Modeling Soybean Rust Spore Escape from Infected Canopies: Model Description and Preliminary Results

Transcription

1 APRIL 2009 A N D R A D E E T A L. 789 Modeling Soybean Rust Spore Escape from Infected Canopies: Model Description and Preliminary Results DAVID ANDRADE, ZAITAO PAN, AND WILLIAM DANNEVIK Saint Louis University, St. Louis, Missouri JEREMY ZIDEK The Pennsylvania State University, State College, Pennsylvania (Manuscript received 26 November 2007, in final form 5 September 2008) ABSTRACT Asian soybean rust, caused by Phakopsora pachyrhizi, an airborne fungal pathogen, is an annual threat to U.S. soybean production. The disease is spread during the growing season by fungal spores that are transported from warm southern locations where they overwinter. Current models of long distance spore transport treat spore sources as constant emitters. However, evidence suggests that the spore escape rate depends on 1) the interaction between spores and turbulence within and above an infected canopy and 2) the filtering capacity of the canopy to trap upward-traveling spores. Accordingly, a theoretically motivated yet computationally simple forecast model for escape rate is proposed using a simple turbulence closure method and a parameterization of the canopy porosity. Preliminary escape-rate forecasts were made using the friction velocity, an estimate of initial spore concentrations inside an infected canopy, and the canopy s leaf area distribution. Sensitivity tests were conducted to determine which biological and meteorological variables and parameters most impact modeled spore escape rates. The spore escape model was integrated with a large-scale spore transport model that was used to forecast spore deposition over U.S. soybean production regions. Preliminary results suggest that varying meteorological conditions significantly impact escape rates and the spread of the disease. 1. Introduction In 2004, Asian soybean rust (SBR), caused by Phakopsora pachyrhizi, was detected for the first time in the continental United States (Schneider et al. 2005). Previously, the disease had spread throughout the world s major soybean production regions. In South America, the disease was particularly severe, resulting in crop losses as high as 80% in areas where the disease was well established (Yorinori et al. 2005). A similar scenario was expected to unfold throughout the United States (Isard et al. 2005). Instead, SBR has not spread as aggressively throughout the United States as it has across South America s soybean growing regions. It is likely that a combination of agricultural practices, better access to fungicide, and Corresponding author address: Zaitao Pan, Saint Louis University, 3642 Lindell Blvd., St. Louis, MO panz@eas.slu.edu midlatitude weather conditions have all limited the severity of SBR. For instance, in the United States, soybeans are planted only during summer, even in warm southern areas, and thus SBR can only survive on alternative hosts, such as kudzu, during winter. Similarly, observations of SBR infection in the United States collected by the U.S. Department of Agriculture (USDA) support findings by Pivonia and Yang (2004) that freezing weather restricts SBR to frost-free areas during winter either directly by killing the pathogen (Melching et al. 1989) or indirectly by defoliating its hosts. This has limited the area in the United States where SBR has been able to overwinter to south Texas, south Florida, and scattered urban heat islands located farther north (USDA 2007). SBR is, however, an annual threat to soybean production during the growing season. USDA observations collected since 2004 indicate that SBR begins to migrate northward during spring and early summer. The precise geographical path of the disease spread has varied each year since Warm and humid weather conditions are DOI: /2008JAMC Ó 2009 American Meteorological Society

2 790 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 favorable for disease development (Pivonia and Yang 2004). Winds are thought to be responsible for the aerial transport of Peronospora tabacina spores (Aylor 2003). Various subsequent studies (Pivonia and Yang 2004; Isard et al. 2005, 2007) have implied that the same mechanisms are responsible for the dispersion of SBR spores. At the present time, there is no cost-effective treatment that successfully eradicates SBR from an infected field without considerable damage to the crop. Also, no known host resistance to SBR has been identified (Hartman et al. 2005). Instead, the disease is controlled by applying fungicide during its early stages (Kemerait et al. 2005; Dorrance et al. 2007). This forces farmers to purchase fungicide as a form of insurance against possible SBRinduced crop losses. If farmers were somehow able to obtain prior knowledge of the risk of infection, they could potentially save money by purchasing and applying fungicide only when needed. Identifying this risk requires knowledge of when and where spores will be transported. Fortunately, aerosol transport by meteorological mechanisms in the atmospheric boundary layer (ABL) and free atmosphere (FA) has been extensively studied and is well simulated by a number of existing models, such as the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the Community Multiscale Air Quality (CMAQ) model, among others. Fungal spores do not begin their life cycle in the atmosphere, however. Instead, they are released from disease lesions located well within infected plant canopies. Their upward transport outward into the surface boundary layer (SBL) has not been thoroughly studied (Isard et al. 2005) and is not yet, to our knowledge, simulated in operational large-scale transport models. Nonetheless, the details of this process are needed to accurately estimate the escape rate of spores from infected canopies. This escape rate is known within the framework of large-scale aerosol transport models as the source strength, a vital initial and boundary condition of the dynamical system. For simplicity, early studies of SBR spore dispersion over the United States by Isard et al. (2005) and Pan et al. (2005) treated escape rates as independent of meteorological conditions. However, research has found that the escape rate of aerosol-like particles from within plant canopies into the surface boundary layer is dependent on wind flow and canopy structure (Zelger et al. 1997; Meroney 1968). This dependency exists because aerosol transport within a canopy, as in the ABL, is predominantly controlled by turbulent motions (Aylor and Taylor 1983). To account for this, Isard et al. (2007) treated the SBR spore escape rate from a canopy as an empirical function of surface wind speed and restricted spore escape to periods when it was not raining. Aylor et al. (2001) simulated the escape rate of potato late blight spores, Phytophthora infestans, from infected canopies using a Lagrangian stochastic (LS) particle trajectory model (PTM). The results depended minimally on biological characteristics of the system only vertical leaf area distribution (LAD) and average spore terminal velocity (y t ) but heavily on the wind flow and its statistical properties obtained from external sources. While the model s predictions were accurate (Aylor et al. 2001), its numerical complexity and dependence on various vertical profiles of turbulent statistics, which are not known a priori, makes it difficult to incorporate into larger-scale transport models. In fact, determining the vertical profiles of turbulent statistics within a plant canopy is still an unresolved problem. Our current work has been to develop a computationally simple, yet theoretically motivated model that simulates the spore escape process. Like the LSPTM, our model computes escape rates using only a few biological variables and the leaf area distribution and average spore terminal velocity. In contrast to the LSPTM, our model determines the statistical properties of the wind flow using observations, closure schemes, and other techniques, instead of requiring those properties as input. The approach has been made simple enough, in theory, as to require only 1) a measurement of the mean horizontal wind speed at a single level above the canopy (or friction velocity) and 2) the LAD. Using this approach, spore source strength over infected fields can be more accurately computed without much computational overhead. Output from largescale transport models can be improved by incorporating these source strengths, which depend on weather conditions and canopy morphology. Finally, with better model output, the detail and accuracy of disease spread forecasts can be improved, which can help farmers more cost effectively mitigate crop loss in areas prone to SBR. 2. Background a. Spore and disease characteristics Rust spores are tiny amorphous particles with nontrivial terminal fall speeds. In nature, they can travel alone or as part of larger clusters. They exhibit a tendency to fall downward during calm weather conditions and are thus heavy particles. The dynamics of spore transport within the canopy is dependent on the temporal and spatial structure of the wind field and its interaction with the plant parts (Aylor and Ferrandino 1985). Spores can initiate SBR when leaves of the host are moist and the temperature is at or above 108C. Under ideal conditions, the disease can develop from a single

