Introduction
Plant disease epidemics develop inside plant canopies, which provide the susceptible host tissue and the conditions necessary for infection by the pathogen. To cause an epidemic, however, the pathogen must be dispersed repeatedly to healthy host tissue. Without this dispersal, an epidemic would simply burn out like a forest fire starved for fuel. Fungus spores are the dispersal agents for a major class of plant diseases, and atmospheric dispersion is the predominant mechanism for transporting the spores of the pathogens to healthy tissue.
Because atmospheric dispersal drives epidemics, the release rate of spores from the plant canopy into the atmosphere Q (spores per meter squared per second) is a crucial quantity. Knowledge of Q is necessary to estimate the spread of disease or to compare management techniques for reducing disease. However, Q is a difficult quantity to measure for spores. The problem is similar to measuring trace gas fluxes from the surface. Although a suite of techniques exists for measuring gas fluxes (e.g., eddy covariance, flux gradient), these methods are generally not amenable to measuring spore emission rates because of the lack of fast-response spore sensors and because of the complexity of the spore release mechanisms (Aylor 1990).
A potential technique for estimating Q is to use a dispersion-model-based method. This method relies on a measurement of the concentration of spores (Cmeasured) at a point P downwind of the spore source. A dispersion model is then used to simulate the release of spores into the atmosphere (e.g., assuming an arbitrary release rate Qmodel), and the spore concentration at point P is calculated (Cmodel). The true spore release rate is found by reconciling the modeled and measured concentrations. The method has been used successfully to estimate trace gases emissions (Wilson et al. 1983; Flesch et al. 1995). The success of the method hinges on an accurate dispersion model, applied faithfully to the actual release conditions. However, modeling the dispersion of plant pathogenic spores is a more difficult task than modeling trace gas dispersion, because Q for spores can depend directly on atmospheric turbulence and because the inertia of spores must be accounted for.
A Lagrangian stochastic (LS) dispersion model represents the best candidate for determining Q. These models numerically mimic the trajectories of “particles” (either marked fluid elements or solid particles) downwind of a source. These models have proved to be accurate and easy to use for calculating the dispersion of atmospheric tracers (Wilson and Sawford 1996). The advantages of an LS model as compared with other kinds of models are 1) the correct prediction of dispersion close to a source, 2) easy incorporation of complex wind flow, 3) grid-free models, and 4) easy incorporation of time-dependent processes. The major difficulty in using an LS model for spore dispersion is theoretical. Plant pathogens are usually transported via “heavy” particles, whose size and mass make modeling atmospheric transport more complex than for “passive” tracer particles. Current theory does not point to a correct way to calculate heavy-particle trajectories. Modeling the dispersion of spores is also made difficult by the need to account for additional physical processes: deposition onto foliage, deposition onto the ground, and, in some cases, washout of spores.
In this paper, our objective is to use an LS-model-based approach to estimate Q for plant pathogenic spores. Following the work of others, we have adapted an LS model for passive tracers to obtain a model for dispersion of heavy particles. We then added algorithms for calculating deposition onto vegetation and the ground and for calculating the washout of spores. This model was then applied to two field experiments to determine Q. The LS-model-based estimates of Q were then compared with independent estimates. We will comment on the accuracy of LS technique in our experiments and on the general applicability of the technique for estimating spore emission rates.
Experiments
The LS simulation model (described in section 3) is compared with particle concentrations from two sets of experimental data. One set of data is taken from an earlier study in which Lycopodium spores were released from line sources inside a wheat canopy (Aylor and Ferrandino 1989). The second set is new data, reported here, in which V. inaequalis ascospores were released naturally by the fungus from a ground-level source in a canopy of mixed grasses. These two case studies present notable contrasts with respect to the size of spores, the height in the canopy where spores were released, and the weather conditions during spore release.
