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Supplemental Information
Title:
Quantitative Analysis of Effects of UV Exposure and Spore
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Cluster Size on Deposition and Inhalation Hazards of Bacillus
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Spores
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Authors:
F. A. Handler2 and Jason M. Edmonds1†
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Affiliations:
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Edgewood Chemical Biological Center
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United States Army
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Department of Defense
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5183 Blackhawk Road
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Aberdeen Proving Ground, MD 21010
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1307 Capulet Ct
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Mclean, VA 22102
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Panasynoptics Corporation
Supplemental Data, Methods, Predictions For Larger Clusters
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Attempts to predict the decay of single spores and clusters with simple
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exponential models, as is done in transport and dispersion models, produces
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different results from predictions based on multihit or Gompertz extended models.
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Figure S1 displays the experimental surviving fractions from Kesavan et. al. 2014 for
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single spores (circles), 2.8 m clusters (squares) and 4.4 m clusters (diamonds).
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Solid lines plot the multihit fit to the single spore data and Gompertz extended
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multihit fits for the 2.8 m and 4.4 m data. The dashed lines plot predictions based
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on fitting a simple exponential model to the data. The exponential fits intersect the
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multihit based predictions at two points, the origin and one point within the range
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of the data set used in the fit. Elsewhere the exponential fits diverge from the
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multihit based models. There is no obvious physical rationale for extending the
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exponential fit parameters to larger cluster sizes, but the simplest approach would
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be some kind of empirical fit of k to cluster size. Figure S2 plots the data-fit values
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of k versus cluster size, shown as solid squares. A lograthmic fit to cluster size
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performs well analytically (fit parameters shown) but it produces unphysical results
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in that it produces k = 0 (no decay) at D = 8.75 m and k > 0 at larger sizes. In
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Figure S1, predicted decay for a simple exponential predicted by the fit in Figure S2
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for 8 m clusters is shown as a dashed line with vertical cross hatches. The solid
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line with cross hatches plots the predicted decay for the Gompertz extended
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multihit model from the text. At 8.75 m the empirically predicted exponential
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would not decay.
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Surviving Fraction
10
10
10
10
10
10
10
10
0
-1
-2
-3
-4
-5
-6
-7
-8
0
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44
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Fluence J/m2
100
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Figure S1. Sizes above are single spores, 2.8, 4.4, and 8 microns.
k (m^2/J)
0.005
0.000
-0.005
-0.010
-0.015
-0.020
-0.025
-0.030
-0.035
-0.040
-0.045
0.000
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y = 0.0183ln(x) - 0.0397
R² = 0.9996
5.000
Cluster Size (microns)
10.000
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Figure S2. Size versus k value from exponential fit. Zero k occurs at D = 8.753
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microns
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Supplemental Data, Methods, Modeling Plume Dispersion and Particle Size
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Effects on Inhalation and Deposited Hazards
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We use standard engineering models for plume dispersion since our aim is
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not to evaluate hazards from specific release scenarios but to compare the relative
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hazards presented by single spores versus spore clusters under generic dispersion
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phenomena. We consider the standard meteorological wind conditions described
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by the various Pasquill-Gifford-Turner classes (Turner 1970), shown in Table S1.
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We considered several wind speeds within the lowest standard wind speed class
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(wind < 2 m/s). In the analysis, we used the more stable configurations given, i.e.
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where a class spans A-B, we used B in the analysis.
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Each PGT class has associated an evolution of the dispersions in the x, y, and
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z directions, which has a resulting Gaussian dispersion pattern characterized by x,
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y, z which are functions of downwind distance the plume travels.
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classes, fits to empirical data have been developed which express the evolution of
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plume standard deviations with downwind distance, of the form 𝜎𝑞 = 𝑎𝑥 𝑏+𝑐𝑙𝑛𝑥 ,
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where q = y or z (for continuous plumes), for a single puff we take y = x, a, b, and c
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are empirical parameters which depend on stability class and coordinate, and x is
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downwind distance (Davidson 1990).
