Robert N. Stabler and John P. Chesick' Haverford College Haverford,Pennsylvania 19041
(
I
A Computer Sirnulation of Stratospheric Photochemistry
The rudiments of the photochemistry of the stratosphere and the significance of the resulting ozone layer as a filter for solar radiation of wavelengths between -240 and 310 nm have been discussed in a previous article (I).The simplest representation for the basic reaction system is found in the set of reactions
+
O3 hu
O(lD)
+ O2
(4)
O('D)+M-O+M
(5)
0+03+202 (6) The waveleneth dependencies of the nhotochemical reactions (1) and ( 4 ) a&ountfor both the a~titubeof theozone layer and the role of ozone as a filter for the 240-310 nm solar radiation band. Reactions (I), (3), and (4) followed rapidly by exoergic reactions (2) are responsible for turning uv radiation into thermal energy in the stratospherr. I'he stratosphere is theretore warmer than the laver below and provides an "in. version layer stability" against convective mixing with the troposphere. Catalytic cycles for the destruction of 0 and 0 3 may be summarized by the pair of reactions
which combine to have the same net effect as reaction (6). Relevant pairs of species which are rffective as X and XO in reactions (7) and (8) are NO and NO?, HO and HO2, and CI and CIO. The pair NO and NO2 is important in limiting the natural levels of O and 0 3 in the stratmpherc tn abot~t6WW% of that expected for thc simple ( u n c a t a l p d ) reaction scheme. The actual destruction rate of 0 + 0 1 hv reaction ( 6 ) is about 20% of the total; the other 80% of the destruction of 0 0 3 comes from the comhined effects of reactions (7) + (8)for all pairs o i X and XO. Measuremenmof the ronrentration-altitude profiles of NO and NO? and data on the rates of product& of these from naturai sources have led to clear indications that additional amounts of NO and NO2 from the exhaust gases of a large fleet of SST aircraft would significantly alter the ozone radiation shield. This environmental mncern has stimulated a substantial research effort in the last six years. Laboratory work in the determination of rate constants of relevant elementary reactions has been pushed with vigor, as well as the collection of much more data on the concentrations and movements of trace species in the stratosphere. Data obtained have generally corroborated results predicted from model calculations involving laboratory rate constants and photolysis cross-sections. The species pair CI and (110 iseven moreefficient on a per molerule basis than is the pair NO and NO2 in the catalytic cycle for o7.one destruction. Further envinmmental concern for the stahility of the ozone shield was aroused hy the pro-
+
1 To
whom correspondence should be addressed.
504 1 Journal of Chemical Educstlon
posal of Molina and Rowland (2)that photodecomposition of chlorofluoromethanes diffusing into the stratasphere from lower levels would provide a source of chlorine atoms leading eventually to environmentally significant changes in the ozone layer. The chlorofluoromethanes CFC13 (F-11) and CFzClz (F-12) are manufactured in large quantities for use a s aerosol propellants and as refrigerant working fluids. The chemical analvsis for these substances in the lower atmosohere corresponds well to that expected for the integrated Goduction to date; the compounds seem to be chemically inert in the lower atmosphere and are transparent t o radiation reaching the earth's surface. However.. thev .diffuse to the stratm~herewith a time constant measured in decades and are photolyzed by uv radiation in reactions of the type
+ hv
-
CFClz + C1 This occurs a t altitudes corresponding to those of the ozone reactions. This process is then predicted to he a source of catalyst species for ozone destruction. This destruction will increase with the growth of the diffusion flux from the troposphere into the stratosphere. These predictions, repeated and elaborated by a number of different groups of atmospheric chemists, have brought on a confrontation with the chemical industry producing these chlorofluoromethanes. Most recentlv. ",an indenendentlv constituted Panel on Atmosnheric Chemistry, sponsored by the National Academy of Sciences, has issued a report (3)of its detailed and critical review of available evidence on this issue. The panel concludes CFC13
All the evidence that we examined indicates that the long-term release of F-11 andF-12 at present rates willcausean appreciable reduction in the amount of stratospheric ozone. In more specific terms, it appears that their continued release at the 1973produetion rates would cause the ozone to decrease steadily until a probable - ~- reduction of about 67.5% is reached. ~. with an uncertaintv range of at least 2-20b, using what are believed 11, he roughly 95% conlidence limits The rime required for the reduction toattain half uf this swadv-statevalue (2 3.75%) would hc 40 to XI ymm. ~~~~
