(a)). It has a total pen area of approximately 0.59 km2 (59 ha) designed for 30,000-head capacity. The feedlot is relatively flat, with median surface roughness of 4.0 cm   . Measurements used in comparing WindTrax and the flux-gradient technique were taken from May through September 2011. Information on feedlot management practices affecting pen conditions, such as manure scraping and water application, and meteorological conditions during this 5-month period were presented in Bonifacio et al.  .
2.2. Field Instrumentation
A three-dimensional sonic anemometer (Campbell Scientific, Inc., Logan, UT) was installed at a 5.3-m tower for measurement of micrometeorological conditions at the feedlot. Eddy covariance measurement was recorded at 15-min intervals and included measured variances and covariances of the three wind velocity components (ux, uy, uz) and air temperature (T). Using formulations presented by Flesch et al.  , corresponding friction velocity (u*), Monin-Obukhov length (L) and surface roughness (zo) were first computed in 15-min intervals before being integrated into hourly values.
Measurements of PM10 concentrations were conducted at two locations simultaneously: 1) within the feedlot, approximately 400 and 200 m from the feedlot’s north and west edges, respectively; and 2) at the sampling site north (5 m away from the fenceline) or south (800 m away from the fenceline) edge of the feedlot if the wind was coming from the north or south, respectively (Figure 1(a)). In computing net PM10 concentrations, measurement within the feedlot was used as downwind concentration and measurement at either north or south sampling site was used as upwind concentration, depending on wind direction. The PM10 concentrations within the feedlot were measured at four sampling heights: 2.0, 3.81, 5.34, and 7.62 m above the feedlot surface (Figure 1(b)). The PM10 concentration at the upwind sampling site was measured at the 2.0-m height only due to limited equipment availability. The PM10 concentrations were measured using tapered element oscillating microbalance (TEOM) samplers (series 1400a, Thermo Fisher Scientific, East Greenbush, NY), a US EPA federal equivalent method for determining PM10 concentrations (designation No. EQPM-1090-079). Monthly routine maintenance (i.e., inlet cleaning, flow audit, and leak test) was performed on TEOM PM10 samplers to ensure quality of data collection. The TEOMs were operated to record PM10 concentrations at 20-min intervals. The 20-min downwind and upwind concentrations were integrated into hourly averages before computing net hourly PM10 concentrations. Calculation of PM10 emission rates were based on hourly data points that had measured downwind and upwind concentrations and positive calculated net concentrations.
WindTrax is based on a reduced transport equation given by:
where the overall mass transport for concentration, C, is defined by convective mass transport in all directions (x, y, z) with corresponding velocity components held constant, and an accumulation term (¶C/¶t)  . The method selected by the developers of WindTrax to solve Equation (2) is the backward Lagrangian stochastic (bLS) approach that describes the evolution of particle position and particle velocity in a backward time frame. The derivation of concentration equations using the bLS approach is explained in detail by Flesch et al.  and Flesch and Wilson  .
WindTrax has an interface that enables mapping of the area source of interest and sampler locations using aerial image files  . The studied feedlot was mapped using available satellite imagery (MapQuest.com, Inc.). In this study, WindTrax simulation inputs included measured hourly net PM10 concentrations and meteorological parameters. From the meteorological inputs, WindTrax estimates other variables required in parameterization of the atmospheric surface layer based on formulations described in Crenna  and Flesch et al.  . In the simulation, the number of particle released was set to 50,000, which is the default value  . The PM10 emission rates calculated with WindTrax were also screened based on criteria described by Flesch et al.  .
Figure 1. Field instrumentation: (a) location of sampling site within the feedlot, and (b) sampling heights for tapered element oscillating microbalance (TEOM) PM10 samplers.
Measurement periods with very strong atmospheric stability (|L| < 10 m), low wind speed (u* < 0.15 m/s), or unrealistic wind profile (zo > 1 m) were considered unreliable and therefore not included in the comparison.
