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Photolysis of Nitrogen Dioxide and Ozone in the Atmosphere of Mexico City JC Ruiz Suarez

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Photolysis of Nitrogen Dioxide and Ozone in the Atmosphere of Mexico City JC Ruiz Suarez Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Photolysis of nitrogen dioxide and ozone in the atmosphere of Mexico City J.C. Ruiz Suarez," L.G. Ruiz Suarez, * T. Castro/ C. Gay/ S. Eidels-Dubovoi' ^Institute Tecnologico y de Estudios Superiores de Monterrey, Campus -Morelos, Apto. Postal 99- C, 62050, Mor., Mexico ^Centro de Ciencias de la Atmosfera, UN AM, Circuito Exterior, Cd. Universitaria, Mexico D.F. 04510, Mexico ^Instituto Mexicano del Petroleo, Gerencia de Quimica Ambiental, Eje Central Lazarao Cardenas 152, Mexico D.F. ABSTRACT We report theoretical photolysis rates for the nitrogen dioxide and ozone in the atmosphere of Mexico City. To estimate the spectral irradiance needed in the calculations, the equation of transfer is solved by the delta-Eddington method. An atmosphere of air, nitrogen dioxide, ozone and dry aerosol is modeled. INTRODUCTION A state-of-the art photochemical kinetics model requires the specification of time-dependant rates for the two most important photolytic reactions: NO + hy > NO + 0 (1) 0 + hv > 0 + 0(*D) (2) Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 324 Air Pollution These reactions take place in different portions of the solar spectrum from 280 nm to 410 nm. Indeed, reaction (2) take place below 340 nm whereas nitrogen dioxide is photolyzed mostly above 340 nm. Photolysis of nitrogen dioxide is the key reaction in photochemical smog. It plays a fundamental role as the sole immediate precursor for tropospheric ozone and it is one of the initiation steps in the oxidative chain of several reactions. Moreover, in some of the current air quality models, reaction 1 is the reaction by which the driving force of the reactive polluted atmosphere, the solar radiation, is fed to the modeled system. Other photodissociation processes are often expressed relative to this reaction. So far, (1) and (2) are the only reactions studied experimentally under atmospheric conditions. These reaction rates have been determined by irradiating a gas mixture, containing the absorbing gas, in a quartz flow tube. Afterwards, one measures the concentration of the reaction product or the secondary reaction products. The reaction rates are then determined from the time of exposure, the initial concentration of the absorbing gas, the concentration of the products and a formula derived from the kinetics in play. The aim of this work was to calculate photolysis rates for the above reactions in the atmosphere of Mexico City. To estimate the spectral irradiance needed in the calculations, the equation of transfer is solved by the delta-Eddington method. An atmosphere of air, nitrogen dioxide, ozone and dry aerosol is modeled. In this work we also present the mathematical algorithm used to solve the system of equations that come out from the application of the delta-Eddington method. In order to validate our results, calculated total irradiances were compared with experimental data Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution 325 obtained with an Eppley radiometer. UV RADIATION TRANSFER MODEL EQUATIONS. The basic equation for scattering of solar radiation in plane parallel atmospheres is: (3) U) _ + — Fo where: T, w, P(/I,M')> Fo, fi and po are, respectively, the optical depth, the albedo for single scattering, the phase function, the solar radiance at the top of the atmosphere, the cosine of the zenith angle and the cosine of the solar zenith angle. In the Eddington approximation the total radiance I(%,p) is expanded as: KT,JI) = IO(T) + p II(T) (-1 s n 3 1) (4) Substituting equation (4) into (3) gives: (Shettle et al, [41) dr A Fo fl (5) The parameter q, the first moment of the phase function, is called the asymmetry factor. Integrating eq. (5) and the product of eq. (5) and p, both Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 326 Air Pollution integrals over p, two first-order differential equations are found: 1JJ~i- - = - 3fl-w(T)ll3J\-w(T)lloo + 4-5-- w(T)Fo e~^° (6) d T Due to the fact that w and q are functions of the optical depth (which is the case for a real inhomogeneous atmosphere) eqs. (6) don't have analytical solutions. However, if we consider the atmosphere as composed of homogeneous layers (each layer having constant w and q) simple solutions may be found within each layer. For the ith-layer (i=l,2,....N) we have: T/\ * if \ „ i - JC.T _i+k.T -T/JIO IO(T) = Io (T) = Ci e i + C2 e i - oc.e ^ T. < T < T. l-l I (7) -T/flo II'(T) = P.f \* T. < T < T. l-l I where: k. P. = (8) 7f ~ 1 a. = 3w.Fo fio 1 + g.