Lycopodium spores released artificially in a wheat canopy
The experiment has been described in detail elsewhere (Aylor and Ferrandino 1989), and only a brief description of the essential elements will be given here. Lycopodium spores were artificially released simultaneously from two line sources located at two heights above the ground in a wheat canopy. Lycopodium spores (physical diameter of ∼30 μm) have a settling speed of 0.019 m s−1 and an equivalent aerodynamic diameter of about 25 μm (Ferrandino and Aylor 1984). For the six realizations of the experiment, the heights h of the wheat canopy were 0.75, 0.85, 0.95, 0.97, 0.91, and 0.95 m. The source heights were 0.53h, 0.47h, 0.53h, 0.52h, 0.44h, and 0.42h for the lower source and 0.89h, 0.79h, 0.80h, 0.78h, 0.74h, and 0.71h for the upper source. The Lycopodium spores used in the two sources were dyed two different colors [red (lower source) and blue (upper source)] to distinguish the two source heights. Aerial spore concentrations were determined using rotorod samplers and suction samplers to collect spores at several heights above the ground downwind from the sources. Wind speed and turbulence were measured above and within the canopy, as was the foliage area density profiles. The release rate of spores (spores per meter per second) was estimated from the weight of the spores released during each trial.
Venturia inaequalis ascospores released naturally by the fungus in a grass canopy
The escape of V. inaequalis ascospores from a grass canopy was studied during the spring of 1997 in Mount Carmel, Connecticut (41°25′N lat, 72°55′W long). The 0.5-ha field contained a mixture of tall fescue and orchard grasses. The field is approximately level and is at the top of a slight rise (Aylor et al. 1993). The V. inaequalis ascospores (physical dimensions ∼6 μm × 13 μm) have a settling speed of about 0.002 m s−1 and an equivalent aerodynamic diameter of about 8.2 μm (Gregory 1973).
Four experimental “spore-release” source plots were established in the grass field. The grass in two of the plots was mowed on a regular basis and the grass in the other two plots was not mowed at all (cf. appendix, Fig. A1). The source of ascospores was scabby McIntosh apple leaves that were spread on the ground in circular areas with a diameter of 4.3 m. Ascospore concentrations were measured at several heights above the ground at the center of these plots. The source plots were separated by 11 m in the north–south direction and by 18.3 m in the east–west direction. The leaves were spread evenly and “nestled” into the short grass using a rake in early December of the previous year. To help to keep the leaves from being scattered by the wind, they were covered with a single layer of highly porous lightweight plastic bird netting (Aylor and Qiu 1996). The V. inaequalis ascospores develop to maturity over a period of time during the spring. The rate at which ascospores become mature first increases, reaches a peak, and then decreases during a period that extends for about 6–8 weeks following the “green-tip” phenological stage of development on McIntosh apple trees (Aylor 1998). They are released into the air during rain events. Aerial concentrations of ascospores were measured during 18 rainy days occurring over the course of 9 weeks in the spring.
Airborne concentrations of V. inaequalis ascospores
Aerial concentrations C (ascospores per meter cubed) of V. inaequalis ascospores were measured using rotorod spore samplers with retracting-type sampling heads (Model 82, Sampling Technologies, Inc., Los Altos Hills, California). The sampling surfaces of the rotorods were coated with a thin layer of high-vacuum silicon grease (Dow Corning, Inc., Midland, Michigan). Rotorods were shielded from rain by 30 cm × 30 cm Plexiglas plates situated about 10 cm above the sampling head. The spore collection rods were placed at heights of 0.15, 0.30, 0.50, and 1.00 m.
The first set of rotorods was operated for 2 h following the start of rain (after the first 0.1 mm of rain) during daylight hours and was then switched off. If rain continued, the duplicate set of rotorods in the second set of sources was then turned on and operated for 2 h. The switching on and off of both sets of rotorods was controlled automatically by a data logger (Model 21X, Campbell Scientific, Inc., Logan, Utah). At the end of a 4-h period, the rotorod samplers were fitted with a fresh set of sampling rods, and the entire sampling sequence was restarted.
Counts of ascospores on the rotorods (obtained using a microscope at 200× magnification) were converted to values of concentration C by accounting for the proportion of the sample surface that was counted, the sampling rate, the duration of the sampling period, and the efficiency of the sampler. The sampling rate (38 L min−1) and capture efficiency (21%) of the rotorod samplers for V. inaequalis ascospores was determined previously (Aylor 1993).