WindTrax can calculate emission rates using one or more concentration measurements  . Use of concentration measurements from several heights and locations, referred to as “overdetermined” simulation, is described to reduce the influence of concentration measurement errors on emission estimation, with the calculated emission rate the best fit for the given set of concentrations   . In the present study, PM10 emission rates determined by WindTrax using single-height and multiple-height measurements were examined. But in comparing WindTrax and the flux-gradient technique, only the multiple-height measurements were used.
In McGinn et al.  , PM10 emissions from Australian cattle feedlots was determined using a version of WindTrax modified to account for effects of gravitational settling on particle motion; however, this modified version still has to be made public. In the present study, the latest WindTrax version available (18.104.22.168, www.thunderbeachscientific.com) was used. Based on a companion study that used AERMOD  , neglecting gravitational settling underestimated PM10 emission rates by 4%.
2.4. Flux-Gradient Technique
For the flux-gradient technique, PM10 emission rate (Q, µg/m2∙s) was calculated as:
where KPM is PM10 eddy diffusivity (m2/s), Cm is measured net PM10 concentration (µg/m3), and dCm/dz is vertical PM10 concentration gradient (µg/m3-m)   . The vertical concentration gradient, dCm/dz, was the derivative of the regression equation derived for sampling heights with concentration measurements  . In Bonifacio et al.  , suitability of the flux-gradient technique in determining PM10 emissions from cattle feedlots had been verified using the criterion presented by Lilly  . Based on ratios of particle relaxation times calculated for different PM sizes to Lagrangian time scales measured at the studied feedlot, feedlot PM with aerodynamic diameter < 35 µm is essentially governed by eddy diffusion  , and thus, suggesting suitability of the flux- gradient technique for PM emissions within this size range.
The KPM was determined from eddy diffusivity for momentum, Km (m2/s), and Schmidt number, Sc (Equation (3))   .
The Sc was set to 0.63, which was the overall value determined for PM10 emissions at the studied feedlot that had hourly median Sc ranging from 0.40 to 1.23  . The Km was given by:
where zm is mean geometric height based on heights with PM10 concentration measurements, and is a nondimensional correction parameter that accounts for atmospheric stability effects  . Prueger and Kustas  provided a summary of different formulations that can be used in calculating. With a general expression given by:
four sets of formulations for were used in this study, with values for a and b summarized in Table 1. Selection of these formulations were based on its appropriateness for representing the feedlot surface: 1) Hogstrom  applies for multiple surface from oceans to forest and was the one used in the companion studies   ; 2) Flesch et al.  is the one implemented in WindTrax; 3) Dyer and Hicks  was derived for plowed field (i.e., with a loose surface layer like that of the feedlot surface); and 4) Hogstrom  has been used in a previous cattle feedlot study  .
For the flux-gradient technique, two screening criteria were implemented. The first criterion required that the corresponding fetch of the uppermost sampling height (7.62-m) fall within the feedlot boundary to ensure that
Table 1. Values of parameters a and b in calculating the nondimensional correction parameter for the flux-gradient technique.
calculated emission rates represented PM10 emitted at the feedlot only and not from outside sources. Calculation of fetch was based on Hsieh et al.  as previously implemented in companion studies   . The second criterion described the vertical concentration profiles appropriate for the flux-gradient technique, such that PM10 concentration should be linear and decreasing with the logarithm of height. Linearity between PM10 concentration and logarithm of height was assessed in terms of Pearson correlation. Preliminary analyses showed that increasing the Pearson correlation criterion lowered the difference in calculated PM10 emission rates between WindTrax and the flux-gradient technique but greatly decreased the number of hourly data points for comparison. With the flux-gradient technique producing higher emission rates, Pearson correlation criteria of 0.75, 0.85, 0.95, and 0.975 resulted to differences of 31%, 28%, 20%, and 19%, respectively, in calculated PM10 emissions between the two methods based on 228, 184, 104, and 58 hourly data points, respectively. Based on these results, a Pearson correlation criterion of 0.95 was implemented for the flux-gradient technique.