3 APRIL 2009 A N D R A D E E T A L. 791 spore in approximately 3 6 weeks (Isard et al. 2005). In the upper canopy, greater ventilation likely reduces the rate of infection in that area by maintaining lower humidity. In the United States, during summer, normal meteorological conditions are usually favorable for disease development (Pivonia and Yang 2004; Pivonia et al. 2005). b. Canopy turbulence Turbulent motions dominate the wind field within dense plant canopies. Plant stalks and leaves form a dense collection of objects that act as a large sink for mean-flow momentum. Sparse canopies are probably not a significant source of SBR spores because of low foliage density and good ventilation. Also, SBR tends to infect soybeans during its reproductive stages when the canopy is dense rather than during its vegetative stages when the canopy is sparse. For this reason, sparse canopies are not considered here. Various features of canopy turbulence important to constructing a model of upward spore transport are reviewed in the following sections. 1) EDDY CHARACTERISTICS TABLE 1. Description of dominant turbulent eddy types within canopies (adapted from Finnigan 2000). Sweep and ejection are the two most frequent eddy types. u9 w9 Eddy type Positive Positive Outward interaction Positive Negative Sweep Negative Negative Inward interaction Negative Positive Ejection The spectral decomposition of turbulent kinetic energy (TKE) in dense canopies is characterized by a scale separation between eddies 1) with sizes on the order of the canopy height h and 2) of sizes comparable to individual leaves and stems (Finnigan 2000). Larger eddies are produced by vertical shear of the mean wind. They are spatially large, intense, long lived, and probably responsible for most transport of heavy particles within a dense canopy. Typically, large eddies traverse the entire canopy vertically. They are also spatially and temporally well correlated, which implies that large eddies are persistent coherent structures embedded in the wind flow. Four classes of large eddies were first described by Lu and Willmarth (1973) (Table 1). Their interaction, frequency, and spatial distribution all determine the nature of spore transport within a dense plant canopy. Observations and analysis by Gao et al. (1989) indicate that there is good spatial and temporal correlation between nearby turbulent motions within plant canopies. This provides strong evidence that largescale eddies transport spores coherently within a canopy and do not simply shuffle spores around. Spores escape during organized wind events instead of diffusing upward. This feature of canopy spore transport is a major logical premise for the physical model of spore escape from canopies presented here. Sweep and ejection eddies are the first- and secondmost frequent and energetic eddy types, respectively. Both types occur in coupled pairs as part of large counterrotating vortices. This eddy arrangement is efficient at sweeping spores located on top and underneath leaves (sweep) and then concentrating the spores into an updraft (ejection). Smaller eddies are usually too small, too weak, and too short lived to contribute significantly to canopy spore transport. Similarly, the contribution to the total TKE of outward and inward interaction eddies has been found to be small except in coherently waving canopies (Finnigan 1979). For this reason, we believe that only sweep and ejection eddy types play a significant role in the transport of SBR spores within dense soybean canopies. 2) TURBULENT STATISTICS Quantifying the number of spores that are transported upward by turbulent eddies is key to simulating spore escape from an infected canopy. Escape rate depends on the strength and frequency of sweep-ejection eddy couplets. The mean wind and variance profiles are closely related to eddy strength and frequency. The mean wind profile is related to the variance profiles via the dynamical systems that describe canopy wind flow (Finnigan 2000). Its vertical shape within dense plant canopies determines both the amount of TKE generated and vertical momentum flux. Mean wind profiles within differing dense plant canopies (Baldocchi et al. 1983; Raupach et al. 1996) possess similar characteristics, with differences attributable to differing vertical leaf area distributions. Generally, in the upper canopy, the wind increases exponentially with height (z). Near the ground, the wind profile is logarithmic. An inflection point separates these two zones (Fig. 1). A secondary local maximum is often found within the stem space, but often ignored in dense canopies. The variance profiles, su 2(z), s w 2(z), and s uw(z) [ u 0 w9, are inhomogeneous with height and in general satisfy the inequality su 2. s w 2 at all levels in the canopy. Also, total TKE increases toward the canopy top. The stress, 2s uw, is negative throughout the depth of most plant canopies. In the lower half, it varies by a small percentage, decreasing to less than 20% of its value outside the canopy. Usually, between z/h and the canopy top, the magnitude of the stress increases tremendously. Above the canopy, the stress satisfies the constant-flux layer condition of a classic surface boundary