~
The effect of this decrease in the ozone layer in increasing the solar flux a t the earth's surface is readily calculable. The environmental impact of such an increase in the uv radiation a t the earth's surface is a separate matter for discussion in terms of expected increases in incidence of skin cancer, effects on various-levels of plant growth, and effects on global climate. This whole topic has proven to be of considerable interest to students in chemistry a t all levels. A discussion of this ties together topics in photochemistry, chemical kinetics and energetics, and other physical-chemical phenomena. I t provides a prime example of the use of rate constants and other information obtained from controlled laboratory studies of nure com~oundsand simole svstems to build an under" standing of a large and complex chemical system of obvious interest and imoortance. A recent article bv Bassow ( 4 ) highlights ways illis issue ran be discussed at ;he secondary sch(r,l level. A l t h ~ g hconsiderilhle simplification can make many spectsof the topicaccessible without extensivederailed computation. more detailed numerical examoles are useful insights into methods and sensit&ity of the calin culated results to assumptions made. The availability of
-
comnuter svstems for students use in manv institutions s u g & ~h i modeling of moderate romplenity rs within reach of the undereraduate level. T h r model mlculation on which this article is hased was largely programmed as a portion of a senior student honors nroiect . . in coniunction with a tonics course in environmental systems. I t is an example of what can be eenerated at the undermaduate level with results which can be &ed in a variety of ways to illustrate aspects of atmospheric ohotochemical svstems which are not obvious from oualitative discussions. The program is versatile. and bv simnle modification of input data &n he adapted without ch;mge in the program structure to utilize a wide variety of reaction schemes. It is currently set up to handle up to 100 chemical reactions involving UP to 60 chemical species. I t was written in Fortran IV for& on an IBM 360144 computer. Disc or tape storage capability is most useful for storage of the compiled programs, hut is not needed for the actual computations. As will be discussed in the next section, this calculation also raises some interesting problems in connection with the integration of the chemical rate equations. This integration must he done for each level in the stratosphere to find the steady state concentrations, starting from the set of rate constants, absorption cross-sections for species undergoing photolysis reactions, the assumed starting concentrations, and the solar flux received from the next higher level. All discussions here are in terms of the stratospheric region, taken in these calculations to be between 15 and 50 km in altitude. However, changes in the input data and trivial changes in three assiznmeut statements in the nroeram would make it possible to model the chemistry a n d beLavior of a higher altitude region such as the ionosphere.
-
integration of Rate Laws
The general problem of the simulation of the kinetics of a multistep chemical reaction is expressed mathematically as the solution to an initial value problem for a system of firstorder ordinary differential equations. The rate of formation of each chemical species is a sum of terms, with each term heine the rate of an elementarv reaction in which the oarticular species is formed as a product or destroyed a reactant. The rate terms involve concentrations of various species and provide the coupling of the variables between the different rate equations. The starting concentrations of all chemical species provide the initial values for the variables, and numerical integration of the set of rate equations then provides the concentrations of all species a t any desired future time. The solution of the type of initial value problem defined by most multistep reaction mechanisms poses particular difficulties hecause of the wide range of time constants in the system of chemical reactions. This problem, known as stiffness, constrains the time sten per iteration (sten size) for conventional numerical integrition techniques such as Euler's method, Runge-Kutta methods, Adam's method, etc., to a small value to preserve accuracy in the variables which depend on the fastest reactions. This leads to grossly excessive computation time for performing the integration over the whole reaction time. Huehert has described here (5) an interesting computer simulation of a photochemical smog system. This calculation used the quasi-steady-state approximation (QSSA) for some species of short lifetimes and used the Euler method for integration of the rate laws for the rest of the species. This integration method simply calculates the concentration increment from the rate expression and a chosen time increment: e.g. ~
