APPLIED AND ENVIRONMENTAL MICROBIOLOGY, OCt. 1989, p. 2641-2647 Vol. 55, No. 100099-2240/89/102641-07$02.00/0Copyright © 1989, American Society for Microbiology

Model To Predict Aerial Dispersal of Bacteria duringEnvironmental Release

GUY R. KNUDSENPlant Pathology Division, Department of Plant, Soil and Entomological Sciences,

University of Idaho, Moscow, Idaho 83843

Received 13 February 1989/Accepted 1 May 1989

Risk assessment for genetically engineered bacteria sprayed onto crops includes determination of off-sitedispersal and deposition. The ability to predict microbial dispersal patterns is essential to characterize theuncertainty (risk) associated with environmental release of recombinant organisms. Toward this end, a particledispersal model was developed to predict recovery of bacteria on fallout plates at various distances anddirections about a test site. The microcomputer simulation incorporates particle size distribution, wind speedand direction, turbulence, evaporation, sedimentation, and mortality, with a time step of 0.5 s. The model wastested against data reported from three field applications of nonrecombinant bacteria and two applications ofrecombinant bacteria. Simulated dispersal of 105 particles was compared with reported deposition measure-ments. The model may be useful in defining appropriate populations of organisms for release, methods ofrelease or application, characteristics of a release site that influence containment or dispersal, and in developingan appropriate sampling methodology for monitoring the dispersal of organisms such as genetically engineeredbacteria.

Recombinant DNA technology offers the possibility ofgenetically modifying microbial control agents for useagainst plant pathogens (13, 14, 15). The number of applica-tions for experimental-use permits to release geneticallyengineered bacteria in small-scale field trials has increased;many requests focus on application of microbial pest controlagents to agricultural crops, since research with these organ-isms has progressed to the point where field tests are neededto evaluate their performance. Genetically engineered organ-isms that have been released include strains ofPseudomonassyringae and Pseudomonas fluorescens from which the icenucleation gene has been deleted (14, 15, 23). These ice-minus strains are intended to competitively exclude icenucleation-active strains involved in frost damage on plantsurfaces. To date, small-scale field releases of aerosolizedgenetically engineered bacteria have been undertaken byAdvanced Genetic Sciences, Inc., and the University ofCalifornia, Berkeley, with a large concurrent investment oftime and money by state and federal regulatory agencies inan attempt to determine microbial dispersal patterns.To assess potential risks associated with field release of

genetically engineered microorganisms, it is necessary firstto efficiently monitor them after release. In the case ofbacteria applied to field plots in aerosol form, we need anability to predict aerial concentrations of viable cells anddeposition patterns around the test site. Prediction of dis-persal patterns under specific weather patterns, prior to fieldtesting, would allow more effective use of sampling re-sources. Such a predictive model could prescribe optimumplacement of sampling devices, probable detection thresh-olds, and the effects of possible weather changes.

Various models have been developed to describe disper-sion of atmospheric particles from sources. Gaussian plumemodels (10, 17, 18) predict concentrations of particles in adownwind plume and are probably the most commonly useddispersion models (18). They assume that turbulence causesairborne particles to randomly disperse, so that an aerosolplume will show increasing scatter around its origin withincreasing distance from the source, characterized by a

bivariate Gaussian (normal) distribution. Variations of thesemodels specify the dispersion parameters as functions ofdownwind distance and atmospheric stability; e.g., Pasquill(17) identified six stability classes based on surface windvelocity, daytime solar radiation, and nighttime cloudiness.Gaussian dispersion models are relatively easy to manipulatemathematically, but one disadvantage lies in the assumptionof a continuous source and uniform wind speed. Duringexperimental field releases of recombinant bacteria, the timespan of interest may be very short (minutes), and a high levelof precision in estimating movement of airborne particles isrequired. Because the particle source is small and discontin-uous in time, minor variations in wind speed and directionover short time periods can significantly affect predicteddispersal patterns. Puff diffusion models calculate the posi-tion of a particle cloud at successive time steps and offer animprovement over simple Gaussian plume models, but theirmain disadvantage lies in the increasing computational diffi-culty as the time step length is decreased or wind vectorschange. Also, they are not flexible enough to easily adapt todifferent plot sizes, particle size distributions, evaporation(which effectively alters aerosol droplet size), and depositionof aerosol particles. Thus, the above models are not highlysuitable for small-scale field releases of microbes.Random walk models follow a discrete number of particles

released from a source, producing a representative picture ofthe entire plume in space and time. Time is also treated as adiscrete variable, meaning that the system is examined atregular intervals (e.g., every second). Such models are wellsuited for computer application, and several random walkmodels have been developed to estimate dispersion of airpollutants (8, 19).

