NASA Contractor Report 158945]

AircraftJHOx and NOXEmission Effects on iStratospheric Ozone andTemperature

L.Glatt and" G. F.Widhopf

THE AEROSPACE CORPORATION"!EL SEGUNDO, CA 90245 I

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K ' - - - - - -- . . „_

CONTRACT NAS1-13970SEPTEMBER 1978 !

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IM/NSAi National Aeronautics and 'Space Administration

'• Langley Research Centeri Hampton, Virginia 23665

NASA Contractor Report 158945

AIRCRAFT HO AND NO EMISSION EFFECTS ONx x

STRATOSPHERIC OZONE AND TEMPERATURE

By L. Glatt and G. F. Widhopf

The Aerospace CorporationEl Segundo, CA 90245

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

AIRCRAFT HO AND NO EMISSION EFFECTS ONx x

STRATOSPHERIC OZONE AND TEMPERATURE

By L. Glatt and G. F. WidhopfThe Aerospace Corporation

SUMMARY

A simplified two-dimensional steady-state photochemical model of theatmosphere, which includes the effects of atmosphere radiation, has beendeveloped to investigate the effect of injection of NOx and HOx on thechemical and thermal structure of the stratosphere.

The model has been developed in two parts. The first part is the de-velopment of the natural atmosphere, and is characterized by the coupledsolution of the energy and the species conservation equations in the strato-sphere with the temperature of the natural atmosphere prescribed. Theresults of this calculation are a coupled solution for the meridional circula-tion and the chemical structure of the natural atmosphere. Included in thismodel is the development of an active water vapor model that accounts forconvection, diffusion, rainout/washout and chemistry. The model of thenatural atmosphere has been run for the fall season, and the water vapordistributions are in good agreement with available data.

The second part consists of the development of a model of the perturbedatmosphere and is characterized by the solution of the coupled energy andspecies conservation equations. In this model, the meridional circulation isprescribed from solution of the natural atmosphere and the energy equationis solved for the temperature perturbation resulting from the injection ofNO and HO pollutants. The model has been used to study the effect on thethermal and chemical structure of the atmosphere of two types of pollutioncases: (a) injection of NOX and HO from a hypothetical fleet of supersonicand subsonic aircraft and (b) injection of HOX from a hypothetical fleet ofliquid-fueled hydrogen aircraft. The results are discussed with regard tostratospheric perturbations in ozone, water vapor and temperature.

INTRODUCTION

| The effect of aircraft pollutants on the state of the atmosphere, espe-j ,cially the ozone layer, has been the subject of intense investigation for a! number of years. In order to study this problem, photochemical models of1 the atmosphere have been developed together with making measurements

of various stratospheric properties. Both of these efforts have led to abetter understanding of various stratospheric phenomena together withproviding numerical atmospheric models that can make state-of-the-artestimates of the potential effect of high flying aircraft on the ozone layer.

Atmospheric models have progressed from the most simple box modelto more sophisticated one-dimensional and multidimensional models. Due tothe complexity of the physical problems, these models have progressed insteps, developing better phenomenology for describing various atmosphericphenomena at each step. In all models, various aspects of the overall prob-lem have been either neglected or modeled in a very simple manner. Ingeneral, the most important phenomena have been included in these modelsand,as a result of continued development some of the initial approximationshave been relaxed. The work reported herein attempts to relax some ofthe constraints of previous models, specifically the omission of active watervapor transport and the uncoupling of the stratospheric temperature distri-bution from changes in atmospheric species concentration. These tempera-ture and species concentration changes can result from the introduction ofpollutants in the stratosphere and are of interest because of the feedbackinfluence these temperature and species concentration perturbations canhave on chemical rate processes, mean atmospheric transport and climate.

This coupling was initially investigated by Ramanathan (ref. 1) using aone-dimensional radiative-convective (radiative equilibrium) model. Atwo-dimensional coupled circulation model of the stratosphere, incorporatingthe effects of radiation, photochemistry and seasonal transport processes,was developed by Rao (ref. 2). This model was used to study the naturalatmosphere and to investigate ozone and temperature perturbations due toNO emissions from a fleet of supersonic aircraft flying at 20 km and 45°Nin the summer hemisphere (ref. 3). However, active water vapor was notincluded in either of these studies, and only a very simple radiation modelwas used by Rao.

Active water vapor transport is of interest for many reasons and hasbeen investigated only recently with limited success. In order to adequatelycalculate the water vapor distribution in the natural atmosphere, the dyna-mic interchange between the troposphere and stratosphere, together with therainout/washout mechanisms in the troposphere, must be considered. Inthe initial stage of development, multidimensional models were not able tohandle active water vapor transport; thus, the problem was circumvented byspecifying the water vapor distributions using available measurements.This, however, did not allow for an active means for treating the HOX poTlu-tion problem. This pollution problem has become much more important inrecent years in determining the effect of aircraft exhaust emissions on the.chemical and thermal structure of the atmosphere. This is a consequenceof the importance of the species OH and the measurement of new reactionrates that increase the relative importance of HO with respect to NO onthe distribution of ozone.

2.'.-

The work to be described in this report consists of the development of asimplified two-dimensional, coupled, radiation-species model of the atmos-phere. Basically, it is a modification of an existing phenomenological photo-chemical model of the atmosphere developed at The Aerospace Corporation(ref. 4). Due to the limited nature of one-dimensional models, it is desirableto have the same technology available in a multidimensional model in orderto more realistically determine any associated effects of pollutants. This isrequired since the more realistic transport and strong latitudinal gradients intemperature, density and solar flux present in a two-dimensional model caninfluence the magnitude and distribution of the resulting atmospheric per-turbations.

The development of this capability requires the solution of the energyequation, which is a balance between the advective and turbulent diffusivetransport of heat and the radiative heating/cooling. In this study, the localradiation flux is evaluated using a comprehensive simplified model developedby Ramanathan (ref. 1). The advective transport of heat is evaluated by cal-culating the meridional wind field. Since the calculation of the meridionalcirculation from the governing continuity and momentum equations is verytime-consuming, due to numerical time step limitations, an approximatemethod is used. This method utilizes the continuity and energy equations tosolve for the meridional velocity components. Since the energy equation isalso utilized to calculate temperature changes, it is apparent that both thetemperature and the wind field cannot be computed simultaneously. The pro-cedure in this work is to evaluate the meridional circulation in the naturalatmosphere and then hold it fixed in the perturbed atmosphere using the energyequation to compute temperature changes in this case.

In order to make these calculations self-consistent, the same radiationmodel must be used to compute both the circulation and temperature pertur-bations. Before the radiation model is used, a two-dimensional evaluation ofthe validity of this model is performed. The calculation of the meridionalcirculation patterns and various aspects of using this approximate method arealso discussed. These results are compared to a similar calculation per-formed by Louis (ref. 5) whose circulation patterns were originally used inthe basic model developed previous to this work. Some inert tracer experi-ments performed using these resulting circulation patterns are described aswell and compared to available data.

A discussion of the water vapor transport model is included, as well as adescription of the coupled species-circulation-radiation model of the naturalatmosphere. Here, the energy, species and continuity equations were solvedsimultaneously using prescribed meridional temperature distributionscompiled from data by Louis (ref. 5). The Aerospace atmospheric modelwhich was used as a basis for the incorporation of these changes is describedin the Appendix. Typical results of this coupled calculation of the naturalatmosphere are also presented.

In order to evaluate the effect of HOX and NOX on the atmospheric distri-bution of various species concentrations and the temperature distribution,the meridional circulation calculated in the natural atmosphere is held fixed,

and the energy equation is used to solve for the associated temperaturechanges. This procedure does not allow for an estimate of the effect of thespecies concentration change on the circulation patterns, and therefore yieldsan upper limit estimate of the temperature changes.

Two aircraft pollution cases are investigated. The first is an injection ofNOX and HOX from a. combined fleet of subsonic and supersonic aircraft flyingin the troposphere and stratosphere. The second case considers a hypo-thetical fleet of liquid hydrogen-fueled aircraft cruising at 20.6 km. Theresults of these calculations are discussed in regard to perturbations inozone and stratospheric temperature.

SYMBOLS

A time constant for rainout in troposphere, s~

c specific heat at constant pressure, cm /s - K

e saturation vapor pressure, atmS

F energy source/sink distribution, K/day

F1 perturbation of energy source/sink distribution, K/day

G(z) function defined by equation (8)

H height of troposphere

H(<£) function defined by equation (8)

h relative humidity2

K.. turbulent eddy diffusivity tensor, km Is

K coefficient of vertical eddy diffusion in troposphere, (K ), km /so zz

p pressure, atm

p reference pressure, atm

Qrp turbulent diffusion of heat, K/day

QR radiative heating, K/day

R gas constant for air, cm /s< -°K

R function defined by equation (7)

r vertical distance from center of earth, km

T atmospheric temperature, K

v meridional velocity, km/s

w vertical velocity, km/s

Y. mass fraction of species i

z vertical distance from earth surface, km

z/H

latitude, degrees

potential temperature, K3

atmospheric density, gm/cm

reduced pressure (p/p ) P

RADIATION MODELING

The solution of the energy equation for the temperature perturbations oralternatively for the meridional circulation requires the distribution ofradiative sources and sinks in the atmosphere. In this regard, a simplified,yet comprehensive and realistic radiation model of the atmosphere, developedby Ramanathan (ref. 1) was utilized in the present study. The model con-siders the stratospheric radiative transfer due to f^O, €©2 and O,. Itincludes solar absorption by six bands of water vapor in the region 0. 9fl -6. 3 £/, by ten bands of CO2 in the regions 2. 0 //, 2. 7fj. and 4. 3 fl , and alsothe ultraviolet and visible absorption bands of ozone. In addition, the modeltreats long wavelength radiation by the vibration-rotation, pure rotation andtwo continuum bands of water vapor, the 9. (>H band of ozone and the fourfundamental and six hot bands of CO2- Specific details of the model are dis-cussed by Ramanathan (ref. 1).

At the initiation of this study, this radiation model had been includedonly in a one-dimensional model, and thus it was necessary to determinewhether the model could predict the meridional distribution of radiative

heating/cooling reasonably well. As a test, the model results were comparedwith the results of a more comprehensive model developed by Dopplick(ref. 6). In this context, it must be emphasized that the atmospheric dis-tribution of radiative parameters (i. e., temperature, cloud cover, ozone andH2O distributions) was not identical in both calculations. For this verifica-tion study, the temperature field was taken from the data compilations ofLouis (ref. 5), the ozone distributions from Wilcox, Nastrom and Beknont(ref. 7), and the tropospheric water vapor from Manabe and Wetherald (ref. 8).The stratospheric water vapor mass mixing ratio was assumed to be 2. 5 ppm.