.~~~
6Ci = Ridt
The expression for the rate of nroduction of snecies i.. R;. .. comes from the mechanism and & simplificatick resulting from the QSSA algebra. The numerical calculation of R; uses the values~ofspecjes concentrations a t the start of th; time
step 6T. The resulting concentration values for species subject to the Euler integration are then calculated a t the end of the time step by
c;(t+ at) = ci(t)+ aci and the QSSA algebra gives the corresponding new concentrations of the short lived species. If the time increment at can he made sufficiently small without requiring a miserably long cornoutation time. the method will eive useful results assuming the QSSA is valid. The difficugy, however, is that the system must he both well behaved and well understood to permit the separation of the long and short time constant reactions and species implied by the use of the QSSA. This approach also implies either reprogramming of the calculation or an elaborate proaram svstem if it is desired to change the - mechanism. For the smog simulation example, the time evolution of the system was of intrinsic interest. In the stratospheric model we are discussing here, the rate laws are intemated startina from some set of initial concentrations to findthe concentrkms present under conditions of constant solar illumination in the &atosphere. The QSSA cannot be simply applied, and the variety of time constants inherent in the reaction system leads to severe stiffness instability problems preventing use of simple integration techniques such as Euler's method. The multivalue predic&corrector method of Gear has been found to be well suited for the integration of chemical rate laws without application of the QSSA. Edelson (6) has discussed this matter in some detail and has led the use of the Gear method for inteeratine the rate laws arisine " from chemical rate equations. Unfortunately, his extensive system for using the Gear integration algorithm is not transportable to another computer system. A relatively compact program system was therefore developed here which permits versatility in varying the chemical reaction scheme without any reprogramming, and utilizes the Gear method for integration of the rate equations without application of the QSSA. This system, HAVCHM. has been incomorated into the main stratosnheric simulationprogram described here and is described inmore detail elsewhere (7).
-
v
Computational Model for Stratospheric Simulation
Although the need to integrate the rate equations to find steadv concentrations under conditions of constant incident solar flux makes time a variable in the course of the computation process, the final output consists of the resulting set of profiles of species concentrations and light fluxas a function of altitude. The calculation is therefore referred to as one dimensional. Two and three dimensional models attempting to include longitudinal and latitudinal variations have been reported, but in general computer capabilities limit the chemical reaction systems to a sub-primitive level. Vertical stirring, turbulence and resulting mass and energy transport processes are crucial in describing the troposphere (i.e. weather) next to the earth's surface. However these processes are relatively less important in descrihina- the stratosnhere, where vertical mixing is quite slow compared to lateral circulation. "State of the art" stratospheric simulations employ an eddy diffusion model to describe vertical transport of some species to and from the stratosphere. This model uses empirical fitting of diffusion coefficient parameters to match observed profiles of tracer substances in the stratosphere. These diffusion parameters are then used to describe vertical transport of substances of interest which are known to have significant sources or sinks outside of the stratosphere. Explicit inclusion of vertical diffusion and therefore time as a variable is important in predicting the future response of the stratosphere to chlorofluorocarbon release in the troposphere near the earth's surface, since the stratosphere is decades away from being in steady state with respect to the current levels of these compounds in the troposphere. In our model the stratosphere is divided into eight equally Volume 55, Number 8, August 1978 1 505