4 792 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 1. Typical profiles of the mean wind, LAD, and LAI in a soybean canopy. Curves were constructed from measurements presented in Baldocchi et al. (1983). Each curve has been normalized for comparison of its shape with the others. layer. Near the ground, the stress is very close to zero, indicating that the canopy elements are efficient sinks of streamwise momentum (Finnigan 2000). 3) TURBULENT VELOCITY PROBABILITY DENSITY DISTRIBUTION The frequency of sweep and ejection eddy couplets can be determined from a joint probability density function (PDF) of turbulent velocities. In general, its shape and magnitude are not easily determined. Measurements of joint PDFs in dense canopies have shown that turbulent velocities are not normally distributed. Vertical velocities are downwardly skewed. Horizontal wind speeds are biased toward larger values, suggesting that intermittent but intense wind gusts are most common (Finnigan 2000). In other words, large clouds of spores probably escape during rare high-wind events. During longer quiescent periods, few spores are transported. Large correlation coefficients, s uw /(s u s w ), in the upper canopy suggest that eddies become larger and more coherent with height. This is represented statistically by a rotation of the turbulent velocity joint PDF about the z axis. Large correlation coefficients greatly reduce the relative importance of outward and inward interactions and increase the relative importance of sweeps and ejections to spore transport. The amount of rotation varies with height. 3. Model rationale a. Canopy spore concentrations Spore escape rates are naturally quite dependent on the supply of spores within the canopy. This supply can be estimated from the number of spores that are produced by infected lesions during a certain period of time. Precise knowledge of the spatial distribution of infected lesions is necessary to determine the number of available spores for lifting per unit area. Unfortunately, the exact location where spores landed to initiate the disease and the inner dynamics of disease spread within the canopy are not well understood or easily simulated at present. For this reason, it is assumed that the horizontal distribution of lesions is random enough so that statistically it is horizontally homogeneous (HH). With this assumption, the horizontally averaged number of lesions per unit area can be written as a function of height alone. The horizontal density of infected lesions (lesion area per ground area) at each height cannot exceed the amount of leaf area. In the absence of more precise data, the number of lesions per unit leaf area was assumed to be constant so that the lesion concentration is proportional to A(z). The release of spores into the air generally occurs once per infected lesion. Spores settle on leaves and stems during low-wind periods. Later, when intense and large enough turbulent eddies sweep and then eject spores from the canopy, a number of those spores make it through the canopy top into the atmosphere. The average number of spores available to turbulent eddies for lifting during a given time period is denoted here as p(z). A simple model for p(z) based on the discussion above is p(z)5 spore production rate lesion 3 lesions leaf area 3a(z)1u(z), (1) where a(z) is the vertical leaf area distribution and u(z) refers to any other spore sources that may exist because of biophysical processes that are not yet resolved. The quantity p(z)dz has units of spores time 21 length 22 and represents the average number of spores available for lifting by turbulent eddies in a vertical section of the canopy bounded by z and z 1 dz during the averaging time period. The portion of Eq. (1) that precedes a(z), henceforth referred to as C, depends on a number of biological and meteorological conditions (dynamics of disease spread, temperature, moisture, amount of UV radiation, etc.) whose influences are not well known at the present time. A crude and simple method for approximating C is to use estimates by Isard et al. (2005) for the number of spores produced per day per hectare in heavily infected canopies. These estimates can be distributed evenly through the period of emission and then divided by the canopy leaf area index (LAI) so that

