Oct 20, 1984 - Vertical and meridional winds for (a), (b), vernal equinox and (c), (d) summer .... GeM, for our purpose we would prefer heating rates based.
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL.
89, NO. D6, PAGES 9589-9602, OCTOBER
20, 1984
ADiabatic Circulation Experiment in a Two-Dimensional PhotochemicalModel P. D. GUTHRIE,C. H. JACKMAN,J. R. HERMAN,AND C. J. McQUILLAN NASA GoddardSpaceFlight Center,AtmosphericChemistryBranch A two-dimensionalphotochemicalmodel based on diabatic circulation has been used to simulatethe behaviorof N20, CFC13(F-11), and CF2Cl• (F-12). The circulationis basedon estimatesof net heating from the ground to 60 kin. Eddy diffusion has been reducedwith respectto other model studieswith
Kzz-- 2 x 103cm• s-• everywhere above100mbar.Resulting tracerprofilesshowreasonable agreement with measuredprofilesin the tropics and fall off much more sharplywith altitude than thoseproduced by modelsusinglarger valuesof Kzz.The agreementobtainedis at leastas good as that obtainedwith adjustable,eddy diffusion parameters.The diabatic circulation treatment is more closelyrelated to real physicalprocessesand thus more easily interpreted.Diffusive mixing appearsto be more important in determiningthe detailsof the tracerdistributionsthan the basicmorphology. INTRODUCTION
Photochemicalmodelshave evolved,over the last 10 years or so, into one of the primary classesof tools usedin studying the chemicalbehavior of the atmosphere.These models now range from box chemistry models to three-dimensionalversions with coupled treatments of radiation, dynamics, and chemistry,and there will always be some problems that require evenmore sophisticatedmodelsthan availablecomputer resourcescan support.One of the first stepsin any attempt to model atmospheric phenomena must be the selection of a modelingtool at an appropriatelevel of physicalapproximation. It is the purposeof this paper to investigatethe ability of a two-dimensional(zonally averaged)model, using transport based on a diabatically driven circulation without substantialeddy diffusion,to provide a good simulationof atmosphericbehavior as measuredby upward flowing long-lived
3-D model. If the 2-D model is basedon highly parameterized eddycoefficientsfrom atmosphericmeasurements,this consistencyis difficult to achieve.Finally, the 2-D modelsprovide an interpretive bridge between the relative simplicity of a 1-D model profile and the inherently more complex and variable 3-D simulations.
There remain conceptual difficulties in interpeting 2-D transport [see,for example,Danielson,1981], and one must be wary not to attempt to push the model beyond the inherent limits of the basiczonally averagedformulation.For example, it seemsunlikely that a 2-D model could properly simulate transportduring a stratosphericwarming event,althoughthe net effectcan be parameterized[Schoeberland Strobel,1980]. The time scalefor a zonally avergedmodel is ultimatelyfixed by the time scalefor zonal mixing (that is, for the atmosphere to "average"a perturbation around a latitude circle),which is of the order of severalweeks.During the recent E1 Chichon tracer distributions. The diversityof atmosphericphenomenahas led to the de- eruption, it took 3 weeks for the leading edge of the aerosol velopmentof a hierarchy(in dimensionality)of models.At one cloud to wrap around and mergewith the trailing edge[Krueextremethereare simplebox models,usefulfor studyingprob- ger, 1983; Robockand Matson, 1983]. In testingthe limits of a lems involving rapid, complex chemistrywhere transport is model basedon a particular transport treatment,simulations unimportant. At the other extreme is the three-dimensional of tracer distributionsallow us to focuson the long-term net interactivemodel, which attemptsto encompassmost of the transport effects. Subsequentstudies will focus on the adeunderlying physical processesof the atmosphere,including quacyof this transporttreatmentin simulatingseasonalcycles limited chemistry.Such modelsare primarily usefulin study- of ozoneand other photochemicallyactivespecies. Many existing2-D models,includingthat usedin this study, ing problems of complex atmosphericmotion and energy can be describedas specifiedtransport models; that is, a flows. In the middle lie the one-dimensional and twodimensionalmodels.The former is often thought of as repre- changein speciesdistributions(e.g.,ozone)doesnot producea changein the atmosphericcirculation.For the senting global average altitude profiles of chemical species, self-consistent while the latter is most usefulfor problemsinvolving latitudi- present study we have chosen to specifythe 2-D transport nal distributionsand seasonalvariationsof speciesof interest. fields at monthly intervals and to