Meteorological measurements
Wind speed and direction, air temperature, relative humidity, and solar irradiance were monitored continuously near the center of the test site using a Model 21X data logger. Wind speed was measured using cup anemometers (Model 014A, Met-One, Inc., Grants Pass, Oregon) located at heights of 0.5, 1.5, and 3.0 m above the ground, and wind direction was measured using a vane (Met-One Model 024A) placed 3.0 m above the ground. Temperature and relative humidity were measured with a probe (Campbell Model 207) that was shielded from the sun and located at a height of 1.5 m. Solar irradiance was sensed by a pyranometer (Model LI-200S, LI-COR, Inc., Lincoln, Nebraska) at a height of 1.8 m. Rainfall amounts were measured using a tipping-bucket rain gauge [Model TR-525 (sensitivity 0.1 millimeters per tip), Texas Electronics, Inc., Dallas, Texas]. The outputs from a leaf wetness resistance grid (Campbell Model 731), the pyranometer, and the rain gauge were used to trigger rotorod spore traps to turn on at the beginning of rainfall during the daylight hours. These instruments were sampled at 10-s intervals and averaged for 1 h during all conditions. During periods of rain, wind speed and direction were averaged, and rainfall amount was totaled every 15 min.
Turbulence was characterized using two three-dimensional sonic anemometers (Gill Instruments, Ltd., Lymington, United Kingdom) at 2.0 m (Research) and 3.6 m (Wind Master) above the ground. The sonic anemometers were sampled at 5 Hz, and variances and covariances of the 3 velocity components (u, υ, w) were recorded every 30 min using a data logger. In addition, to help to characterize wind in the grass canopy, wind speed profiles were measured in and above the grass using hot-wire anemometers and sensitive cup anemometers for selected periods during fair weather.
Ascospore release rates estimated using a laboratory spore release tower
A laboratory estimate of the ascospore release rate QT (spores per meter squared per second) was made at least biweekly during the experiment. A spore tower was used for this estimate. The spore tower, which consists mainly of a vertically oriented wind tunnel and volumetric spore samplers, is described in detail elsewhere (Aylor and Qiu 1996). The tower gives the release rate for a standard number of leaves. To obtain the release rate of ascospores per unit area of ground in the field plots, we scaled the tower results with the number density of diseased leaves in the source plots (Aylor and Qiu 1996). Values of QT to be compared with LS model estimates of Q were determined by extrapolating the most recent spore-tower determinations of QT before and after a natural release of ascospores in the field. During release events lasting several hours, the number of mature ascospores in the source leaves becomes depleted as a consequence of their being released. The depletion of ascospores during a rain event was assumed to be proportional to the time course of the concentration measured in the field. During the course of several extended spore release periods, C was found to decrease exponentially at a rate of about 39% per hour.
LS model for spore dispersion
The LS models are most commonly used to simulate the trajectories of passive tracers. In a passive model, the trajectory of a background fluid element is calculated, and this trajectory will reflect the continually changing fluid velocity as the fluid element travels through the turbulent atmosphere. Complications arise when applying LS models to spore transport; we must account for the effects of inertia and gravity on spore trajectories. According to Wilson (2000), two modifications are necessary to convert a passive LS model to a spore-trajectory LS model. First, the settling velocity υS of the spore must be added to the vertical velocity calculated by the passive LS model. This is to represent the vertical velocity of the heavy particle as it travels through turbulence. The second modification is to reduce the turbulence timescale of the passive LS model to reflect the turbulent conditions “seen” by the spore. These simple changes create an accurate LS model for particles smaller than 300 μm in diameter (Wilson 2000). In this section, we detail our LS trajectory model.
Even with an accurate spore trajectory model, we must include other important processes that affect spore dispersal. In the following section, we outline the trajectory model and our algorithms for foliage and ground deposition of spores and for washout of spores by rain.
Two-dimensional dispersion treatment
Because of the nature of our experimental data, it is possible for us to model spore dispersal in two dimensions (2D), calculating trajectories in the alongwind and vertical directions (x, z). This simplification from 3D to 2D reduces model complexity and the number of model inputs required. In the Lycopodium experiment, spores were released in a line roughly perpendicular to the wind, and concentration was measured downwind of the line source centerpoint. This can be modeled as an infinite crosswind line source, with lateral (y) dispersion neglected. In the Venturia inaequalis ascospores experiment, the source was a circular plot, and concentration was measured above the center of the plot. We can model this as an infinite crosswind area source (expansive crosswind rectangular source). Although this is not a totally faithful representation of a circular source, we believe the error associated with this simplification is small in our case. This view is based on 3D simulations of a circular, passive-tracer ground source. In neutral and stable stratification (the situation in this study) and for the plot size of interest here, the results suggest our 2D treatment will yield concentrations that are only 1%–5% too high (in unstable cases, this error would be larger because of increased lateral dispersion).