5 APRIL 2009 A N D R A D E E T A L. 793 spore production rate C ffi 3 1 area LAI. (2) For typical leaf area distributions of a soybean canopy, C ; spores m 22 h 21. b. Estimating vertical escape rate The number of spores that exit the canopy during the averaging time period can be approximated by summing the number of spores that are lifted from every thin slab volume within the canopy. Theoretically, this number can be estimated from the joint turbulent velocity PDF. The logic that motivates this theory can be more easily understood if a simplified scenario is analyzed first. 1) A SIMPLIFIED CASE Assume that at an instant in time many spores are uniformly distributed on a plane located some distance above the ground but beneath the canopy top. Coherent sections (closed neighborhoods) of the plane correspond to zones where the vertical velocity exceeds the terminal velocity of the spores. The proportion of spores that are lifted upward from the plane is thus the ratio of the area enclosed by these eddies to the entire area of the plane (Fig. 2). Since eddies are coherent and spatially well correlated, the shape and location of the shaded neighborhoods will generally persist to the canopy top. This implies that spores embedded in these zones will reach the canopy top if they encounter no obstructions along the way. 2) MORE REALISTIC CASE Within a soybean canopy, inert spores require both vertical and horizontal gusts to be transported. Initially, the horizontal gust must overcome any frictional forces between the spore and the substance it is resting atop. Similarly, the vertical component must exceed the spore s terminal velocity. Thus, the three-dimensional structure of sweep and ejection eddies is ideal for spore transport. If, at a point chosen at random within the canopy, the measured velocity contains a horizontal component (u9. 0) capable of spore transport, then it is quite likely that spores embedded in that eddy will be transported to the canopy top. This is true because the measured velocity is most likely embedded in a sweep, which naturally evolves into an ejection from the canopy. These eddies are large-scale, coherent, spatially and temporally wellcorrelated structures, which suggests that strong sweeps evolve into strong ejections, not weak ejections. Inside horizontally uniform foliage, one can argue that the value of the integrated joint-velocity PDF over the subdomain u9.u t and w9.y t, where u t and y t are the horizontal velocity and terminal velocity thresholds at a FIG. 2. Schematic of spore lifting by localized updrafts. Shaded regions to which arrows point correspond to zones where the turbulent vertical velocity exceeds the average spore terminal velocity (y t ). level z, respectively, is the expected value of the proportion of upwardly lifted spores from z during the averaging time period. This subdomain corresponds to the proportion of sweep and ejection eddy couplets that is able to transport spores. This reasoning relies heavily on the premise that the horizontal distribution of turbulent eddies is completely random, so that there are no preferred horizontal subsections of the canopy where certain eddy types tend to reoccur. Also, it assumes that spores available for lifting are also randomly distributed on leaves, so that spatial distribution of these spores is spatially uncorrelated with the position of sweep and ejection eddies. c. Integration of the joint velocity PDF The volume under the PDF bounded by u9.u t and w9.y t is equal to the proportion of space time that is occupied by eddies capable of transporting spores. Both u t and y t represent the average amount of momentum in the horizontal and vertical directions required for spore transport. Whether or not spores embedded in a randomly selected eddy will arrive at the canopy top depends on an eddy s temporal persistence. However, eddies are coherent structures that are well correlated in space and time. Also, their vertical size is usually on the order of h. This implies that a spore embedded in a randomly selected sweep or ejection eddy whose velocity exceeds the critical values has a very high chance of being carried all the way to the canopy top as long as it encounters no obstructions. d. Filtering capacity of the canopy Upwardly transported spores can be scattered or filtered out of vertical eddies when they collide with

6 794 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 obstructing plant parts. In fact, the canopy itself forms a complexmazeofobstacles.thismazeisnotrigid,however. Leaves deform easily with the wind and open up temporary pathways for spore transport. On the other hand, plant parts can also generate small-scale eddies that deflect a percentage of spores out of large-scale updrafts. Strong eddies will likely open pathways for spore escape, while weaker eddies will be unable to transport spores. A proposed parameterization of the net impact of canopy filtering on spore escape is discussed next. ANALOGY TO OPTICAL DEPTH Because canopy elements, particularly leaves, are not rigid and can deform easily when large-scale turbulent motions are present, upward traveling spores can be likened to light traveling through a fluid. At the quantum scales, particles that compose a fluid are nonstationary and their exact locations cannot be known. Also, the position of individual photons interacting with particles at quantum scales cannot be known. Together these uncertainties are similar to the uncertainty of a spore s position relative to a leaf and of a deformed leaf s morphology during a possible interaction between the two. While the analogy is crude, it is used here to propose a relationship between the average number of spores that are lifted to the canopy top from a level z during a time period and the average number that actually escape: c out 5 p(z) 3 PDF (z) 3 exp f c LAI(h) ð h z a(z9) dz9, (3) where f c is an empirical quantity, called the filtering coefficient, that must be determined from experimental data and may depend on the intensity of the turbulence. The exponential in Eq. (3), referred to here as the filtering factor, can also be written as f f 5 exp{ f c [LAI(z) 2 a(z9) dz9 and the ratio [LAI(z) 2 LAI(h)]/LAI(h) represents the proportion of total leaf area that a spore must traverse while traveling upward between z and the canopy top. Larger values of LAI probably reduce the chance that a spore will navigate through the leaves without colliding or being scattered out of an eddy. Similarly, the filtering mechanism should, in theory, scatter spores out of updrafts and reduce the spore escape rate. Since LAI(z) 2 LAI(h) is always negative, the exponential term in Eq. (3) is less than 1 if f c is made to be positive. It is assumed that f c is independent of the canopy leaf area distribution because the impact of A(z) is already parameterized in Eq. (3) outside of f c. However, turbulent intensity may impact f c by influencing the frequency of strong LAI(h)]/[LAI(h)]}, where LAI(z) 5 Ð z 0 wind gusts that are able to open pathways in the canopy for spore escape, thus reducing the canopy s filtering capacity. 4. Procedure Methods for reproducing the turbulence and calculating the spore escape rate were devised. Different approaches (described below) were used to create a model ensemble and diversify its members. Sensitivity tests were conducted for all members to determine which model variables and parameters most affect the modeled spore escape rate. a. Probability density function An exact reproduction of the turbulent velocity PDF in canopies requires the resolution of the turbulence closure problem. Nonetheless, this model s usefulness would be greatly diminished if it were incapable of constructing, even if only approximately, the turbulent PDF using as little input as possible. Thus, in the absence of a more precise formulation for the turbulent PDF, a bivariate normal Gaussian distribution with correlation s uw /(s u s w ) and standard deviation s u and s w was employed as an approximation to the true PDF. Two different methods were used to construct the mean wind and variance profiles using the friction velocity and canopy leaf area distribution. The first method (method A) is a closure model developed by Massman and Weil (1999). In a second method (method B), the mean wind profile was fit empirically, and the approach of Raupach and Thom (1981) was used to determine the stress profile. Variance profiles were then obtained from the turbulent stress using ratio profiles for s uw /s 2 u and s w/s u obtained from measurements presented in Finnigan (2000), Katul and Chang (1999), and idealized constructions. Horizontal homogeneity was assumed so that the turbulent velocity PDF was the distribution of turbulent velocities, u9 and w9, over an extensive thin-slab volume (Finnigan 2000) over a given averaging time period. The averaging time period t was chosen to match the averaging period used to calculate the mean wind or friction velocity, either of which can serve as input to the model. b. Leaf area distribution Various leaf area distributions were used to test the model (Fig. 3). Clark 1979, HN 1980, and HPD 1980 were obtained from Baldocchi et al. (1983). Zidek 8/23 was measured during a field experiment described later in this section. Together they are referred to here as measured (Fig. 3a). A x 2 distribution was also used as a

