Attenuation of UVC Solar Radiation as a Function of Altitude ( 0 ≤ z ≤ 100 km ) : Rayleigh Diffusion and Photo Dissociation of O 2 Influence

In this paper, we present an analysis of attenuation for UV-C radiation ( 290 nm λ ≤ ) as a function of the altitude z ( ) 0 100 km z ≤ ≤ by calculating the interaction ratio between the UV-C radiation and the molecular species susceptible of interact with UV-C radiation. The Rayleigh scattering spectral cross sections were calculated, the UV-C spectral cross sections of the species susceptible of interact with UV-C radiation and the UV extraterrestrial (ETR) solar spectrum were standardized with wavelength steps of 1 nm, and The International Standard Atmosphere model (ISO 1972) was adapted to calculate the molecular density. These data were utilized to calculate the photodissociation and Rayleigh scattering ratios as a function of the altitude and to determine to what measure the photodissociation and the Rayleigh diffusion were determinants of the attenuation of UV-C radiation. It became clear that the photo dissociation of O2 is the primordial mechanism of attenuation for the UV-C radiation, but the Rayleigh diffusion appears like a mechanism that encreases the photon flux, raising the performance of the O2 photodissociation. The attenuation capacities of N2O, CO2 and water vapor (H2O) over the UV-C radiation are all similar, although smaller (less than 0.6%), and this is due to their low concentration. The O3, has the theoretical greater attenuation capacity, but it is found in mid-range altitudes ( ) 15 40 km z ≤ ≤ , where the residual UV-C photons has almost vanished by O2 photo dissociation or Rayleigh diffusion, so the real effect over the UV-C attenuation is minimum. How to cite this paper: Pinedo-Vega, J.L., Ríos-Martínez, C., Navarro-Solís, D.J., Dávila-Rangel, J.I., Mireles-García, F., Saucedo-Anaya, S.A., Manzanares-Acuña, E. and Badillo-Almaraz, V. (2017) Attenuation of UV-C Solar Radiation as a Function of Altitude (0 ≤ z ≤ 100 km): Rayleigh Diffusion and Photo Dissociation of O2 Influence. Atmospheric and Climate Sciences, 7, 540-553. https://doi.org/10.4236/acs.2017.74039 Received: September 15, 2017 Accepted: October 20, 2017 Published: October 23, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access J. L. Pinedo-Vega et al. DOI: 10.4236/acs.2017.74039 541 Atmospheric and Climate Sciences


Introduction
It is well known that UV-C radiation does not reach the surface of the Earth.However, there is no precise knowledge about its spectral attenuation.
The attenuation of UV radiation, in general, is the result of the interaction of the photons with the species or molecules that are susceptible to interact.The photons extinguish themselves upon reacting, transferring their energy to the molecules either causing the breaking of their molecular bonds or the dissociation of the molecule.Due to its nature, this type of interaction is called photodissociation.
The spectral photodissociation ratio ( )