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Gaussian distribution, given by
For the PGT
The puff evolves in 3 dimensions as a
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𝐶(𝑥0 ; 𝑥, 𝑦, 𝑧, 𝑡) =
2𝑁
3
(2𝜋)2 𝜎𝑥 𝜎𝑦 𝜎𝑧
2𝑁
3
(2𝜋) ⁄2 𝜎𝑥 𝜎𝑦 𝜎𝑧
𝑒𝑥𝑝 {−
(𝑥0 −𝑣𝑤 𝑡)2
2𝜎𝑥2
𝑒𝑥𝑝 {−
(𝑥0 −𝑥(𝑡))
2𝜎𝑥2
2
𝑦2
𝑧2
− 2𝜎2 − 2𝜎2 } =
𝑦
𝑧
} (S1)(Equivalent to equation 7 in the text)
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where x0 = vwindt0 = the x position reached by the center of the puff after t0 seconds,
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x = y and z evolution is approximated by the empirical plume relations, evaluated
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at t0. This approximates the puff as distributed at t0, moving with velocity vw past x0
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without evolving the distribution in time as it passes. We assume the z-distribution
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of material is reflected in the positive z direction, hence the factor 2 multiplying N in
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the numerator. Since we are interested in the concentration at y = z = 0, the
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appropriate expression of concentration is on the right in equation S1. The time the
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plume center takes to reach downwind distance x0 is given simply by t = x0/vw and
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and we evaluate results for downwind distances of 0.5km, 1km, 2.5km, 5km, and
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10km.
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To assess the total effects on hazards at various distances downwind, we
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estimated the concentrations downwind that result from the plume spreading of the
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material being dispersed. This is given by equation S1 with x(t) = x0 and we
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incorporate the effect of UV degradation due to solar exposure simply by
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multiplying the concentration by the surviving fraction as a function of times of
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exposure at distances downwind as
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𝑥0
𝐶 (𝑥0 , 𝑡 = 𝑣 ) =
𝑤
𝑥
2𝑁×𝑆(𝑡= 0 )
𝑣𝑤
3
(2𝜋)2 𝜎𝑥 𝜎𝑦 𝜎𝑧
(S2)(Equation 8 in the text)
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We use the times calculated by t = x0/vw and standard plume dispersion solar
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elevation angles and sky cover categories ((Turner 1970) page 6), given in Table S2
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for estimating the suspension time and resulting total UV insolation for particles
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deposited at varying distances downwind.
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The fluence is reduced as a function of solar elevation angle by the increase in
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attenuation due to increasing optical path length through the atmosphere. The
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reduction is given by the commonly used Beer-Lambert law 𝐼(𝜃) = 𝐼0 𝑒 −𝛼𝑚(𝜃) .
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Measured values for the atmospheric extinction coefficient for UV radiation depend
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on variables such as location, local aerosol concentrations, and humidity, but are on
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the order of 2.0 for clear sky (Kirchoff 2001). Tabulated values of m(θ) provide
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m(45°) = 1.41 and m(25°) = 2.36, so that the Beer-Lambert expression gives the
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intensity reductions with elevation angle as 0.44 and 0.07 for 45° and 25°,
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respectively (Kasten and Young 1989). With these values, the adjustment factors to
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multiply solar exposure time to yield germicidal effective dose are presented in
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Table S3.
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The deposited hazard on the centerline is given by the plume concentration times
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the particle deposition velocity, vD, integrated over the time the plume passes the
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downwind distance x0,
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∞
𝑁
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𝐷(𝑥0 , 𝑦 = 𝑧 = 0) = ∫0 𝑣𝐷 𝐶(𝑥0 ; 𝑡)𝑑𝑡 = 2𝜋𝜎
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(S3)(Equation 9 in the text)
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𝑣𝐷
𝑦 𝜎𝑧 𝑣𝑤
𝑥0
[ 1 + erf (
√2𝜎𝑥
)]
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where we have integrated the Gaussian plume passing the point x0 as characterized
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by its distribution at x0 and constant for the time the plume passes.
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velocity, vD, is calculated with standard empirically calibrated models (Ian Sykes, et .
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al. 2006, pp 67-75) (20) as 𝑣𝐷 = 𝑣𝑔 + 𝑣𝑑 where vg is the gravitational settling
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velocity and vd is the dry deposition velocity as a function of the friction velocity u*
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and a deposition velocity E, 𝑣𝑑 =
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speed as used here, and the deposition efficiency is given by 𝐸 = 1 − (1 − 𝐸𝐵 )(1 −
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𝐸𝐼𝑀 )(1 − 𝐸𝐼𝑁 ). EB corresponds to Brownian diffusion, EIM to turbulence induced
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impaction, and EIN to interception of vertical surface components such as elements
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of a vegetative canopy (Sykes 2006). For simplicity we focus on relatively smooth
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deposition surfaces such as soil, sand or concrete and in such cases EIN = 0, 𝐸𝐵 =
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0.8 𝑆𝑐−0.7 , 𝐸𝐼𝑀 = 1+ 𝐼𝑀
𝐴
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Schmidt number, with 𝜈 the kinematic viscosity of air, and 𝜗 the particle diffusivity
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coefficient.