7 APRIL 2009 A N D R A D E E T A L. 795 FIG. 3. (a) Measured and (b) idealized LADs used as input to the spore escape model during sensitivity tests. two-parameter fit for A(z). Also, a uniform distribution, a parabola fit, and two triangular distributions, with one concentrating most of the leaf area near the top of the canopy and the other in the bottom, were used to test the sensitivity of the model to different distributions of leaf area. This group of LAD profiles was classified as idealized (Fig. 3b). The model was designed to reproduce a smooth leaf area density distribution using discrete values of LAI measured over thin horizontally extensive slabs of the canopy. The discrete values were then converted into a smooth cumulative leaf area index function that depends only on height. Finally, the leaf area density was determined by differentiating the smooth LAI function with respect to height. Smooth curves were preferred over discrete representations because of the numerical simplicity of method A and method B closure schemes, as well as the low vertical resolution of some measurements of LAI. This design implementation made it simple to use field measurements of LAI as input. c. Field experiment Data from a field experiment were used to narrow the range of f c used in Eq. (3). The experiment was conducted over a soybean field near Quincy, Florida, during the period spanning from 22 to 28 August The field consisted of mature soybeans and was heavily infected with SBR. The field was part of the USDA soybean rust sentinel monitoring network. Rows were about 18 cm apart and the leaf area distribution evolved little throughout the experiment. Its shape and evolution is illustrated in Fig. 4. SBR was determined to be at 99% incidence and 33% severity on 21 August. Also, there was active sporulation at the lower, middle, and top of the canopy. To measure the leaf area distribution, leaves were cut at height increments of 10.0 cm from the ground to the top of the canopy. The cut leaves were placed in sealed plastic bags and labeled according to their height within the canopy. The leaves were then scanned to create a digital image in tagged image file format (TIFF). Finally, the leaf area at each 10.0-cm height increment was estimated using a computer program. The program mapped each pixel in the various TIFF images of the leaves to grayscale and categorized each pixel into white or nonwhite categories. The number of nonwhite pixels were counted for each image and divided by the total number of pixels cm 22. From this value, the LAI was calculated at each height increment by dividing the total leaf area by the total ground area (2500 cm 2 ). Naturally released spores were collected by rotorod impaction samplers mounted at 0.5, 1.0, 1.5, and 2.5 h. These samplers were placed at the corners of a 3 m 3 3 m square located near the field s center to minimize the amount of airborne spores originating from other infected soybean fields. During each trial, spores were collected continuously over 15-min intervals. Afterward, the rotorod slides were packaged in plastic containers and refrigerated. Spores on each slide were counted under 1003 magnification to determine the total count. The volume of air V sampled during each trial is given by V 5 Wldpst, where W is the rod width in meters, l is the rod length in meters, d is the head diameter in meters, s is the number of rotorod revolutions per minute, and t is the time in minutes. After estimating the volume of air sampled, the concentration C of spores per rotorod was estimated using C 5 p/v, where p is the total count of spores.

8 796 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 4. LAD measured at different dates during the field experiments. A three-dimensional sonic anemometer (CSAT3) and a Vaisala temperature/rh probe (HMP45C) were located between 2 and 3 m away from the collection square and also approximately 1 m above the canopy top. Mean wind speed, air temperature, heat flux, relative humidity, and 1-min covariance were synchronously measured during each of the 12 separate trials. Spore escape rates during each of the 15-min-long trials were estimated as the ratio of the average concentration observed at z h to the average concentration at z h, where the average was defined as the mean spore concentration of the four different towers at each corner of the collection square. The data collected during the trials were used to run the model and generate spore escape rates as a function of f c. d. Skewness and spore clustering Significant spore clustering was observed during the Florida field experiment. This raises the possibility that the average spore terminal velocity may be quite different than the terminal velocity of a single spore. For this reason, the dependence of model-predicted escape rates on terminal velocity was investigated. A range of values for y t was used to calculate escape rates for a variety of leaf area distributions. A skewed PDF was not incorporated in the model because the dependence of skewness on both the leaf area distribution and turbulent intensity cannot be easily determined. However, it is well known that the skewness of turbulent velocities within canopies is not negligible. In plant canopies, sweeps are more frequent and ejections are less frequent than indicated by a bivariate approximation. For this reason, the integrated area over these regions was artificially increased (decreased) for sweeps (ejections) by altering the values of y t and u t together during some sensitivity tests. Both the potential effects of spore clustering and varying skewness were investigated by perturbing y t and u t. e. Large-scale transport The spore escape model developed here was coupled with HYSPLIT_4 (Draxler and Hess 1997) to form a large-scale spore transport model with dynamic spore source strengths. The coupling was accomplished by modifying the HYSPLIT_4 source code to modulate fixed emission rates dynamically via the escape rate model using the friction velocity and an LAD profile for soybean. The fixed emission rates were chosen as an upper bound on the number of spores emitted by an infected canopy according to estimates by Isard et al. (2005). Infected counties were identified using data available from the USDA (2007). Spore sources were modeled in HYSPLIT_4 as continuously emitting point sources with an initial area approximately equal to the area covered in soybean fields within each infected county. Meteorological data obtained by running the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model (MM5; Grell et al. 1995) with a temporal resolution of 6 h, a horizontal spatial resolution of 52 km, and 23 levels in the vertical were used to drive the HYSPLIT_4 simulation. The internal friction velocity computed by HYSPLIT_4 was used as input to the spore escape component of the coupled model. Wet deposition was simulated using HYSPLIT_4 s default parameterization scheme with no pollutant solubility, Henry constant equaling 0, a cloud removal ratio of , and a below-cloud removal time constant of Dispersion was simulated using the particle-puff hybrid method and concentration was calculated at 0, 10, and 500 m above the ground. All aspects of the procedure described above, with the exception of the model coupling, have been used at Saint Louis University and Iowa State University to generate forecasts of SBR spore dispersion for soybean producers and the research community during the past several growing seasons. The coupled model was created to investigate the potential effects of dynamic spore sources on these long-range forecasts of spore dispersion. Several simulations, each 2 weeks long, were conducted for the 2007 growing season using both the coupled model and an uncoupled version with the same features as the coupled model except that constant rates of emission were used. The simulation period was chosen to be long enough so that substantive large-scale dispersion of SBR spores could occur, but short enough