R z
λ can be defined as the number of molecular photodissociation produced by the solar radiation of each wavelength λ at any altitude in the atmosphere.This must be proportional to the spectral photon flow ( ) and to the molecular density ( ) λ σ known as the cross section, represents the probability of reacting or of molecular photodissociation which is specific to each wavelength λ for each molecular species.
The total photodissociation ratio at each altitude z is the integral of the spectral photodissociation ratio ( ) ( ) ( ) ( ) The attenuation of the residual spectral photon flux at each altitude z can be calculated by subtracting the number of reactions of photodissociation from the spectral photon flux at the altitude The initial spectral photon flux 0λ φ can be calculated from the spectral irra- diance 0 I λ received at the top of the atmosphere or ETR spectrum where, hc E λ λ = , is the photon energy, h the Planck constant and c the speed light in vacuum.
The molecular density at altitude can be expressed in terms of the pressure and the average temperature with the equation ( ) ( ) ( ) λ alternate.The temperature in the stratosphere, for example, can be characterized through three temperature gradients-the lower one positive, the highest one negative, and an isothermal layer in between-until reaching the mesopause.
The temperature gradients n λ have an approximately linear nature in each layer n of the atmosphere Through integration, the temperature inside the layer n can be expressed as where n T y n z are the temperature and altitude base of each layer.
According to The International Standard Atmosphere, between 0 and 100 km the standard atmosphere is comprised of 8 layers [1].
For a layer with gradient 0 n λ ≠ , the molecular density is given by ( ) ( ) where g is the acceleration due to gravity.
While for one isothermal layer 0 n λ = , or one without a temperature gradient the molecular density is given by ( ) The species susceptible to reacting with UV-C radiation are O 2 , O 3 , CO 2 , H 2 O and N 2 O.The corresponding cross sections are consulted in The MPI-Mainz UV/VIS Spectral Atlas [2].
The first claim of this paper is to determine to which measure these molecular species are determinant in the attenuation of the UV-C radiation.The region for the study of the attenuation of UV-C radiation is the homosphere ( ) . The homosphere-the region in which the composition of air and the molecular weight are approximately constant-contains 99.79% of the total mass reported in the atmosphere, and it is also the region where the molecular species susceptible to reacting with UV-C radiation reside.
In this paper, the homosphere is discretized in 100 m steps and the attenuation of UV-C radiation has been restricted to the perpendicular diffusion towards the surface of the Earth.

ETR Solar Spectrum
The Gueymard extraterrestrial (ETR) spectrum ( ) to it being the only one found in literature that begins in 0.5 nm.The Gueymard spectrum covers the spectral region from 0.5 nm to 280 nm in 1 nm steps, 280 to 400 nm in 0.5 nm steps, from 400 nm to 1705 nm in 1 nm steps, 5 nm steps from 1705 nm to 4000 nm, and variable steps beyond 4000 nm [3].
The integral of the Gueymard spectrum is equal to 1366.1521372347W/m 2 , which is in the same order as the Solar Constant UV-C irradiance is 10.712521 W/m 2 , representing 0.7841% of the whole solar spectrum.In Figure 1 the UV-C region of the Gueymard spectrum is presented.
By the Gueymard spectrum having variable wavelength steps, in this paper the spectrum was standardized with wavelength steps of 1 nm centered on multiples of 0.5 nm.The error propagated by this standardization was evaluated by comparing the integrals of the original and the homologated spectrums.The difference between the original integral of UV-C irradiance and the standardized integral of UV-C irradiance was 0.132 W/m 2 , which equals a relative error of 0.1272%.

Cross Sections
In Figure 2 the cross sections of the principal molecular species of the atmosphere that absorb UV radiation are presented.
The cross section of O 2 (black line) extends until 250 nm and given its concentration in the atmosphere (0.20953) it is one of the most determinant species in the attenuation of the UV-C radiation between 0 and 244 nm.
Under 150 nm, the most important cross sections are those of N 2 O and CO 2 (magenta and blue line).Nevertheless, the capacity for attenuation of these species cannot be too important, due to their low concentrations in the atmosphere given their relatively reduced concentration in the troposphere, they also cannot have an important attenuation capacity for the UV-C radiation.
The ozone, for its part (red line), is the only species whose cross sections are important between 200 nm and 300 nm, the region of the spectrum in which the ETR solar irradiance is in the range of 10 W/m 2 ; although its concentration is relatively reduced (3.5 × 10 −7 ), the ozone must play a significant role in the attenuation of the UV-C radiation.