2.5. Data Analyses
In this study, analyses include: 1) for each emission estimation method, comparison of PM10 emission rates derived using data sets that differed in heights and number of heights included (Table 2); and 2) comparison of PM10 emission rates calculated with WindTrax and the flux-gradient technique. For WindTrax, PM10 emission rates estimated using single-height measurements (i.e., data sets 7 and 8) was also verified. Linear regression analyses were performed in comparing any two PM10 emission rate estimates. In addition, paired t-test was done when comparing PM10 emission rates of WindTrax and the flux-gradient technique. In the comparison, a 5%- significance level was applied. For hourly net PM10 concentrations, overall values were reported as averages. But due to its skewed and asymmetric distributions, PM10 emission rates were reported as medians.
3. Results and Discussion
A total of 74 hourly data points passed the screening criteria defined for both methods and was included in all data sets used in the comparisons (Table 2). Based on calculated L, 70 of these data points had unstable atmospheric conditions. In terms of time of the day, numbers of hourly data points were 7, 20, 27, and 20 for the 0100 h to 0600 h, 0700 h to 1200 h, 1300 h to 1800 h, and 1900 h to 2400 periods, respectively.
3.1. Net PM10 Concentrations
Hourly average net PM10 concentrations are shown in Figure 2. The PM10 concentrations at all four sampling heights exhibited diurnal trends, with the highest concentrations measured during the early evening period, which started to increase at 1900 h and ended at 2300 h, and the lowest during early morning period (0200 h to 0300 h) (note: no data point for 0400 h and 0500 h). From the 74 hourly data points, average net PM10 concentrations were 305 ± 351, 189 ± 194, 142 ± 145, 107 ± 117 µg/m3 for 2.0-, 3.81-, 5.34-, and 7.62-m heights. As shown in Figure 3, PM10 concentration had a very strong linear relationship (R2 = 0.98) with the logarithm of sampling height (note: for illustration purposes, median concentrations and corresponding upper and lower standard deviations were used). On average, PM10 concentration decreased by 34 ± 41 µg/m3 for every 1 m increase in height. Within the day, the highest vertical PM10 concentration gradient was measured from 1900 h to 2000 h, in which the concentration decreased by 103 ± 100 µg/m3 for every 1 m increase in height, whereas the
Table 2. Description of data sets used in PM10 emission rate estimation using WindTrax and the flux-gradient technique.a
a. For WindTrax only.
Figure 2. Hourly average net PM10 concentrations for the four measurement heights from May through September 2011 (n = 74). Error bars represent standard deviations.
Figure 3. Plot of net PM10 concentrations against the logarithm of measurement heights (n = 74). Error bars represent upper and lower standard deviations.
lowest was measured from 0100 h to 0300 h (8 ± 1 µg/m3∙m).
3.2. WindTrax-Based PM10 Emission Rates
Ranges of hourly PM10 emission rates for the eight data sets are plotted in Figure 4. Diurnal trend in calculated PM10 emission rates was observed for all data sets, with the highest PM10 emission rates calculated for the1900 h to 2200 h period (47 to 128 µg/m2∙s), followed by the 1400 h to 1500 h period (50 to 80 µg/m2∙s). Based on overall median hourly values, highest PM10 emission rates were obtained with data set 8 (i.e., 2.0-m height only), with a value of 37 µg/m2∙s, followed by data sets 5, 6, 3, and 1 with values of 34.8, 33.6, 32.8, and 32.6 µg/m2∙s, respectively. On the other hand, the lowest PM10 emission rates were calculated using data sets 2, 4, and 7, with overall median values ranging from 29.1 to 30.5 µg/m2∙s. These results indicate that use of the 2.0-m height, which was the lowest sampling height, in determining hourly PM10 emission rates with WindTrax led to emission estimates higher by almost 27%.
Slopes and R2 values from regression analyses are summarized in Table 3. For WindTrax, high linearity was observed between any pair of data sets, with R2 values ranging from 0.88 to 1.00. It was observed that the highest linearity was determined when comparing any two data sets as long as they had the same lowest measurement height―e.g., data sets 3 and 1 both with the lowest height at 2.0 m, data sets 4 and 2 both with the lowest
Figure 4. Hourly median PM10 emission rates calculated with WindTrax. Shaded area represents the range of emission estimates calculated using all the eight data sets.