The initial results for the meridional distribution of radiative heating/cooling rates were not in good agreement with Dopplick's results. Aftercareful analysis of these results, it was found that the disagreement was dueto the method in which the solar flux was evaluated. The solar heating fluxwas evaluated in the original radiation model using an average daylight valueof the cosine of the solar zenith angle. This model does not properly evaluatethe diurnally averaged solar radiation needed in a two-dimensional applica-tion. To correct this aspect of the model, it was necessary to integrate thesolar radiation flux over a 24-hour period. The results obtained after theabove modification was incorporated in the model are shown in figure la andcompared with those of Dopplick (fig. lb) for the fall season (where the fall sea-son refers to the northern hemisphere). Dopplick's calculations were availableonly below 32 km, whereas the present calculations were performed for theregion 15-50 km. The present calculations were limited to altitudes above15 km, since the present radiation model is not valid in the troposphere.Comparison of figures la and lb shows good agreement between the twomethods in the region 15-32 km. Figures 2 through 4 show the results of thenet radiative heating rates for the winter, spring and summer seasons,respectively, which, although not shown, are also in good agreement withDopplick's results.

Thus, the radiation model developed by Ramanathan provides an adequatedescription of the stratospheric radiative sources and sinks in the naturalatmosphere, provided the diurnally averaged solar flux is evaluated properly.Because of its simplicity, it is well suited for use in a photochemical modelof the atmosphere. In this regard, it can be used to evaluate the requiredradiative contribution in the energy equation for the solution of either themeridional circulation or the temperature perturbations.

MERIDIONAL CIRCULATION

The computation of the meridional circulation by solving the primitiveequations can be very time-consuming, primarily due to the requirement of asmall time step in order to insure that a stable numerical solution is ob-tained. For this reason, approximate methods have been developed. Ingeneral, these methods reduce the number of partial differential equations totwo. These two equations are solved for the horizontal (v) and vertical (w)components of the meridional circulation, with the remaining variables

such as density and temperature prescribed. In most cases, one of theequations is the continuity equation, whereas the second is either the energyequation [Murgatroyd, et al. (ref. 9) and Louis (ref. 5)] or the zonalmomentum equation [Vincent (ref. .10)]. The two-dimensional AerospaceCorporation model used as a basis for the present investigation originallyemployed the meridional circulation patterns computed by Louis (ref. 5).However, because of the differences in the radiation and turbulent diffusionmodels used by Louis and that used in the present work, the meridionalcirculation patterns must be recalculated. This is necessary in order toobtain a consistent evaluation of the energy equation that will allow a deter-mination of temperature perturbations resulting from the introduction ofpollutants into the stratosphere.

The method used in the present calculation follows along the lines ofLouis (ref. 5). The major differences in the computation of the meridionalcirculation are the methods in which the radiative heating and eddy flux ofsensible heat are modeled. The following paragraphs outline the basic equa-tions and the method used in computing the seasonal circulation.

The basic equations are the energy equation

QR

and the continuity equation

+ rcos0 J?r (Pv cosrid(j> +-- (pw) = 0dz ^ (2)

R/c7T = (p/p ) pwhere 0 is the potential temperature, 7T = (p/p ) p is the reduced pres-

sure, p is the density, v, w are the meridional and vertical velocity com-ponents, respectively, and T ^ O n . The terms Qj- and Q^ are the diabaticheating terms due to turbulent diffusion and radiation, respectively. Theheating due to radiation is computed using the model developed by Ramanathan(ref. 1) a.s described in the previous section. The heating due to the turbulenteddy flux is computed using an eddy diffusivity model [see Reed and German(ref. 11)] and is given by

, l d dOH ?TT I, is. , -o—

r o<p \ 0z dz

00S-T,O<p

(3)TC 50^J^t 5 r<pz OZ

K7T-T

O(p

where K-. is the given eddy diffusivity tensor. The specific components ofKj4 used In this computation are those developed by Luther (ref. 12) and modi-fied~by~Gfatt and Widhopf "(ref". "'13)." In the above^mbdeT,'"we have account"e"d~"for both the horizontal and vertical flux contributions to the turbulent heating.For the calculation of the meridional circulation, the potential temperatureand density are given. Thus, equation (1) can be written as

(4)season

where F represents the distribution of energy sources and sinks. Aspointed out by Louis (ref. 5), the term dp/dt in the continuity equation is atleast two orders of magnitude smaller than the other terras and thus can beneglected. Therefore, equation (2) becomes

r cos<

Equations (4) and (5) can now be solved for v and w. Although the compu-tation of v and w is straightforward, the computed values of w musts ati s f y

7T/2

/ pw cos 0 d<f> = 0 (6)i

-7T/2

since v .= 0 at both poles.

Since the method is only approximate, equation (6) generally will not besatisfied. Thus, an iterative procedure is required which allows the func-tion F to be perturbed in order to satisfy equation (6). The sequentialsteps of the solution procedure are:

(1) Solve for w from equation (4).

(2) Compute v from equation (5).

(3) Evaluate the left-hand side of equation (6).

(4) Perturb FQ by F1 (z,0) so that the w computed by equation (4)with the latest values of v satisfies equation (6).

i (5) Recompute v from equation (5) using the new values of w computed\ in equation (4). .

(6) Repeat steps (4) and (5) until the values of v at consecutive intera-tions differ by a given C.

Since equation (6) is an integral constraint on w, there exist manychoices for F1 (z,<£) which will satisfy this integral constraint. Thus, theproblem of nonuniqueness of the meridional circulation can exist when thismethod is used. A sensitivity study has been performed to assess the effectof varying F1 on the computed winds; the results will be discussed later.

By satisfying equation (6), we require

/""[-7T/2 l

cos <f)

-7T/2

7T/2> F - — Z£TL o r Q<b

cos <f> d<f) = R

(7)

To simplify the integration, we assume pF'/(90/9z) can be separated intothe product of two functions, one a-function of z and the other a functionof <f>, i.e.,

PF' _= G(z) (8)

Substituting equation (8) into the left-hand side of equation (7) and solvingfor G(z) yields

G(z) =

L7T/2

(9)

cos (ft d<f>

When equation (9) is substituted into equation (8), the following expressionfor F' (z,0) is obtained.

(10)R H(0)-7T/2y H«^

_-7T/2

) cos 0 d0

The function H(0) must now be chosen. Louis (ref. 5) selectedH(0) = cos0. This function concentrates the perturbation around the equatorwhere cos(f> is unity and introduces a zero perturbation at the poles. How-ever, since the circulation is most important, from the standpoint of trans-port, at latitudes less than 50°-60°, an attempt should be made to reduce theperturbation in this region. In the present analysis, H(0) is chosen to beunity, since for this function the perturbation is evenly distributed from poleto pole. The ratio of the perturbations for the function H($) = cos0 (=F'L)

,9

and H(0) = 1 (=F ' ) can easily be obtained using equation (10), i.e.,F ' /F'L = 7T/(4 cos0). Thus, for (j) < 45°, the perturbation using H(0) = 1is less than or equal to that for the case H(0) = cos<£. This is desirable,since large perturbations are inconsistent with the method.

This method was used to calculate the meridional circulation for each ofthe four seasons. The required inputs to the model are B,p and the concen-trations of Oo, CO-, and H-,0. The seasonal distributions of temperature[Louis (ref. 5)], which are used in the basic two-dimensional model, wereutilized in this calculation. The pressure was obtained from the hydrostaticequilibrium relationship and the density calculated from the perfect gasequation of state. Using the pressure and temperature, the potential tem-perature can be obtained. The mass mixing ratio of CO? is assumed to beuniform with a value of 488 ppm [Ramanathan (ref. 1)], while the monthlyozone distributions are taken from Wilcox, Nastrom and Belmont (ref. 7).

The water vapor distribution is based on a relative humidity formulationtaken from Manabe and Wetherald (ref. 8). This water vapor model wasdeveloped after careful analysis of data in the troposphere demonstrated thatthe meridional distribution of relative humidity was nearly similar for thedifferent seasons and, thus, one could use the data to approximate an averagerelative humidity distribution. Manabe and Wetherald found the verticaldistribution of relative humidity could be represented by

h =* - °. °2)1 - 0.02

where h0, is the relative humidity at the earth's surface, p the pressureand POS the surface pressure. When p/p^ is less than 0.02, the relativehumidity becomes negative; it is therefore necessary to specify the humiditydistribution for small values of p/p*. According to the measurements ofMastenbrook (ref. 14), the stratosphere is very dry and the mixing ratio isabout 2 x 10 gm/gm of air. Thus, the mass mixing ratio is given by

0 . 6 2 2 h e g ( T )YH90 = p - h e (T) (12)

Li S

and

.-6(YH,o) = 2.0 x 10

min

where e (T) is the saturation vapor pressure at temperature T.S «

Since the Ramanathan radiation model has a number of approximationswhich are only valid in the stratosphere, the model does not give an adequaterepresentation for the tropospheric radiation. With a tropospheric jradiationmodel not available, the coupled continuity and energy equations

10

could only be solved in the stratosphere (i.e., above 15 km). The meridionalcirculation in the troposphere was taken from the data of Newell, et al.(ref. 15). This technique was also used by Louis (ref. 5).

The meridional circulation for each of the seasons has been computed andthe results shown in figures 5 through 8. In each case, the corresponding

^circulation as computed by Louis (ref. 5) is also shown. Comparison of thetwo calculations indicates similar type circulations during the winter and /summer seasons (figs. 6 and 8), jwhejr^ajsjthjijl^ ^S™L/appreciable differences (figs. 5 and 7). Since the results of these calculationsare dependent on the modeling of the radiation, turbulent diffusion, as well asthe method used to satisfy the integral constraint, it is therefore important toinvestigate the sensitivity of the solution to variations of modeling in theseareas. These are shown for the fall season in figures 9 through 11 whichdepict the vertical velocity component w at (/> - 0°, 30°N and 60°N lati-tude. The curves labeled (a) are the results obtained using the present tech-nique. Curves (b) are the results obtained by Louis (ref. 5). Curves (c) arethe results obtained using the. present model with one exception; the contri-bution due to eddy flux [eq. (3)] is replaced with that given by Louis (ref. 5).Curves (d) are the results obtained using the present model, except that inequation (8) H($) = cos$ rather than unity. Finally, curves (e).are theresults obtained using the present model with H(<£) = cos0 and Qjr given byLouis (ref. 5 ).