Rayleigh Scattering
Another phenomenon that must influence the attenuation of the radiation UV-C is the Rayleigh scattering or the Rayleigh diffusion.
The Rayleigh scattering theory was proposed at the end of XIX century by John William Strutt (British physicist known like Lord Rayleigh).Using Electromagnetic Theory Rayleigh assumed that the molecules of the air, at being pushed into their excited state by the electromagnetic radiation of the sun, are converted into oscillating dipoles that re-emit the radiation in 4π esterora- dians.
The expression for the Rayleigh scattering cross section R σ for standard air −790 mm Hg, 15°C and containing 300 ppm CO 2 is the Penndorf equation [5] presented like the classic equation in many textbooks (e.g.[6]) where s n is the refractive index of air, is the depolarization term or the King factor and δ is the depolarization factor which describes the effect of molecular anisotropy.
For the refractive index s n , Peck and Reeder [7] proposed the formula for 300 ppm CO 2 ( ) ( ) where ( ) 1.034 3.17 10  ( ) Figure 4 shows the Rayleigh cross sections calculated using the Peck and Reeder refractive index s n and Bates King factor.The discontinuities for 200 nm λ < reappear.
In Table 1, we present the values of R σ reported by Penndorf [5], Bodhain [9] and Bucholtz [10] as well as the values calculated using the Equations ( 10)-( 14) for the concentrations of CO 2 360, 380 and 400 ppm.The differences between authors are around 10 −27 cm 2 ; meanwhile the differences for the different concentrations of CO 2 are around 10 −29 cm 2 .For the purpose of the calculations of attenuation of UV-C radiation, those minute differences do not cause a great impact.

Limitations
The spectral cross sections available in literature present important differences between authors and no one author has uniform wavelength steps.It is known that the cross sections vary with temperature, but it was not possible to take into account this dependence, seeing as no data exists that permits taking the gamma temperatures that exist in the atmosphere.The majority of the cross sections used in this work were measured at 298 K, with exceptions of the higher part of the spectrum of O 2 , whose cross sections were measured at 202 and 243 K, and   the cross sections of CO 2 which were measured at 310 K.
In the case of the ozone, values for the cross sections which are under 110 nm were not found.Nevertheless, under this wavelength the Irradiance is equal to only 0.00517 W/m 2 , in such a way that the error generated due to the omission of this region must be very small.In the case of the Rayleigh scattering cross section the only reliable values are those calculated for wavelength 200 nm λ > , with this in mind the Rayleigh scattering for this wavelength was omitted.
The ETR solar spectrum and the cross sections were standardized into wavelengths through interpolation and/or extrapolation and into wavelength steps of 1 nm were situated values of 0.5 nm.The error generated was evaluated by comparing the integral of the original and homologated spectrums.The relative differences between the integrals under the curve from the reported cross sections and the standardized cross sections were: in the case of O 2 : 9.818 × 10 −5 , in the case of the O 3 : −0.01599; in the case of CO 2 : 0.040026, in the case of N 2 O: 5.3782 × 10 −5 , and in the case of H 2 O: 0.00243.
In Figure 5(a) the photodissociation ratio of O 2 is presented as a function of altitude, considering the O 2 as the only species that produces attenuation of the UV-C radiation.Two regions of interaction between the UV-C radiation and O 2 molecules are observed, one in the upper layers of the homosphere (z > 80 km), and the other between 0 and 40 km-which is approximately the region in which one would find the distribution of the ozone in the atmosphere.
In Figure 5(b), UV-C Irradiance is presented as a function of the altitude that corresponds to the residual flow of UV-C radiation reacting strictly with the O 2 .Between 100 and 80 km, the molecules of O 2 only attenuate around 18% of the UV-C radiation.Between 80 km and 50 km, it is observed that the residual quantity of the UV-C radiation is constant.Left is an irradiance of 8.79 W/m 2 of the 10.71 W/m 2 which are produced from the sun.Between 40 and 0 km, the O 2 attenuates another 76.4% of the UV-C irradiance which is composed of lower energy photons.Nevertheless, if the UV-C radiation interacts exclusively with the O 2 it would not be able to attenuate completely with the UV-C radiation given that on the Surface of the Earth (sea-level), a residual irradiance around 0.6 W/m 2 (5.6% of the UV-C ETR).
Partial conclusion, the O 2 is not the only species that prevents the UV-C radiation from reaching the surface of the Earth.

