## 1. Introduction

The widespread adoption of genetically modified (GM) maize has led to a need to better understand the dispersal of maize pollen in the atmosphere because of concerns over the potential contamination of non-GM maize by pollen from GM maize. To address this need, we have studied the properties of maize pollen and atmospheric transport that are important to this process. In particular, we have measured maize pollen’s fall velocity (Aylor 2002), rate of dehydration (Aylor 2003), and viability as a function of time and atmospheric conditions (Aylor 2004); have measured pollen concentrations from near the surface to 90 m above ground level (AGL; Aylor et al. 2006); and have constructed detailed models of transport in the maize canopy and adjacent atmospheric surface layer (SL; Aylor and Flesch 2001; Aylor et al. 2003) and in the convective boundary layer (CBL; Boehm and Aylor 2005). These studies, along with several others (e.g., Klein et al. 2003; Loos et al. 2003; Jarosz et al. 2004; Ma et al. 2004; Yamamura 2004), are clarifying maize pollen transport in the atmosphere.

Maize pollen is primarily released under drying conditions from midmorning through early afternoon, a time of day when, during fair weather, the atmospheric boundary layer is typically becoming increasingly convective. Under convective conditions, turbulent transport within the boundary layer is dominated by updrafts and downdrafts extending from near the surface to the top of the boundary layer at a typical height of 500–2000 m AGL. These large eddies can carry maize pollen from its near-surface release point to the top of the CBL and back to the surface again at a distance several kilometers from its release location over a period of tens of minutes. Therefore, to model the longer distance dispersal of maize pollen it is necessary to use a model that mimics the large-scale updrafts and downdrafts that dominate the CBL.

We have implemented a CBL Lagrangian stochastic (LS) model following Luhar (2002) and modified it to include the effects of particle fall velocity. This model mimics the skewed, vertically inhomogeneous turbulence characteristic of the CBL through the use of vertically varying vertical velocity variance, long correlation time scales, and positively skewed vertical velocity probability distribution functions (PDFs; Boehm and Aylor 2005; Luhar and Britter 1989; Luhar et al. 1996; Luhar 2002). In the LS framework, the trajectories of a large number of particles are calculated based on the turbulent statistics of the wind flow of interest, and the corresponding concentration field is determined by compiling the locations of all particles at all times. Compared to large-eddy simulation (LES), this framework is relatively simple and computationally efficient and allows for more rapid dispersal calculations over a range of atmospheric conditions, although it requires independent information about the wind flow field.

Maize pollen is released near the top of the maize canopy, 2–3 m above the surface. As a result, the turbulent wind flow within and just above the canopy and deposition on the plants and ground determine the fraction of the pollen released that is available for long-distance transport. However, the turbulence parameterizations used in the CBL LS model were developed for the bulk of the CBL based on laboratory measurements, field experiments, and LES results and may not be accurate very near the surface. This is particularly true under windy, less convective conditions where wind shear generates a significant amount of turbulence near the surface.

Therefore, in this paper the turbulence parameters in our one-dimensional CBL LS model were modified to more accurately reflect the effects of wind shear near the surface. These modifications, along with supporting turbulence data, are presented in section 2. Section 3 describes measurements of airborne maize pollen that provide data for testing the modified model. These measurements are compared with model results in section 4. Section 5 summarizes our findings.

## 2. Application of a CBL LS model near the ground

### a. Turbulence parameterizations

In this section, our CBL LS model is modified to more accurately represent conditions near the ground, especially under less convective conditions when shear-driven turbulence becomes important in this region. To provide guidance in making these modifications, we first compare near-surface values from the Luhar (2002) turbulence parameterization used in our CBL model (Boehm and Aylor 2005) with near-surface turbulence measurements and with the parameterization in our SL model (Aylor and Flesch 2001; Aylor et al. 2003). Throughout this article, “CBL” refers to the model using the pure-CBL model parameterization of Luhar (2002), while “merged” refers to the model using the modified parameterization presented later in this section. The term merged is used because the modified parameterization is a combination of the pure-CBL and SL parameterizations.

On a total of 11 days during the summers of 2004 and 2005, measurements from a 3D sonic anemometer (Research Unit, Gill Instruments Ltd., Lymington, England) 3.25 m above a freshly cut alfalfa field were recorded onto a laptop computer at a rate of 20.8 Hz. These data covered a period of 3–8 h during midmorning through midafternoon on each day and include a wide range of atmospheric stability and wind conditions. The analyses presented in this section were performed over periods of about 26 min (2^{15} measurement points for use in an FFT routine).

Figure 1 compares the measured vertical velocity standard deviation, *σ _{w}*

_{,obs}, with the parameterized values for both the SL and CBL models at the 3.25-m measurement height over all the averaging periods. The SL model values,

*σ*

_{w}_{,SL}, were parameterized based on the friction velocity

*u*

_{*}and the Monin–Obukhov length

*L*(Aylor and Flesch 2001), and the CBL model values

*σ*

_{w}_{,CBL}were parameterized based on the convective velocity scale

*w*

_{*}and the boundary layer depth

*z*(Luhar 2002). The boundary layer depth was estimated from National Weather Service soundings and from profiles of potential temperature, water vapor mixing ratio, wind direction, and wind speed from the Eta Data Assimilation System (see section 3d).