Comparison.of curves (a) and (c) shows the sensitivity of the results tothe modeling of QE« The largest differences are seen to be at 30°N. Louisused data published by Newell, et al. (ref. 15). These data are questionabledue to the facts that: (1) the computed fluxes are essentially the ones due tostanding eddies only, and (2) the data in the upper stratosphere only coverthe we stern half of the northern hemisphere. In the present calculations, wehave used an eddy diffusivity model to describe the eddy flux of heat [equa-tion (3)]. This model accounts for both gradient and countergradient fluxesof heat. We should emphasize that we are not suggesting that the eddy dif-fusivity model predicts the fluxes of heat any more or less accurately thandoes the use of the data, but is one method of accounting for the eddy fluxesand is consistent with the two-dimensional diffusion coefficients used in theatmospheric model.

Comparison of curves (a) [H(</>) = 1] and (d) [H(^») = cos</>] shows theso-called "nonuniqueness " in the method of satisfying the integral constraint[eq. (6)]. The smallest differences occur near (j> = 30°N, since this is theregion where the heating sources are the largest. At other locations, thestrength of the sources and sinks are smaller and the perturbations becomemore pronounced, i.e., see 0 = 0°, 60°N. This nonuniqueness is actually afailure in the method and arises when the computed perturbations F1 are nolonger small when compared to F . For the results presented, the non-uniqueness becomes apparent at the higher altitudes (i.e., above 25 km).However, the breakdown in this region is due to the poor description of thecontribution to the heating due to the eddy flux, and thus a larger F1 isrequired to satisfy equation (6). Comparisons of curves (b) and (e) show the

11

sensitivity of the solution to the differences between the radiation modelsused in the present calculation and that of Louis (ref. 5). As previouslydiscussed, the present computation includes a radiation model developed byRamanathan (ref. 1) to compute the heating due to O^, CO? and H?O, whereasLouis used a number of different computer codes to account for each of theradiating species [for details, see Louis (ref. 5)]. For the present results,the largest difference occurs at 0 = 60°N. In general, below 30 km, themagnitude of the radiation heating is less than 1 °K/day; thus there canexist a substantial effect if the models are predicting differences on the orderof tenths of a degree per day;

In general, we cannot distinctly separate out the effects of both radiationand eddy flux modeling due to the integral constraint imposed by equation (6).This is because a modification of either of the above effects will require adifferent perturbation to satisfy equation (6) and in a manner that may over-shadow the actual local physical effects.

Short of solving the complete system of primitive equations for the cir-culation, these approximate methods are adequate and should suffice for thephenome no logical models in which they are to be used, as long as one keepsin mind the sensitivity of the results to the technique in modeling the physicalprocesses. Some filtering of the computed results as done by Louis (ref. 5)may also be necessary.

As a further evaluation of these computed circulation patterns, inerttracer calculations were performed for carbon-14 and tungsten-185. Theseresults are described in the next section.

TRACER STUDIES

In order to test the present meridional circulation pattern, the disper-sion of carbon-14 and tungsten-185 were calculated using the new meridionalcirculations computed in the previous section. Figures 12 through 14 showthe measurements of carbon-14 distribution [Telegadas (ref. 16); Johnston(ref. 17)] as a function of time for the latitudes <j> = 10°N, 30°N, and 70°N.Also shown are the results of the latest calculations as well as the previousresults obtained using Louis' circulation [Widhopf, et al. (ref. 22)]. At 10°N,the latest circulation overpredicts the peak concentration of carbon-14. At30°N, although the earlier profiles show the peaks occurring at 1-2 km higheras well as lower concentration below the peak, these distributions approachthe data over the next year or so. At 70°N, a similar situation occurs; i.e.,by January 1965 the calculations adequately predict the data.

Figure 15 shows the results of the tungsten-185 simulation for the peakconcentration in the equatorial region for both Louis' circulation and thepresent circulation. Along with these results are the data obtained by Friend(ref. 18) and Gudiksen, et al. (ref. 19). Notice that the new circulationadequately simulates the decay of the peak equatorial concentration oftungsten-185 as a function of time.

12

It must be pointed out that the turbulent diffusion coefficients used inthese calculations were those obtained by Glatt and Widhopf (ref. 13) whichare modifications to the original coefficients of Luther (ref. 12). This modi-fication involved using Louis' (ref. 5) circulation and adjusting the diffusioncoefficients in the high latitude regions employing the carbon-14 data as aguide. With these new coefficients, the tungsten-185 simulation was then run.In the present calculation, the seasonal circulation was computed using thesediffusion coefficients. Thus, any modifications to the diffusion coefficients tobring the present results into better agreement with the data (as was done forthe carbon-14) must be performed in an iterative manner since the diffusioncoefficients couple back to the calculation of the season circulation. Thistype of study was not within the scope of the present work. However, thesetests demonstrate the adequacy of the present transport.

Before a coupled radiation-species-circulation model can be developed tostudy the effects of HOX pollutants on the stratospheric ozone and tempera-ture, a consistent model of the natural atmosphere must be developed. Inparticular, an adequate water vapor model must be used. The developmentof such a model is described in the next section.

WATER VAPOR MODELING

The investigation of the effects of HOX pollutants on the stratosphericozone and temperature requires an active water vapor model. This modelmust account for transport by meridional winds, diffusion by turbulent eddies,chemical production and/or depletion, and include the effects of evaporationand precipitation.

From a physical standpoint, a steady-state water vapor distribution canonly exist if the difference between the evaporation from the surface E, andthe precipitation P, integrated over the entire globe vanishes. Since themajor portion of the water vapor is located in the troposphere, a troposphericwater vapor model must be developed.

Before development of a two-dimensional model is initiated, one canmake use of a simplified one-dimensional model in order to determine theeffects of boundary conditions, transport, chemistry and rainout on the levelof water vapor. The lowest order one-dimensional model is based on theassumption that under steady-state conditions in the troposphere, a balanceexists between the divergence of the vertical eddy flux and the rainout ofwater vapor (i.e., precipitation), with chemistry being a higher order effect.This latter assumption is subsequently verified by actual computation.

To elaborate on the model, consider a region of depth H in which boththe vertical eddy diffusivity KQ and residence time A (i.e., the timeconstant for rainout) are both independent of altitude. Mathematically, thegoverning equation for the steady-state distribution of water vapor is given by

K ^-4 - A Y = 0 (13)o , i. odz

13

where Y is the mass fraction of water vapor. The boundary conditions imposed on equation (13) are

Y(0) = Ys;< (14a)

Y(H) = Y (14b)

where Y^ is the value of the surface mass fraction of water vapor and YTTis the value of the mass fraction of water vapor in the stratosphere. Thesolution of equation (13) subject to equation (14) is given by

Y, sinh [X (1-z)] + Y sinhY = — S 1 _ (15)

sinh A

where z = z/H and X = H ^/A /K . The first question that arises is, Doesthis model give a reasonable upward flux at surface, i.e., is the overallevaporation process modeled? The flux at the surface is given byF* = -K (dY/dz),,, and can be found by differentiating equation (15). Theresulting expression is

F^ = \/A0

K0 [Y* tanh X - YH/sinh X] (16)

A computation of F^ requires an estimation of the various parameters in theabove expression. At 30°N latitude, Junge (ref. 20) estimated the averageresidence time of water vapor in the atmosphere to be about eight days, andthe height of the troposphere is about 15 km. The value of the stratosphericmass fraction is about 2. 5 x 10 [see Harries (ref. 21)]. A typical vahie ofK used in_ one -dimensional calculations of the atmosphere is .~10~-> km /sand thus, X =* 6. The form of boundary condition at the surface is taken fromManabe and Wetherald (ref. 8) and is given by

0.622 h e (T)

where e • (T) is the saturation vapor pressure, and h;,, and p% are the surfacerelative humidity and pressure, respectively. Typical values of Y# are onthe order of 10"^ to 10" . Under these conditions, the surface flux can beapproximated by

14,

When the values of AQ, K and Y# are substituted into equation (18), thesurface flux is found to be about 0. 2 x 10"? km/s. Existing data [junge(ref. 20)] show F# — 0. 3 x 10""^ km/s; thus the computed surface fluxes areconsidered reasonable. Figure 16 shows the results of two separate calcula-tions using The Aerospace Corporation's one-dimensional photochemical at-mospheric model along with observational data taken from Mastenbrook (ref.14) and Oort and Rasmussen (ref. 30) interpolated for 30°N latitude. Thevalues of the parameters are not unreasonable and have been chosen in orderto show the calculated distributions of water vapor that not only bracket theobserved data, but in addition yield reasonable agreement. Curve (a) corre-sponds to the values: A0 = 5. 8 x 10~6 dayl (two-day rainout period), K =2 x 10~5 km^/s, Y>>- = 0. 24 x 10-2 gm/gm-air; whereas curve (b) correspondsto AQ = 2 x lO-6 s-1 (5. 8-day rainout period), Ko = 0. 66 x 10~B km2/s,Y# = 0 .69 x 10"^ gm/gm-air. These calculations give surface fluxes of about0.25 x 10"' km/s. These calculations were carried out for two differentchemistry models; namely, an original chemical model used by Widhopf, et al.(ref. 22) (see Table I) and that currently published by the NASA workshop (seeTable II). Even though certain key hydroxyl reaction rates were changed, theresults for the water vapor distributions are relatively insensitive to thischange. The numerical results of the one-dimensional model were comparedwith equation (15) using the corresponding parameters and found to differ byless than two percent, thereby confirming the fact that the water vapor profileis'mainly controlled bythe transport/rainout mechanisms in the troposphere.

Extension of the one-dimensional model to two dimensions is generallystraightforward. The average residence time of the water vapor as a func-tion of latitude is taken from Junge (ref. 20). In addition, the transportdue to circulation as well as both gradient and countergradient turbulentfluxes of water vapor is included.

Regarding the assumption of A being constant in the troposphere equalto an average value estimated from data, it should be emphasized that themodel was not developed to predict the actual precipitation at each point inthe troposphere (which is not known, anyway) but to simulate the total pre-cipitation in a column at each latitude (since the data can only show totalprecipitation that reaches the surface). In addition, since the amount ofprecipitation is proportional to the amount of water vapor present, most oftfie~ pfecipitatfbn occurs in the first 5-6 km, and this agrees™reasonably wellwith observations of cloud cover.

We should also point out the lack of success in attempting to develop awater vapor model based on a relative humidity formulation. In this type ofmodel, the relative humidity is monitored; when its value reaches a certainpredetermined level, precipitation is assumed to occur. The results of thistype of model did not yield a dry stratosphere as observed by Mastenbrook(ref. 14).

With a two-dimensional model of the water vapor available, a simplifiedcoupled-radiation species and circulation model of the natural atmospherecan be put together. The description of the model of the natural atmosphereis given in the next section and includes the water-vapor distributions cal-culated using this model of rainout/wash out.

