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 [8] [15] . 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. [8] .

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 (u_x, u_y, u_z) and air temperature (T). Using formulations presented by Flesch et al. [23] , corresponding friction velocity (u_*), Monin-Obukhov length (L) and surface roughness (z_o) 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) [24] . 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. [25] and Flesch and Wilson [24] .

WindTrax has an interface that enables mapping of the area source of interest and sampler locations using aerial image files [26] . 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 [27] and Flesch et al. [23] . In the simulation, the number of particle released was set to 50,000, which is the default value [26] . The PM₁₀ emission rates calculated with WindTrax were also screened based on criteria described by Flesch et al. [28] .

Measurement periods with very strong atmospheric stability (|L| < 10 m), low wind speed (u_* < 0.15 m/s), or unrealistic wind profile (z_o > 1 m) were considered unreliable and therefore not included in the comparison.

WindTrax can calculate emission rates using one or more concentration measurements [26] . 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 [26] [29] . 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. [9] , 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 (2.0.8.8, www.thunderbeachscientific.com) was used. Based on a companion study that used AERMOD [17] , neglecting gravitational settling underestimated PM₁₀ emission rates by 4%.

For the flux-gradient technique, PM₁₀ emission rate (Q, µg/m²∙s) was calculated as:

where K_PM is PM₁₀ eddy diffusivity (m²/s), C_m is measured net PM₁₀ concentration (µg/m³), and dC_m/dz is vertical PM₁₀ concentration gradient (µg/m³-m) [30] [31] . The vertical concentration gradient, dC_m/dz, was the derivative of the regression equation derived for sampling heights with concentration measurements [18] . In Bonifacio et al. [8] , suitability of the flux-gradient technique in determining PM₁₀ emissions from cattle feedlots had been verified using the criterion presented by Lilly [32] . 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 [18] , and thus, suggesting suitability of the flux- gradient technique for PM emissions within this size range.

The K_PM was determined from eddy diffusivity for momentum, K_m (m²/s), and Schmidt number, S_c (Equation (3)) [33] [34] .

The S_c was set to 0.63, which was the overall value determined for PM₁₀ emissions at the studied feedlot that had hourly median S_c ranging from 0.40 to 1.23 [8] . The K_m was given by:

where z_m is mean geometric height based on heights with PM₁₀ concentration measurements, and is a nondimensional correction parameter that accounts for atmospheric stability effects [34] . Prueger and Kustas [31] provided a summary of different formulations that can be used in calculating. With a general expression given by:

(5),

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 [35] applies for multiple surface from oceans to forest and was the one used in the companion studies [8] [18] ; 2) Flesch et al. [23] is the one implemented in WindTrax; 3) Dyer and Hicks [36] was derived for plowed field (i.e., with a loose surface layer like that of the feedlot surface); and 4) Hogstrom [37] has been used in a previous cattle feedlot study [38] .

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

calculated emission rates represented PM₁₀ emitted at the feedlot only and not from outside sources. Calculation of fetch was based on Hsieh et al. [40] as previously implemented in companion studies [8] [18] . 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.

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.

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

a. For WindTrax only.

lowest was measured from 0100 h to 0300 h (8 ± 1 µg/m³∙m).

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

^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).

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 f_m formulations (i.e., total of 24 data set-f_m formulation combinations). Similarly, a diurnal trend in calculated PM₁₀ emission rates was observed for all data set-f_m 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 f_m, and, equivalently, K_PM (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-f_m 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 f_m formulations, Hogstrom [35] produced the highest PM₁₀ emissions rates whereas Flesch et al. [23] had the lowest. With respect to Hogstrom [35] , Flesch et al. [23] 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. [23] 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-

^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 K_PM. 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).

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 [33] [38] [41] . 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. [41] and Flesch et al. [33] ), area source evaluated (i.e., feedlot in this study, lagoon in Wilson et al. [41] ), 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. [38] ), and approximation of eddy diffusivity (i.e., similar to companion studies [8] [18] , the procedure implemented followed Prueger et al. [34] ). 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 f_m formulations from Flesch et al. [23] .

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 f_m and K_PM, and higher vertical concentration gradient calculated. And as mentioned above, use of the

^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, f_m formulation from Flesch et al. [23] , 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 f_m formulation for data sets that included the 2.0-m height was the one from Flesch et al. [23] based on regression analyses and paired t-test. For data sets 2 and 4 (i.e., no 2.0-m height), the suggested f_m formulation was the one from Hogstrom [37] , followed by Dyer [39] and Dyer and Hicks [36] in second, and Hogstrom [35] in third―still, these three formulations produced PM₁₀ emission estimates that were not significantly different from each other (P ≥ 0.41). Nevertheless, regardless of f_m formulations for the flux-gradient technique, the high linearity observed indicates the possibility of developing conversion factors between the two emission estimation methods.