_{i}In reflection on the well-established success of the SL formulation, excellent agreement is found between *σ _{w}*

_{,obs}and

*σ*

_{w}_{,SL}over the entire range of values (Fig. 1a). In contrast, the agreement between

*σ*

_{w}_{,obs}and

*σ*

_{w}_{,CBL}is not so good. There is generally good agreement for small values of

*σ*

_{w}_{,obs}, but poor agreement as

*σ*

_{w}_{,obs}increases. To aid in understanding these differences, Fig. 1b shows

*σ*

_{w}_{,CBL}/

*σ*

_{w}_{,obs}as a function of |

*L*|. The points for which

*σ*

_{w}_{,obs}and

*σ*

_{w}_{,CBL}show good agreement

*(σ*

_{w}_{,CBL}/

*σ*

_{w}_{,obs}∼1) correspond to small values of |

*L*| (highly convective conditions), while the points with poor agreement correspond to large values of |

*L*| (less convective conditions). Under highly convective conditions, turbulence is driven largely by buoyancy, even near the surface, so that the buoyancy-driven CBL model accurately represents the turbulence parameters. In contrast, under less convective conditions, wind speeds tend to be stronger and shear-generated turbulence becomes more important. However, the CBL LS model does not adequately represent this additional source of turbulence and as a result underestimates the turbulence parameters, including

*σ*, near the surface.

_{w}*κ*is the wavenumber,

*α*is a constant with a value of 0.52, and

*P*(

_{u}*κ*),

*P*(

_{υ}*κ*), and

*P*(

_{w}*κ*) are the power spectra of

*u*,

*υ*, and

*w*, respectively. For a given averaging period, the values for ε calculated from the three spectral components agreed closely.

Again, reflecting on the success of the SL formulation, good agreement is found between ε_{obs} and ε_{SL}, with only a slight offset (Fig. 2b). In contrast, in behavior similar to that for *σ _{w}*, some agreement is found between ε

_{obs}and ε

_{CBL}for small values of ε

_{obs}, but poor agreement is found for larger values. As was the case for

*σ*, this behavior is a result of the inability of the CBL model to account for shear-generated turbulence, which becomes more important as conditions become less convective and wind speed increases.

_{w}These analyses show that near the surface, the turbulence parameterization in the CBL LS model agrees with the measurements and SL LS model parameterization under highly convective conditions, but agrees less well as conditions become less convective and windier. This is reflected in Figs. 3a–d, which show, for both models, the parameterized profiles for *σ _{w}* and ε under two sets of atmospheric conditions: strongly convective with light winds and weakly convective with strong winds. For the highly convective case, the two models show reasonable agreement near the surface, while in the weakly convective case, the agreement is much poorer.

### b. Merged parameters

Therefore, to more accurately model long-distance dispersion under weakly convective, windy conditions, it was necessary to modify the CBL model turbulence parameter profiles to incorporate the effects of shear-generated turbulence. In particular, profiles were needed that transition from SL model values near the surface to values that represent the combined effects of buoyancy- and shear-generated turbulence in the bulk of the CBL.

*w*

_{*}is the convective velocity scale (Deardorff 1970),

*u*

_{*}is the friction velocity,

*z*is the boundary layer depth,

_{i}*L*is the Monin–Obukhov length, and

*k*is the von Kármán constant. The first term depends on CBL variables and is identical to the constant expression for ε used in our CBL model (Boehm and Aylor 2005; Luhar 2002), while the second term represents the additional TKE dissipation that is required when shear-generated turbulence is added and depends primarily on SL variables. The merged ε profile decreases rapidly from SL to CBL values under convective conditions, but much more gradually under less convective, windy conditions (Figs. 3c–d).

A merged profile was also required for *σ _{w}*. Model results and observations have shown that under the moderately sheared conditions considered here,

*σ*in the bulk of the CBL is similar to

_{w}*σ*under highly convective conditions with light winds, with the largest impacts of shear-driven turbulence near the surface (Dosio et al. 2003; Ohya and Uchida 2004; Moeng and Sullivan 1994; Sykes and Henn 1989). The merged

_{w}*σ*parameterization presented by Rotach et al. (1996) gives larger

_{w}*σ*values under sheared conditions than have been modeled and observed.

_{w}*σ*profile that is a blending of the Luhar (2002) CBL parameterization and the measurement-based neutral profile of Brost et al. (1982):The primary weighting in

_{w}*σ*

^{2}

_{w,merged}is based on the following velocity scale (Zeman and Tennekes 1977; Moeng and Sullivan 1994; Dosio et al. 2003):

*w*

^{3}

_{m}=

*w*

^{3}

_{*}+ 5

*u*

^{3}

_{*}

*w*

^{3}

_{*}. This velocity scale is based on scaling of the TKE equation and was shown by Moeng and Sullivan (1994) to provide a suitable scaling for second-order turbulence moments. The exponential factors in the weighting cause the profile to exponentially transition from the neutral (SL) value at the surface to the weighted average with a scale height of |

*L*|.

Profiles of *σ _{w}*

_{,merged}and ε

_{merged}are included in Figs. 3a–d. Under highly convective conditions, the contribution of shear-driven turbulence is minimal so that the modifications have little impact and the merged profiles are nearly identical to the CBL profiles. The most noticeable difference occurs in ε near the surface, where it quickly transitions from the SL model to the merged model values over the lowest 50 m of the boundary layer.

Under weakly convective conditions with strong winds, the modifications have a more significant impact. The profile for *σ _{w}*

_{,merged}transitions from the larger SL value at the ground to the merged value over about the lowest 200 m of the boundary layer. Above this level, the merged profile is almost identical to the CBL profile. Under these same conditions, ε

_{CBL}transitions more gradually, taking about the entire depth of the boundary layer to go from the SL value to the merged value.