In this report, a microcomputer simulation model is pre-sented that predicts dispersal and deposition patterns foraerosolized bacteria in field trials. It is apparently the firstattempt to formulate a random walk model suitable forpredicting short-range movement of bacteria from field trialsites. The model can accommodate short-term variations inwind speed, direction, and turbulence. The model is further

2641

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

APPL. ENVIRON. MICROBIOL.

designed to accommodate variations in particle size distri-bution, evaporation, and mortality. Model predictions ofbacterial deposition are compared with reported field obser-vations (16, 23).

MATERIALS AND METHODS

Model description. The general form of the simulator is arandom walk model. The model describes the motion anddispersal of a large number (105) of particles released from apoint or area source. The trajectory of each particle isdivided into discrete time steps (0.5 s), during which thehorizontal and vertical velocity components of each particleare held constant. The program tracks the x, y, and zcoordinates of each particle over time.

Deterministic elements in the model include particle sed-imentation due to gravity, advection by prevailing wind,evaporation, mortality, and collection of particles by sam-pling devices. In the model, advection is either based onaverage wind speed and direction or calculated by using adata file of wind speed and direction measured at discretetime intervals. The model calculates horizontal movement,i.e., change in the x coordinate (Ax) and y coordinate (Ay) ofeach particle as follows:

Ax = wind speed cos(wind angle) (1)

Ay = wind speed sin(wind angle) (2)

where wind speed is in meters per second and wind angle isin radians. Terminal velocity (i.e., sedimentation rate) waspredicted by using Stokes' Law, which describes the termi-nal velocity of a smooth spherical object falling in a fluidmedium. For microbial aerosols suspended in air, assumingthat the density of the medium is negligible compared withthe density of the falling object, Stokes' Law simplifies to

V, = 0.0121 r2 (3)where V, is the terminal velocity of the falling object (metersper second) and r is the radius of a spherical aerosol dropletin micrometers (7). For purposes of the simulations pre-sented here, it was assumed that particles were released atterminal velocity, the height of the plant canopy was 0.2 m,and the wind speed within the canopy was 0 m sec-

Stochastic elements in the model include particle (droplet)sizes and turbulence dispersion vectors. Particle sizes areassumed to be lognormally distributed; mean and variance ofthe distribution are specified in advance of the simulationrun. Dispersion due to turbulence was assumed to be ran-dom normally distributed (mean = 0 m) in the parallel,perpendicular horizontal, and perpendicular vertical direc-tions to prevailing winds (Fig. 1). The model assumes nocovariance relationships between successive time intervals.Standard deviations were selected by running simulationswith different values and determining those that generatedGaussian dispersion patterns (at 100 m, 1 m sec-1 windspeed), similar to those predicted by standard Gaussianplume dispersion models for Pasquill's atmospheric stabilityclasses (10). For simulations presented herein, standarddeviation values of 2.19 and 2.00 m in the horizontal andvertical planes, respectively, were used to simulate turbulentconditions. For all stochastic elements, a Monte Carloroutine selects random normal deviates by using a randomnumber-generating routine and look-up table (5, 22).