Table 3. Linear regression between any two data sets (x, y) applied in WindTrax in terms of determined PM10 emission rates.a,b
aIn performing regression, data set x was treated as the independent variable and data set y as the dependent variable. bValues presented are slopes from regression analyses; values in parentheses are corresponding R2 values.
height at 3.81 m, etc. On the other hand, comparing any two data sets that differed in the lowest measurement height (i.e., one at 2.0 m while the other at 3.81-m) resulted to the lowest linearity. The percentage difference between any two data sets ranged from 0% to 18%, with an average of 8%. Similarly, the difference in calculated PM10 emission rates lowered when comparing any two data sets that had the same lowest measurement height whereas increased when the lowest measurement heights differed. In addition, the difference was largest when comparing the single-height measurement at 2.0-m (data set 8) to multiple-height measurements with the lowest height at 3.81-m (data sets 2 and 4) (Table 3).
3.3. Flux-Gradient Technique-Based PM10 Emission Rates
Plotted in Figure 5 are ranges of hourly PM10 emission rates calculated with the flux-gradient technique using the first six data sets (1 to 6, Table 2) and four fm formulations (i.e., total of 24 data set-fm formulation combinations). Similarly, a diurnal trend in calculated PM10 emission rates was observed for all data set-fm formulation combinations, with the highest emission rates calculated for the 1900 h to 2200 h (44 to 154 µg/m2∙s) and 1400 h to 1500 h (43 to 102 µg/m2∙s) periods. Unlike with WindTrax, however, exclusion of the 2.0-m height measurement in emission estimation led to a slightly different profile ? for combinations using data sets 2 and 4, the 1400 h to 1500 h period (43 to 96 µg/m2∙s) had higher PM10 emission rates than the 1900 to 2200 h period (44 to 81 µg/m2∙s). Comparing data sets 1 and 2, exclusion of the 2.0-m height slightly increased fm, and, equivalently, KPM (average of 32%) but significantly lowered the calculated vertical PM10 concentration gradient (36%). Between 1400 h to 1500 h and 1900 to 2200 h periods, it was the latter that had the largest decrease (48%) in concentration gradient―this explained why the 1900 h to 2200 h period no longer had the highest PM10 emission rates calculated for the day.
Overall median hourly PM10 emission rates for all data set-fm formulation combinations ranged from 27 to 47 µg/m2∙s, with the highest values derived when using data set 3―i.e., with the 2.0-m height (lowest) but without the 7.62-m height (highest). Among the four fm formulations, Hogstrom  produced the highest PM10 emissions rates whereas Flesch et al.  had the lowest. With respect to Hogstrom  , Flesch et al.  resulted to emission rates lower by 10% to 12% while the other two differed by 1% to 3% only. This was not surprising as a (Equation (5)) from Flesch et al.  had a setting less than half of those from the other three for unstable conditions (Table 1).
For the flux-gradient technique, slopes and R2 values from regression analyses are summarized in Table 4. Similar to WindTrax, the following applies for the flux-gradient technique: 1) high linearity (R2 > 0.74) was observed between any pair of data sets; 2) the highest linearity was obtained when comparing data sets with the same lowest measurement height (e.g., data sets 2 and 4, 1 and 5, etc.); and 3) the lowest linearity was determined when the data sets differed in the lowest measurement height (e.g., data sets 2 and 3, 3 and 4, etc.). Un-
Figure 5. Hourly median PM10 emission rates calculated with the flux-gradient technique. Shaded area represents the range of emission estimates calculated using all the eight data sets.