Another important parameter in LS models is the local vertical velocity decorrelation time scale, *τ*. This time scale is often parameterized as *τ* = 2*σ*^{2}_{w}/*C*_{0}ε, where *C*_{0} is a constant (set to 3 in this study). Under highly convective conditions, *τ*_{merged} is virtually identical to *τ*_{CBL} (Figs. 3e–f) because of the corresponding very minor modifications to *σ _{w}* and ε. On the other hand, under weakly convective conditions with strong winds, the modifications reduce

*τ*by a factor of about 2 through the bulk of the CBL.

The modifications to the *σ*_{w} profile also have an impact on vertical velocity skewness (not shown) *S _{w}*, defined by

*S*

_{w}=

*σ*

^{2}

_{w})

^{3/2}, where

*σ*in the merged model result in very small values for

_{w}*S*near the surface, in agreement with the SL model, while under light wind convective conditions, the values for

_{w}*S*in the merged model are very similar to the CBL model values. The values for

_{w}*S*calculated from our sonic anemometer data (not shown) are in reasonable agreement with the merged model values.

_{w}Most CBL LS model studies have used a vertically constant mean horizontal wind based on the assumption that horizontal momentum is well mixed through the CBL. This is generally a good assumption under highly convective conditions with light winds, but as wind shear is added and conditions become less convective, the wind profile becomes less well mixed. Therefore, we have incorporated into our merged model the wind profile used in our SL LS model. This profile is the logarithmic wind profile modified to include the effects of stability (Aylor and Flesch 2001). For the cases analyzed in this paper, the wind direction was constant up through the remotely piloted vehicle (RPV) measurement height. The sensitivity of the results to wind direction is examined in section 4d(5).

By including horizontal wind shear and turbulence (through *σ _{u}*), we have partially extended the one-dimensional model of Boehm and Aylor (2005) to two dimensions. However, to maintain the relative simplicity of the CBL model formulation, we have not incorporated the covariance terms (Thomson 1987) that potentially become important as wind shear increases. The covariance terms are included in our SL model used in determining the pollen source strength, however, and further research is needed to determine the impact of leaving them out of our merged model.

To illustrate the impacts of the modifications on model results, Fig. 4 shows results from simulations of the dispersal of weightless particles under weakly convective conditions with strong winds incorporating both the Luhar (2002) parameterization (Fig. 4a) and the new, merged parameterization (Fig. 4b). The results using the Luhar (2002) parameterization show the typical CBL dispersion pattern of rapid initial plume ascent, leading to an elevated maximum, followed by gradual descent and mixing. The reduced *τ* in the merged parameterization reduces the time that a typical particle caught in an updraft maintains its upward motion. As a result, the initial plume ascent is more gradual, the plume is more spread out, and the concentration in the upper maximum is reduced.

## 3. Measurements and methods

### a. Maize pollen measurements

Measured maize pollen concentrations were used to test our LS models. These measurements were made on the Cornell Animal Science Teaching and Research Center near Dryden, New York (42°26′30.0″N, 76°14′30.0″W), on each day during the period 21–28 July 2005. This 500-ha dairy farm is largely a mosaic of 20- to 40-ha maize and alfalfa fields. In this section, the methods used to obtain the aerial pollen concentrations, the pollen source strengths, and the meteorological parameters required as inputs for the model simulations are described.

Maize pollen was sampled at altitudes up to 250 m AGL using airborne remotely piloted vehicles outfitted with petri-plate (PP) samplers (Aylor et al. 2006). Between 2 and 4 (average of 3.25) 30-min sampling periods were carried out on each day during the experiment, with between 2 and 4 (average of 2.73) successful RPV samples obtained during each period. A successful sample was one in which at least 2 PP samplers were exposed and retrieved and for which flight data were available. The sampled pollen was manually counted under a microscope and the counts were converted to flight-track average concentrations. To provide data for testing the merged model, the RPVs were vertically stacked, with flight heights varied depending on atmospheric conditions. Typically, one RPV was flown 50–100 m AGL, a second 100–200 m AGL, and a third 230–260 m AGL. The mean altitudes during sampling ranged from 57 m AGL to 259 m AGL.

To help define the maize pollen source strength, pollen was also sampled near or at the surface using several methods. First, the aerial concentration of pollen near the surface was measured using rotorod (RR) samplers with retracting-type sampling heads (Model 82, Sampling Technologies, Inc., Los Altos Hills, California) deployed at heights of 3, 5, and 9 m AGL on a tower in both Fields 7 and 16, located near the RPV flight paths (Fig. 5). Four consecutive, 1-h RR sampling periods (covering the times of the RPV flights) were conducted on each day during the experiment, during which one RR sampler was exposed at each height in each field. The RRs sampled the air at a rate of 38 L min^{−1} and collected maize pollen with an efficiency of 0.8 (Noll 1970; Aylor 1993).

