### Abstract

- Top of page
- Abstract
- Introduction
- Methodology
- Results
- Discussion
- References
- Supporting Information

The inactivation of pathogenic aerosols by solar radiation is relevant to public health and biodefense. We investigated whether a relatively simple method to calculate solar diffuse and total irradiances could be developed and used in environmental photobiology estimations instead of complex atmospheric radiative transfer computer programs. The second-order regression model that we developed reproduced 13 radiation quantities calculated for equinoxes and solstices at 35^{°} latitude with a computer-intensive and rather complex atmospheric radiative transfer program (MODTRAN) with a mean error <6% (2% for most radiation quantities). Extending the application of the regression model from a reference latitude and date (chosen as 35° latitude for 21 March) to different latitudes and days of the year was accomplished with variable success: usually with a mean error <15% (but as high as 150% for some combination of latitudes and days of year). This accuracy of the methodology proposed here compares favorably to photobiological experiments where the microbial survival is usually measured with an accuracy no better than ±0.5 log_{10} units. The approach and equations presented in this study should assist in estimating the maximum time during which microbial pathogens remain infectious after accidental or intentional aerosolization in open environments.

### Introduction

- Top of page
- Abstract
- Introduction
- Methodology
- Results
- Discussion
- References
- Supporting Information

The inactivation of airborne microbial pathogens is relevant to public health and biodefense [1, 2]. The main biocidal agent affecting bioaerosols is solar radiation consisting of a direct solar UV and a diffuse UV component, this later being produced by the multiple scattering of light by ambient atmospheric aerosols and gasses and by the multiple reflections of UV by the underlying surface or ground [3]. Predicting the direct and diffuse solar UV in the wavelength range 280–320 nm (which is known as UVB) is key to predict the environmental survival and consequent risk posed by virulent microorganisms in general [4] and in particular of virulent microorganisms airborne in aerosols after broadcasted by infected patients during epidemics or by germs aerosolized after a biological attack. Although considerable advances have been made to predict the survival of microorganisms deposited on surfaces or suspended in liquids [5-8], the prediction of viability of bioaerosols in the atmosphere remains lacking.

In a recent paper [3], we described the use of MODerate resolution atmospheric TRANsmission (MODTRAN) (a software program [9, 10] developed by Spectral Sciences Inc. [Burlington, MA] and the US Air Force Research Laboratory [Wright-Patterson Air Force Base, OH]) to predict the direct and diffuse solar UVB fluxes received by bio-aerosols at various altitude, sea-level meteorological visibility distances, and surface (ground) albedos in a clear-sky atmosphere. The effect of relative humidity (RH) was accounted for in MODTRAN simulations within the visibility distance parameter (see Sea level visibility range in the Supplementary Information). MODTRAN is a numerical code that is commonly used to address diffuse sky radiance, multiple scattering and band models gas absorption. MODTRAN has been extensively verified and validated [11]. However, MODTRAN is complex (the user must be an expert in MODTRAN to be able to use it correctly) and its application is time consuming (many MODTRAN “runs” are needed to compute UV daily energy). In addition (true for any numerical code), the output from MODTRAN is “numbers” for each run, thus intuitive insight for the effect of key parameters on the output is lost. Although MODTRAN produces adequate predictive results, its requirements of extensive computer memory (GigaBytes) and prolonged running time (hours) generally limit the program to highly specialized atmospheric applications with intensive supporting computer power. The goal of this study was to investigate whether a relatively simple method to calculate solar diffuse and total irradiances received by aerosols could be developed and easily used by photobiologists or other scientists who are not always able or willing to devote extensive resources and training to utilize complex atmospheric radiative transfer computer programs.

### Methodology

- Top of page
- Abstract
- Introduction
- Methodology
- Results
- Discussion
- References
- Supporting Information

We considered solar photons irradiating aerosols according to the radiative transfer model detailed in the Supplementary information and in [3]. We used the microbial action spectrum (microbicidal potency at various wavelengths with respect to the survival measured after exposure to 254 nm UV radiation which is near the peak of DNA absorption and microbial damage) previously published [12]. After variable analysis, we selected nine quantities: (total, diffuse and direct daily action energies), , , (daily action energies that are normalized by atmospheric ambient maximum flux measured at noon). , and correspond to the fraction of total daily action-energy that is diffused, to the ratio of direct ambient daily energy to total daily action energy, and to the fraction of total ambient flux at noon that is diffused, respectively. Superscripts denote diffuse, direct and total = diffuse + direct. Subscript “a” denotes action energy which is obtained by weighing the ambient UVB spectrum with respect to the action biocidal spectrum (4), *i.e*. it is the net radiation that damages microbes. Lack of subscript (*i.e*. ) refers to UVB daily energy in the atmosphere in the absence of microbes; *F*_{max} is ambient flux at noon (see Eqs. S1, S2, S4, S5 in the Supplementary Information). Calculation of each of these is described in the Supplementary Information (Eq. S6) and their tabulated values are also in the Supplementary information (Tables S1–S4). From these nine quantities, we derived four additional ambient quantities (Eq. S7): (total, diffuse and direct ambient fluxes at noon), and *E*^{dir} (ambient direct daily energy). An example of using and to estimate the maximum number of days necessary to inactivate influenza virus in aerosols suspended at midlatitude under a specific set of atmospheric conditions has been previously described [3] with a discussion of the difference between spherical actinic fluxes and MODTRAN plane radiances. In this work all radiation quantities (energy and flux) are for radiation on horizontal plane (*i.e*. a plane whose normal is the zenith) and the diffuse radiation is from photons that are scattered from all directions (*i.e*. downwelling and upwelling photons that cross a plane from above and below, Eq. S1 in Supplementary information).