9 APRIL 2009 A N D R A D E E T A L. 797 so that significant spread of the disease was unlikely, thereby avoiding the need to update spore source locations during a simulation. Each simulation produced spore deposition forecasts for the eastern half of the United States. For both simulations, a single leaf area distribution, Clark 1979, was used at all spore source locations and at all time steps. Thus, only the impact of varying model turbulence regimes on the long distance dispersion of SBR spores was analyzed using the above method. 5. Preliminary results a. Sensitivity tests Spore escape rate was quantified by the escape proportion E, defined as the ratio of spores that exit the canopy to the total possible spores available for lifting during the averaging period t: E [ No. spores escaped. (4) ð h 0 p(z, t) dz Figure 5 shows the dependence of E on the friction velocity u * for the leaf area distributions used to run the model. The curves depict large variations in E over the typical range in u * of 0 1 m s 21 for the atmosphere, implying that varying meteorological conditions have an important impact on spore escape rates. Over the range 1, u *, 2.5 m s 21, the variation in E was much smaller. Increases in u * beyond 2.5 m s 21 resulted in negligible increases in E for all the leaf area distributions tested. Overall, E increases rapidly but at a decreasing rate and asymptotes to a value not much larger than E(u * m s 21 ) for all LADs tested. A possible reason for this asymptotic behavior is that at higher turbulent intensities all the spores capable of being lifted are transported out of the canopy. However, E is still less than unity because the canopy s filtering capacity always traps some spores inside. The general shape of the E curves is in close agreement with results from the LSPTM discussed in Aylor et al. (2001). The normalized escape rate proportion (Ê) was used to compare the results of various sensitivity tests. It was defined as ^E [ E(u )/E max, where E max [E(u m s 1 ) when sensitivity to u * was being investigated (Fig. 6). The results of most significance tests are shown in Table 2. The normalized escape rate proportion was quite sensitive to variations in u *, f c, y t, u t, and the LAD. Stronger winds resulted in larger escape rates. Larger filtering coefficients reduced Ê and smaller terminal velocities allowed more spores to escape. FIG. 5. Escape proportion E as a function of the u * for LADs shown in (a) Fig. 3a calculated using method A and (b) Fig. 3b calculated using method B. Artificially skewing the PDF by reducing u t and simultaneously increasing y t resulted in an increase in Ê for all leaf area distributions tested. However, only the trend, not the magnitude of this increase, is meaningful because the relative change of u t and y t was arbitrarily determined. Also, these perturbations lead to a vertically uniform shift in integrated area, whereas in canopy turbulence, the skewness of the joint velocity PDF likely varies considerably with height. Variation in Ê among different leaf area distributions was less than 30%, which corresponds to a difference in E of about 20%. Using traditional estimates of p(z) by Isard et al. (2005) (10 6 spores per meter squared per

10 798 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 actual range for h t, measurements of the coefficient of friction between spores and the top of leaves are most likely required. b. Observations and the filtering coefficient FIG. 6. Normalized escape proportion Ê calculated using method A for LADs shown in Fig. 3a, showing the sensitivity of escape rates to different LADs. hour in a heavily infected canopy between early morning and noon), this variation amounts to about spores per meter squared per hour. In less heavily infected canopies, this variation could be smaller. Significant spore clumping was observed during the Florida field experiment. For a single spore, y t is about 2 cm s 21. For large clumps, depending on the geometry, y t could be as large as 8 cm s 21. When y t ranged between 0 and 10 cm s 21, Ê varied up to 12%. Larger y t reduced E, and also led to a larger sensitivity of E to the LAD used, resulting in a larger separation between the curves in Fig. 5 at large u * and y t. The horizontal threshold velocity led to variations in Ê as much as 25% over the range of 0 10 cm s 21. However, there was no reason to believe that u t can actually vary over this range. Therefore, the results of this test simply revealed a trend in Ê when forced by changes in u t. To determine an Measurements collected during the Florida field experiment contained evidence supporting the description of eddy structure and characteristics provided in section 2. One-minute covariance measurements showed some evidence of intermittency and scale separation (Fig. 7). The covariances were computed at small time scales and thus somewhat mirror instantaneous turbulent motions. Maxima in the 1-min covariances corresponded to strong eddies. The separation between peaks was indicative of distinct temporal separation between eddies and implies that even the larger eddies were short lived. Clumps ranged from a couple of spores to many spores. Because single spores were rare, a terminal velocity of about 8 cm s 21 corresponding to larger clumps was assumed for running the model using meteorological conditions observed during the experiment. Modelpredicted Ê for these conditions depended heavily on the choice of filtering coefficient f c. Estimates of Ê calculated from observations corresponded to the model predictions for f c in the range of , with a standard deviation of about 1.8 (Fig. 8). While this narrows down the possible value of f c, variation in Ê over this range is still very large (Table 2). c. Coupled experiment with a large-scale transport model The domain-averaged 2-week accumulated spore deposition predicted by the coupled HYSPLIT simulations was always less than that predicted by the uncoupled simulations. In most cases, coupled and uncoupled model-accumulated deposition shared basic spatial features that differed in size and intensity. In rare cases, Method A TABLE 2. Results from the various sensitivity tests. Method B Domain DE DÊ O(DS)* DE DÊ O(DS)* Remarks LAD (0 2.5 m s 21 ) 1% 20% 1% 30% % 10% 1% 15% 10 5 Fig. 5 h t (0 0.1 m s 21 ) 8% 20% 10% 25% % 20% 15% 25% 10 5 Ê decreases within increasing h t, almost linearly y t (0 0.1 m s 21 ) 10% 6% 12% % 8% 10% 10 5 Ê decreases within increasing y t, almost linearly LAI (2 4),5% 7% 10 4,5% 7% 10 4 Ê decreases with increasing LAI h (1 1.5 m) 5% 10% 5% 20% % 5% 5% 12% 10 5 Ê increases with increasing h when using method A but decreases with increasing h when using method B f c (0 16) 75% 100% % 100% 10 6 Ê decreases at a decreasing rate with increasing f c * Largest variation in number of escaped spores based on estimates by Isard et al. (2005).