A biological measure of the potential amount of pollen available to be released in a field each day during sampling was obtained by determining the amount of mature, ready-to-be-released pollen in the tassels of individual plants and then scaling this by the number of plants per field. Typically, pollen release begins at a low level when the first few anthers are exposed, then increases to a peak amount after 3–4 days, and then steadily declines toward zero as the contents of the anthers are exhausted. The total amount of pollen produced (i.e., mature and ready to be released) per tassel over the course of a day in Fields 7 and 16 was estimated by harvesting tassels from 12 plants in each field on each day during the experiment. The tassels were covered on the evening preceding harvest with a breathable plastic bag (Pantek, Montesson, France) covered by a brown paper tassel bag (Lawson, Northfield, Illinois, No. 402—“Showerproof’d”). Early the next evening, the bagged tassels were harvested by cutting the stalk below the tassel and were stored upside down in a dry place. The number of pollen grains produced in individual harvested tassels was estimated by comparing the total mass of pollen collected after drying with the mass of individual pollen grains. This method yielded the daily production of pollen per plant, *q _{P}* (grains plant

^{−1}day

^{−1}).

A Burkard 7-day volumetric spore sampler (Burkard Scientific Sales, Ltd., Rickmansworth, Hertfordshire, England) was operated continuously near the RR tower in Field 7 with its sampling orifice at the average tassel height. The seasonal and diurnal patterns of pollen release were determined by counting the number of pollen grains impacted as a function of time along the sampling tape. The diurnal pattern of pollen deposited on the sampling tape, showing peak pollen release during midmorning–early afternoon, with very little release at night, agreed with the findings of other studies (Jarosz et al. 2005; Aylor et al. 2006).

### b. Pollen source strength determination

The maize pollen source strength, *Q* (grains per meter squared per second), the number of pollen grains released per unit area per unit time, is a key model input parameter used to scale the pollen contributions from the various fields. It was determined for Fields 7 and 16 using the RR-measured pollen concentrations in these fields in combination with our SL LS model, following the method described by Aylor et al. (2006). In this method, the model is run for the weather conditions observed during the RR sampling period and *Q* is determined as the value of the source strength for the modeled area sources surrounding the modeled RR tower for which the modeled pollen concentrations at the RR heights best match the measured concentrations.

Four *Q* values were obtained for each field on each day, corresponding to the four daily one-hour RR sampling periods. The sum of these four *Q* values was multiplied by 3600 (seconds per hour) to obtain *A*, the total number of pollen grains released per unit ground area over the combined 4-h sampling period. The values for *A* were compared with the total number of pollen grains released per unit area per day determined from the tassel bags. In this comparison, *A* ranged from 4% to 62% of (*q _{P}* ×

*N*) in Field 7 and from 0.3% to 10% of (

_{P}*q*×

_{P}*N*) in Field 16, where

_{P}*N*

_{P}is the population density of 5.4 and 7.9 plants per meter squared for Fields 7 and 16, respectively.

The focus in the present study is on longer-distance transport in the CBL, where the sampled pollen may include contributions from several fields at various distances. Limited resources made it impractical to measure *Q* in every cornfield at the site. Therefore, the visual assessment of pollen production was used to estimate *Q* for most of the fields at the site over the RPV sampling periods.

The daily potential pollen production in most fields on the research farm and surrounding farms in the valley, including Fields 7 and 16 for calibration purposes, was determined by visiting the fields and visually estimating 1) the percentage of the plants in the field with fully extended tassels, 2) the percentage emerged anthers on the extended tassels, and 3) the pollen content and release potential in the emerged anthers, categorized as either light, moderate, heavy, or none (empty). This category was determined by gently tapping the tassel over a collection surface and assessing the amount of pollen collected. In addition, anther color was used to indicate the amount of pollen contained in the anthers (full anthers are yellow and empty anthers are pale gray). These measures were combined to arrive at a rating (1–11) representing the fraction of the seasonal total pollen production estimated to be available for release on a given day. Not every field was visited on every day; on most days, only those fields located near to or upwind of the RPV flight paths were visited.

Finally, *Q* for the majority of the fields where only visual evaluation was available was determined as follows. First, the rating (1–11) was converted to a daily release (actually a 4-h value) using the idealized curve in Fig. 6a. Values of *Q* for each 1-h sampling period were obtained by multiplying the 4-h value in a given field by the proportion of the 4-h release occurring during that hour in Field 7 (Fig. 6b).

### c. Meteorological measurements

To model maize pollen dispersal, the state of the atmosphere during sampling must be known. Therefore, a variety of meteorological measurements were made at the farm.

First, a tethersonde system (Model TT12, Vaisala Inc., Boulder, Colorado) was used to profile the wind direction, wind speed, temperature, and relative humidity up to about 360 m AGL (maximum allowed by the Federal Aviation Administration at our site) by continuously raising and lowering the tethersonde between the surface and this height, except when strong winds (>10 m s^{−1}) limited profiling to lower heights. The tethersonde wind data were used in real time during the experiment to help determine the RPV flight tracks and the averages of various combinations of the profiles were used in generating model input parameters.

Second, a 3D sonic anemometer was used to measure turbulence statistics 3.25 m above a freshly cut alfalfa field located near the tethersonde (Fig. 5). The average values of the 3 components of the wind velocity (*u*, *υ*, *w*) and sonic-derived temperature (*T*), the variance of each quantity, and the covariances between the quantities were saved over 2-min intervals. These 2-min averages, variances, and covariances were then compiled to obtain values corresponding to the RPV sampling periods (typically around 30 min). The compiled data were used in calculating the turbulence parameters required by the models.

Finally, to supplement the wind data obtained from the tethersonde system and sonic anemometer, the wind direction and speed were measured near the sonic anemometer at a height of 3.25 m using a standard cup anemometer, wind vane, and datalogger (Model 014A and Model 024A, Met-One, Inc., Grants Pass, Oregon, and Model 23X, Campbell Scientific, Inc., Logan, Utah). These instruments were sampled at 10-s intervals and averaged for 10 min.