Evaporation of aerosol droplets. Evaporation significantlyaffects the trajectory of aqueous sprays. Seymour and Byrd(21) developed equations to account for simultaneous varia-

* -ILOCATIONI(

Sedimentation

PARTICLE DISPLACEMENT VECTORS

Turbulence Components(a) Parallel to wind(b) Perpendicular to wind(c) Vertical

(a)(LOCATION] -

(t.At) c

t (c)

Mean advectionFIG. 1. Diagrammatic representation of particle displacement

vectors used in the simulation model. For each simulated 0.5-s timeinterval, vectors representing sedimentation, advection, and turbu-lence are summed to calculate the new position (location(,+A,)) ofeach simulated aerosol droplet. Turbulence vector b representsmovement perpendicular to the plane of the page.

tion in droplet diameter, fall velocity, and evaporation rate.For this model, using graphs published by Seymour andByrd (21), linearly interpolated estimates were made ofparticle diameter change due to evaporation over 0.5-s timeperiods (Fig. 2). Estimates were derived on the basis ofconditions of 50% relative humidity, 25°C temperature, and760 mm of Hg atmospheric pressure. Minimum particlediameter was set at 1 rLm.

Mortality of bacteria in droplets. The model contains aprovision to predict exponential decline of bacterial numbersin droplets. However, in the Tulelake simulations presented,overall mortality was arbitrarily estimated at 99.9%. Al-though this estimate is consistent with published values forsome aerosolized bacteria (12), estimates vary widely amongstrains and weather conditions. Mortality in aerosol has notbeen empirically determined for the specific strains simu-lated here.

Collection on fallout plates. In simulations, it is assumedthat particles falling to a height of 0.01 m were deposited onthe sample surface (i.e., petri dish of a selective medium).Deposition is monitored on 1-M2 blocks of a 50-M2 grid, and

Diameter los per 0.5 sec (pm)

1-50 51-100 0-150 151-200 >200Particle Diameter (pm)

FIG. 2. Rates of particle diameter change due to evaporation, asused in the simulation model. Rates were derived from linearinterpolation of published graphs, based on conditions of 50%relative humidity, 25°C temperature, and 760 mm of Hg atmosphericpressure (19). Minimum particle diameter was set at 1 ,um.

2642 KNUDSEN

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

MODEL TO PREDICT AERIAL DISPERSAL OF BACTERIA

counts (colony-forming units) are adjusted to representdeposition that would have occurred in 10-cm-diameterfallout plates (assumption: fallout plates are efficient collec-tors). The model also has the capability of tracking particlesthat move outside the monitored area.Model algorithm. Sequential steps in the simulation and a

description of the model are provided in the Appendix.Testing the model. (i) Release of nonrecombinant Pseudo-

monas syringae at Tulelake, Calif. Three field releases ofnonrecombinant strains of Pseudomonas syringae, reportedby Lindow et al. (16), were simulated. In simulations, it wasassumed that particles were released uniformly over a grid (7by 7 m), at a height of 0.5 meters, at time = 0 (16). For eachsimulation run, movement of 105 individual particles wasmonitored for 30 min. Predicted deposition on a grid (50 mby 50 m) in and around the test site was determined andadjusted to represent deposition that would have occurred in10-cm-diameter fallout plates. Counts were adjusted to ac-count for the ratio of particles simulated to particles actuallysprayed, and mortality was arbitrarily estimated as de-scribed above. Predictions of more than 4,000 CFU per platewere set equal to 4,000 CFU per plate, the highest valuereported as countable by Lindow et al. (16).

(ii) Release of recombinant Pseudomonas syringae and P.fluorescens at Brentwood, Calif. Field releases of P. syringaeand P. fluorescens in two fields (24 m by 43 m in size),monitored by the California Department of Food and Agri-culture (23), were simulated. Following field trials, theCalifornia Department of Food and Agriculture periodicallysampled off-site vegetation of various plant species fromtransects located at various distances from treated plots forpresence of the released bacteria (23). Reported resultsindicated only presence or absence of the recombinantbacteria in specific samples (23). The model was run toindicate the extent of off-site dispersal of bacteria underprevailing weather conditions by simulating deposition in 70regularly spaced 25-M2 areas in and around plots. A simpli-fying assumption was made that bacteria were sprayeduniformly over each field. Because equal numbers of P.syringae and P. fluorescens were sprayed on each field, onlyone simulation was run for each field.