11 APRIL 2009 A N D R A D E E T A L. 799 FIG. 7. One-minute covariance measured over an infected soybean field in Florida on 28 Aug Measurements were collected over a 15-min interval that began 20 min after noon. the coupled simulation produced deposition patterns that were quite different than those produced by the uncoupled simulation. Some examples that illustrate the differences between output produced by the two models for the late summer and early autumn of 2007 are summarized in the next paragraph. Uncoupled model deposition for 11 August 2007 (Fig. 9b) has a maximum centered in upstate New York that was absent in the coupled model s output (Fig. 9a). Over the same period, accumulated deposition was higher in the coupled simulation over a small region centered around the Mississippi River just south of Memphis and across southwest West Virginia and northern Virginia. All of these differences were at least three orders of magnitude. Comparisons of cumulative disease spread between 1 August (Fig. 9c) and 15 September 2007 (Fig. 9d), and again between 1 September (Fig. 10c) and 19 October 2007 (Fig. 10d), for both models indicate no disease development in many of the high-deposition areas across Kentucky, much of Tennessee, West Virginia, and Virginia. Much of this region was affected by a summer drought where conditions were not favorable for disease development. However, across Pennsylvania and upstate New York, conditions were more favorable for disease development. The uncoupled model indicates a relative maximum of spore deposition across upstate New York and Pennsylvania. Nonetheless, no disease development is detected throughout the summer and early autumn. This seems to suggest that spores were not actually transported to that region. This is in agreement with ouptut from the coupled model, which shows no deposition over the same area. FIG. 8. Filtering coefficients determined by running the model using the same conditions observed during the Florida field experiment and comparing model output with observed estimates of E. Diamonds enclosed within the dashed lines lie within one std dev of the mean. Along the Mississippi River between Louisiana and Missouri, considerable disease spread occurred during the later period (1 September 19 October), during which warm weather persisted and moisture increased. Some early signs of disease development in this region were also visible in Fig. 9d. The coupled model predicted higher 2-week accumulated deposition for 11 August 2007 over the southern portion of this region than did the uncoupled model. However, in the northern portion of the same region the uncoupled model predicted higher deposition. Another simulation ending on 14 September 2007 (Fig. 10) illustrates a case where output from the coupled and uncoupled models differed very little. When compared with observations of disease spread between 1 September (Fig. 10c) and 19 October 2007 (Fig. 10d), both simulations seemed to predict spore spread that precedes disease spread in both the eastern and western portions of the domain. The coupled simulation predicts a slightly more northerly extension of deposition across southern Illinois and Indiana, where the disease began and spread significantly by mid-october. This spread was probably limited by cold weather in mid-november across the Midwest. 6. Summary and discussion Long-distance dispersion of pachyrhizi spores begins when spores are released from infected canopies. The escape rate depends on the intensity of canopy turbulence and biological factors, such as the leaf area

12 800 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 9. Cumulative spore deposition (spores m 22 ) predicted for 11 Aug 2007 by the (a) coupled simulation and (b) uncoupled simulation; USDA SBR observations for the period preceding (c) 1 Aug 2007 and (d) 15 Sep 2007, about 5 weeks after the time for which the forecasts in (a) and (b) are valid. distribution, which can influence both canopy turbulence and intensity of the spore source. Our preliminary results show that variability in the escape rate due to varying meteorological conditions can alter the amount and location of spore deposition over regions far from the source. This confirms the belief that the escape rate is a key initial and boundary condition on the dynamical system that governs large-scale spore transport. In our implementation of a spore escape model, only the friction velocity u * and the vertical leaf area distribution of a soybean canopy are needed as input. Several other model parameters are treated as constants. The

13 APRIL 2009 A N D R A D E E T A L. 801 FIG. 10. As in Fig. 9, but for (a),(b) 14 Sep 2007, (c) 1 Sep 2007, and (d) 19 Oct computational requirements for running the model are small, making it easy to incorporate into larger-scale particle transport models without much additional computational overhead. Results from the spore escaperate model (Fig. 5) have very similar shapes to those generated by more computationally demanding Lagrangian stochastic particle trajectory models (Aylor et al. 2001). Spore deposition forecasts produced using a preliminary implementation of a Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT) coupled with the spore escape model proposed here were, in some cases, more consistent with the observed spread of SBR in 2007 than were HYSPLIT-generated deposition forecasts produced without the spore escaperate model. Although these improvements were not