### d. Meteorological model inputs

The LS models require several meteorological inputs. The determination of these inputs using a combination of the meteorological measurements made at the farm and data from external sources is described in this subsection.

Wind direction was based on measurements from the tethersonde system, the sonic anemometer, and the surface weather station. Under steady wind conditions when all the measurements agreed, the near-surface wind direction was easy to determine. On other occasions, when the wind was unsteady or the measurements disagreed, the near-surface wind direction was more difficult to determine and in a couple of very light wind cases was not meaningful. The variation in wind direction with height potentially has a big influence on the pollen sampled by the RPVs. The wind direction tended to be most variable for the first flight on a given day and then became more constant with height as the boundary layer became well mixed.

The wind speed profiles in the models were based on *u*_{*} and *L*. Initial estimates for these surface layer parameters were determined from the sonic anemometer data using *u*_{*} = (^{2} + ^{2})^{1/4} and *L* = −*u*^{3}_{*}*T**kg**u*_{*} from data rotated into the mean wind direction was not used since it produced undefined values for *u*_{*} under light and variable wind conditions. Under steady wind conditions, both methods gave essentially the same answer since after rotation 〈*υ*′*w*′〉 ∼ 0.

The values of *u*_{*} and *L* used in the model were determined by comparing the theoretical wind speed profiles based on *u*_{*} and *L* calculated by the above method with the corresponding wind speed profiles measured by the tethersonde system. In cases when the theoretical and measured wind speed profiles agreed, the values used for *u*_{*} and *L* were similar to the estimates from the sonic anemometer data. On the other hand, in cases when the theoretical and measured wind speed profiles agreed less well, the sonic anemometer estimates for *u*_{*} and *L* were adjusted to match the tethersonde profiles. This typically occurred when atmospheric conditions were changing or unsteady so that surface layer similarity theory is less reliable. In several cases, the profiles were well mixed over the lowest few tens of meters and then stable above. Since the focus of this paper is on dispersion in the CBL, these cases were not modeled in this study.

The CBL and merged models require the boundary layer depth, *z _{i}*, as input. On a typical day during the summer at the experiment location,

*z*

_{i}can exceed 1000 m, well above our tethersonde limit of 360 m AGL. Thus, additional data were used to estimate

*z*during the experiment, primarily model data from the Eta Data Assimilation System (EDAS), a data assimilation system based on the National Centers for Environmental Prediction (NCEP) Eta Weather Forecasting Model. The EDAS data were obtained from the Air Resources Laboratory (Silver Spring, Maryland) of the National Oceanic and Atmospheric Administration through their Web site (see online at http://www.arl.noaa.gov/ss/transport/archives.html). Data were obtained over the duration of the experiment for the grid point at 42.44°N, 76.50°W, the point nearest to the experiment site in the 40-km resolution data. The data included profiles of temperature, potential temperature, relative humidity, and the wind components. In the lower atmosphere, data were available at 25-mb intervals from 1000 to 700 mb, or one data point about every 250 m from the surface through about 3000 m. The data were available at 3-h intervals, with the times of most interest to this study being 1200–2400 UTC [0800–2000 eastern daylight time (EDT)].

_{i}The EDAS data were compared with National Weather Service (NWS) radiosonde data from the “Atmospheric Soundings” Web site (http://weather.uwyo.edu/upperair/sounding.html) maintained by the Department of Atmospheric Science in the College of Engineering at the University of Wyoming. These data consisted of soundings launched at 1200 UTC (0800 EDT) and at 0000 UTC (2000 EDT) from Albany, Buffalo, and Upton, New York. Unfortunately, no soundings were available around midday when the atmosphere is most convective and the boundary layer is deepest. Useful information was still obtained from these soundings as on many days the atmosphere was still convective at the time of the evening sounding.

For each EDAS profile during daylight hours, *z*_{i} was estimated as the height of the top of the mixed layer in the following variables: potential temperature, water vapor mixing ratio, wind direction, and wind speed. In some cases, this height was similar in all the variables, while in other cases it differed from variable to variable and *z _{i}* was estimated using a blend of all the variables. For the 1200 UTC and 0000 UTC assessments, the EDAS

*z*estimates were compared with values estimated from the NWS radiosonde data following a similar method. The agreement between the estimated values was generally best for the 0000 UTC (2000 EDT) profiles when the signature of the midafternoon convective boundary layer was still visible. In these comparisons,

_{i}*z*was generally greater in the NWS radiosonde profiles than in the EDAS profiles.

_{i}The convective velocity scale *w*_{*} was calculated using (Deardorff 1970) *w*_{*} = (−*z _{i}u*

^{3}

_{*}/

*kL*)

^{1/3}, where

*k*= 0.4 is the von Kármán constant. Fortunately,

*w*

_{*}depends on

*z*to the one-third power and is forgiving to a fair amount of uncertainty in its value. The sensitivity of the model results to

_{i}*z*and

_{i}*w*

_{*}is discussed later in the paper.