Simulation parameters. Parameters used in simulation runswere as follows. Unless otherwise noted, the followingparameters represent measurements taken during field trialsand reported by Lindow et al. (16) or Supkoff et al. (23): (i)particle diameter, geometric mean = 100 ,m (assumed); (ii)particle diameter, standard deviation = 0.25 x log1o of meandiameter (assumed); (iii) cell densities (colony-forming unitsper milliliter) = 8.1 x 107 (plot 1), 6.4 x 108 (plot 2), and 1.8x 1010 (plot 3) for Tulelake and 2 x 108 for Brentwood; (iv)total volumes sprayed = 4 liters per plot (Tulelake) and 40liters per field (Brentwood); (v) wind speeds = constant 1.5m/s (plot 1), 1.3 m/s (plot 2), and 0.7 m/s (plot 3) (measuredat 1 m height) for Tulelake and 0.5 m/s for Brentwood; (vi)mean wind direction (origin) = W-NW (Tulelake); S-SE(Brentwood); (vii) atmospheric stability class = A (turbu-lent) (standard deviations of turbulence vectors used were2.19 m in the horizontal plane and 2.0 in the vertical plane).

Plotting observed and simulated results and analysis ofresiduals. (i) Tulelake. Observed deposition of bacteria (16)was plotted by using a computer program (Surfer, GoldenSoftware, Inc., Golden, Colo.) that interpolates a grid fromirregularly spaced data points (i.e., plate counts from exper-iments of Lindow et al.). An inverse-distance griddingmethod was used, and the grid was smoothed by using cubicspline interpolation. Similarly, results obtained in simulation

runs were gridded and plotted, but using all 2,500 data pointsfor each 50-m by 50-m field plot.

Linear regression of predicted versus observed colonycounts for the 36 sample sites (fallout plates) in each of theTulelake field release trials was performed. Lindow (14)found that colony counts at different distances from the plotsgenerally followed an exponential decline gradient; thus,regression of loglo predicted versus loglo observed colonycounts was also performed. Zero values were converted to0.1 prior to log transformation.

(ii) Brentwood. Simulation results (deposition in 25-M2areas) were gridded and smoothed as described above andwere then plotted as a topographic map. Because the re-ported data could not distinguish deposition results betweenone treated field and the other, simulation results for bothfields were added and combined into a single topographicmap. Mortality was not incorporated into Brentwood simu-lations, since their purpose was primarily to predict relativedensities of bacterium-containing aerosol droplets. The ex-tent of predicted dispersal was compared with reportedobservations of bacteria recovered from vegetation samples(23).

RESULTS

Deposition patterns observed in Tulelake field trials andsimulations are shown in Fig. 3. Simulated deposition pat-terns (i.e., predictions of bacterial colonies on fallout platescontaining a selective medium) were generally very similarin shape to those observed in field trials. As reported byLindow et al. (16), asymmetric patterns of bacterial dispersalfrom the spray sites was observed in the general downwinddirection. The highest bacterial counts were obtained withinplot boundaries or close to and downwind from plots, andthese results were also obtained in simulations. Simulateddeposition patterns were similar for each spray event, re-flecting the similar meteorological conditions that prevailed.For plot 3, where the lowest wind speed prevailed, thesimulated downwind dispersal gradient was somewhatsteeper, but dispersion perpendicular to the wind was

slightly higher (Fig. 3). Few bacteria were detected morethan 1 m upwind of any inoculated plot, and again theseresults were predicted by the simulation. Although bothobserved and simulated deposition patterns indicated higherrecovery from higher spray concentrations, deposition dif-ferences in both cases were much smaller than differences inspray concentration.

Regression analysis of predicted versus observed colonycounts for Tulelake data (both arithmetic and log trans-formed) are shown in Fig. 4. For each set of results,duplicate points at (0, 0) and (4,000, 4,000) were included inthe regression analysis but are shown as single points on thegraphs. Residuals (observed-predicted) can be visualized asdeviations from the line of slope = 1 (dotted line). Forarithmetic data, slopes for plots 1, 2, and 3 were 0.96, 1.01,and 0.62, respectively, and r2 values were 0.95, 0.89, and0.69. For log-transformed data, slopes were 0.91, 0.84, and0.63, with r2 values of 0.94, 0.80, and 0.68 (a perfectpredictive model would result in slope and r2 values of 1.0).