Spore trajectory model
For heavy particles (e.g., unit density spheres with diameters >300 μm), it would be necessary for us to solve simultaneously the equations of motion for the fluid and for the particle. Wilson (2000) and others before him found that for small particles (diameter < 300 μm) it is not necessary to solve the particle equation of motion. This is fortunate because of the extreme computational demands that would be added by the particle equation of motion due to the very small time step implied by the drop equation of motion. The equivalent aerodynamic diameter of V. inaequalis ascospores is about 8.2 μm (particle relaxation time τR is about 0.2 ms), and the aerodynamic diameter for Lycopodium spores is about 25 μm (τR about 2 ms). The diameters of both particles are well below the limit determined by Wilson (2000), and their motions in the atmosphere can be adequately described by the model given here.
Timescale correction
Because of their relatively small settling speeds, the effect of f on the calculated motion of spores is small. For the V. inaequalis ascospore experiments (friction velocity u∗ values were ≥ 0.06 m s−1), we estimate that f was greater than 0.99 above midcanopy height and greater than 0.95 at heights within a few centimeters above the ground. For the Lycopodium experiments (u∗ ≥ 0.30 m s−1), we estimate that f is greater than 0.96 above midcanopy height and greater than 0.83 within a few centimeters above the ground.
Spore deposition on vegetation
Spore deposition on ground
Spore washout by rain
Model requirements
The model assumes a steady wind field and requires vertical profiles (as a function of height above the ground) of several time-average wind statistics. For model inputs, we require the following:
•Spore characteristics
1) The settling velocity of the spore υS.
•Atmospheric properties
2) The average horizontal Eulerian wind velocity U(z) (and the gradient ∂U/∂z);
3) the Eulerian velocity variances
σ2u σ2w uw σ2u σ2w uw 4) Lagrangian timescale TL.
•Canopy information
We conceptually divided the plant canopies into two vegetation classes, leaf and stem, and then specified
5) (i) leaf area density (m−2 m−3) as a function of height, (ii) characteristic leaf angle as a function of height, and (iii) characteristic leaf dimension; and
6) (i) stem area density (m−2 m−3) as a function of height, (ii) characteristic stem angle as a function of height, and (iii) characteristic stem dimension.
Calculating C and Q
Results
Lycopodium experiments
Concentration profiles
The shapes of LS model calculated profiles (40 000 particles released per source) are in generally good agreement with the shapes of the Lycopodium concentration profiles measured above the canopy (Figs. 1a–f). The agreement between modeled and observed concentration profiles in the lower canopy is less good. The measured concentrations have been scaled by a constant (for each profile) factor Qmodel [Eq. (17)], which was determined by a least squares regression to fit the concentrations measured by each of the four rotorod samplers located above the canopy (section 3h). This was done for each of the 6 experiments, giving 12 different Qmodel estimates.
Comparing Qmodel with Qmeasured
A measured rate of Lycopodium spore release Qmeasured was determined by weighing the spores and their emitters before and after each release period. The LS model predicted release rates that on average were about 20% smaller (blue spores) or 3% larger (red spores) than release rates estimated by weighing the spores, both for the source located near midcanopy height and for the source located in the upper canopy (Table 1). There was a significant linear relationship between Qmodel and Qmeasured (significance level P = 0.02) for releases from both source locations.
Venturia inaequalis experiments
Concentration profiles
Rain occurred and ascospore concentrations were measured above the experimental plots on a total of 18 days during the experiment. On several of these days, multiple concentration profiles (each one a 2-h average) were measured, depending on the duration of the rain event. Over the course of the season, V. inaequalis ascospore release rates [estimated using the laboratory tower; cf., section 2b(3)] ranged from less than 100 to more than 15 000 ascospores per meter squared per second (Fig. 2).
The shapes of a total of 92 individual concentration profiles were compared (4 profiles out of a total of 96 collected were not included because of low counts). The vertical profiles of concentration are plotted in four groups according to the height of the top of the grass leaf area in the source plots (Fig. 3).
Concentrations of ascospores decreased rapidly with height above the ground, consistent with a ground-level source. We fitted the LS model to the concentrations at z = 0.15 m by dividing these concentrations by a single number, which is a modeled ascospore release rate [Eq. (17)]. On a log scale, this amounts to a simple horizontal translation along the log(Cu∗/Q) axis and does not affect the slope of the C profiles. The shapes (slopes) of the measured normalized concentration profiles (Cu∗/Q) were fitted well by the LS model using TL [Eq. (A4)] with the premultiplier set equal to 0.4 [using Eq. (A4) with the premultiplier equal to 0.5 as written tended to predict somewhat higher concentrations and smaller slopes than were measured].