### e. Modeled concentration along flight track

Following the method used by Aylor et al. (2006), model-derived concentrations corresponding to each RPV sample were calculated using the LS models. First, the models were run for the atmospheric conditions corresponding to the RPV flight of interest, producing as output the crosswind-integrated concentration (CWIC) as a function of downwind distance and altitude. The model-predicted concentration along the RPV flight track was then determined by calculating for each point along the track the downwind distance from, crosswind distance from, and altitude above each point in all of the fields. The concentration at the RPV location was calculated from the CWIC corresponding to the downwind distance and altitude by assuming a Gaussian crosswind spread and multiplying the CWIC by the appropriate factor for the determined downwind and crosswind distances. The Gaussian distribution used *σ*_{y} calculated based on Pasquill–Gifford stability class B. Finally, the average concentration was calculated along the entire flight path, and this value was compared with the concentrations measured by the PP samplers. In a previous paper, we found little sensitivity of modeled concentrations to stability class, with about a 1% difference between results using classes A and D (Aylor et al. 2006).

## 4. Results and discussion

### a. Measured concentration profiles

Table 1 details the 26 RPV flight experiments and corresponding weather conditions. Because the main focus was on testing the impact of our modifications to the CBL LS model, our analysis concentrated on the 14 out of 26 experiments (shown in Fig. 7a and bolded in Table 1) that were convective through the depth of the sampled layer (up to 250 m AGL) and had reasonably well-defined wind directions. The remaining sampling periods (shown in Fig. 7b) either had a poorly defined wind direction, had approximately neutral stability for which the CBL model is not valid, or consisted of a shallow developing mixed layer (∼50 m) overlaid by a stable boundary layer. The large variability in observed concentrations results from the large range in weather conditions and source strengths during the experiment. The atmospheric profiles corresponding to the stable cases generally consisted of a shallow unstable layer near the surface overlaid by a stable layer. In Table 1, separate parameters are given for the shallow unstable and stable layers, as well as the transition altitude between the two layers.

### b. Pollen source strength

Table 2 gives our best estimate of *Q* for the 14 sampling periods included in the analysis for fields that were near to the RPV flight tracks and more distant fields that contributed at least 1% to the modeled concentrations for any of the RPV samples, as determined from model runs to be presented later. These source strengths were used as inputs into the calculations of the modeled concentrations.

### c. Comparison between modeled and measured concentrations

Figure 8a compares the concentrations obtained using the merged model, *C*_{merged}, with the measured concentrations, *C*_{obs}. Although *C*_{merged} generally agrees with *C*_{obs}, there is significant scatter. On average, the merged model underpredicts the measurements by about a factor of 2.4, while, for comparison, the CBL model overpredicts the measurements by about the same factor (Table 3). Similar calculations show that the SL model overpredicts the measurements by a factor of 1.6. The geometric standard deviations show greater scatter in the SL than in the merged model results. The scatter in the model results was due to several factors, including inherent uncertainty due to the shortness of our averaging times compared with convective time scales (Fox 1984; Willis and Deardorff 1976; Stein and Wyngaard 2001), the intermittent nature of the pollen source (Aylor 1990), uncertainties in pollen source strength, particularly for the more distant fields, uncertainties in model parameter calculations, and sensitivity of the models’ applicability to stability and other parameters.

The PDF of log(*C*_{merged}/*C*_{obs}) is plotted in Fig. 8b. This distribution agrees well with the lognormal distribution corresponding to the geometric mean and standard deviation (Table 3). This type of distribution is consistent with the results of Aylor et al. (2006). The goodness of fit of the lognormal PDF was quantified using the coefficient of determination *r* ^{2}. For the results in Fig. 8b, *r* ^{2} = 0.60, indicating that the lognormal distribution explained about 60% of the scatter. Similar calculations with the SL model results yielded *r* ^{2} = 0.30, so that for this model the lognormal distribution explained less of the scatter.

Figure 9 plots *C*_{merged}/*C*_{obs} and *C*_{SL}/*C*_{obs} with respect to |*L*|. While this ratio exhibits dependence on |*L*| for both models, the dependence is stronger for the SL than for the merged model. The greater sensitivity to |*L|* in the SL model is most likely a consequence of the tendency for the SL model to allow particles to ascend unboundedly as conditions become increasingly unstable, whereas the parameters in the merged model were designed to progressively reverse the direction of motion of upward moving particles to mimic downdrafts. Therefore, there is a greater tendency for the SL model to overestimate the concentration of airborne particles as |*L*| decreases.

### d. Sensitivity studies

#### 1) Turbulence parameterization

The sensitivity of the modeled concentrations to the turbulence parameterization modifications presented in section 2 was examined by comparing *C*_{merged} with concentrations modeled using the CBL parameterization, *C*_{CBL}. The concentrations obtained using the merged model are consistently less than those obtained using the CBL model (Fig. 10a).

The ratio between the concentrations obtained using the two models has an interesting dependence on *L* (Fig. 10b). For |*L*| < 20 m, *C*_{merged}/*C*_{CBL} decreases as |*L*| increases, while for |*L*| > 20 m, *C*_{merged}/*C*_{CBL} increases slightly as |*L*| increases. This dependence on *L* is related to the impacts of the new parameterization on *σ _{w}* and

*τ*(Fig. 11). The V-shaped form of the graph in Fig. 10b is mainly due to the interplay between

*σ*and

_{w}*τ*near the surface, where their dependence on

*L*is “inversely” related. That is,

*σ*increases while

_{w}*τ*decreases with increasing |

*L*|. In general, a greater fraction of the particles in the CBL will escape from the near-surface region as both

*σ*and

_{w}*τ*increase, so that their inverse relationship results in a complex relationship between |

*L*| and the fraction of particles that are available for long-distance transport in the CBL. The airborne concentration in the CBL is directly related to this “escape fraction,” which in this paper is arbitrarily defined as the fraction of the particles released in the model that are transported downwind a distance of at least 50 m before descending below a height of 1 m.