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settling time constant given by vg/g and 𝑣∗ is the average local friction speed based
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on the fluctuating surface momentum flux, but independent of the horizontal
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direction of the flux. EB and vg are independent of the friction velocity and for 1 μm
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and 10 μm particles are, at T = 25°C, and P = 1 atm, 7.6e-5 and 3.5 e-3 cm/s (1 m)
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and 1.38e-5, 0.3 cm/s (10 m). We calculate the friction velocity as given by the
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well-known logarithmic velocity profile law corrected for stability, using standard
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adjustments for stability class via the Monin-Obukhov length (Sykes 2006). We
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have used the more stable value where several classes are given; for example, if the
𝐴
𝐼𝑀
𝐸𝑢∗2
𝑢𝑟
The deposition
. Here ur = vw is the reference velocity, or wind
𝑤𝑖𝑡ℎ 𝐴𝐼𝑀 = 0.08𝑆𝑡(1 − 𝑒 −0.42𝑆𝑡 ) , where 𝑆𝑐 = 𝜈/𝜗 is the
The Stokes number is 𝑆𝑡 =
(𝑢∗2 +𝑣∗2 )𝜏𝑔
𝜐
where τg is the gravitational
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class has A-B, we chose B. The resulting friction velocities determine the dry
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deposition and are given in Table S4.
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To estimate the depletion of the plume concentration resulting from the
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amount deposited, we recall equation (S3) above for the deposition on the
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centerline, and note that integration of the Gaussian over –∞ y < ∞ removes the
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√2𝜋y dependence. We further note that for the values of x0 and x here the erf
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function is essentially 1, so we replace the bracketed term with 2. The result for the
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number of released particles adjusted for total depletion by deposition of the plume
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during dispersion from plume initiation at xl to downwind distance x0 is
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(S4)(Included in equation 10 in the text)
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The integral term in equation (S4) can be evaluated by using an approximate but
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integrable form for z, 𝜎𝑧 = 𝑎𝑥 𝑏+𝑐𝑙𝑛𝑥 ≈ 𝛼𝑥 𝛽 , where and  are empirical constants
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determined for each PGT stability class. We determine  and  simply by linear
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regression of ln(x) on ln(z), the results of which are given in Table S5. Using the
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simplified power law for z, equation (S4) gives the depletion due to deposition as
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2 𝑣𝐷
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𝑁𝑆 (𝑥0 ) = 𝑁𝑆0 [1 −
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in equation 10 in the text)
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1
√2𝜋 𝑣𝑤 𝛼(1−𝛽)
1−𝛽
(𝑥0
1−𝛽
− 𝑥𝑙
)]
(S5)(Included
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Figures S3 and S4 show the depletion fraction due to deposition for strong and
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moderate sunlight, respectively. The differences are due to the effect of sunlight on
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the PGT classes for each wind speed (see Table S1) and the resulting differences in
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the empirical plume spread as a function of downwind distance. Since we evaluated
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the more stable choice for each class, the strong sunlight case has PGT Classes
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(A,A,A,B,B,C,C) and the moderate sunlight case has (B,B,B,B,C,D,D) for the wind
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speeds evaluated (.2,.5,1,,2,3,5,6) m/s. Since the amount of sunlight affects the
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stability class, the deposition at a given wind speed varies with sunlight case
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considered.
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From Figure S3 we observe that deposition depletion of the 10 m plume still
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leaves more than 75% of the concentration intact. From Figure S4, for the moderate
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sunlight case, deposition depletion of the 10 m plume still leaves more than 40% of
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the concentration intact. Thus for both the strong and moderate sunlight cases,
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depletion is relatively negligible (compared to orders of magnitude differences)
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with respect to UV degradation when comparing single spores to 10 m cluster
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hazards.
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Surface
Wind
(m/s) at
10 m
0.2
0.5
1
2
3
Day
Incoming Solar Radiation
Strong
A
A
A
A-B
B
Moderate Slight
A-B
B
A-B
B
A-B
B
B
C
B-C
C
Night
Overcast Conditions
Heavy
D
D
D
D
D
Thin
D
D
D
E
D
Slight
D
D
D
F
E
xdw
meters
A
A
A
A-B
B
5
6
C
C
C-D
D
D
D
D
D
D
D
D
D
C
C
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Table S1. Standard PGT Meteorological Classes.