(l-cj.) . = 3w.Fo I L Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution 327 In order to determine the coefficients Ci and Cz we must use boundary conditions for Io and h at the top and bottom of the atmosphere and at the N-l layer interfaces (Shettle et al, [4]). This gives 2N linear equations which, in principle, are easly solved. However, a flexible computer code, dealing with any choice of N, T., w. and 9., is not a trivial task. Here we present a simple algorithm to construct the matrix and the independant vector for the linear system AX=B where: t-c* c' c" c* c* d ^ * 1' ^1' 2' 2 2 and a = 1 + — P 11 3 1 a = 0 ; j=[2,N] . a =1- p 1,N+1 3 1 a = 0 for j=[N+z,2N] a. = t exp[-kr._ ] for J=(I,NI and i=[2,Nl f i i=j+i t = ]-i I-J I 0 otherwise a = t exp[k T. ] for j=[i,N] and i=(2,N] a. = t P expl-kr. 1 for i=u,N-u and J=H,NI l+N,j J J l-l 1-1 J=i+l 1 Uj 0 otherwise a. = -£ P exptkr.] for i=[i,N-il and J=U,N] L+N, j + N J j I a =0 for j=[l,N-U 2N,j Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 328 Air Pollution a = [l-,4 + — P (l+4)]exp(k T ] 2N.2N 3 N ^ N N a = 0 for J=N+1,2N-1 2N,J b= —j3 + a 1 3 *1 1 b. = («•i-f <V exp[-T._^o] for i=(2,NJ (p. -0.) exp[-T. /Ma<] for i=(2,N] Vi-r oFo] exp[-r /MO] V "' N T N N with 4 =surface albedo. Total irradiances are calculated from, FTOT(T) = F^(T) + F^(T) + TT^O Fo e" (9) where: 271J1 (I(Io+Mh)Mdo M (10) J -i« Here, F^(T) and F^(T) are the upward and downward directed diffuse irradiances. To calculate the reaction rates, one has to evaluate actinic fluxes instead of total irradiances (Madronich, [1]). This is done by evaluating the following integral: = 271 (11) Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution 329 PROCEDURE The atmospheric composition is assumed to be made of air, ozone, nitrogen dioxide and aerosols. The atmosphere is divided in 50 layers from zero to 50 km of altitude. At this stage of the work, the aerosols are considered to exist only at the surface boundary layer. Because of the large size of the aerosols (d z 1.0 Jim), the incident beam of light induces high-order modes of polarization and Mie theory is required to estimate their extinction coefficients and asymmetry factors. The refractive index for this particle is n = (1.65-0.005i). The parameters T, w and q, are wavelength dependant. We calculate them every 5 nm in our range of interest. Extraterrestial solar fluxes were taken from WMO [51. The concentration profiles for ozone and nitrogen dioxide were reported in Ruiz-Suarez et at [21. Calculations were carried out in a Micro VAX 3100. The main and auxiliary programs (FOTON), were coded in FORTRAN 77. In order to compare the model results with Eppley measurements, only direct and surface downward scattered radiation were taken into account. RESULTS Eppley UV radiation measurements were recorded from November 1990 to February 15, 1991 on the roof of the Atmospheric Sciences Center of the National University building. Measurements made on January 22 and 28, 1991 were chosen for making comparisons (Fig. 1,2). Calculated photolysis rate constants for N02 and 03 on January 22 are shown in Fig. 3. Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution 330 "5 i5 i i i i IB LOCAL TIME(hs) Fig. 1 Experimental and theoretical Irradiance for January 22,1991. 8 10 11 12 13 14 15 LOCAL TIME(hs) Fig. 2 Experimental and theoretical irradiance for January 28,1991 Transactions on Ecology and the Environment vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution 331 0.007 0-007 8 9 10 11 12 13 14 15 16 17 18 LOCAL TIME(hs) Fig. 3 Reaction rates for NO2 and O3 as a function of local time for Jan. 22/91 CONCLUSIONS In this paper we have shown the core of our implementation of the delta-Eddington model.
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