snaced levels. from 50-15 km in altitude. Each level receives the s d s r flux passed from the level ahove and acts as a filter in reducing some of the intensity lor the level helou,due to the absorption of the molecules c&ulated to he present in the 5-km thick layer centered a t the altitude of the level. There is no explicit inclusion of atmospheric transport. T o compensate for this, the concentration profiles of certain molecular species which have sources or sinks in the troposphere below must be held constant using available experimental data to provide srahle concentration ~ I I I I : ~ . The calculation is initialized with the input uf the in( idcnt solar flux a t 50 equally spaced wavelength values and the photoabsorption cross-sections for species undergoing photolysis reactions at these wavelengths.The temperature profile and starting concentration profiles are input for Nz, 02, and other species of fixed concentrations. Approximately known profiles of other variable species may also he input to speed the calculations, but are not required. The method of input of the reaction scheme has a simplicity and flexibility which we feel to he a special feature of the program. Chemical species are defined by labels which can he any comhination of symbols readable under an A8 format in Fortran. Reactions are input as a series of cards, one per reaction. Each reaction card contains a label for the reaction to permit positive matching with rate constant data input separatelv. The reaction card also contains the labels for UD to three ieacrant species and up to three product species. ?he n u m b r and identitirs ( ~ t t h e isvecies e inwlved in the reaction then define the calculation and usage of the corresponding reaction rate term. The total of all different species labels found on the set of reaction cards defines the list of chemical species to be considered in the reaction scheme. The names of species whose concentrations are to be held constant are specified with an input list. The actual calculation begins by evaluation of the firstorder photolysis rate constants for each photochemical reaction at the highest level from the incident solar flux matrix and molecular absorption data using the relationship
Here I(X;) is solar flux a t the wavelength hi in photons cm-2 (wavelength interval)-', and q,(X;) is the product of quantum yield and absorption cross-section, in cm2 molecule-', for molecule j, also at the wavelength interval centered a t Xi. The integration of the rate equations is performed for this level until a satisfactory steady state is established for the concentrations of all species at this level. The solar flux matrix is then calculated for the next level using the Beer-Lambert law to correct for the attenuation caused hv the concentrations of absorbers just calculated for the level above. Thus the flux a t Xi at level j 1isohtained from the value a t level j immediately above using the relation
+
where L is the spacing between levels (the absorption path length), and n,, is the concentration of absorbing species k in the region centered a t level j. X is an average solar zenith angle wh~chcorrects for the oblique path followed by the sun's rays, which are not on average perpendicular to the earth's surface. A value of 45' is suggested for this angle (3). Likewise, the input incident solar flux matrix is reduced 50% from the full sun intensity toallow for a diurnal averaging of intensity (3). After rate law integratibn to steady concentration values is comnleted for each level. the final outnnt is obtained. This consists of the complete set of rate constants, concentrations, rates of all reaction*. iind the solnr flux distribution for pach altitude. The comp~ktespecies concentration matrix is also output as a card image file to permit punched output for plotting or input for subsequent calculations. 506 / Journal of Chemical Education
Sample Results Reactions (1)-(6) comprise the scheme for the simplest renresentation of the stratospheric ozone svstem. 