14 802 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 very impressive, we believe improved implementations of the spore escape model have the potential to substantially improve forecasts of SBR spore dispersion. In the current implementation, there is still large uncertainty in several model parameters. For instance, although the filtering coefficient used in the parameterization of the canopy porosity is thought to lie between 0 and 6 based on a field experiment conducted over a soybean field in Florida, spore escape rates still vary nontrivially over this range. Also, a bivariate Gaussian approximation to the probability distribution of turbulent velocities within the canopy was used for simplicity, but the true PDF is skewed in favor of sweeps and ejections. It is likely that use of a better representation of the turbulent velocity PDF will substantially improve forecasts of escape rate. Finally, with adequate tuning, a spore escape model makes it feasible to develop a fully coupled model of disease spread. Such a model could simulate all aspects of rust spread: from spore transport to deposition; from disease initiation to new spore development. The simulation would mimic the dynamic nature of the disease, in which its evolution depends on its prior history and meteorological conditions as an external forcing. In this way, disease forecasts could be generated early in the year for an entire growing season, which could help farmers more effectively mitigate the spread of the disease. However, the spore escape model is only a single, although crucial, component of a fully coupled disease spread model. Several other components are needed. These include a biological model of the disease within a canopy, responsible for the evolution of the disease once spores are deposited, a reliable long-range meteorological forecast model, and a long-range dispersion model that satisfactorily simulates wet and dry deposition. Acknowledgments. The authors thank Roland R. Draxler of NOAA for providing the HYSPLIT source code, Lulin Xue for assistance with HYSPLIT, Xun Li for providing information concerning the biology of SBR, and the anonymous reviewers for offering excellent constructive criticism that has greatly improved this paper. Support was provided by the Iowa Soybean Association, U.S. Department of Agriculture/PIPE, Syngenta Corporation, and the U.S. Department of Energy/ NICCR. Funding for the field experiment reported in section 4a was provided by the USDA, Cooperative State Research, Extension, and Education Service (under the Animal and Plant Biosecurity Program Grant 872 AG ). We thank these agencies for their support. REFERENCES Aylor, D. E., 2003: Spread of plant disease on a continental scale: Role of aerial dispersal of pathogens. Ecology, 84, , and G. S. Taylor, 1983: Escape of Peronospora tabacina spores from a field of diseased tobacco plants. Phytopathology, 73, , and F. J. Ferrandino, 1985: Escape of urediniospores of Uromyces phaseoli from a bean canopy. Phytopathology, 75, , W. E. Fry, H. Mayton, and J. L. Andrade-Piedra, 2001: Quantifying the rate of release and escape of Phytophthora infestans sporangia from a potato canopy. Phytopathology, 91, Baldocchi, D. D., S. B. Verma, and N. J. Rosenberg, 1983: Characteristics of air flow above and within soybean canopies. Bound.-Layer Meteor., 25, Dorrance, A. E., M. A. Draper, and D. E. Hershman, 2007: Using foliar fungicides to manage soybean rust. Ohio State University Extension Bull. SR-2007, 111 pp. Draxler, R., and G. D. Hess, 1997: Description of the HYSPLIT_4 Modeling System. NOAA Tech. Memo. ERL ARL-224, 27 pp. Finnigan, J. J., 1979: Turbulence in waving wheat II. Structure of transfer. Bound.-Layer Meteor., 16, , 2000: Turbulence in plant canopies. Annu. Rev. Fluid Mech., 19, Gao, W., R. H. Shaw, and U. K. Paw, 1989: Observation of organised structure in turbulent flow within and above a forest canopy. Bound.-Layer Meteor., 47, Grell, G., J. Dudhia, and D. Stauffer, 1995: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NACR Tech. Note NCAR/TN-3981STR, 138 pp. Hartman, G. L., M. R. Miles, and R. D. Frederick, 2005: Breeding for resistance to soybean rust. Plant Dis., 89, Isard, S. A., S. H. Gage, P. Comtois, and J. M. Russo, 2005: Principles of the atmospheric pathway for invasive species applied to soybean rust. Bioscience, 55, , J. M. Russo, and A. Ariatti, 2007: The Integrated Aerobiology Modeling System applied to the spread of soybean rust into the Ohio River Valley during September Earth Environ. Sci., 23, Katul, G. G., and W. H. Chang, 1999: Principal length scales in second-order closure models for canopy turbulence. J. Appl. Meteor., 38, Kemerait, R. C., P. Jost, D. Sconyers, D. Phillips, J. Brock, J. Clark, and J. Kichler, 2005: Summaries of Southeastern University fungicide efficacy trials. Proc. National Soybean Rust Symp., Nashville, TN, APS. [Available online at plantmanagementnetwork.org/infocenter/topic/soybeanrust/ symposium/presentations/kemerait.pdf.] Lu, S. S., and W. W. Willmarth, 1973: Measurements of the structure of Reynolds stress in a turbulent boundary layer. J. Fluid Mech., 60, Massman, W. J., and J. C. Weil, 1999: An analytical one-dimensional second-order closure model of turbulence statistics and the Lagrangian timescale within and above plant canopies of arbitrary structure. Bound.-Layer Meteor., 91, Melching, J. S., W. M. Dowler, D. L. Koogle, and M. H. Royer, 1989: Effects of duration, frequency, and temperature of leaf wetness periods on soybean rust. Plant Dis., 73, Meroney, R. N., 1968: Characteristics of wind and turbulence in and above model forests. Atmos. Environ., 7,