Release rates of Venturia inaequalis ascospores
By matching the modeled and measured concentrations for each measured profile, we obtained a series of values for estimated spore release rate Qmodel. For each sampling day, we calculated the total spore release per unit ground area per day, qmodel (spores per meter squared per day), by first multiplying each value of Qmodel by the duration of a sampling period (i.e., 7200 s) and then by summing all of these values for a given day. Spore release rates Qtower for each sampling period were estimated using the laboratory tower results and the number density of source leaves on the ground, as described in section 2b(3). In a similar manner, we used the spore release rates Qtower estimated using the laboratory spore tower to obtain values for total spore release per unit ground area per day for the tower qtower (spores per meter squared per day). These “daily” values of qmodel and qtower were highly correlated [qmodel = 0.81qtower (variance r2 = 0.44; degrees of freedom df = 17; P < 0.002)] (Fig. 4). There is an obvious outlying point (occurring on yearday 126) to remind us of the great difficulty of directly determining Q for ascospores. If this one outlier is removed, then the regression instead becomes [qmodel = 0.55qtower (r2 = 0.66; df = 16; P < 0.000 05)]. Nevertheless, the generally good agreement [particularly in the season's total (Fig. 4b)] suggests that the LS model can be used in conjunction with measured concentration values to obtain reasonable estimates of spore release rates that would otherwise not be possible to obtain.
Discussion and conclusions
Modeling the spread of plant disease by aerially dispersed pathogens requires knowledge of the number of pathogenic spores deposited on susceptible plant tissue at various distances from a source. Given the aerial concentration of spores surrounding susceptible plants (or in the vertical column of air above the plants if wet deposition is involved), it is possible to quantify the number of infections that are likely to occur (Aylor and Kiyomoto 1993). Unfortunately, the ability to predict C is extremely limited because of the difficulty of determining the rate of spore release from a source, owing mainly to the microscopic nature of spores and to the lack of a fast-response sensor for discriminating fluxes of spores of specific pathogens. Our LS model gave reasonable estimates of Q both for Lycopodium spores released inside a wheat canopy from elevated line sources (Table 1) and for V. inaequalis ascospores released naturally by the fungus during rain from ground-level area sources (Fig. 4).
On both theoretical grounds and an examination of our results, we have lower confidence in our model predictions of Lycopodium concentrations within the wheat canopy than above (Fig. 1). This lack of confidence is due to the difficulty in accurately measuring winds in a plant canopy and to the unresolved complexity of the wind flow within the canopy. Also, our model predictions in the canopy were characterized by large stochastic uncertainty. We attribute this to the small number of model spores that remain airborne deep in the canopy at the sampling location and to the high turbulent intensity in the canopy. These factors combine to give a relatively large variability in CLS predictions in the canopy. Another factor creating lower confidence is the greater uncertainty of Cmeasured in the canopy. Suction samplers, which were used of necessity owing to the close proximity of the canopy's various elements, are less accurate than rotorods because of anisokinetic sampling errors (Hinds 1982).
An outlying point for V. inaequalis ascospores occurred on yearday 126 (Fig. 4) during a period of rapid biological development (maturation) of the ascospores (Fig. 2). It is highly likely that our spore tower determination underestimated the peak spore release in this case. In view of the difficulty of estimating Q for ascospores from direct measurements, we strongly favor the LS model determinations of Q.
An important issue when using a model to simulate spore dispersal is the difference between actively and passively released spores. The model we have outlined here is appropriate for actively released spores, that is, spores that are released quasi-continuously, independent of the ambient wind speed (e.g., Lycopodium and V. inaequalis experiments). However, a key model assumption is invalid for passively released spores whose release rate varies with the ambient wind velocity. This is the assumption that the wind velocity is described by Gaussian statistics (pdfs). It is reasonable to suppose that actively released spores experience the entire velocity pdf. Based on the dispersion results of Flesch and Wilson (1992) and Wilson (2000), it is reasonable to use Gaussian statistics. However, passively released spores are different. The liberation and the initial stages of dispersal of this type of spore occur during wind gusts that are above a particular threshold wind speed (Aylor and Parlange 1975; Aylor 1990). Although our model can theoretically accommodate situations in which spore release occurs in such truncated (censored) wind statistics (Legg 1983), it is likely that the inaccuracy of using Gaussian pdfs will become pronounced, and a more sophisticated model will be required to quantify the dispersal of spores that are passively liberated from lesions into the air during gusts.