### Results

- Top of page
- Abstract
- Introduction
- Methodology
- Results
- Discussion
- References
- Supporting Information

In our attempt to replace the vast output of MODTRAN with a simple regression model, we captured the nonlinearity of the radiation quantities (shown in Fig. 1) by developing a second-order regression model as a function of altitude, ground albedo (*i.e*. reflectivity) and visibility range. The attenuation in the atmosphere is an exponential process with optical depth (*e.g*. Beer's law for the direct component of the solar UV) that is nonlinear with altitude, as is shown in the curvature (steeper at lower altitudes) of the direct daily action energy (Fig. 1c). The nonlinear effect of altitude is also evident in the curvature of the surfaces in Fig. 1b and in the nonuniform spacing of the surfaces in Fig. 1a (*e.g*. the spacing between the 1 and 3 km surfaces is larger than the spacing between 3 and 5 km). The nonlinear effect of visibility is evident in the curvature of the surfaces in Fig. 1a for the diffuse daily action energy, in Fig. 1c for the direct daily action energy and in Fig. 1d for the total (diffuse + direct) daily action energy, where the polarity of the curvature is concave near the ground and convex at higher altitude. As altitude increases, the curvature of the surfaces decreases. We searched for the lowest order polynomial that showed reasonable agreement with the results produced by MODTRAN and that ensured numerical stability of the regression model (see Supplementary information section S2.2). We treated each variable independently (for simplicity and for preserving straightforward interpretation) and did not allow interaction (cross-terms) between variables (*e.g*. or ). We finally chose a second-order polynomial *y*(*h*, *alb*, *vis*), where *y* is any of the nine quantities listed in the Supplementary information Tables S1–S4 with seven coefficients, *w*_{1}–*w*_{7} (determined with least-squares fit to MODTRAN data) for a given set of atmospheric conditions (*η*, *ψ*), as represented by

- (1)

In Eq. (1), *η* is a given latitude and day of the year, *ψ* denotes the atmospheric physical parameters (vertical distribution of gasses, temperature, optical properties, etc.), *h* the altitude aboveground is in kilometer, *vis* is sea level visibility distance in kilometer, *alb* is surface (ground) albedo in fraction (range 0–1). See units for the nine *y* quantities in SI Eq. S6. With Eq. (1), we can deduce four more quantities (see SI Eq. S7), thus, a total of 13 radiative quantities can be derived with our second-order regression model. We chose not to treat the atmospheric trace gas ozone as a regression variable (although it affects the UV radiances due to its strong UV absorption). Our regression model is for a given atmosphere for which the temperature and pressure profile as well as the altitude distribution of trace gasses is set. Different atmospheric models have different ozone profiles (see fig. 2 in ref. [3]). We developed a regression model for three atmospheres; the 1976 US Standard and two midlatitude atmospheres. We did not detect any variation in UV solar flux that could be attributed to variations in water vapor relative humidity when the regression was done with the visibility parameter (see discussion in SI section S2). Thus, for a given atmosphere we only address the effect of altitude (location of the microbial aerosols), the albedo of the ground coverage and the visibility condition (affected by aerosols in the atmospheric boundary layer). The reasons leading us to select a second-order regression model and the physical reasons for the good fit of the data are further discussed in the SI (section S3.1).

The coefficients in Eq. (1) were determined by least-square fit of the nine quantities calculated by MODTRAN data corresponding to the 1976 U.S. Standard atmosphere and a midlatitude atmosphere at two different seasons (spring–summer and fall–winter) and for two ambient aerosols models (for urban and rural environments), at the dates of the two solstices and the two equinox dates. We previously reported that plane irradiances calculated by MODTRAN underestimated spherical actinic irradiances [3]. Therefore, Eq. (2) only provides a maximum number of radiation days, *n*_{days}, needed for inactivating a specific germ at altitude *h* (km) in a given atmospheric model, visibility distance (km) and ground albedo, given by

- (2)

where *y* can be any of (Jm^{−2}) and *E*_{I} (Jm^{−2}) is the inactivation energy of a specific germ for a given survival level (*e.g*. 1−log_{10} or 2−log_{10} inactivation kill 90% or 99% of the microbial populations, respectively). Hence, Eq. (2) predicts the maximum number of radiation days a germ will survive before its population is depleted to these levels.