Table 4. Linear regression between any two data sets (x, y) applied in the flux-gradient technique in terms of determined PM10 emission rates.a,b
aIn performing regression, data set x was treated as the independent variable and data set y as the dependent variable; bValues presented are slopes from regression analyses; values in parentheses are corresponding R2 values.
like with WindTrax, use of different data sets, which varied in heights and number of heights included, led to larger difference (<56%) in calculated emission rates (Table 4). The lowest differences were obtained when comparing data sets 2 and 4 (2%), data sets 1 and 5 (4%), and data sets 3 and 6 (6%) whereas the largest when comparing data sets 3 and 4 (56%) and data sets 2 and 3 (40%). In general, relatively higher PM10 emission rates were calculated when: 1) changing the lowest measurement height from 3.81 m to 2.0 m (e.g., data sets 4 and 5) or including the 2.0-m height (e.g., data sets 1 and 2), equivalent to what was observed with WindTrax; and 2) changing the highest measurement height from 7.62 m to 5.34 m (e.g., data sets 5 and 6) or excluding the 7.62-m height (e.g., data sets 1 and 3). Results also indicate that the most critical heights when implementing the flux-gradient technique would be the lowest and the highest measurement heights used in approximating the vertical concentration gradient and KPM. As long as the lowest and the highest measurement heights remain the same, removal of heights in between would likely lead to very small change in estimated emission rate. Comparing data sets 2 and 4, 1 and 5, and 3 and 6, removal of other heights led only to 2%, 4%, and 6% change in calculated PM10 emission rates, respectively (Table 4).
3.4. Comparison of WindTrax and the Flux-Gradient Technique
Previous studies reported that between WindTrax (bLS model) and the flux-gradient technique, it was the latter that tended to have the lower emission estimates    . In the present study, however, the flux-gradient technique produced the higher PM10 emission rates in general. This difference in findings could be attributed to difference in measurement design when implementing the flux-gradient technique, including measurement heights (i.e., 2.0 to 7.62 m range in this study, <2 m only in Wilson et al.  and Flesch et al.  ), area source evaluated (i.e., feedlot in this study, lagoon in Wilson et al.  ), emissions measured (i.e., PM10 in this study, gases/tracers in previous), comparison procedure (i.e., hourly data points in this study, seasonal and annual means in Todd et al.  ), and approximation of eddy diffusivity (i.e., similar to companion studies   , the procedure implemented followed Prueger et al.  ). As discussed below, the only time the flux- gradient technique gave the lower PM10 emission rates in this study was with the combination of data sets that excluded the 2.0-m height and fm formulations from Flesch et al.  .
Slopes and R2 values from performing regression analyses between WindTrax and the flux-gradient technique are summarized in Table 5. In terms of their calculated PM10 emission rates, WindTrax and the flux-gradient technique had relatively high linear relationship (0.73 ≤ R2 ≤ 0.89). The highest linearity was observed between the two methods using data set 5―i.e., with two measurement heights, the lowest (2.0 m) and the highest (7.62 m) in the measurement set-up. Based on slopes (Table 5), the percentage difference in estimated emission rate between WindTrax and the flux-gradient technique ranged up to 38%. The lowest differences (<8%) were observed when using data sets 2 and 4, which did not include the 2.0-m height measurements in emission estimation. Meanwhile, the difference was largest when using data set 3 (29% to 38%) followed by data set 6 (19% to 27%), both of which included the 2.0-m height but excluded the 7.62-m height. These results suggest lower difference between WindTrax and the flux-gradient technique when estimating emission rates using the 7.62-m height and, in contrast, neglecting the 2.0-m height. Note that for both methods, use of the 2.0-m height measurements resulted to higher PM10 emission rate estimates―for the flux-gradient technique, this was due to lower fm and KPM, and higher vertical concentration gradient calculated. And as mentioned above, use of the
Table 5. Linear regression between WindTrax and the flux-gradient technique for all data set-fm formulation combinations  .a,b
aFor comparison purposes, WindTrax was treated as the independent variable and the flux-gradient technique as the dependent variable in the regression analyses; bValues presented are slopes from regression analyses; values in parentheses are corresponding R2 values.
7.62-m height, which considerably reduced the estimated vertical concentration gradient, significantly lowered the emission rate calculated by the flux-gradient technique.