*T*and

_{E}*T*for escape and deposition, respectively. The probability of escape

_{D}*P*is determined using Aylor (1999):

_{E}*T*is expressed in terms of a diffusion time scale involving a length squared divided by an average diffusivity:where

_{E}*h*is the source height and

*γ*> 1. In this equation it is assumed that escape occurs (i.e., there is negligible local return of pollen grains released from the source) at some distance (

*γ*– 1)

*h*above the source. For the heavy particles considered here, the deposition time scale is taken simply aswhere

*β*< 1 and it is assumed that downward moving particles that reach a height of (1 −

*β*)

*h*are deposited (i.e., there is a perfect sink at this height). Combining Eqs. (4)–(6) gives the escape probability:where

*a*

_{1}is an empirical constant (=

*γ*

^{2}/

*β*) that has a value of about 3.8 (see Fig. 11). The V-shaped curve in Fig. 10b is a direct consequence of Eq. (7) and the dependence of

*σ*and

_{w}*τ*on

*L*.

Escape fractions for the model runs using the CBL and merged parameterizations, denoted *F _{E}*

_{,CBL}and

*F*

_{E}_{,merged}, respectively, were calculated as the fraction of particles that remained airborne for a downwind distance of at least 50 m from the computational source. Escape fractions for these model runs were also calculated using Eq. (7). In these calculations,

*σ*and

_{w}*τ*were calculated using the corresponding parameterization at the release height

*h*= 2.5 m,

*υ*= 0.26 m s

_{S}^{−1}, and

*a*

_{1}= 3.75, corresponding with the model deposition height,

*z*

_{dep}= 1 m. Since the V-shaped curve in Fig. 10b corresponds to the ratio

*C*

_{merged}/

*C*

_{CBL}, the corresponding quantity when considering the escape fraction is

*F*

_{E}_{,merged}/

*F*

_{E}_{,CBL.}This latter ratio shows good agreement with the corresponding ratio between the theoretical curves for the two model parameterizations (Fig. 11c). Because of the connection between the escape fraction and aerial concentration, it is concluded that Eqs. (4)–(7) adequately represent the dependence of

*C*

_{merged}/

*C*

_{CBL}on

*L*in Fig. 10b.

#### 2) Relative contribution of near and far sources

The sensitivity of the results to the relative pollen contribution by sources located near the RPV flight tracks (hereinafter denoted “near-RPV sources”) and far from the RPV flight tracks is now examined. Fields 5, 6, 7, 13, 14, and 16 were considered near-RPV sources (Fig. 5), while the remaining fields were considered far from the RPV flight tracks. Averaged over all the flights under consideration, the near-RPV sources contributed 83% and 63% of the measured airborne pollen as modeled using the merged and SL models, respectively.

The level of agreement between the modeled and measured concentrations depended strongly on the percentage contribution by near-RPV sources (Fig. 12). For the merged model results (Fig. 12a) with a near-RPV source contribution greater than 95%, the geometric average of *C*_{merged}/*C*_{obs} is 0.94, while for the remainder of the flights the value is 0.071. For comparison, the geometric averages of *C*_{CBL}/*C*_{obs}, broken down in a similar manner, were 4.85 and 0.49, respectively. The flights with a large near-RPV source contribution correspond to the most convective conditions with small |*L*|, as indicated by the size of the bubbles in Fig. 12a. Thus, under highly convective conditions, the merged model shows much better agreement with the measurements than does the CBL model. This reinforces the results presented in Fig. 9a, where the merged model agreed well with the measurements for the smallest |*L*|. The CBL model agreed better with the observations for cases in which sources far from the RPV made a significant contribution to the modeled pollen. However, there were fewer of these cases (12) than there were cases with a large near-RPV source contribution (29), so that the results are less significant. In addition, the pollen source strengths for the more distant sources are less well known than those for the near-RPV sources, so that there is greater room for error in the modeled concentrations when the more distant sources make a significant contribution. Note that the cases with the lowest near-RPV source contribution (left-hand side of Fig. 12a) all show agreement within a factor of 10.

The impact of near-RPV source contribution is even more striking for the SL model (Fig. 12b), where for flights with a near-RPV source contribution greater than 95% the geometric average of *C*_{SL}/*C*_{obs} is 16.9, while for the remainder of the flights the value is 0.20. Again, the bubble sizes indicate that the flights with a large near-RPV source contribution correspond to more convective conditions. Thus, consistent with the results presented in Fig. 9b, the SL model significantly overpredicts the measured concentrations under highly convective conditions when near-RPV sources made a large contribution. These results underscore the inappropriateness of using a SL model at heights greater than about 0.1|*L*|.

#### 3) Lower boundary condition (deposition height)

The merged model used a simple lower boundary condition. Particles were released at a height of 2.5 m (maize tassel height) into air parcels with initial vertical velocities corresponding to the model vertical velocity PDF at this height. The particles were then deposited if their movement took them below a designated deposition height, *z*_{dep} (= 1 m for the runs in this paper). The values from Eq. (7) show reasonable agreement with the dependence of the modeled escape fractions on |*L*| (Fig. 13).

To examine the sensitivity of the model results to *z*_{dep}, runs were performed using the merged model with *z*_{dep} = 2 m and *z*_{dep} = 2.5 m. Geometrically averaged over all the RPV samples, increasing *z*_{dep} from 1 to 2 m and to 2.5 m reduced the modeled concentration by 24% and by 58%, respectively. No significant dependence on |*L*| of the impact of changing *z*_{dep} was found.