SI Tables S1–S4 provide measures of the accuracy of the regression model presented here. The tables present mean absolute error, 90 percentile confidence interval (*e.g*. a 0.05 significance level for double-sided hypothesis testing), standard deviation of error and correlation coefficient between our model and the MODTRAN data. The error is defined as: *error* = [*y*(*h*, *alb*, *vis*) - MODTRAN(*h*, *alb*, *vis*)]/MODTRAN(*h*, *alb*, *vis*). The regression model reproduced MODTRAN radiation quantities with acceptable accuracy (mean accuracy of *ca* 2% from data in the SI Tables S1–S4). The largest error was *ca* 6% for radiation fields and on 21 December. For all other quantities, the error was <5%. This accuracy is excellent compared with microbiological laboratory experiments where the survival level of microorganisms to UV radiation, measured in log-scale units is usually within accuracy no better than ±0.5 log_{10} units. The correlation coefficient between the data estimated by the present regression model and MODTRAN was high (>0.9, and in most cases >0.95), showing that our model explain much of the variation in the MODTRAN data. For example, the unexplained portion of MODTRAN data by our regression model is only 1 − *ρ*^{2} = 0.1 (*i.e*. 10%) for an observed correlation coefficient *ρ* = 0.95.

The accuracy of our regression model appeared satisfactory, but its utility was limited to a specific latitude (35°) and day of the year (equinox and solstice dates). One option to expand the model to other latitudes and times of the year was to recompute regression coefficients (SI Eq. S10) for the desired latitude/date, a process that is time consuming and involves a vast number of MODTRAN runs. As an alternative, we attempted to scale (in an empirical fashion) the regression model from a reference latitude and date (chosen as 35° latitude for 21 March) to any desirable latitude and day of the year. The difficulty in latitude/date scaling is due to nonlinear effect of sun-angle θ (a complicated geometric function of latitude and date, see SI Eq. S3) on the radiation fields, and furthermore the fact that the daily action energy is a complicated integral of all sun-angles θ during a day. We empirically scaled from the reference latitude and date to any desired latitude and date by the functions of zenith angle and length of daylight for the six quantities, , , , , , by,

- (3)

where *θ*(*lat*, *day*) is the solar angle (see SI Eq. S3) at noon time (*hour *= 12 in Eq. S3) at a given latitude and date, and daylight (*lat*, *day*) is the daylight length in hours. For example, the total daily action energy for 45^{°} latitude on 1 August for a 1976 U.S. Standard atmosphere with rural aerosols at spring–summer (SI Table S1) is given by Eq. (3) as

where the magnitude-scaling constant is computed from Eq. S3 for 21 August (233rd day of the year) at 45° latitude where *θ* = 32.63° (at noon) and ; and for the reference 21 March (80th day of the year) at 35° latitude where *θ* = 35.11^{o} (at noon). The empirical scaling relationship was derived by considering: that daily energies are related to length of daylight; that fluxes at noon time (*e.g*. , , ) are proportional to cos (*θ*_{noon}) [*θ* in Eq. (3)] and that some of the contribution to the diffuse radiances is due to diffuse reflection by the ground albedo (modeled as a Lambertian surface in MODTRAN) to a point located on the zenith at elevation *h*. We note that powers of cosine angle [*e.g*. 2nd, 3rd and 4th powers, used in our scaling Eq. (3)] appear in determining irradiances produced by the geometry of diffuse sources (Chapter 8 in Ref. [13]).