In terms of their calculated PM10 emission rates, WindTrax and the flux-gradient technique were not significantly different (0.05 < P < 0.90) from each other when using data sets 2, 4, and 5, the first two as the data sets that did not include the 2.0-m measurement height. For data set 1, in which all the four measurement heights were used, fm formulation from Flesch et al.  , when used in the flux-gradient technique, was the only one in which the two methods did not significantly vary (P = 0.09) in estimated emission rates. To have closer estimates with WindTrax, the suggested fm formulation for data sets that included the 2.0-m height was the one from Flesch et al.  based on regression analyses and paired t-test. For data sets 2 and 4 (i.e., no 2.0-m height), the suggested fm formulation was the one from Hogstrom  , followed by Dyer  and Dyer and Hicks  in second, and Hogstrom  in third―still, these three formulations produced PM10 emission estimates that were not significantly different from each other (P ≥ 0.41). Nevertheless, regardless of fm formulations for the flux-gradient technique, the high linearity observed indicates the possibility of developing conversion factors between the two emission estimation methods.
This study compared WindTrax and the flux-gradient technique as methods for estimating PM10 emissions from large commercial beef cattle feedlots. Using PM10 concentration measurements at several heights and measured meteorological conditions at a Kansas cattle feedlot, the two emission estimation methods were compared using different concentration data sets, which varied in terms of heights and number of heights included, and several formulations for the flux-gradient technique’s nondimensional correction parameter fm. From the analyses, the following conclusions were made:
・ Between the two methods, WindTrax was least sensitive to changes in heights and number of heights used in calculating emission rates. In this study, percent change in PM10 emission rates estimated by WindTrax ranged up to 18%, which was relatively small compared to the change observed for the flux-gradient technique (≤56%). Still, in each method, high linearity was observed among PM10 emission rates calculated using different concentration data sets.
・ For both methods, higher PM10 emission rates were obtained when using the 2.0-m height, the lowest height in the measurement set-up, in emission estimation. On the other hand, PM10 emission rates calculated with the flux-gradient technique lowered when using the 7.62-m height, the highest height in the set-up.
・ For the flux-gradient technique, the most critical heights were the lowest and the highest heights used in calculating the vertical concentration gradient. As demonstrated in this study, neglecting other heights in between resulted only in percent change of 2% to 6%.
・ In general, the flux-gradient technique produced the higher PM10 emission rates. Only by excluding the 2.0-m height and using fm formulations from Flesch et al.  made the flux-gradient technique calculate emission rates lower, but not significantly different, than those by WindTrax.
・ For all fm formulations evaluated, the smallest difference in estimated PM10 emission rates was observed between WindTrax and the flux-gradient when using data sets without the 2.0-m height (≤8%). It should also be pointed out, however, that in this study, the flux-gradient technique was implemented with a very strict criterion for linearity (Pearson correlation = 0.95) between PM10 concentration and measurement height. Using a lower criterion would likely lead to higher difference in calculated PM10 emission rates between the two methods (e.g., Pearson correlation = 0.75 increased the difference by 50%).
Results from this study could serve as reference for and in developing conversion factors between WindTrax and the flux-gradient technique. The procedures presented for both methods can be used in determining PM emission rates from large commercial cattle feedlots. It must be emphasized, however, that the version of WindTrax implemented neglected gravitational settling effects; as noted, this might underestimate PM10 emissions by 4%. Based on meteorological conditions measured at the cattle feedlot studied, the flux-gradient technique was found to be applicable in estimating emission rates for PM with aerodynamic diameter ≤ 35 µm  ; above this range, it is recommended to utilize a different emission estimation method that can account for gravitational settling effects.
This study was supported by USDA National Institute of Food and Agriculture (Project No. 2009-35112-05244), USDA Agricultural Research Service, and Kansas Agricultural Experiment Station (contribution number 14- 410-J). Technical assistance provided by the following is acknowledged: Darrell Oard, Dr. Li Guo, Dr. Orlando Aguilar, Dr. Howell Gonzales, and Curtis Leiker, formerly of Kansas State University, Manhattan, KS; Dr. Kenwood Scoggin of USDA, Agricultural Research Service, Ames, IA; and Dr. Bernardo Predicala of Prairie Swine Centre Inc., Saskatoon, Saskatchewan, Canada. Cooperation of feedlot operators and KLA Environmental Services, Inc. is also acknowledged.
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