15

NATURAL ATMOSPHERE

In order to assess the effects of the injection of pollutants on the chemicaland thermal structure of the atmosphere, one must have knowledge of thestructure of the natural atmosphere. The computation of the coupled chemi-cal, thermal and dynamic structure of the atmosphere tends to be very expen-sive from a computational standpoint. To alleviate this problem, one canconsider a simplified atmospheric model in which the perturbed thermal struc-ture of the atmosphere is not coupled back to the dynamics. A consistent cal-culation of the perturbed structure can be performed by prescribing thenatural atmosphere by a coupled solution of the species conservation and energyequations with the temperature specified. The results of such a calculationwould yield the meridional circulation as well as the chemical structure of thenatural atmosphere. The perturbed chemical and thermal structure of theatmosphere can then be obtained by solving the coupled species conservationand energy equations, using the computed meridional circulation of the naturalatmosphere. Although there is no coupling of the chemical and thermal struc-ture to the dynamics, the resultant temperature perturbation obtained can beconsidered to be an upper bound, since all the perturbed energy is convertedinto a. temperature change, rather than allowing a portion of it to perturb thecirculation. This model of the natural atmosphere is described below.

The coupled model of the natural atmosphere is a modification of TheAerospace Corporation's atmospheric model. This original model was asteady-state seasonal phenomenological photochemical model of the atmospherein which the hydrodynamic variables (mean atmospheric density, temperature,turbulent diffusion coefficients and mean meridional winds) are specified andused to solve the system of species conservation equations for the meridionaldistribution of trace species. The details of this model are described in theAppendix. The modification necessary to complete the model of the naturalatmosphere was to couple the method of computing the meridional circulationto the solution of the species conservation equations. The resultant coupledmodel was then used to calculate the chemical and dynamic structure of thenatural atmosphere. The water model outlined previously was also incorpo-rated.

To demonstrate the feasibility of such a model, the natural atmospherewas simulated for the fall season (northern hemisphere). The coupled calcu-lation was run until a steady-state solution was achieved. Figure 17 illustratesthe data taken from'Gebhart, et al. (ref. 23), Sticksel (ref. 24) and London(ref. 25) for the latitudinal distribution of total ozone column for the fall sea-son. Also shown are the results of two calculations for the natural atmosphere.Curve (a) is an initial calculation carried out using the chemical system andassociated reaction rate coefficients tabulated in Table I. This is essentiallythe chemical system used by Widhopf, Glatt and Kramer (ref. 22) to estimatethe effect on ozone due to NOX emissions from a combined fleet of supersonicand subsonic aircraft projected to be operational in 1990. Curve (b) is the re-sult of a similar calculation in which the important reactions involving NOo and

16

N2Og have been included together with use of the latest updated reaction ratesfrom the NASA summary (ref. 51), as shown in Table II. The effects of day/nightaveraging were also included in this latter calculation. The converged solu-tion, curve (a), shows good agreement with the data in the northern hemis-phere (maximum difference, about nine percent). The ozone column in thesouthern hemisphere (maximum difference, about 16 percent) is not in as goodagreement with the available data as is the northern hemisphere calculation.The results given by curve (b) show a substantial increase in the Oo column"tKroughout the meridional plane [approximately a 50 percent increase fromcurve (a) near the northern polar region]. This result is essentially due to •the change in the reaction rate for the reaction R I O : NO + HC^-^OH TTSTO?from a value of 2. 3 x 10~^ to 8 x 10, a factor of about 35 increase.Since the major destruction of ozone through NOX occurs by the reaction R7,O3 -f NO-*O2 + NO2, the effect of increasing RIO is to reduce the effect ofR7. This result has also been observed in our one-dimensional model as wellas by other investigators in both one-dimensional and two-dimensionalmodels. Since the reaction rate RIO has been verified, it is possible thatthere may be other phenomena which have not been properly accounted for,either by having an incorrect reaction rate constant, not including pertinentchemical systems, or an incorrect prescription of the dynamics. However,to date, the latest set of reaction rates corresponding to curve (b) is thestate-of-the-art; thus, until further refinement is made, these rates are usedfor current atmospheric model simulations. Due to the coupling of the diffu-sion coefficients to the computation of the circulation, it is beyond the scopeof this work to investigate the sensitivity of the resultant ozone distributionto modifications in both the diffusion coefficients and chemical system.

Figure 18 shows the vertical distribution of ozone for various latitudes. - . ? . ..100N, 60°N and^ 80°N) corresponding to curves (a) and (b) in figure 17.The results" fb> solutiori"(a~) are in agreement with~~data [Wilcox "(ref. 7), andHering and Borden (refs. 26 through 29)], with the peaks generally beingabout 2 km lower than the peaks in the data. The results for solution (b) showa large increase in the ozone level throughout the meridional plane.

Figure 19 shows the resultant converged solution of water vapor profilesat 0°N, 30°N and 60°N corresponding to solution (b). Included is the cor-responding data of Oort and Rasmussen (ref. 30) for the tropospheric watervapor. The calculated results are in very good agreement with the data at0°N and 30°N, and slightly low at 60°N. However, these reduced values at60°N are most probably associated with the lower boundary value used in thecalculation. The calculation also produces a very dry stratosphere with amass fraction of 2.5-3 x 10-6 gm/gm-air. The water vapor results cor-responding to the chemical system in Table II are essentially the same since,as pointed out previously, chemistry is a higher order effect on the watervapor profiles.

Figures 20 and 21 show the resultant converged solution for the meri-dional heating distribution and circulation pattern. Comparison of figure 21and figure 5 shows the computed ozone profiles give similar type streamlinepatterns in the northern hemisphere as those obtained using the prescribedozone profiles by Wilcox, et al. (ref. 7). However, the circulation patternin the southern hemisphere has changed somewhat.

A 7

One important result has been in regard to the N^O profiles. In theoriginal calculation by Widhopf (ref. 4), which used the meridional cir-culation calculated by Louis (ref. 5), the ^O at high altitudes was shown tobe high when compared to data [Ehhalt, et al. (ref. 31), Farmer, et al.(ref. 32), Murcray, et al. (ref. 33), and Schutz, et al. (ref. 34)]. Thesehigh values were attributed to the N2O being controlled by the meridional cir-culation at the high latitudes, convecting it upward and then diffusing itmeridionally. In the present calculation, the computed circulation in thehigh latitudes produces a lower upward velocity than does that of Louis andthus lowers the value of ^O. This can be seen in figure 22.

Thus, the coupled model developed for the natural atmosphere has beenfound to produce distributions of water vapor and ozone that are in reasonableagreement with data. With this fact in mind, an investigation of the effectsof NOX and HOX pollutant injection on ozone and stratospheric temperaturecan be made.

PERTURBED ATMOSPHERE

The development of an atmospheric model to investigate changes in boththe chemical and thermal structures of the atmosphere, arising from theinjection of pollutants, involves coupling the individual speliies conser-vation equations to the energy equatiqn. In this model, the circulationis held fixed as computed in the natural atmosphere; thus, the coupling of thetemperature perturbations to the meridional circulation is not considered.Because of this lack of coupling, one can expect the calculated temperatureperturbations to be an upper bound, since all the energy changes go intodriving the temperature perturbation. The temperature perturbations arecoupled back into the reaction rate coefficients in the computation of thechemical structure of the perturbed atmosphere. The formulation of theenergy equation is described below.

The energy equation expressed in terms of the potential temperature isgiven by equation (19)-

+ - (19)E 7T x '

To simplify the calculation, equation (19) can be written in terms of the perturbation of potential temperature

,at r o<p dz E TT + TT

(20)x '

* • •

where QJj, is given by equation (3) with B replaced by #' and Q' is Q_ - (QR) .Here, the term (QR)O is the resultant distribution of radiative sources ana osinks obtained for the natural atmosphere, and QR is the total radiativeheating or cooling in the perturbed atmosphere. The term 7T1 /7TQ (Q^)o is, ingeneral, smaller than QU (less than one percent near the tropopause andabout eight percent near 50 km) and thus can be neglected. Therefore, equa-tion (20) cari tre approximated by

Equation (21) is solved in the domain -90°^ 0 £ 90° and 15 < z < 50 km.The lower boundary of 15 km has been chosen since the radiation modeldeveloped by Ramanathan (ref. 1) is valid only in the stratosphere. Thesolution of the energy equation down to the surface requires the need of avery complex tropo spheric radiation model, which is not available at thepresent time. Equation (21) requires four boundary conditions on 0'. At thepoles we have prescribed 90' /d& = 0, whereas at the upper and lower bound-aries we have prescribed O01 fQz = 0. The use of the lower boundary conditionwill be discussed later in this section.

The energy equation is solved using a combined leap-frog and Dufort-Frankel finite -difference scheme similar to that used for the solution of thespecies conservation equations. The energy equation is coupled to the speciesequations in the following manner: As the new mass fractions Y?+ arecomputed, they are used to evaluate the radiation term in the energy equationto compute 0' at time (n+l)At. The maximum time step for which the cal-culation was found to remain stable was about one day and was used in thecomputation of both species and temperature perturbations. With 0* known,the actual temperature T = 07T is found; thus T' = T - TQ (where TQ is thetemperature distribution in the natural atmosphere) can be evaluated. Thenew temperature is then coupled back to the reaction rates for the computa-tion of the new species mass fraction. The calculation is continued until asteady- state solution- is obtained.

A discussion of the results of two separate investigations of the effectsof the injection of NOX and HOX pollutants on the chemical and thermal struc-ture of the atmosphere follows.

19

Case 1: Perturbed Atmosphere--NO. and HOX X.

Since the initiation of this study, the importance of including the effectsof subsonic flying aircraft has become apparent. This is a result of the factthat the subsonic aircraft fleets were found to produce a greater amount ofNO than the higher flying SSTs; this potentially results in an overall increaseof total ozone rather than a decrease [Widhopf, et al. (ref. 22)]. Table IIIshows a recent estimate (upper bound) supplied by the FAA (ref. 35) regardingthe NOX emissions from a combined fleet of supersonic and subsonic aircraftprojected to be operational in 1990. This table includes emissions from pres-ent subsonic type aircraft that nominally cruise at 9-H km, advanced sub-sonic aircraft that cruise in the altitude range of 12.5-14.5 km, and super-sonic aircraft of the Concorde-Tupolev type that nominally cruise at 18 km.The variation of NOX emissions with both altitude and latitude is seen to belarge. The major source of emissions (about 80 percent) results from thesubsonic fleet and is deposited mainly between 9 and 13 km. The total amountof NOX emissions for this estimate is 2.81 x 10° kgm/yr.