0 2 and total gar (A{) pn,fdec are fixed at the experimental values, and the prwedure descrihed was fdlowed to find the Oc.0, and O(lI)) profiles of concentration versus altitude. he excited state (ID) oxygen atoms will play a key role in the catalyzed systems and hence reactions (4) and (5) are included here. From about 370-800 nm, the Chappius ozone absorption .. rvgion, the photolysis of ozone is important as n destruction steu for t h ~ species. s However, the light flux is not significantly changed by ozone absorption in this region of thespectrum, in marked contrast to shorter wavelengths. Thus this visible region photolysis is most simply treated by including a firstorder ozone decomposition reaction with rate constant computed from the Chappius region absorption cross-sections and the visible region solar flux. Rate constants are taken from the most recent best estimates published in the NRC report (3),and solar flux data, absorption cross-sections, and Oz and M profiles are taken chiefly from Banks and Kockarts (8).The ozone profile is reasonable.. eiven the a~nroximations of the model and most " .. particularly the relatively coarse treatment implied in the eieht level calculation. The total ozone column. assuming a constant concentration a t each level for the 5 km thickness, is 1.15 X 10'9 molecules/cm2, or a thickness of 0.43 cm of gas a t S.T.P. Natural Catalyzed System
The natural stratosphere contains traces of water vagor and NzO which are present as a result of diffusion from the troposphere below. The N 2 0 is formed from bacterial reduction of nitrate and nitrite in the soil, and is the chief source of fixed nitrogen in the stratosphere. The following is a minimum set of reactions representing the chemistry resulting from these species
-
OPD) + H20 20H OH+O~+HOI+OZ H02+O-OH+02 HO* + OH H20 0 2 Nz0 + OPD) 2NO NO+O~-NOZ+O~ NOn+O-NO+02 OH+NOz+M-HNOz+M HN03 + hv+ OH + NOz NOz+hu-NO+O HOz + NO -OH + NOz
-
-
+
(9) (10)
(11) (12)
(13) (14)
(15) (16) (17)
(18) (19)
Reactions (10) and (14) are seen to he particular examples of the general reaction ( I ) , and reactions (11) and (15) are examples of the general reaction (8). Reaction (16) is shown as a third-order reaction; the OH NO? comhination process is actually in the pressure dependent transition region between second- and third-order behavior at stratopheric pressures. Many other interconversion reactions of lesser importance involving species such as NOa can be written and included. The upward diffusion of N2O pruluces NO hy reaction 113); this NO inout to the NO,-svstem is balanced bv downward . diffusion df HN03 with subsequent rainout in the troposphere. In the absence of explicit inclusion of diffusion effects, the concentration profiles of HzO, HN03, and Nz0 must be held constant if stable results are to be obtained from integration of the rate law system. These profiles were taken from the experimental results shown for these species in the NRC report (3), as were the rate constants, with the exception of
+
and Molina (11) provide photostationary state profiles for these species assuming continuation of the 1973 fluorocarbon production rates to stationary state conditions in the stratosphere. T h e fluorocarbon production is averaged over the surface of the earth, and different choices for eddy diffusion coefficients are tried. When we use the "best estimates" for the fixed concentration profiles and include the reactions (20)-(26). . . . . , we obtain the ozone orofile also shown on the fieure. T h e tutal ozone rolumn is redured by 4%. in contrast to rhe value of ahout 7'b oxedicted hv t he more exwnsive calculations including diffusion effects i3, 11). The shift of the ozone orofile to lower altitudes is correctlv comouted hv our scheme. ?he rates of reactions (201 and ( 2 0 , thephotolisesof C F ~ C I ~ and CFCI?. when summed over altitude eive total rates on an s-I, in area basi'hf 1.9 X In7 and 1.4 X lo7 molecules satisfactorv aereement with the aloha1 averaged production rates for these species of 1.6 X ib7and 1.1 x 10~molecules cm-2 s-l. I
I 6
5
10 11 log C(rnoleeules/cm~) 7
8
8
12
13
Calculated concentrations vwsus altitude. 0 Natural system: 0,. HO,, NO, reactions. A Natural catalyzed system with CI, reactions and chlarofluaromethane photolysls a more recent (13) value for k2. A value of 1.0 was chosen for the quantum yield of reaction (17) a t all wavelengths. This is a matter of some controversy (9).T h e results ofinclusion of reactions (9)-(19) along with (1)-(6) are also shown in the figure. T h e total 0 3 column is reduced to 82% of the value calculated for the "pure"uncatalyzed case, with a mole fraction for NO NO2 between 0.1 X 1W9 and 5 X 1W9, depending on altitude. Calculated concentrations of 0, NO, NO2 and OH are in eood aereement with exoerimental data (3). although NO2 i s a hit low a t lower altitudes. Values for OPD) and HOo are satisfactorilv close to thwe obtained in the much more detailed calrulations of McElroy, et al. (121.The rate of reaction (1 3) summed uvrr altitude gkea a total of 1.6 X 10" molerules NO ~ m - ~ s from - ' this source. This is satisf~rtorilv rlose to the better estimate (12) . . of about 0.9 X 10holecules NO ~ m s-1 - for ~ this value.
+
Perturbation by GI, from Fluorocarbon Photolysis For this we add the following reactions to reactions (1)-(6) and (9)-(19).