Gusts and lulls in the wind have another potential effect on dispersal. In the absence of vertical fluctuations of the wind, spores released near the ground would settle onto the ground in a matter of seconds. If lulls in the wind last for too long, then the dispersal of a substantial number of spores might be extremely limited. A characteristic timescale for spores to be deposited on the ground by sedimentation is τS = dS/υs, where dS is the vertical distance that a spore is energetically projected into the air by the fungus, and υS is the settling speed of the spore in still air. For V. inaequalis ascospores, the value of dS is between 3 and 7 mm (Aylor and Anagnostakis 1991), and υS is 0.002 m s−1 (Gregory 1973). Together, these lead to values of τS in the range 1.5–3.5 s. Lulls in the wind near the ground in a grass canopy rarely lasted for more than 3 s (Aylor et al. 1993). Their average length was closer to 1 s, which is considerably less than τS. Thus, it does not appear that lulls generally last long enough or are frequent enough to bias significantly our calculations of deposition of V. inaequalis ascospores by sedimentation. Based on this, we likely are justified in our use of Gaussian pdfs to calculate the motions of ascospores near the ground. This may not be the case for larger spores (with substantially greater settling speeds) that are released this close to the ground. In this case, many spores would be deposited right at the source, leaving only those that travel in gusts (see previous paragraph) to be dispersed.
Venturia inaequalis ascospores become airborne during periods of rain. Earlier studies (Aylor and Ducharme 1995) showed that the fluctuations in vertical and horizontal components of wind velocity within a few meters above the ground are in good agreement with those found during conditions of fair weather and near-neutral atmospheric stability. Thus, for purposes of modeling the initial aerial dispersal of V. inaequalis ascospores, it probably is reasonable for us to have used the description of velocity variances determined in studies during fair weather (appendix A). As far as we are aware, there are no studies during rain to guide us in a choice of TL different than the one we took for our studies.
Quantifying the rate of release of spores and their escape from a canopy is a crucial first step in evaluating risk of disease spread, whether from naturally occurring pathogens or from pathogens purposely introduced as biocontrol agents (De Jong et al. 1999). The release rate Q is determined by the biology of the pathogen interacting with the environment and is a highly dynamic process. The dispersal of spores released inside a plant canopy is determined by the physical characteristics of the spores and the canopy, the height of spore release in the canopy, and the vertical profiles of wind speed and turbulence in and just above the canopy. Additional challenges of modeling spore dispersal (as compared with trace gases) arise from the spore's small but finite inertia and sedimentation, microscopic size, and proximity of the source to surfaces. Our LS model realistically describes these physical effects.
We successfully used a Lagrangian stochastic model–based approach to estimate the release of spores into the atmosphere. This problem is nearly intractable by other methods. Our estimates of Q appear to be excellent, considering the complexity of the problem. This indicates accuracy of not only the LS model but also of the deposition algorithms and shows the quality of the meteorological inputs. Thus, the application of an LS model provides a new tool that significantly advances the ability to model the aerial dispersal of microscopic biological aerosols and furthers the application of meteorology to management of plant diseases.
Acknowledgments
We thank P. Thiel and J. Severino for able technical assistance and F. Ferrandino and Y. Wang for helpful comments on an earlier draft of the manuscript. This material is based upon work supported in part by the Cooperative State Research, Education, and Extension Service, U.S. Department of Agriculture, USDA-NE-IPM 97-04077.