With the increased understanding of the HOX chemical cycle, it has becomeapparent that the effects of HOX injection are important in determining thechemical and thermal structure of the atmosphere. Ramanathan (ref. 1)studied the sensitivity of the stratospheric temperature to changes in watervapor using a one-dimensional radiative-equilibrium model. His resultsshowed the necessity of including HOX injection for correctly predicting thethermal structure of the atmosphere. Two-dimensional calculations of Rao(ref. 3) did not include these HO effects.

J\.

The calculations to be described considered a modification of the FAAestimate of NOX injection rates in order to account for an increased fleet ofsupersonic aircraft. This amounted to an increase of NOX injection ratesabove 15 km by the factor 500/142. The HOX injection rates were obtained bymultiplying the final NOX injection rates by the ratio of their emission indices1250/17. For the present calculation, NOX was injected as N©2 and HOX asH2O. The initial conditions used for the calculation were obtained from theresults of the natural atmosphere.

The perturbed atmosphere was simulated for a period of four years afterwhich a steady-state solution was attained. Figure 23 shows the latitudinaldistribution of total ozone column change. The maximum increase in totalozone is three percent and occurs about 40°N latitude. This latitude cor-responds to that for peak NOX and HOX injection rates. Also shown, however,is the ozone column change above 15 km. Thus, it can be seen that morethan two-thirds of the total column increase occurs below 15 km. The inter-esting result here is the production of ozone in the stratosphere. Comparisonof the present results with those obtained by Widhopf, et al. (ref. 22), whereNOX was the only pollutant injected, show a similar result in the troposphere;however, a slight reduction of ozone occurred in the stratosphere (maximumtotal ozone column change of 1.4 percent during the fall season).

20

The increase of ozone in the stratosphere in the present calculations isattributed to the injection of water vapor. Figure 24 shows the resultantdistributions of t^O at 0 = 0° and 40°N for both natural and perturbed at-mospheres. The increase in ozone above 15 km is due to the reduction in theeffectiveness of the NOX catalytic destruction cycle by I^O. In addition, theincrease of the reaction rate for NO + HC>2 — *-OH + N©2 can have a large effecton the reduced effectiveness of the NOX destruction cycle. For the pure NOXinjection case, this catalytic cycle is

+ O(3P)— »NO + O R6

NO + O3— > NO 2 + O2 R7

However, the additional injection of H^O forms OH and HO- through reactions

0(1D) + H20) — *OH + OH R32

OH— »>O + HO R9

The increased concentration of HO.., reduces NO through the reaction

HO2 + NO— *OH + NO2 RIO

Although O^ is depleted through R9, the depletion of O$ through R7 has beenreduced considerably due to reduction in NO through RIO. In addition,is reduced through the reaction

OH + NO2 + M— »HNO3 + M R12

which in turn reduces the NO produced by the photodissociation of NO?, i. e.

+ hi/— -*NO + O(3P) R4

The net result is a decrease in the effectiveness of the catalytic destructioncycle and an increase in ozone.

In the troposphere, the effect of the combined injection of NOX and HOis a production of ozone. This ozone increase is due to the increased concen-tration of O(^P). As pointed out by Widhopf, et al. (ref. 22) in the strict NOX

21

injection case, the increase in O( P) was initiated by the oxidation ofmethane by OH, which then cycled through the smog chain to produce HC>2.The HO2 reacted with NO to produce NO2 which then photodissociated toproduce O(3p), i.e.

HO2 + NO — *OH + NO2 RIO

NO2 + hi /— *NO + O(3P) R4

The additional injection of HOX increases the effectiveness of smog chain onthe production of O( P) since H~O is converted to OH by the reaction

O(1D) + HO— *OH + OH R32

3The concentration of O( P) is also increased directly by the reaction

OH + OH— *H_O + O(3P) R38L*

3This increase in O( P) increases the ozone level through the reaction

O2 + O(3P) + M— *O3 + M R5

Thus, the combined effect of the injection of NOX and HOX for these cal-culations is to increase ozone in both the troposphere and stratosphere. Itshould be pointed out that these results are based on the new reaction ratemeasurement for RIO which has been increased by a factor of 35 over previousrecommended value (Table I). Since the mechanisms in both stratosphere andtroposphere are strongly dependent on the reaction HO2 + NO — *OH + NO2,and have resulted in a- substantial increase in the ozone columns in the naturalatmosphere above observed levels, one should not draw any immediate definiteconclusions in regard to the magnitude of the production of ozone for this NOand HOX pollution case. The increased ozone levels in the natural atmosphereare particularly disturbing, and it is possible that other reaction rates involv-ing the hydroxyls are still inaccurate and could influence the present results.This is an important area of future investigation, and possible candidates arehydroxyl reactions involving production or depletion of O(^P) and thosedepleting ozone.

Figure 25 shows the corresponding resultant steady-state meridional dis-tribution of temperature perturbation (T 1) in °K. The results exhibit twointeresting features. First, the contours of T1 are shown to be nearly sym-metrically centered around the equator in the region 40°S to 40°N between

22

15 and 25 km. Second, the maximum temperature perturbation, which is ap-proximately 5. 9°K, is located at the lower boundary near the equator. How-ever, the temperature perturbation is less than one degree above 19 km. Inorder to gain some understanding of the resultant perturbations, we mustexamine the physical mechanisms that produce these perturbations.

Since the complete energy equation is solved in this investigation, thesteady-state distribution of T1 is achieved by a balance of convection, diffu-sion and radiation of perturbed energy. The perturbations are initially gen-erated through the radiation term by a perturbation in water vapo? and ozoneafter which the convection and diffusion come into play by redistributing theperturbed energy. Since the time scales for transport are much longer thanthose for the chemistry changes, the perturbed atmosphere must be simulatedfor a number of years before a steady-state condition is attained.

From an analysis of the steady-state solution, it was determined that theheating due to radiation (Qt>) in the equatorial region near the lower boundaryis produced by the 9. 6;U On band due to the increase in ozone concentration.In addition, heating due to the 15)U CO2 band occurs because of the increasedamount of water vapor aloft which reduces the cooling by CC>2 through theH_O overlap region. At higher altitudes, the atmosphere is cooled by theincreased water vapor through the t^O emission band. The peak cooling isless than -0.5°K. In the equatorial region aloft, there exists a region ofpositive temperature perturbation which is due to the vertical diffusion of per-turbed energy from the lower regions. The nearly symmetric contours ofT1 in the equatorial region are a result of the closed circulation cell (seefig. 21) which redistributes the perturbed energy in the region 15 to 25 km.

Since the maximum temperature perturbation occurs at the lower boundaryand is of substantial magnitude, it is important to investigate the effect of thelower boundary condition on the resultant perturbations. For this study, aone-dimensional version of the two-dimensional model was used. In this case,the energy equation [eq. (21)] reduces to

(22)V <U I A*^J \S *J / /»

\ / o

Under steady-state conditions

QL7T

O

23

As might have been expected, equation (23) requires the total vertical fluxof perturbed energy to be constant, i.e.

F1 + F' = constant (24)

where F1 = -K (d0 ' /dz) and F1R = - jf (Q^/7rQ) dz. We consider two differ-

ent bounlary conditions for this investigation. The first condition,90' Idz = 0, is identical to the boundary condition used in the two-dimensionalcalculation, and the second is T1 = 0 at the lower boundary. The secondboundary condition is physically unrealistic for the present injection casesince the major portion of the injection is below 15 km. However, some phy-sical insight can be gained by using such a boundary condition.

Figure 26 shows the resultant one-dimensional distribution of tempera-ture perturbation for both boundary conditions, i.e., (a) d0 ' /dz = 0 and(b) T' = 0. For these calculations, we have used the injection rates at 30 Nlatitude. Use of the boundary condition c^'/dz = 0 results in a verticaltemperature distribution similar to that obtained in the two-dimensional cal-culation, with the peak temperature perturbation occurring at the boundarywith a value of approximately 0. 5°K and the crossover point from positiveto negative perturbations occurring at about 21 km. For the two-dimensionalresult (fig. 25) at 30°N latitude, the peak value of T1 is approximately 1°Kand occurs at the lower boundary with the crossover occurring at 20 km.Due to the large latitudinal gradient in T1 calculated in the two-dimensionalresults, it is not unrealistic that the one-dimensional calculations predict T1

to be about one-half that obtained with the two-dimensional calculations.

Use of the second boundary condition T1 = 0 results in a much lowerpositive temperature perturbation (T1 « 0. 08°K) and is found to occur 1 kmabove the boundary. Above 25 km, these results show less cooling than inthe c\0'/dz = 0 case; however, below 25 km, there is more cooling (or lessheating) for the T1 = 0 case. These results are consistent since the T1 = 0case allows a finite transfer of energy downward at the lower boundary, thusallowing for an energy removal mechanism which did not exist for the caseo-0'/dz = 0.

Since the results exhibit the strong sensitivity of the temperature pertur-bation to the lower boundary condition, the resultant maximum temperatureperturbation of 5. 9°K for the two-dimensional calculations would appear tobe on the high side. In addition, as pointed out earlier, since the tempera-ture perturbations are not coupled back to the dynamics, one should alsoexpect the magnitude of the calculated temperature perturbation to be on thehigh side. However, it is not clear at this time what the appropriate lowerboundary condition should be. It is evident, at this'time, that the only logicalmethod of alleviating the problem of the lower boundary condition is to solvethe energy equation down to the surface and prescribe T1 = 0 at this point.This method requires the use of a complex tropospheric radiation model,which is not available at this time, fbut which should be developed.

24,

Case 2: Perturbed Atmosphere — H^O

In recent years, there has been considerable interest in the developmentof new types of propulsion systems for high-flying aircraft. Prior to imple-mentation of these systems, it is important to determine whether any detri-mental effects to the atmosphere will arise from their use. In particular,the use of liquid hydrogen has been under consideration as a new type of fuelfor these high-flying aircraft. Since the exhaust emissions from this typeof system contain HOX, and with the recent knowledge of the increased rela-tive importance of HO chemistry on the ozone layer, it is important toinvestigate this potential problem area.

The hypothetical fleet used in this study consists of 200 liquid hydrogen-fueled aircraft- flying six hours per day at an altitude of 20. 6 km through thelatitudinal corridor 35°N-55°N. The exhaust emissions were specified to bein the form of water vapor at a rate of 28.5 kgm/s. These emissions wereuniformly distributed through the corridor 35°N-55°N and between 20 and21 km. Starting with the natural atmosphere as the initial condition, theperturbed atmosphere was simulated for a period of two and one-half yearsafter which a steady- state solution was essentially attained. For this calcu-lation, the chemical system used was that shown in Table I as modified byTable II. The meridional circulation was taken from the results of the naturalatmosphere (fig. 21).