-
CF& + hv 2C1+ CF2 CFCI3+ hv 2CI + CFCl c1+o3-c1o+o2 ClO+O-C1+02 CIO + NO C1+ NOz C1+ CHI HCI + CH3 HO + HCI HzO + C1
--
(20) (21) (22)
(23)
(24) (25) (26) Although the primary photochemical act in each of the reactions (20) and (21) is to free a single C1 atom, a second atom is prohably liberated in subsequent processes. The species CF2, CFCI, H, and CH3 are less important in subsequent processes than other species in reactions already included and are not shown as reactants in further steps in our simplified scheme. These species are therefore not treated as variables in the rate law integrations. CHI, CF2C12, and CFCb have their sources in the troposphere; our reaction scheme without diffusion sources cannot allow replenishment of these species as they are consumed by chemical reactions, and hence the concentration profiles of these species must be fixed. HCI likewise requires diffusion processes to balance the effects of reactions of types (25) and (26) and must have a fixed concentration profile in the absence of such diffusion terms in the rate law for the species. Rowland
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Educational Usage
For any calculation with a model, i t is usually found that it is changes in computed results with changes in the model which are most reliable rather than the absolute values of computed results. An acceptable model should, however, be expected to produce reasonable values a s well. Thus the utilizations of the stratosoheric models eenerallv involve the study of effects of pertu;hations to the model s&lem, such as those nrovided hv additions of NO. from SST exhaw&. or the addit& of thehalogen r e a ~ t i o ~ s y s t ewith m varying fluorocarbon burdens. or varvine . .. diffusion coefficients. Absolute values of results frim a model ralrulation mar give insight into dominant terms. or simolifirations which mieht he made in understanding particular system. T h e sensitivity of the oerturbation induced changes in the svstem to values of parameters in the model is of primary roncern in assensing the reliability of such ralculated perturhatinn effects. In thr rvent that budgeflromputer arress nmsiderations limit the utilization of the program system descrihed here, it is suggested t h ~ ar minimum sef of ralrulations might he those for the three different reartion systems described here. This would provide complete sets of reaction rates, concentrations, etc., which would provide the numerical basis for answering questions of the following sort.
a
1) Compare and explain the variation of rates and rate conatants
with altitude for the photochemical reactions. 2) Some reactions interconvert the odd oxygen species 0 and Oa and other reactions carry out a net change in the sum (01+ [Os]. Express d([O]+ [Os])/dt in terms of the relevant rates of reactions in the mechanism. and evaluate the relative imoortance of renrtio>> I f i j and reactions of NO, and HO, catal!lie ryrles in the deatruetim o f 0 and 02.How does the rerult depend on altitude? 3) Obtain a simple expression for [Os]l[O] in terms of the dominant rate constants and concentrations, using the calculated rate terms to suggest approximations for mid stratosphere altitudes. (see ref. ( I ) ) 4) A resoonse heard to a statement of the fluorocarbon orohlem is: "Since the tofa! nmounl of mone present in the rtratosphcre is small. solve the prohlem hy periudir~llysending up rockets loaded with mone tu replenish the wpply." Considering the stratospheric rates of ozone decomposition, comment (with numhera) on this proposal. 5) Show that 0 and 0s are essentially in rapid photostationary equilibrium, compared to formation and destruction rates for the total of odd oxygen species. 6) A large supersonic transport, as described in 1971,is estimated to produce about 3.6 X lo6 kglyr of NOn in its exhaust gases when in regular operation. a) Compute the area rate of production of NOn, in molecules em-28-1, by a fleet of 100 such aircraft, if the source is assumed to,he distributed evenly over the surface of the earth. b) Compare the answer in (a) to the natural NO, source rate given by integrating the rate of reaction (13) over altitude ~
~
Volume 55, Number 8, August 1978 1 507