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APPENDIX
Wind Speed and Turbulence Characteristics andModel Parameters
The model assumes a steady wind field and requires vertical profiles (as a function of height above the ground) of several time-average wind statistics. These include the average horizontal Eulerian wind velocity U(z) (and the gradient ∂U/∂z), the Eulerian velocity variances
Wind profile shapes and parameter values were obtained from several earlier studies (Aylor et al. 1993; Wilson et al. 1981; Wilson et al. 1982; Raupach et al. 1991). Vertical profiles of u, σw, and σu in and above a grass canopy were assumed to scale with u∗ and h in concert with findings for a wide range of canopy types, heights, and densities (Raupach et al. 1991). Statistics were defined in three regimes: inside the canopy, above the canopy, and in the roughness sublayer (Kaimal and Finnigan 1994; Mahrt 2000; Raupach 1989; Raupach et al. 1980, 1991). The depth of the roughness sublayer extends for a vertical distance of about 2(h − d) above the displacement height (Mahrt 2000; Raupach 1994). For the relatively short, dense [leaf area index (LAI) ∼ 2–4] canopies used in this study, the roughness sublayer is expected to extend about 0.3h above the top of the canopy (∼0.3 m for the wheat and ∼0.1 m for the grass), that is, the height zw of the roughness sublayer above the ground is about 1.3h. In the roughness sublayer, the Reynolds stress is essentially constant, and, for canopies having LAI greater than 1, the average wind speed does not deviate significantly from surface layer values (Kaimal and Finnigan 1994; Raupach 1994; Raupach et al. 1996). In the roughness sublayer, the σw and σu both decrease by about 10%–15% from above the sublayer to the top of the canopy, and the magnitude of the correlation coefficient ruw increases from about −0.32 above to −0.45 at z = h (Kaimal and Finnigan 1994). The following sections describe the wind statistics used in our model.
Above the canopy
The Lycopodium experiments were conducted during conditions when atmospheric stability was close to neutral or slightly to moderately unstable, values of L in meters for the six realizations of the experiment were estimated from the data given in Aylor and Ferrandino (1989) to be −100, −40, −100, −40, −10 000 (neutral), and −40, respectively. Best fits to the average wind speed profiles above the canopy yielded values of d/h equal to 0.7 for the first five realizations and equal to 0.62 for the last realization of the Lycopodium experiment. The values of z0/h were 0.11, 0.08, 0.08, 0.065, 0.11, and 0.10, respectively, for the six realizations of the Lycopodium experiment. The V. inaequalis experiments were conducted during overcast, rainy (frontal rain) conditions, and calculations were done using the equations for stable conditions, with L equal to 10 m, d/h equal to 0.7, and z0/h equal to 0.06 for all cases. Values of u∗ were obtained by fitting measured horizontal wind profiles for the Lycopodium experiment and from mean uw measured using a 3D sonic anemometer (Research Model, Gill Instruments, Ltd., Lymington, United Kingdom) for the V. inaequalis experiment.
Above the roughness sublayer
Inside the roughness sublayer
In the layer between h and zw (h ≤ z ≤ zw), the values of σu and σw were assumed to decrease linearly from the values given by Eqs. (A6)–(A9) to values at the top of the canopy that were about 15% smaller than the values above zw (Kaimal and Finnigan 1994). This yielded values σu(h) = 2u∗, σw(h) = 1.1u∗, and ruw(h) = −0.45.
Inside the canopy
The value of the attenuation factor γ1 was taken equal to 4 in the wheat canopy, in agreement with findings in a corn canopy (Wilson et al. 1982), and was taken equal to 2.5 in the grass canopy (Aylor et al. 1993). The standard deviations of the wind σw and σu were taken to decrease exponentially with depth inside the canopy with the same length scale, h/2.4 (so that γ2 = γ3 = 2.4) (Aylor et al. 1993), and 〈uw〉 was assumed to have a length scale of h/3.9 (γ4 = 3.9). The vertical variations of σw/u∗ and σu/u∗ chosen for inside the canopy are in general agreement with the findings of others in nonforest canopies (Raupach et al. 1991; Wilson et al. 1982).
The values of several properties of the spores and the canopies used in the model are given in Table A1. Values for the vertical distribution of the leaf area density for the Lycopodium/wheat canopy experiment was taken from Fig. 1 of Aylor and Ferrandino (1989). For the V. inaequalis/grass experiments, the grass in two of the source plots, and in a 20 m by 20 m area surrounding each of these plots, was mowed to a height of about 0.06 m every 7–10 days (Fig. A1). The grass in the other two source plots and in the 20 m by 20 m areas surrounding each of these sources was not mowed. By the end of the season, the top of the leaf area in the unmowed plots reached about 0.7 m, and the seed heads reached a height of about 1.0–1.2 m (Fig. A1a). The grass was relatively sparse and had an average LAI at the end of the season of 2.1 ± 0.4 m2 m−2. Most of the plant area density was concentrated close to the ground, with about 73% of the area occurring below a height of 0.2 m (Fig. A1b). The height h of the canopy used for normalizing the canopy wind flow measurements in the unmowed plots, was taken to be the top of the dense leaf area, which was about 0.3 m at the end of the season.