Figure 27 shows the resultant meridional distribution of percent changein ozone column. The peak change in the northern hemisphere is about 0. 16percent increase, and occurs at 50°N, whereas in the southern hemispherethe change is about 0.28 percent increase and occurs at 70°S. In the equa-torial region (40°S-20°N), a 0. 12 percent decrease in ozone has occurred.Also shown is the column change above 15 km. Note that there is a decreasein ozone below 15 km except in the equatorial region where no change isobserved. The mechanism for ozone increase in the stratosphere with regardto HOX injection has been discussed in the previous section. The decreasein ozone below 15 km (and up to 25 km in the equatorial region) is due tothe reduction in O(3P) by HO,, as well as by the depletion of Oj by OH, i.e.

+ O(3P)— vOH + O R15

O(3P) + M— *0 + M R5

OH— "O + H0 . R9

Figure 28 shows the resultant water vapor profiles at 0°N and 40°N. In theregion of injection, the water vapor concentration has increased by about 25percent. The changes in total ozone column in the southern hemisphere aredue to the water vapor being convected and diffused southward (see fig. 21).

." 25

Figure 29 shows the resultant meridional distribution of temperature-perturbation in °K. The maximum positive temperature perturbation of0. 7°K occurs at the lower boundary near the equator. The peak negativeperturbation is -0.7°K and occurs near the northern polar region at about21 km. Note the nearly symmetrical contours centered around the equatorbelow 20 km. This result is similar to that found in the NO and HOX

injection, although not as wide and with a much lower zero contour. Thecooling is initiated through the radiation term in the energy equation by theincreased water vapor concentration after which convection and diffusion comeinto play in redistributing the energy. The heating in the equatorial region isdue to the increased concentration of ozone as well as the increase in watervapor aloft which reduces the cooling of the 15jU CC>2 band through the f^Otransmissivity factor. Convection and diffusion then again become importantin redistributing this energy.

The physical aspect of the lower boundary condition with regard to theresulting temperature perturbations has already been discussed, and it shouldbe emphasized that it also applies here. However, based on these results,it appears that the present hypothetical fleet of liquid hydrogen-fueled aircrafthas a minimal effect on both the thermal and chemical structure of the atmos-phere.

CONCLUSIONS

This study was initiated to provide the ability of including active HOperturbations in stratospheric pollution studies and to investigate any resultingstratospheric temperature changes. The primary results of this investiga-tion are:

(1) The Ramanathan radiation model provides a very good description ofthe meridional stratospheric heating and cooling rates, provided the solarradiation is calculated using a diurnal averaging technique.

(2) The computation of the meridional circulation using the energy andcontinuity equations (given the temperature distribution) has been found to besensitive to the prescription of both turbulent diffusion coefficients as well asthe radiation model. Due to the requirement of satisfying an integral con-straint on the vertical velocity when using this approximate technique, theresultant circulations are, in general, not unique.

(3) The resultant seasonal meridional circulation patterns computedusing the approximate method have been used to study the dispersion of inerttracers (carbon-14 and tungsten-185). The results of this study have shownthe adequacy of these computed circulation patterns in describing the decayof these inert tracers.

26

(4) An active water vapor model was developed which is simple in con-cept and yields two-dimensional steady-state water vapor distributions thatare in agreement with available tropospheric measurements. The model alsoyields a dry stratosphere in agreement with available data. In addition, thecalculated precipitation is in relatively good agreement with measurements,being approximately 75 percent high in the region 0-30° latitude and within25 percent of the measurements at higher latitudes.

(5) The inclusion of the latest chemical reaction rates has been found toproduce more ozone (approximately 25 percent) in the natural atmospherethan has been previously calculated and/or measured. This result indicatesthe possibility that other chemical species are important, although presentlynot included, or that certain reaction rates are still uncertain, in particularthose involving the hydroxyls.

(6) A coupled species-radiation model was developed to study active NOXand HO pollutant problems. It has been found herein,that transport is veryimportant in determining the distribution of the temperature perturbation inthe stratosphere. Thus, one-dimensional calculations may be limited in thisregard.

(7) At the initiation of this study the pollution emitted by high flyingsupersonic aircraft was to be investigated. However, subsequent work byHidalgo and Crutzen (ref. 52) and Widhopf, et al. (ref. 22) indicates that theemissions by subsonic aircraft flying in the troposphere are important in theoverall evaluation of the effect of aircraft emissions on atmospheric ozone.In this regard, the effect of NOX and HOX emissions from a modified FAAprojected fleet of both supersonic and subsonic aircraft was investigated andfound to produce a maximum total ozone column increase of three percentlocated at 40°N latitude. In addition, the maximum calculated temperatureperturbation was 6°K and occurred at the lower boundary (15 km) near theequator. It should be emphasized that these results were obtained using thenewly measured higher rate for the HC>2 + NO reaction which yields approxi-mately a 25 percent overprediction of the total ozone column--in the naturalatmosphere [see item (5)]. The necessity of choosing the lower boundary at15 km was due to the fact that the Ramanathan radiation model is only valid inthe stratosphere. For this case, in which 80 percent of the NO and HO hasbeen injected in the troposphere, the correct lower boundary condition for thetemperature perturbation is uncertain. From a sensitivity study performedusing a one-dimensional version of the two-dimensional model, the resultanttemperature perturbations have been found to be sensitive to the lowerboundary condition, and it would appear that the present boundary conditionused in the two-dimensional model has overestimated the temperature pertur-bation. In addition, the method of computing the temperature perturbation bydecoupling the circulation from the calculation would also lead to an over-prediction in the results. Thus, the 6°K perturbation is considered an over-estimation of the actual effect. It has become apparent that the inclusion of atropospheric radiation model is a necessity in order to accurately determinethe temperature perturbation, especially in the case of subsonic injections.Such a model is not available but should be developed in the near future.

27

(8) The effect of stratospheric HO emissions by a hypothetical fleet ofZOO liquid hydrogen-fueled aircraft cruising at 20.6 km was found to beminimal with regard to both temperature and ozone (less than 0.25 percentincrease in ozone and a maximum temperature perturbation of 0. 7°K).

28

APPENDIX

Basic Atmospheric Model

The model is a phenomenological photochemical model of the atmos-phere in which the hydrodynamic variables (mean atmospheric density,temperature, turbulent diffusion coefficients, and mean meridional winds)are either specified from observations or obtained indirectly from obser-vations as a function of time during the year and used to solve the system ofspecies conservation equations for the meridional distribution of tracespecies throughout the year. The original formulation of the model, dis-cussed in Widhopf and Taylor (ref. 36) and Widhopf (ref. 4), is basicallydesigned to examine relatively small changes in the ozone concentration as afunction of the time of year throughout the meridional plane, since any re-sultant changes in the species concentration occurring as a result of theintroduction of a pollutant are not coupled back to the atmospheric dynamicsor temperature distributions.

The governing species conservation equation is derived following thegeneral procedure outlined by Reed and German (ref. 11) for representingthe turbulent transport flux due to large-scale eddies. In the meridionalplane this equation, written in terms of the mass mixing ratio, is of the form

6lpvY.cos0

COS0

_ _rd0

pk ,0z

dY. dY+ pk -, ,00

pr (2k

+

zz

ZZ

tan0) + (2kz0 - k00tan^

+ (Al)

.thw^here Y^ is the mass mixing ratio P-lp of the i"" chemical species, p isthe local mean atmospheric density, t is the temporal variable, r = z + R(where Re is the mean radius of the earth and z is the altitude measured6

from and normal to the earth's surface), <f is the latitude, (J- is the photo-chemical rate of production/depletion of the i"1 species, and S. is the localsource/sink effect. The components of the tensor k^o represent the diffu-sion coefficient in the respective directions arising from large-scale eddymotions, while v and w are the components of the mean circulation in themeridional and vertical directions, respectively. This equation is solvedfor each of the trace species considered.

29

Chemical Model

The chemical system considered in this investigation includes the fol-lowing species: O(1D), O(3P), O2, O3, NO, N2O, NO2, OH, H2O, HO2,HoQ2, HNO3, N, H, N2, CO, CH4, NO3 and N2O5. Smog-type reactionsinitiated by the oxidation of methane by OH, which may be important in thelower regions of the atmosphere, are also included [Crutzen (ref. 37)].These reactions also include the species CH3, CHO, CH2O, CH3O, CH3O2

and CHoO2H. The specific reaction system and the associated reaction-ratecoefficients used in this investigation are tabulated in Tables I and II. Thischemical system is based essentially on that recommended by the NASA-CFMReport.

Computation of the absorption of solar radiation is an integral step indetermining the chemical structure of the atmosphere, since many of theimportant reactions in the atmosphere are photochemical processes. Usingthe solar flux data compiled by Ackerman (ref. 38), the diurnally averagedlocal photodissociation rates J- are calculated at every location in the at-mosphere at each time step by a technique developed by Kramer and Widhopf(ref. 39). The time variation of the solar zenith angle with latitude and solardeclination is included in the determination of J-. The absorption crosssections utilized to compute J- for the various species are outlined inWidhopf (ref. 4).

The effect of chlorine in the atmosphere was not included in this investi-gation. From NAS studies (ref. 40), -the inclusion of chlorine should attenu-ate the effect of NO,, destruction of ozone due to the formation of CjtONO0.x

Boundary Conditions

The computational domain considered in this investigation extends fromthe north to the south pole, with a ten-degree meridional resolution; and fromthe surface to 50 kilometers, with a vertical resolution of Az = 1 km from thesurface to 35 kilometers, and Az = 2 . 5 km up to the upper boundary. At thepolar regions, a zero latitudinal flux is assumed.

A fixed ozone concentration [6(10) molecules/cc] was imposed at thelower boundary, as interpreted from the meridional distributions compiled byDutsch (ref. 41) and Hering and Borden (refs. 26-29) [as summarized in thedata compilation of Wu (ref. 42)]. The concentration of N2O at the lowerboundary was prescribed as an average value (0.481 ppmm) interpreted fromthe tropospheric measurements of Schutz, et al. (ref. 34), and Goldman,et al. (ref. 43). The latitudinal variation of the mass mixing ratio of CO atthe surface was interpreted from the measurements of Seiler (ref. 44). Themass mixing ratio of CH, (0. 75 ppmm) at the lower boundary was specifiedfrom the measurements of Ehhalt, et al. (ref. 31). Injection of NO and NO2resulting from the anthrophotogenic activities were specified at the lowerboundary as interpreted from the estimates of Bobbins and Robinson (ref. 45).