Simulated deposition patterns for the Brentwood trials are

shown in Fig. 5. The lowest contour level indicated repre-sents predicted deposition of 103 droplets per M2; subse-quent contour levels are in increments of 5 x 104 droplets.Because the correlation between deposition and samplerecovery has not been quantified, the contour map should beinterpreted as indicating relative deposition levels and thus

VOL. 55, 1989 2643

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

2644 KNUDSEN APPL. ENVIRON. MICROBIOL.

V4,

*aLS zzir 0oSv CII %s 0

H-Isc Zcy-3y - n-7d

fr

Z,9&Z a610 pl.

9siC SiS n-

6Cr0 IC/SCr *e/SD/ 919=1 60 0

"sIczIyW13 n&.9

.0.-

0:..o

>~~~~~~<

0 0

co~~~~~~~~~~co

).. ,0 O

U.0.

6biE 0zer 06Z 0991 0£CO 0 .0-H$J'O Zs13S - n O2

U U ~~~~~~~~~~~~~~~~~~~~~~U

CZ

0

0~~~~~~~~~~~~~~06

a- _

1-SIIX.3 - ~ .)

.0oI0

CZ

-

~ Q) C

0 0

U _

0. EUOC

w~_

zo~

-i ~~~~~~~~~00-_

.) 00

n0..

,~~~~~~z ] O .w3<~~~~~~1.:O

°~~~~~~~~~~~~~~~~~~~~~~~-4-a

0nc

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

MODEL TO PREDICT AERIAL DISPERSAL OF BACTERIA

0 I tu Ls &a 4

cu bwwdo twa) M 0.1 1 0 0c o_sww

0 CA 1 U Ls La 4U Obmd T

CF"ia* P10i

O1000 Plot 02 o

t0 0 0-0/ -

10 O X,

0.1 / ,0' 0 0 03 0

O 01- 1__- _ 10_ 90 I0

I11 XCPW% Obwwd

l00

FIG. 4. Observed and predicted recovery of bacteria for 36 sample sites (fallout plates) in each of three Tulelake field release trials. Linearregression (solid line) of predicted versus observed and of log1o predicted versus log10 observed counts was performed; slopes and coefficientsof determination (r2) for each regression equation are shown. Zero values were converted to 0.1 prior to log transformation. Residuals(observed-predicted) can be visualized as deviations from the line of slope = 1 (dotted line). For each set of results, duplicate points at 0, 0and 4,000, 4,000 were included in the regression analysis but are shown as single points on the graphs.

relative likelihood of recovering recombinant bacteria fromsamples. Following spray application, high numbers ofrecombinant bacteria (>104 CFU/g of leaf tissue) wererecovered within treated plots (23). Simulation results agree

with that finding. Recombinant bacteria were not detected inoff-site mixed vegetation samples 1, 3, or 7 days afterspraying but were detected in several samples after 14 days(site C was not sampled on days 1 and 3). Sites whererecombinant bacteria were recovered are indicated in Fig. 4.Of seven mixed-vegetation sites sampled, recombinant bac-teria were recovered from three. Of these, one (site B) was

located primarily in an area (north and west of plots) wherepredicted deposition was >5 x 104 droplets per m2 and two(sites C and D) were located in locations where predicteddeposition was between 1 x 103 and 5 x 104 droplets per M2.Sites where recombinant bacteria were not recovered wereeither in areas of between 1 x 103 and 5 x 104 droplets perm2 (sites E and F) or <103 droplets per m2 (sites A and G).

DISCUSSION

For the Tulelake trials, simulated deposition patterns (i.e.,predictions of bacterial colonies on fallout plates containinga selective medium) were generally very similar in shape to

those observed in field trials. However, potential sources oferror include possible underestimation of turbulence coeffi-cients, use of a constant mean wind speed, or error inestimating the particle size distribution. Average windspeeds used in the simulation were those measured at a

height of 1 m, although Lindow et al. (16) did observegenerally higher wind speeds at heights of 2, 3, and 10 m.