#### 4) Boundary layer depth

To examine the sensitivity of the results to *z*_{i}, concentration calculations were performed using 0.5 and 1.5 *z _{i}*. In these calculations, the dependence of

*w*

_{*}on

*z*was included. Geometrically averaged over all the RPV flights, halving

_{i}*z*

_{i}led to a 29% increase in the modeled concentrations, while multiplying

*z*by 1.5 led to a 14% decrease in the modeled concentrations. The impact of changing

_{i}*z*did not significantly depend on |

_{i}*L*|. The increase in the modeled concentration with decreasing

*z*is a result of the reduced volume occupied by the boundary layer in this case. If this were the only cause, halving

_{i}*z*would be expected to double the modeled concentrations. The concentration is kept from doubling because reducing

_{i}*z*also leads to a decrease in

_{i}*w*

_{*}, which in turn reduces the intensity of the convection and the escape fraction.

The focus in this paper is on relatively low altitudes along the initial plume ascent in the CBL. At these altitudes, the plume is dominated by the near-surface parameters and is not dramatically impacted by *z _{i}*. On the other hand, longer distance transport will be much more sensitive to

*z*, as pollen ascends to greater heights before being deposited.

_{i}#### 5) Wind direction

The sensitivity of the modeled concentrations to wind direction was examined by modeling the concentrations with the wind rotated both clockwise and counterclockwise by 45°. Combining the results for both rotation directions, it was found that (geometrically averaging all the RPV samples) rotating the wind direction reduced the modeled concentration by about 32%. This reduction is a result of our attempt during the experiment to place the RPV flight tracks downwind of large source areas. Thus, any rotation in wind direction will tend to reduce the sampled concentration, and this is reflected in the decrease in modeled concentration.

## 5. Summary

Our long-term goal is to describe the transport of pollen under the range of atmospheric conditions normally encountered, ranging from highly convective conditions to stable conditions. Under highly convective conditions with light winds, existing CBL LS models adequately describe this buoyancy-dominated transport through the bulk of the CBL. However, as conditions become less convective and windier, shear-generated turbulence, not accounted for in current CBL models, becomes more important, especially near the surface. Conditions near the surface are very important when modeling the dispersal of particles released in this region. Therefore, our CBL LS model was modified to partially incorporate the impacts of this shear on the turbulence parameters (*σ _{w}* and ε) in the model, resulting in the model referred to in this paper as the merged model. To maintain the relatively simple framework used in the CBL model, the terms representing the covariance between horizontal and vertical velocity fluctuations were not incorporated in the merged model. These terms, which are included in our SL model (Aylor and Flesch 2001), were used to determine the source strength of pollen from the cornfields. The impact of neglecting these terms in the CBL model as wind shear increases is a topic for future studies to determine.

Considering all the cases included in our analyses, the merged LS model underpredicted the measured concentrations by a factor similar to the amount that our CBL LS model overpredicted the concentrations. However, under the most convective conditions, the merged model, on average, was within 5% of the measurements, a significant improvement over previous CBL models. The SL model significantly overestimated the concentrations under highly convective conditions due to the lack of an adequate mechanism for turning particles around once they begin to ascend.

The scatter in the comparison of the concentrations modeled with the merged model and the measurements is partially due to inherent uncertainty over the relatively short averaging periods employed in the study and also to uncertainty in the values of the parameters used as input for the model runs. Such scatter is to be expected in a study that brings together so many components, and the best measure of model performance is obtained by averaging results over a number of cases with relatively similar conditions.

The merged LS model produced reasonable results over a range of conditions. However, a number of the sampling periods were conducted under stable conditions, in which the profile consisted of an unstable layer overlaid with a stable layer. The dispersal of pollen under such conditions remains a challenge to model using the relatively simple LS framework being tested here, and doing so would require the use of a number of tunable parameters (e.g., transition height, entrainment rate, etc.). These conditions typically occur when the atmosphere is in a state of transition from the nighttime stable boundary layer to the daytime convective boundary layer. Perhaps (numerical) prognostic meteorological models, simulating such meteorological conditions, coupled with Lagrangian particle models for dispersion, will be able to address this complex problem.

We thank P. Thiel, T. Testa, G. Neumann, D. Wooley, D. McKenna, C. Hanzel, M. Johnson, B. White, L. Belgoolere, M. Testa, and E. Lowery for excellent technical assistance. This work is supported in part by Hatch Funds; by the Cooperative State Research, Education, and Extension Service, U.S. Department of Agriculture, under Agreements 2001-52106-11528 and 2004-33522-15044; and by a grant from Pioneer Hi-Bred International, Inc.

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Summary of RPV sampling periods. Periods in bold type were used in the analysis. Periods with two *u*_{*} and *L* values consisted of a shallow unstable layer near the surface up to the height indicated in the *z _{i}* column, overlaid by a stable layer with parameters indicated in the columns subscripted “stable.” In the wind direction (Θ) column, PD stands for “poorly defined” and LV stands for “light and variable.”

Source strength, *Q* (grains per meter squared per second), for all fields near the RPV flight tracks and more distant fields that contributed at least 1% of the modeled pollen for either the merged or SL model. The columns are labeled with the field numbers (see Fig. 5).

Comparison of the geometric mean and std dev of the ratios between the modeled and observed pollen concentrations (*C*).