In Table S5 shown in the SI, we compared the values of these six quantities listed for the 1976 U.S. Standard atmosphere and midlatitude summer atmosphere with rural and urban aerosols (noted as atmospheres A, B, C and D in the SI Table S5) to those in the reference atmosphere (21 Mar and 35° latitude) to latitudes 25°, 35° and 45° for four dates (1 February, 1 May, 1 August and 1 November). The average error of all 288 entries corresponding to different dates, latitudes and types of aerosols in Table S5 was 13%. This 13% error is higher than the average error of 2% in SI Tables S1–S4. This is due (in part) to the error magnification (Eq. S11) when the reference atmosphere is used instead of the appropriate (“error-free”) latitude/date atmosphere. However, our empirical scaling partially compensates for the use of slightly more inaccurate reference atmosphere regression coefficients, and the magnitude of the total errors of our estimates is within errors generally accepted in microbiology. The worst accuracy obtained was when the reference atmosphere (21 March at midlatitude summer atmosphere) was used for predicting midlatitude winter atmosphere at months of the winter season (November and February), especially for and for at 45° latitude (with their largest observed errors of *ca* 150% and *ca* 70%, respectively). The overall correlation between MODTRAN latitude/date data and our latitude/date scaled model is quite high (>0.9) for the six radiation fields in spite of the large errors in some fields (*e.g*. even for the 150% error for in November the correlation was >0.95). This relatively high correlation implies that most of the variation in MODTRAN data can be explained by affine (gain and offset) transformation of . Our relatively simple approach of scaling with Eq. (3) from known data for a given reference date and latitude to a different desired date and latitude enables the estimation of the solar UV irradiance received by airborne pathogens with <50% error (achieved for most of our latitude/date scaling) and can be useful in predicting UV solar inactivation of microbes in the atmosphere as microbial survival is estimated in logarithmic scale with a large uncertainty (within ±0.5 log_{10} units). If a better accuracy than the one achieved with our empirical scaling [Eq. (3)] is ever desired, then, a full-scale computation can be performed as described in Tables S1–S4, whereby a mean absolute error *ca* 2% should be achieved. Alternatively, a similar regression model could be computed for a coarse grid of latitude/dates (*e.g*. for each month and every 2° of latitude intervals). However, any error reduction below the 2% would be attained after considerable effort that seems unnecessary in view of the accuracy already obtained and the noted limitations generally accepted in the concentration of microorganisms

### Discussion

- Top of page
- Abstract
- Introduction
- Methodology
- Results
- Discussion
- References
- Supporting Information

Previous attempts to fit MODTRAN output with a regression model were made for a limited number of specific limited parameters (*e.g*. UV transmission [14], water temperature retrieval [15] or radiance along a specific flight line [16]. To our knowledge, this is the first time that a comprehensive regression model including multiple variables (13 quantities given in SI Eqs. S6–7) has been achieved to describe with usable accuracy a complex radiative transfer scenario in the atmosphere as a function of altitude, ground albedo and sea level visibility distance. The novelty and usefulness of the regression model described herein are that it can “replace” MODTRAN for estimating inactivation of microbes by solar UV radiation suspended in the atmosphere within experimental microbiological errors.

The action spectrum used in this work represents microbial survival at various wavelengths with respect to the survival measured after exposure to 254 nm UV radiation (near the peak of DNA absorption and microbial damage). Microbial sensitivity is generally expressed by the D_{37} survival rate which corresponds to the irradiance needed to produce, in average, an inactivating hit per microorganism (which experimentally corresponds to a decrease in the measured survival to 37% of the microbial amount originally irradiated). Although the action spectrum was built using D_{37} values measured at various wavelengths, other survival levels can also be employed, *e.g*. the survival levels for 1 − log_{10} or 2 − log_{10} are 10% and 1%, respectively [3, 12]. Microbial survival can thus be estimated by combining the microbial sensitivities that have been measured or estimated previously ([5, 8, 12], reviewed in [17]) with the atmospheric radiances calculated by the method described here for aerosols suspended at different altitudes under various conditions.

With lesser effort (than MODTRAN computations) and more modest computational capabilities, the regression model presented here could be employed to estimate the survival of microbial aerosols at any date and atmospheric conditions (at a given altitude, visibility and over specific ground types). The relatively simpler approach provided by the regression model presented here would indicate the microbial inactivation level that should be expected after each radiation day within the error of the model. The inactivation level per radiation day can be obtained by calculating the total daily energies [ obtained by computing Eq. (3)] and dividing this daily action energy standardized to 254 nm by the microbial sensitivity at 254 nm (either D_{37} or as number of log_{10} inactivation per day), which is known for many bacterial and viral organisms [12, 17]. Thus, our regression model could be used for airborne germs at elevation *h* at a given latitude and date *η* Eq. (1) in a given atmosphere *ψ* (*e.g*. Tables S1–S5), over a ground with albedo *alb* and MODTRAN sea level visibility distance is *vis* (observed visibility is *ca vis*/2, see SI section S2.1). The regression model for [7th row in Tables S1–S4, and if latitude/date scaling is needed also use Eq. (3)] can then predict the daily action energy (microbicidal daily energy, , relative to the microbe's sensitivity to 254 nm light). The prediction of maximum number of radiations days required to inactivate an airborne germ to a given survival level can be (relatively easily) computed with Eq. (2) and this approach was previously demonstrated for influenza-A virus (fig. 6 in ref. [3]).

The approach, equations and procedure presented in this study should assist in estimating the time during which microbial pathogens remain infectious after accidental or intentional release in the atmosphere. The demonstrated success of our regression model should encourage other researchers to seek similar approaches for other complex MODTRAN applications.