UV-C Attenuation by the Rayleigh Diffusion
In Figure 6

Attenuation of the UV Radiation Spectrum: Ozone's Role in UV Attenuation
In Figure 8  To simulate the actions of the ozone, a profile of the concentration of the columns of the ozone was taken randomly, characteristic of a region with a value of 238 DU.In fact, it is the ozone that completes the elimination of the residual 0.14 W/m 2 of the photodissociation of O 2 .
On the other hand, the UV-B range, at ground level ( 0 z = ) only leaves 3.0529 W/m 2 of the ETR UV-B irradiance (18.6707W/m 2 ); meanwhile the UV-A irradiance only 23.3126 W/m 2 at ground level of the ETR UV-A irradiance (83.584W/m 2 ).This is a good approximation of what goes on.

UV-C Attenuation by N2O, CO2 and Water Vapor
Although under the wavelength of 150 nm the cross sections of these molecular species are elevated (Figure 1), due to its low concentration and the fact that the irradiance of the spectrum in this region is very weak, these species are not important in the attenuation of the UV-C radiation.If the attenuation is due to these exclusively, the reduction of the UV-C radiation would be around 0.06 W/m 2 .

Conclusions
Combining the air's Rayleigh diffusion and photodissociation of O 2 , the profile of dissociations of O 2 as a function of the altitude was obtained to describe the attenuation of the UV-C radiation in the atmosphere.This method demonstrates that the dissociations of O 2 occur in two regions of the atmosphere.In this altitude, 18% of the UV-C radiation is attenuated through the photodissociation produced by photons of high energy ( 240 nm

λ ≤
).These photodissociations contribute to the elevation in the temperature of the lower part of the ionosphere, but at these altitudes the liberated atoms of oxygen don't produce molecules The profile of the photodissociation ratio of O 2 is similar to the conditions for distribution of O 3 in the atmosphere.This permits the explanation that the ozone resides in the stratosphere because that is where the majority of the photodissociation ratio of O 2 exists.
Additionally, this paper permits the emphasis that not only the photodissocia- ratio between the UV-C radiation and the molecular species susceptible of interact with UV-C radiation.The Rayleigh scattering spectral cross sections were calculated, the UV-C spectral cross sections of the species susceptible of interact with UV-C radiation and the UV extraterrestrial (ETR) solar spectrum were standardized with wavelength steps of 1 nm, and The International Standard Atmosphere model (ISO 1972) was adapted to calculate the molecular density.These data were utilized to calculate the photodissociation and Rayleigh scattering ratios as a function of the altitude and to determine to what measure the photodissociation and the Rayleigh diffusion were determinants of the attenuation of UV-C radiation.It became clear that the photo dissociation of O 2 is the primordial mechanism of attenuation for the UV-C radiation, but the Rayleigh diffusion appears like a mechanism that encreases the photon flux, raising the performance of the O 2 photodissociation.The attenuation capacities of N 2 O, CO 2 and water vapor (H 2 O) over the UV-C radiation are all similar, although smaller (less than 0.6%), and this is due to their low concentration.The O 3 , has the theoretical greater attenuation capacity, but it is found in midresidual UV-C photons has almost vanished by O 2 photo dissociation or Rayleigh diffusion, so the real effect over the UV-C attenuation is minimum.

Figure 3 . 2 CO
Figure 3. Refractive index of air s n for

Figure 5 .
Figure 5. (a) Density of the reactions to the interaction of UV-C radiation and the 2 O molecules; (b) Residual irradiance from the UV-C radiation upon reacting with 2 O

Figure 6 .Figure 7 .
Figure 6.(a) Density of the reactions of the Rayleigh diffusion with the UV-C radiation; (b) Residual Irradiance of the UV-C radiation due to the Rayleigh diffusion

Figure 8 .
Figure 8. UV spectral irradiance for different altitudes, causing the photodissociation of the 2 O , of the 3 O , and the Rayleigh diffusion to intervene. photodissociation.
of O 3 is what contributes to the generation of the temperature gradient in the stratosphere.In fact, the number of photodissociation of O 2 is four times the number of photodissociation of O 3 .This is meanwhile the photodissociation ratio of O 2 of one column of the atmosphere about 1 cm 2 from the surface is of 0.135 DU of O 3 per second.