From observation of residuals in Fig. 4, it is apparent thatpredictions were least accurate for plot 3. Several of thoselarge residuals result from the apparent location of the plumebeing more to the south than to the southeast, as predictedby the model (also visible in Fig. 3). Because both observa-tions and predictions of colonies too numerous to count werearbitrarily set at 4,000 CFU per plate, the fit of eachregression line is probably better than if true recovery valueswere known.Because bacteria are living organisms and not inert parti-

cles, prediction of their dispersal in space is complicated bythe concurrent need to predict their mortality. The death rateof airborne bacteria or bacteria on surfaces is a function bothof cellular physiology (2) and of environmental factors,including temperature (2, 3), relative humidity (2, 3, 11), andsolar radiation (3, 20). UV radiation, especially, can be lethalto exposed microbes. One common way of accounting for

4 -

Plt Hia

a

0~~~~~a -

4 - ° 0 a'.

PI@t D /

am.

a 0

I00

0o."

C >"

a~~~~~~~~~~~~~~4 - 0 .9'

plot #'°3a o

0~~~~~~~~

VOL. 55, 1989 2645

plot M1000

0

a ..100 0

0

10 siowrs-OA4

I

&I a

---

---

a .-.1000 Plot #3 a 8

0 00

100 00 a 0

0 slow O."10 0 rt-

I

0.1 .13r, a 0 a

AA. .. ,,.I

0 ai I li 2 Lo 3 &S 4CFUfi%ft Obowvod (ThavemMe)

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

APPL. ENVIRON. MICROBIOL.

FIG. 5. Simulated deposition patterns for aerosolized bacteriasprayed in field trials at Brentwood, Calif. (21). The lowest contourline represents a predicted deposition of 103 droplets per M2;subsequent lines are in increments of 5 x 104 droplets per M2. Thetwo rectangular plots where bacteria were sprayed are indicated bybold lines. Prevailing winds were from the southeast. Seven sites (Athrough G) where mixed vegetation was sampled for presence ofrecombinant bacteria are indicated; all except site E are linetransects. Recombinant Pseudomonas syringae (S) or P. fluorescens(F) organisms were recovered within plots and from sites B (S andF), C (S), and D (S).

mortality of microbes during dispersal has been to introducean exponential decay factor to account for microbe deathwith increasing aerosol age due to environmental stress(e.g., solar irradiation or desiccation) (1, 3). Lighthart andFrisch (12) were among the first to incorporate an exponen-

tial microbial death rate into a modified Pasquill particledispersion model to predict concentrations of viable airbornemicrobes at different locations downwind from a pointsource, assuming a continuous emission source and un-

changing meteorological conditions. They pointed out thepaucity of data describing death rates for microbes in thenatural environment and the need for caution in substitutinglaboratory measurements. Because of this important effectof mortality, it is difficult to critically evaluate the scale (asopposed to the shape) of simulated deposition. More re-

search is needed in this area. However, variations in themortality rate in simulations would affect, primarily, thescale rather than the shape of simulated dispersal patterns.As predictive ability about mortality of airborne bacteria isimproved, the utility of the model in helping optimizesampling methods will be increased.For the Brentwood trials, the model predicted off-site

dispersal patterns that were in qualitative agreement withresults from the reported off-site vegetation samples. Unfor-tunately, vegetation samples from upwind sites were appar-

ently not obtained (23); such information would be helpful infurther testing the model. Again, the need for more informa-

tion about mortality of bacteria in aerosols is emphasized, aswell as correlation of area deposition with samples obtainedfrom vegetation. Also, it is not known whether the belatedappearance of recombinant bacteria at some sample sitesresulted from movement subsequent to the initial dispersalevent or as an artifact of the sampling method (23).Because the output of the model, as shown, depicts the

deposition of droplets containing bacteria (e.g., a droplet is acolony-forming unit), colony counts will not differ signifi-cantly between spray concentrations. However, the modelalso keeps track of actual numbers of bacterial cells in eachdroplet and thus has the flexibility to predict cell numbers insamples obtained by devices such as the all-glass impinger,used to monitor actual numbers of cells in aerosol samples.The model would also be appropriate to predict recoveryfrom air samplers (all-glass impingers or Andersen- or Rey-nier-type samplers) located at any (x, y, or z) coordinate, andthe software was designed to easily incorporate this option.Concerns about possible environmental effects of geneti-

cally engineered microorganisms released into the environ-ment include uncertainty about their survival, fate, andpossible interactions with indigenous organisms. Research-ers as well as regulatory agencies need tools to assess thedispersal and survival of bacteria in the atmosphere andsubsequent downwind deposition. Development of predic-tive models is not a substitute for appropriate field testingbut will help in establishing appropriate sampling methodsfor monitoring field releases, including determination of thefactors influencing various detection methods, the limits ofdetection, periodicity of sampling, and the rationale formonitoring procedures. The model presented in this report isone such tool.