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Sky Cover
Solar Elevation angle
> 60°
60°>x>35° 35°>x>15°
4/8 or less
Strong
Moderate
Slight
5/8 to 78 Low cloud Moderate Slight
Slight
5/8 to 7/8 Middle
Slight
Slight
Slight
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Table S2. Solar radiation corresponding to the “Strong,” “Moderate,” and “Slight”
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categories (Turner, 1971)
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Exposure Adjustment
Solar Elevation angle
> 60°
60°>x>35°
35°>x>15°
Factor x Tsolar
Sunlight =
Strong
Moderate
Slight
Summer
0.5
0.22
0.035
Winter
1
0.44
0.07
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Table S3. Exposure time adjustment for solar elevation angle.
Surface
Wind
(m/s) at
10 m
0.2
0.5
1
2
3
5
6
Day
Incoming Solar Radiation
Strong
0.02
0.05
0.11
0.20
0.31
0.50
0.60
Moderate
0.02
0.05
0.10
0.20
0.30
0.50
0.60
Slight
0.02
0.05
0.10
0.20
0.30
0.50
0.60
Night
Overcast Conditions
Heavy
0.02
0.05
0.10
0.20
0.30
0.50
0.60
Thin
0.02
0.05
0.10
0.14
0.30
0.50
0.60
Slight
0.02
0.05
0.10
0.10
0.21
0.50
0.60
Table S4. Friction velocities for the various PGT classes, in meters/second.
PGT Class
A < 3.1 km
A > 3.1 km
B
C
D
b
2.117
2.944
1.069
0.9147
0.6616
a
-8.506
-15.06
-2.830
-2.201
-1.140
Table S5. Fit values of z given by 𝜎𝑧 = 𝑎𝑥 𝑏+𝑐𝑙𝑛𝑥 to 𝜎𝑧 = 𝛼𝑥 𝛽 for PGT Classes A to D
determining and . Differences between the two expressions are on the order of
5% or less.
Figure S3. Depletion of the plume due to deposition during transport and
dispersion up to downwind distances shown. PGT Classes shown are for the case of
strong sunlight. Figure S3(a) shows deposition fraction for 10 m clusters. Figure
S3(b) shows results for single spores. Letters A, B, C label the relevant PGT classes.
Horizontal axis is downwind distance in km. Note the difference in deposited
fraction scales between Figure S3(a) and S3(b).
Figure S4. Depletion of the plume due to deposition during transport and
dispersion up to downwind distances shown. The depletion fraction is given by
equation S5 above. PGT Classes shown are for the case of winter, moderate sunlight.
Black solid and dashed lines correspond to B class cases, the gray double line
indicates the C class case (for 3 m/s wind speed), and the single gray solid and
dashed lines indicate D class cases. Figure S4(a) is for 10 m clusters and Figure
S4(b) for single spores. (Note the difference in vertical scales.)
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Supplemental Data, Results, Effects of particle size on projected hazard –
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without deposition depletion and dose-response adjustments
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To assess the order of magnitude differences between clusters and single
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spores, we first estimate and compare surviving concentrations and depositions for
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single spores and 10 m clusters without adjusting for 1) depletion of the plume
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due to deposition and 2) differences is infective dose-response due to particles size.
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These results display the order of magnitude of the differences due primarily to UV
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degradation differences.
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For the range of weather conditions encountered in hazard estimates, as
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characterized by the PGT classes, we compare the downwind inhalation hazard
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(Figure S5a) presented and the downwind deposition hazard (Figure S5b) based on
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the standard plume dispersion models and particle deposition rates as described
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above, and the survival rates for solar exposure derived from the experimental data.
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We used the times calculated given by t = x0/vw and solar elevation angles reported
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in Table 5 for estimating the suspension time and fluence received for particles
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deposited at varying distances downwind. We find that the combined effects of
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solar degradation and size dependent deposition result in 10 m clusters presenting
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from a few to up to 10 orders of magnitude greater deposition and inhalation
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hazards than single spores, depending on meteorological conditions and downwind
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distance. The differences in deposited hazards presented by the two sizes are
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increased, relative to the inhalation hazards, due to the difference in deposition
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rates as a function of particle size. The two lowest speed cases plotted end at 2.5 km
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and 5 km, indicating that at greater distances, the hazard is below the numerical
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accuracy of the calculations, essentially zero.