30

The species O(3P), O(*D), OH, HO2, N and H were taken to be in photo-chemical equilibrium at the lower boundary because of their relatively shortlifetimes, while HNC>3, NO2, NO and H2O2 were removed from the tropo-sphere by simulating atmospheric rainout/washout. HNOo was removed atthe average rates defined by Junge (ref. 46 ), while NO2, NO and H2O2 wereassumed to be removed at one-tenth this rate.

The species O(3P), O(1D), O3, OH, HO2, H2O2> N and H were assumed .to be in photochemical equilibrium at the upper boundary, while the massmixing ratios of NO2, N2O, CH%, CO and HNO3 were analytically continuedto the upper boundary by a second-order extrapolation in space and time de-scribed by Widhopf (ref. 4' ) and Widhopf and Taylor (ref. 3,6). This extra-polation allows the use of centered spatial differencing at this boundary, whilealso eliminating the necessity of specifying a boundary condition for thesespecies at this location. It is an accurate and stable method of evaluating

. conditions at computational boundaries [Victoria and Widhopf (ref. 47/)] when'•' ' the physical mechanisms interior to the computational domain govern the

boundary value. This is the case for N2O, NO2, CH4, CO and HNO3 whichare being transported up into the higher regions of the stratosphere.

Transport Data

The meridional distributions of both the mean density and temperaturewere specified using the data obtained from ten years of observations whichwere analyzed and compiled by Louis (ref. 5). These averaged data arespecified from the surface to 68 km for the entire meridional plane and foreach of the four seasons.

Luther (ref. 12) has analyzed the heat transfer, temperature and windvariance data of Oort and Rasmus sen (ref. 30) using the procedure outlined byReed and German (ref. 11) for defining the components of the anisotropicturbulent eddy diffusivity tensor. The three components (k^0, k0z and kzz)are specified for the northern hemisphere from the surface to 60 km.Values for the components of the diffusivity tensor in regions where obser-vational data were not available were obtained by Luther by_extraj3oj.a.tion,

I- i '•' - • using the results of Hunten~(Fef.~ 48) and Newell, et al. (ref. 49). __ /~~Thlfse c^¥ffrcTents~are specified for each month alid were initially used to

parameterize the components of the turbulent diffusivity tensor. The valuesfor the southern hemisphere were obtained by reflecting the northern hemi-spheric values, shifted by six months, and applying them appropriately inthe southern hemisphere. However, in testing these transport coefficientsagainst the dispersion of inert tracers in the atmosphere, they were found notto be totally adequate [Widhopf (ref. 4)] and were improved by numericalexperimentation. The results are described by Widhopf, et al. (ref. 22).

Numerical Scheme

An accurate (second order in space and time) time-dependent numericalfinite difference scheme developed by Widhopf and Victoria (ref. 50) , whichis explicit in space and implicit in time and efficiently overcomes the "stiff"nature of the chemical system, is used to solve the governing individualspecies conservation equations. Details of the scheme as applied to thisproblem are discussed in Widhopf (ref. 4) and Widhopf and Taylor (ref. 36).

32 '

REFERENCES

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33

12. Luther, F.M. : Monthly Values of Eddy Diffusion Coefficients in theLower Stratosphere. Preprint 73-498, AIAA (Denver, CO), July 1973.

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14. Mastenbrook, H. J. : The Variability of Water Vapor in the Stratosphere.J. Atmos. Sci., vol. 28, 1971, pp. 1495-1501.

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16. Telegadas, K. : The Seasonal Stratospheric Distribution and Inventoriesof Excess Carbon-14 from March 1955 to July 1969. U.S. AtomicEnergy Commission, Health and Safety Lab., Report No. 243, 1971,pp. 3-86.

17. Johnston, H.S., Kattenhorn, D., and Whitten, G. : Use of ExcessCarbon-14 Data to Calibrate Models of Stratospheric Ozone Depletionby Supersonic Transports. J. Geophys. Res., vol. 81, 1976, pp.368-380.

18. Friend, J. P., Feely, H. W., Krey, P. W., Spar, J., and Walton, W. :Discussion on HASP Results. Defense Atomic Support Agency, DADA1300, vol. 3 (Washington, D. C.) , 1961.

19. Gudiksen, P.H., Fairhall, A.W., and Reed, R .J . : Role of MeanMeridional Circulation .and Eddy Diffusion in the Transport of TraceSubstances in the Lower Stratosphere. J. Geophys. Res., vol. 73,1969, p. 1729.

20. Junge, C.E.: Air Chemistry and Radioactivity. Academic Press,New York and London, 1963, p. 10.

21. Harries, J.E. : The Distribution of Water Vapor in the Stratosphere.Rev. of Geophysics and Space Sciences, vol. 14, no. 4, 1976, pp. 565-575.

22. Widhopf, G.F., Glatt, L., and Kramer, R. F. : Results of a Phenomeno-logical Time-Dependent Two-Dimensional Photochemical Model of theAtmosphere. AIAA Journal, vol. 15, 1977, p. 1322.

23. Gebhart, R., Bojkov, R., and London, J. : A Comparison of Observedand Computer Models. Beitrage zur Physik der Atmosphare, vol. 43,1970, pp. 209-227.

24. Sticksel, P.R.: The Annual Variation of Total Ozone in the SouthernHemisphere. Mon. Wea. Rev., vol. 98, 1970, pp. 787-788.

34-;

25. London, J. : The Distribution of Total Ozone in the Northern Hemis-phere. Beitrage zur Physik der Atmosphare, vol. 26, 1963, pp. 254-263.

26. Hering, W. S. : Ozonesonde Observations over North America, 1.Research Report AFCRL-64-30(I), Air Force Cambridge ResearchLaboratories, Bedford, MA, 1964.

27. Hering, W.S., and Borden, T.R. , Jr.: Ozonesonde Observations overNorth America, 2. Environmental Research Papers no. 38, AFCRL-64-30(11), 1964.

28. Hering, W. S., and Borden, T. R., Jr.: Ozonesonde Observations overNorth America, 3. Environmental Research Papers no. 133, AFCRL-64-30(111), 1965.

29. Hering, W. S., and Borden, T. R., Jr.: Ozonesonde Observations overNorth America, 4. Environmental Research Papers no. 279, AFCRL-64-30(IV), 1967.

30. Oort, A.H., and Rasmussen, E.M.: Atmospheric Circulation Statistics.National Oceanic and Atmospheric Administration, NOAA prof, paper 5,1971.

31. Ehhalt, D.H., Heidt, L.E., Lueb, R. H., and Roper, N. : VerticalProfiles of CH4, H2, CO, N2O and CO2 in the Stratosphere. Pro-ceedings of the Third Conference on CIAP, A. J. Broderick and T.M.Hard, eds., Dept. of Transportation, DOT-TSC-OST-74-15, Feb. 1974,pp. 153-160.

32. Farmer, C.B., Raper, O. F., Toth, R.A., and Shindler, R .A . : RecentResults in Aircraft Infrared Observations of the Stratosphere. Pro-ceedings of the Third Conference on CIAP, T.M. Hard and A. J.Broderick, eds., 1974, pp. 234-245.

33. Murcray, D.G., Goldman, A., Murcray, F.H., Williams, W. J.,Brooks, J.N., and Barker, D.B.: Vertical Distribution of MinorAtmospheric Constituents as Derived from Airborne Measurements ofAtmospheric Emission and Absorption Spectra. Proceedings of theSecond Conference on CIAP, A. J. Broderick, ed., 1973, pp. 86-98.

34. Schiitz, K., Junge, C., Beck, R., and Albrecht, B. : Studies of Atmos-spheric N2O. J. Geophys. Res., vol. 75, 1970, pp. 2230-2246.

35. Oliver, R.C., Bauer, E., Hidalgo, H., Garner, K. A., and Wasylklwskyj,W. : Aircraft Emissions: Potential Effects on Ozone and Climate, AReview and Progress Report. Dept. of Transportation, Report No.FAA-EQ-77-3, 1977, p. 404.

35

36. Widhopf, G. F., and Taylor, T. D. : Numerical Experiments onStratospheric Meridional Ozone Distributions Using a ParameterizedTwo-Dimensional Model. Proceedings of the Third Conference onCLAP, A.J. Broderick.and T. M. Hard, eds., Dept. of Transportation,DOT-TSC-OST-73-4, Feb. 1974, pp. 376-389.

37. Crutzen, P. J. : A Discussion of the Chemistry and Some Minor Con-stituents in the Stratosphere and Troposphere. Pure and AppliedGeophysics, vols. 106-108, 1973, pp. 1385-1399.

38. Ackerman, M. : Ultraviolet Solar Radiation Related to MesosphericProcesses. Mesospheric Model and Related Experiments, G. Fiocco,ed., Springer-Verlag, New York, 1971, pp. 149-159.

39. ; Kramer, R., and Widhopf, G. F. : Evaluation Daylight or Diurnally/ Averaged Photolytic Rate Coefficients in Atmospheric Photochemical/ Models. To appear in J. Atmos. Sciences, Sept. 1978.

40. Halocarbons: Effect on Stratospheric Ozone. National Academy ofSciences, 1976.

41. Dutsch, H. A.: Photochemistry of Atmospheric Ozone. Advances inGeophysics, vol. 15, H.E. Landsberg and J. Van Meighem, eds.,Academic Press, New York, 1971, pp. 219-322.

42. Wu, M. F.: Observations and Analysis of Trace Constituents in theStratosphere. Environmental Research and Technology, Inc., AnnualReport, Contract DoT-OS-20217, 1973.

43. Goldman, A., Murcray, D.G., Murcray, F.H., and Williams, W.T. :Balloon-Borne Infrared Measurements of the Vertical Distributions ofN2O in the Atmosphere. Journal of the Optical Society of America,vol. 63, July 1973.

44. Seller, W. : The Cycle of Atmospheric CO. Tellus, vol. 26, nos. 1,2,1974, pp. 116-.135.

45. Robbins, R. G., and Robinson, E» : Sources, Abundance and Fate ofGaseous Atmospheric Pollutants. American Petroleum Inst.,(Washington, D. C.) , 1971.

46. Junge, C.E.: Air Chemistry and Radioactivity. Academic Press,New York and London, 1963, p. 10.

47. Victoria, K.J., and Widhopf, G. F. : Numerical Solution of the UnsteadyNavier-Stokes Equations in Curvilinear Coordinates: The HypersonicBlunt Body Merged Layer Problem. Third International Conference onNumerical Methods in Fluid Mechanics, University of Paris-Orsay,Lecture Notes in Physics, vol. II, no. 19, Springer-Verlag, Berlin,1972.