APPENDIX

Sequential steps in the simulation are as follows.I. INPUT simulation parameters:

A. Particle (aerosol droplet) size: mean and standard deviationB. Colony-forming units per milliliter in spray suspensionC. Total volume sprayed on plotD. Estimated atmospheric stability class (i.e., turbulence)E. Average wind speed or data file of wind speed measure-

mentsF. Average wind direction or data file of direction measure-

mentsII. Calculate total number of particles sprayed on plot

III. BEGIN simulation of 1,000 particles:A. Initialize deposition to zero for sampling grid and devicesB. For each particle, initialize:

1. Location over plot (x, y, z coordinates)2. Radius and calculated volume3. Calculated colony-forming units per particle

C. MAIN PROGRAM LOOP (for i = 1 to total run time, inseconds)0.5-S SUBLOOP (forj = 1 to 2; subloops per second)

PARTICLE SUBLOOP (for k = 1 to 1,000 particles)(1) Check if particle has already been deposited; IF

(true) THEN go to (NEXT PARTICLE) ELSE(2) Check if the particle is in the plant canopy (z <

0.2 m) If (true) THEN wind speed and turbulenceare set equal to zero.

(3) Calculate advection (mean wind speed and direc-tion) vector

(4) Calculate sedimentation vector(5) Calculate turbulence vector parallel to wind(6) Calculate turbulence vector perpendicular to

wind(7) Calculate vertical turbulence vector(8) Sum vectors to determine new coordinates (x, y,

z)

2646 KNUDSEN

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from

MODEL TO PREDICT AERIAL DISPERSAL OF BACTERIA 2647

(9) Determine whether particle is deposited or sam-

pled at new position. If so, update deposition-sampler record

(10) Calculate mortality of bacteria in particle(11) Calculate new radius of particle due to evapora-

tionNEXT PARTICLE;

NEXT 0.5 S;NEXT SECOND;

D. Update output file with results of current simulationE. IF <100,000 particles simulated so far, THEN go to (III)

ELSEIV. Close output file; END.

The model is written in Turbo Pascal (Borland International, Inc.,Scotts Valley, Calif.) on an IBM System/2 Model 50 microcomputerand will run on any compatible microcomputer. The model iscopyrighted under the name GEMDRIFT (1989, Idaho ResearchFoundation, Inc., Moscow, Idaho) and may be used with permis-sion.

ACKNOWLEDGMENTS

I wish to thank J. L. Armstrong and R. J. Seidler, U.S. Environ-mental Protection Agency, M. V. Walter, NSI Technology ServicesCorp., and S. E. Lindow, University of California, Berkeley, forsuggestions and criticism that were helpful in initial development ofthis model.

LITERATURE CITED

1. Akers, A. B., and W. D. Won. 1969. Assay of living, airbornemicroorganisms, p. 59-99. In R. L. Dimmick and A. B. Akers(ed.), An introduction to experimental aerobiology. John Wiley& Sons, Inc., New York.

2. Anderson, J. D., and C. S. Cox. 1967. Microbial survival. InAirborne microbes. Proceedings of the 17th symposium, Soci-ety for General Microbiology, Cambridge. Cambridge Univer-sity Press, Cambridge.

3. Dimmick, R. L., and R. J. Heckly. 1969. Theoretical aspects ofmicrobial survival, p. 347-374. In R. L. Dimmick and A. B.Akers (ed.), Introduction to experimental aerobiology. JohnWiley & Sons, Inc., New York.

4. Dunteman, J. 1987. Complete turbo pascal. Scott, Foresmanand Co., Glenview, Ill.

5. Ehrlich, R., S. Miller, and R. L. Walker. 1970. Relationshipbetween atmospheric temperature and survival of airbornebacteria. Appl. Microbiol. 19:245-249.