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The inhalational hazard and deposition hazard for the 1 m/s wind case are shown at
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various distances for strong, moderate, and slight sunlight for winter (Figure S6a)
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and summer (Figure S6b) to illustrate the behavior of the hazards as a function of
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varying insolation. In each of the figures, solid lines plot the values for the 10 m
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clusters and dashed lines plot the values for single spores. Black lines correspond to
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strong sunlight, blue to moderate sunlight, and green to slight sunlight. All of the
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figures are for the 1 m/s wind speed case. Figures S6c and S6d, respectively, give
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the surviving dispersed fraction of released single spores and 10 m clusters, the
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surviving inhalation hazard, as a function of down wind distance, for the case of 1
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m/s wind speeds, for summer and winter, with strong, moderate and slight
223
insolation.
224
225
The main difference between winter and summer deposited hazard as a function of
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UV degradation is due to the solar insolation reduction by a factor of 0.5 for
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summer. The main difference between the single spore and 10 µm cases at small
228
distances (less exposure time and less UV decay) is due to the larger deposition
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velocity of the 10 µm clusters relative to single spores. For slight insolation, UV
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decay is relatively small for both single spores and 10 mm clusters and the
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difference between the two sizes remains relatively the same.
The overall
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magnitudes in the slight insolation cases (green, Figure S6) decreases largely due to
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the spread of the plume and resulting decrease in concentration along the plume
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centerline. For strong and moderate insolation, the 10 µm reduction due to UV
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decay is relatively small, within an order of magnitude at all distances, whereas the
236
single spore hazard is reduced by another 5 (Summer) to 10 (Winter) orders of
237
magnitude, as dispersion distance increases to 10 km.
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239
The main difference between winter and summer inhalation hazard as a function of
240
UV degradation is due to the solar insolation reduction by a factor of 0.5 for
241
summer. For inhalation hazards, the difference between the single spore and 10 µm
242
cases at small distances is smaller than the deposition cases and is due to the slight
243
UV degradation that occurs in the short time to disperse to 0.5 km. The inhalation
244
hazard is essentially independent of the particle size.
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decay is relatively small for both single spores and 10 µm clusters and the hazards
246
for the two sizes remain relatively the same, i.e. the green solid and dashed lines
247
overlap. The overall magnitudes in the slight insolation cases (green, Figure S6)
248
decrease largely due to the spread of the plume and result in a decrease in
249
concentration along the plume centerline. For strong and moderate insolation, the
250
10 µm reduction due to UV decay is relatively small, within an order of magnitude at
251
all distances, whereas the single spore hazard is reduced by another 3 (Summer) to
252
9 (Winter) orders of magnitude, as dispersion distance increases to 10 km (Figure
253
S6).
For slight insolation, UV
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255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
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Figure S5. Inhalational and deposition size dependent hazard. (a) summarizes
the surviving, deposited hazard presented by single spores versus 10 m clusters,
for winter, mid latitude, strong sunlight and various wind speeds, as a function of
the same distances downwind from the plume release and integrated over the time
taken by the plume to pass the given downwind distance. The dashed lines show
the fraction of released single spores that survive in the time required to disperse to
the indicated downwind distances and are deposited at that distance as the plume
passes, according to the deposition velocity of particles of the given sizes. The solid
lines indicate the surviving released values for 10 m clusters. The different colored
lines indicate different wind speeds, with 0.2 m/s being the lowest, and 6 m/s being
the highest. (b) surviving, dispersed inhalation hazard integrated over the time
taken for the plume to pass the given downwind distance presented by single
(dashed lines) spores versus 10 m clusters (solid lines), for winter, mid latitude,
strong sunlight and various wind speeds (0.2, 0.5, 1, 2, 3, 5, 6 m/s), as a function of
distance downwind from the plume release. All values are along the centerline of
the plume. The dashed lines shows the fraction of released single spores that
survive in the time required to disperse to the indicated downwind distances. The
different colored lines indicate different wind speeds, with 0.2 m/s being the lowest,
and
6
m/s
being
the
highest.
Figure S6. The inhalational hazard and deposition hazard for the 1 m/s wind case
are shown at various distances for strong, moderate, and slight sunlight for winter
(Figure S6a) and summer (Figure S6b), S6c and S6d, respectively, give the surviving
dispersed fraction of released single spores and 10 m clusters, the surviving
inhalation hazard, as a function of down wind distance, for the case of 1 m/s wind
speeds, for summer and winter, with strong, moderate and slight insolation.