36

48. Hunten, D.M. : The Philosophy of One-Dimensional Modeling. Pro-ceedings of the Fourth Conference on CLAP, T.M. Hard and A. J.Broderick, eds. Dept. of Transportation, DOT-TSC-OST-75-38,Feb. 1975, pp. 147-155.

49. Newell, R.E., Wallace, J.M., and Mahoney, J. R. : The General Cir-culation of the Atmosphere and Its Effects on the Movement of TraceSubstances, Part 2. Tellus, vol. 18, nos. 2 ,3 , 1966, pp. 363-380.

50. Widhopf, G.F., and Victoria, K. J. : On the Solution of the UnsteadyNavier-Stokes Equations Including Multicomponent Finite Rate Chemis.try. Computers and Fluids, vol. 1, 1973, pp. 159-184.

51. Chlorofluoromethane and the Stratosphere. R. D. Hudson, ed., NASAReference Publication 1010, NASA Goddard Space Flight Center,Greenbelt, Maryland.

52. Hidalgo, H. and Crutzen, P.J.: The Tropospheric and StratosphericComposition Perturbed by NOX Emissions of High Altitude Aircraft.J. Geophys. Res., vol. 82, 1977, pp. 5833-5866.

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41

LATITUDE

(a) PRESENT MODEL

80N

60 40 -6020 0 -20 -40

LATITUDE

(b) DOPPLICK (REF. 6)

FIG. 1. FALL SEASON NET RADIATIVE HEATING (°K/DAY)

-80S

42

50

40

6

WQD

30

20

10

80° 60N

40 20 0 -20

LATITUDE

-40 -60 -801

S

FIG. 2. WINTER SEASON NET RADIATIVE HEATING ( K/DAY)

43

50

40

, 30

W

H 20

10

o80" 60 40N

20 0 -20 -40 -60 -80

LATITUDE

FIG. 3. SPRING SEASON NET RADIATIVE HEATING (°K/DAY) .

50

60 40 20 0 -20 -40 -60 -80*N

LATITUDE

FIG. 4. SUMMER SEASON NET RADIATIVE HEATING (°K/DAY)

44

80N

60 40 20 0 -20

LATITUDE

-40 -60 -80V

S

(a) PRESENT MODEL

°90° 60N

30 0 -30 -60 -90

LATITUDE

(b) LOUIS (REF. 5)12FIG. 5. FALL SEASON INTEGRATED MASS FLUX (10 gm/sec)

45

80 60 40 20N

(a) PRESENT MODEL,

50

-20 -40 -60 -80

LATITUDE

LATITUDE

(b) LOUIS (REF. 5)

12FIG. 6. WINTER SEASON INTEGRATED MASS FLUX (10 gm/sec)

46

50

40

I1 30

WQ£>

20

10

80° 60 40 20 0 -20 -40 -60 -80°N S

LATITUDE

(a) PRESENT MODEL

50

40

•? 30

wg£ 20

10

o90"N

60 30 0 . -30 -60

LATITUDE

-901

S

(b) LOUIS (REF. 5)12FIG. 7. SPRING SEASON INTEGRATED MASS FLUX (10 gm/sec)

47

50

40

a&, 30

WQ£H 20HJ<

10

80 60 40 20 0 -20 -40 -60N

LATITUDE

(a) PRESENT MODEL

-801

S

50

40

6* 30

HQIDH 20

10

0

-i.o

.o90" 60N

(b) LOUIS (REF. 5)

30 0 -30 -60

LATITUDE

-90S

12FIG. 8. SUMMER SEASON INTEGRATED MASS FLUX (10 gm/sec)

48

50

45

40

1 3 5w"Q

HP 30

25

20

15 I

= 0

PRESENT METHODLOUIS MODEL (REF. 5) .PRESENT MODEL WITH Q,FROM LOUIS (REF. 5)PRESENT MODEL WITHH(<£) = cos(f>LOUIS MODEL WITH QRFROM RAMANATHAN(REF. 1)

I

-0.10 -0.05 0 0.05 0.10 0.15

VERTICAL VELOCITY, w - cm/sec

FIG. 9. FALL SEASON VERTICAL VELOCITY

PROFILE AT 0 = 0°N • ' - . . -

49

50

40

g 35

WQ

H 30

25

(a)(b)

~— (c)

(d)

-— (e)

20

15

30°N

PRESENT METHODLOUIS MODEL, (REF. 5)PRESENT MODEL WITH Qn

FROM LOUIS (REF. 5)PRESENT MODEL WITHH(<£) = cos(f>LOUIS MODEL WITHFROM RAMANATHAN(REF. 1)

R

I

-0.25 -0.20 -0.15 -0.10 -0.05

VERTICAL VELOCITY, w - cm/sec

FIG. 10. FALL SEASON VERTICAL VELOCITY

PROFILE AT </> = 30°N

0. 05

50

50

45

40

35

WQt>HH 30

25

20

15

= 60°N

— (d)

(a) PRESENT METHOD(b) LOUIS MODEL (REF. 5) .(c) PRESENT MODEL WITH Q

FROM LOUIS (REF. 5)PRESENT MODEL WITHH(0) = COS0

LOUIS MODEL WITH Q-(e)FROM RAMANATHAN

UREF - n I I

R

-0.15 -0.10 -0.05 0 0.05

VERTICAL VELOCITY, w - cm/sec

0. 10

FIG. 11. FALL SEASON VERTICAL VELOCITYPROFILE AT 0 = 60°N

51

o>•a13

laniinv

52

53

CM

CM CM

54 .

.MM.

OOu_ --1

^ 0^ LJ-a. . LU5^ ss

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M

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OF

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ICAT

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EASU

REM

ENTS

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AL

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ified

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sion

coe

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111

^_CNCN

LiLLQ

PRES

ENT

MOD

ELw

innn

PF

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A

|i

CVJ

r CVJ

CVJ

CVJ

CVJO OO CVI

JOS/^dp ' 581 - N31S9Nm MV3d

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00

CVJ

w Soo EH Pn

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2 w

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CVJ

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56

CO

s500

o~ 400

H

O

<HO

300

20°

100

0

STICKSEL (REF. 24) AND LONDON (REF. 25) - FALLGEBHART, ET AL (REF. 23) - OCTOBER(a) TABLE I CHEMICAL SYSTEM(b) TABLE I .+ TABLE II CHEMICAL SYSTEM

80°N

60 40 20 0 -20 -40 -60 -80°S

LATITUDE

FIG. 17. TOTAL OZONE COLUMN DISTRIBUTION FORTHE NATURAL ATMOSPHERE DURING THEFA LL SEASON

57

.50

40

30

20

10

10°N 40°N

1 6(10)'

50

40

30

20

10

WILCOX, ET AL (REF. 7), OCTHERING AND BORDEN (REFS. 26-29), AUTUMN(a) TABLE I CHEMICAL SYSTEM(b) TABLE I + TABLE II CHEMICAL SYSTEM

7(10)12

80°N

7(10) 12

OZONE CONCENTRATION - molecules /cm

FIG. 18. FALL SEASON OZONE PROFILES IN THENATURAL ATMOSPHERE

58

oCO

§ ai ~H W2 %W 3co £

s i». 3* P

2 2 2o o <;o o ^

D m vD [Hi ii ii ^i ii N Q

5- -6- -Q. o

1 ' 2, o

o o1 O CO

1 II II

[ -e- -e-

2oo

II

•e-

O o D

(M

O

2 9

H<

hOOHHH

xt—i

SCOCO

WffiH2

Otf

> W

<} co

O

o•'1

- aanxinv

59

80N

60 40 20 0 -20

LATITUDE

-40 -60 -80V

S

FIG. 20. FALL SEASON NET RADIATIVE HEATING(°K/PAY) FOR THE NATURAL ATMOSPHERE

50 r

20 0 -20 -40 -60 -8080° 60 40N

LATITUDE

12FIG. 21. FALL SEASON INTEGRATED MASS FLUX (10 gm/sec)FOR THE NATURAL ATMOSPHERE

60

—I 00

-I <*

-I 00

-i vc

•*

H

ffltM^

(\3i— 1OpH

. 00

. vO

. ^

PO

~H

i-H

'Oi-H

rO

Su-

CO

(1)i— i3UIl\cv

i— iOaia0M

HvIC

EN

TR

A

^H

Ouo

ooz

HffiA

O•5!;H<;^

J<«p.H

gft&0111

tOFIL

ES

]

!rAO

00!5

ro*00

•

0H

h

*~,oo

soCO0)

1-4r«rJo0)

1— 1

2

83CO

JJ<hC1iHH

tfPQ

61

W 6

gu

U 3en

OH 2gWU

H

0

ABOVE SURFACE

80V

N60 40 20 0 -20

LATITUDE

-40 -60 -80S

FIG. 23. PERCENT OZONE CHANGE DISTRIBUTION FOR NOX + HOINJECTION CASE DURING THE FALL SEASON X

62

45

40

35

Q 30

25

20

15

40°N

NATURALATMOSPHERE

HO + NO

-6H2O MASS MIXING RATIO (10" gm/gm-air)

FIG. 24. WATER VAPOR PROFILES FOR HO + NO INJECTIONDURING THE FALL SEASON

x x

63

50

40

I' 30

ID

§ 2°10

-0.1.5

\ \\\

80° 60 40 20 0 -20 -40 -60 -80°N S

LATITUDE

FIG. 25. TEMPERATURE PERTURBATION FOR NO + HOINJECTION CASE (°K) DURING THE FALL^EASdN

64

50

45

40

35

HQ

30

25

20

(a)

(b) T1 = 0

\

15|__-0.4 -0.2 0.2 0.4 0.6

FIG. 26. VERTICAL DISTRIBUTION OF THE TEMPERATUREPERTURBATION (30°N) CALCULATED USING AONE-DIMENSIONAL MODEL

/ 0.6

8ufc

OU

IONO

0.4

0.2

0

HUrt -0.2s

-0.4

I I I I I I

/

l80°N

ABOVE 15 km

//*-ABOVE// SURFACE

I I I I I60 40 20 0 -20

LATITUDE

-40 -60

FIG. 27. OZONE COLUMN CHANGE FOR H2O INJECTIONCASE DURING THE FALL SEASON

66

wQ

40

35

30

20

15

40°N

NATURALATMOSPHERE

H2O INJECTION

H_O MASS MIXING RATIO (10~6 gm/gm-air)L*

FIG. 28. VERTICAL PROFILES OF WATER FORINJECTION DURING THE FALL SEASON

67

50

g 40

H

Q 30

H

P20

10

0 j I

80N

60 40 20 0 -20

LATITUDE

-40 -60 -80'S

FIG. 29. TEMPERATURE PBRTURBATJON FOR H2OINJECTION CASE (°K) DURING THEFALL SEASON

68

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+ original

70