6. Ehrlich, R., S. Miller, and R. L. Walker. 1970. Effects ofatmospheric humidity and temperature on the survival of air-borne Flavobacterium. Appl. Microbiol. 20:884-887.

7. Gregory, P. H. 1973. Microbiology of the atmosphere, 2nd ed.John Wiley & Sons, Inc., New York.

8. Hanna, S. R. 1979. Some statistics of Lagrangian and Eulerian

wind fluctuations. J. Appl. Meteorol. 18:518-525.9. Hanna, S. R., G. A. Briggs, J. Deardoff, B. A. Egan, F. A.

Gifford, and F. Pasquill. 1977. Summary of recommendationsmade by the AMS workshop on stability classification schemesand sigma curves. Bull. Am. Meteorol. Soc. 58:1305-1309.

10. Hanna, S. R., G. A. Briggs, and R. P. Hosker, Jr. 1982.Handbook on atmospheric diffusion, publication no. (DOE/TIC)11223. Technical Information Center, U.S. Department ofEnergy, Washington, D.C.

11. Hatch, M. T., and R. L. Dimmick. 1966. Physiological responsesof airborne bacteria to shift in relative humidity. Bacteriol. Rev.30:597-602.

12. Lighthart, B., and A. S. Frisch. 1976. Estimation of viableairborne microbes downwind from a point source. Appl. Envi-ron. Microbiol. 21:700-704.

13. Lindemann, J. 1985. Genetic manipulation of microorganismsfor biological control, p. 116-170. In C. E. Windels and S. E.Lindow (ed.), Biological control on the phylloplane. Am. Phy-topathol. Soc., St. Paul, Minn.

14. Lindow, S. E. 1985. Ecology of Pseudomonas syringae relevantto the field use of ice- deletion mutants constructed in vitro forplant frost control, p. 23-35. In H. 0. Halvorson, D. Pramer,and M. Rogul (ed.), Engineered organisms in the environment:scientific issues. American Society for Microbiology, Washing-ton, D.C.

15. Lindow, S. E. 1986. Strategies and practice of biological controlof ice nucleation active bacteria on plants, p. 293-311. In N.Fokkema (ed.), Microbiology of the phyllosphere. CambridgeUniversity Press, Cambridge.

16. Lindow, S. E., G. R. Knudsen, R. J. Seidler, M. V. Walter,V. W. Lambou, P. S. Amy, D. Schmedding, V. Prince, and S.Hern. 1988. Aerial dispersal and epiphytic survival of Pseudo-monas syringae during a pretest for the release of geneticallyengineered strains into the environment. Appl. Environ. Micro-biol. 54:1557-1563.

17. Pasquill, F. 1961. The estimation of the dispersion of windbornematerial. Meteorol. Mag. 90:33-49.

18. Pasquill, F. 1974. Atmospheric diffusion, 2nd ed. Ellis HorwoodLtd., Publisher, Chichester, United Kingdom.

19. Reid, J. D. 1979. Markov chain simulations of vertical disper-sion in the neutral surface layer for surface and elevatedreleases. Boundary-Layer Meteorol. 16:3-22.

20. Riley, R. L., and J. E. Kaufman. 1972. Effect of relativehumidity on the inactivation of airborne Serratia marcescens byultraviolet radiation. Appi. Microbiol. 23:1113-1120.

21. Seymour, K. G., and B. C. Byrd. 1965. Wind tunnel evaluationof spray drift potential. ASAE paper no. 64-609C. AmericanSociety of Agricultural Engineers.

22. Snedecor, G. W., and W. G. Cochran. 1967. Statistical methods,6th ed. The Iowa State University Press, Ames, Iowa.

23. Supkoff, D. M., L. G. Bezark, and D. Opgenorth. 1988. Moni-toring of the winter 1987 field release of genetically engineeredbacteria in Contra Costa County, report BC 88-1. CaliforniaDept. of Food and Agriculture, Sacramento, Calif.

VOL. 55, 1989

on February 19, 2018 by guest

http://aem.asm

.org/D

ownloaded from