throughout the stratosphere. What are the implications of these results? Is the answer to question (2) relevant in this discussion? c) What (qualitatively)would he the changesexpected in the profiles of HNOa, NO, NOn,and Os, and also the total OR column if the SST exhaust (calculated in (a)) were added to the stratosphere at altitudes between 15 and 22 km? d) Why is a diffusion term in the rate law for HNOsneeessary to see in a quantitative way the effects of SST injections on the [NO,] and therefore the effectson the ozone shield? If comuuter time is available to exnlore variants on t h e three cillwlnrims desrrihed, thrn thesensitivity of the model tochanye~in thr parametersshould heexplored. The profiles tor HNO,, H?O, CH,, HCI. and the fluororarhons are ohvious quantitirs t c ~he wried. Sgmr of the rate ron-tantn are less well kna8u.n indior ilrr more crucial than othrrs. These should he varied hetween thr limifs of prohahle error. Vnriation of the O2 absorption cross-section; below 210 nm (in the banded Schumann-Runge region) should he tried. This provides an opportunity for a discussion of continuous versus banded absorption spectra. Liaht absorption processes may be important for a particular ahsorhing molecule because of resulting atten~intionof the light flux, hecnuse theahsnrptions induce chemical reaction. or for the combination of these ef- ~ , fects. Ozone shows all of these possibilities. Finally, entry into the rapidly evolving literaturp in this subject providwexperience for an advanced undergraduate in apprrciating margins of error and uncertainty. The needs and methods are seen for making reasonable estimates for uncertain quantities in a tonic area which has been in a rauid state of flux since 1971 when the political-ecological implications of stratospheric photochemistry began to he clearly of serious import. ~~~~~~~
~
~~~
~~~~~~
Computatlon Requirements The IBM 360144 computer execution time for a complete calculation with the largest reaction scheme described here (25 reactions, 9 variable species, 10 fixed species) was -16 min, with integration until the relative concentration changes of all variable species were less than ]@after each integration sten. T h e execution time was 3 min for the uncatalvzed schkme with six reactions and three variable species. The ~ B M 360144 computer is similar to the more common IRM 360150 computer in central processing unit execution time. Computer dollar costs obviously depend on institutional computer price structures and policies regarding direct charges (if any) for educational usage. Charges a t "commercial rates" may be in
508 1 Journal of ChemicalEducation
the neighborhood of $3 to $16 for each calculation described here. 'or all Fortran The complete computer core requireme IV generated programs, arrays, and library supplied I/O and arithmetic routines was 96.1 Khytes with Fortran programs dimensioned for 60 chemical species and 100 chemical reactions. A more reasonable set of dimensions, given other limitations of the model. is nruhablv for 30 chemical species and 100 reacti(,ns. This dimensioning would reduw corr requirements hv 17.8 Khstvs to reuuire 78.3 Khvres. or ahout 20 K array elements, of storage for the compl&e executable program. The number of chemical species is more important than the number of chemical reactions in determining storage requirements and computation time. Arithmetic for the integrat,ion process is performed in double precision. T h e main program for the stratospheric simulation and a subroutine for output of various stages of the calculation comprise 332 Fortran statements. T h e rest of the program system consists of -740 Fortran statements for the Gear in- . tegration subroutine and additional subroutines which handle the coding of the input reaction information and compute the necessary derivatives for the integration process. These suhroutines also comprise the largest part of our HAVCHM system for rate :aw integration using the Gear method.
..
Program Avallabillty Programs and input data are obtainable as a card image file on 9 track magnetic tape, 800 b.p.i.; a 400-ft reel will easily hold the whole system. Send a hlank tape and $15 t o cover domestic postage and costs, or alternately $30 to cover domestic postage and costs and a non-returnable tape for the programs and documentation to John P. Chesick. Literature Cited (11 Chnick, J.P.,J.CHEM.EUUC.,49.722 (1972). (2) Molinn, M.J., and Rowland, F. S., Nature, 249,810 (1974).
(a) Panel on Atmnspherb Chemistry, National Resoarch Council, "Halocarbona: Effects on Stratospheric h o n e ? Nstiond Academy of Scieneea, Washington. D.C.. 1976. (4)
(5)
Basmw.H..
J.CHEM.EDUC.54.371 (1977). (1971).
Huehert,R.J.,J.CHEM.EDUC.,51.644 (19741.
($1 F%airon,D.,J.CHEM. EUUC.52.642
(7) Stabler. R. N..and Cherick. J. P., In,. J . Cham.Kin., tobepuhlished. ( 8 ) Ranks, P. M.. and Kockarts. G.. "Aeronomy: Academic Press,New York, 1973. (9) MeConnell,J.C.,snd McE1my.M. R., J. olAtmos. Sci. 30.1465 (1978). (10) Johnston, H.S..Arclr. Chem. Rex. 8.289(1977). (11) Rowlsnd,F.S..andMolina, M. J..Reus. nfUenpkys. nndSpnco Thy.., l3.1(1975). (121 McElroy, M.R. Wofsy.S. C.. Penner, J.E.,and McConnell.J.C.,J. Amos S c i . 31. 287 (19741. (1%)Hudaon, R. D.. (Editor) "Chloronnommethaner and the Stratosphere: NASA Ref. Puhl. 1016. NASA Scientific and Tech. Info. Office 1977.