Normalized concentrations Cu∗/Q of Lycopodium spores released from line sources inside a wheat canopy. Data (symbols) and LS model calculations (lines) are for spores released at height z ∼ 0.5h (triangles, dashed lines) and at z ∼ 0.7h (circles, solid lines). There were six experiments with the following values of h (m) and u∗ (m s−1): (a) h = 0.75, u∗ = 0.49; (b) h = 0.85, u∗ = 0.30; (c) h = 0.95, u∗ = 0.43; (d) h = 0.97, u∗ = 0.35; (e) h = 0.91, u∗ = 0.38; (f) h = 0.95, u∗ = 0.39. The value of h/d used was 0.7 for (a)–(e) and 0.62 for (f); the value of z0/d used was 0.11, 0.08, 0.08, 0.065, 0.11, and 0.10 for (a)–(f), respectively. Measurements were made downwind from the source at distance x = 1 m for (a) and at x = 2 m for (b)–(f)
Citation: Journal of Applied Meteorology 40, 7; 10.1175/1520-0450(2001)040<1196:ESRRUA>2.0.CO;2
Potential release rate QT of ascospores (circles) from diseased apple leaves collected in the field on the days indicated. Results were determined on the day of collection using the laboratory spore-release tower and the area density of source leaves in the experimental plots [cf. section 2b(3)]. Spore concentration profiles were measured in the field during rain events on 18 different days indicated by (+) along the top of the graph
Citation: Journal of Applied Meteorology 40, 7; 10.1175/1520-0450(2001)040<1196:ESRRUA>2.0.CO;2
Normalized concentration profiles of Venturia inaequalis ascospores (Cu∗/Q) vs height above the ground. Profiles were measured outdoors in the center of 4.2-m-diameter source plots. Measured values (filled diamonds) are compared with model calculations using Eq. (A4) as written, with the premultiplier equal to 0.5 (dashed lines) and 0.4 (solid lines). The horizontal bars are the standard deviations of the mean, and n is the number of profiles combined in the means (combined total of 92). Upper row plotted on linear–linear scale; lower row plotted on linear–log scale
Citation: Journal of Applied Meteorology 40, 7; 10.1175/1520-0450(2001)040<1196:ESRRUA>2.0.CO;2
Comparison of measured and modeled daily ascospore release. (a) Daily total release of Venturia inaequalis ascospores predicted by the LS model qmodel, compared with qtower determined using the laboratory spore tower (open diamonds). The regression (solid line) is y = 0.81x (r2 = 0.44; df = 17; P < 0.002); the dashed line is the 1:1 line. (b) Cumulative daily release of Venturia inaequalis ascospores predicted by the LS model (solid line) qmodel compared with qtower determined using the tower (dashed line). The two lines are not significantly different (P = 0.68) according to a Kolmogorov–Smirnov two-sample test
Citation: Journal of Applied Meteorology 40, 7; 10.1175/1520-0450(2001)040<1196:ESRRUA>2.0.CO;2
Fig. A1. Height and leaf area density of grass (LAD) in plots where concentration profiles of Venturia inaequalis ascospores were measured. (a) Grass heights in the experimental plots during the course of the spore-release season. In the mowed plots (solid triangles), the grass height follows a saw-tooth pattern; in the unmowed plots, the height of the leaf area (diamonds) and the stems and seed heads (circles) increased steadily to a maximum at about yearday 160. (b) Vertical profile of LAD in the unmowed experimental plots at the end of the season. Shown are the average (symbols) and standard deviations (horizontal bars) of LAD
Citation: Journal of Applied Meteorology 40, 7; 10.1175/1520-0450(2001)040<1196:ESRRUA>2.0.CO;2
Comparison of measured spore release rates Qmeasured [data from Aylor and Ferrandino (1989), Table II] and release rates predicted by the LS model Qmodel for Lycopodium spores released from line sources inside a wheat canopy (see section 2a). For the upper-level canopy source (blue spores): Qmodel = −0.13 (P = 0.94) + 0.80 (P = 0.022)Qmeasured. For the midlevel canopy source (red spores): Qmodel = −1.91 (P = 0.43) + 1.34 (P = 0.017)Qmeasured. For both sources combined: Qmodel = −0.27 (P = 0.87) + 0.94 (P = 0.004)Qmeasured
Table A1. Values of {+}υ{-}s and canopy physical properties used for simulating the two experiments