neglectfeedbackprocesses The two-dimensionalmodelsare particularly suitedto studies causedby changesin the distributionsof radiatively active of photochemicalphenomenawhere the transport of source species.A number of attemptshave beenmade to includesuch and reservoir speciesis important, but the model time re- a coupling[e.g., Garcia and Solomon,1983; Harwood and Pyle, quired producesa prohibitive computationalload if one uses 1975; Vupputuri,1978], but the problem of incorporating the a 3-D model.For example,in a 2-D model one can perform details of transport feedbacksin a two-dimensionalapproxiseveralmultiyear simulationsto test sensitivitiesto variations mation, especiallywhen the eddy contributionsbecomelarge of groundsourceswithin a reasonable amountof computer in comparison to the mean circulation, has not been comtime. Such modelscan also be usedto provide realisticinitial pletely resolved. Although the goal of most photochemicalmodeling efforts distributionsfor 3-D models, as for the initial NO,, distriis to simulate the behavior of a large number of interacting bution for the 3-D ozone studies of Cunnold et al. [1975]. However, this proceduredependson the degreeto which the chemicalspecies,the resultingcomplexitymakesit quite diffi2-D transport representsa zonal average consistentwith the cult to disentanglethe effectsof the various approximations and parameterizationsemployed.For example,if the seasonal This paper is not subjectto U.S. copyright.Publishedin 1984 by the AmericanGeophysicalUnion. Paper number 4D0715.
variationsin profilesof speciessuchas thosein the NO,• and HO,• familiesare not properlysimulted,is this to be attributed to an inaccurate treatment of transport or to an insufficient 9589
9590
GUTHRIE ET AL.' DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
DIRBATIC 0.1
!
HERTING RRTESfDEG/DAYI
HEAT DRIVEN ,
•
'
,
'
i
'
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'
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HERTING RRTES[DEG/DRY}
HEAT DRIVEN ,
i
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,
,
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O. O0
LATI rUEIE fDEGREES I
3U. O0
60. O0
Dt•Y =
90. O0
-90. O0
-60. O0
-30. O0
30.0
O. O0
30. OO
LRTI TUOE •DEGREES I
DAY--
180.0
Fig. 1. Diabaticheatingratesusedfor northernhemisphere: (a) vernalequinox,(b) summersolstice.
reproductionof the annual ozone cycleas a result of a limited chemicaltreatment?Our strategyis to decoupletheseeffects for the purposesof assessing the model approximationsbefore attempting to modify those approximationsin order to do a full photochemical simulation. In order to study a specific transport parameterizationwe have specifiedozone on the basisof an observed(over 1 year) distributionfrom Nimbus 7 data [McPeters et al., 1984], updatedmonthly. The O2 mixing ratio does not vary, but the column density above a given point changesas the model atmosphererespondsto seasonal variationsin temperature.Thus the calculatedlocal ultraviolet flux should be a good approximationto that of the real atmosphere. The first step is to considerthree precursoror sourcegases: N20, F-11, and F-12. All three have sourcesat the ground and sinksprimarily through stratosphericphotolysis.Thus we are using an experimental circulation to transport photochemicallysensitivetracesthrough a reasonablyrealisticradiation field. The degreeto which the model simulatesthe actual atmosphericbehavior of those tracers is then a test of the ability of the circulation parameterizationto simulate actual atmospherictransport. A demonstratedability to do so is a necessarycondition for usingthis circulationin more complex photochemicalsimulations.
Newton-Raphsoniteration with explicit forward time differencingat eachpoint and alternatingdirectionof integrationin both coordinates(the "angled" derivative schemeof Roberts and Weiss [1966]). The spatial finite differencesare centered fourth order in the interior
and one-sided fourth order at the
boundaries.(Seethe Appendix A for further discussionof numerical technique.)The boundary condition on the transport fields is zero transversevelocity at each boundary. Species boundary conditionsmay be specifiedas constant mixing ratio, specifiedflux (which may be time and latitude dependent), or specifieddepositionvelocity.Although any combination of advective and eddy-diffusivetransport parameters can be formally accommodated,the model is optimizedfor primarily advectivetransport; this is discussedfurther below under "Transport." CHEMISTRY
The chemical production and loss terms in equation (1) representsumsover many individual chemicalprocesses. They are of the form
Pn--E SiJni q-E KnijSiSj q-E Knij•SiSjS• i u u• Ln--E Jniq-E KnjSjq-E KnjkSjSk i
j
(2)
jk
where the $'s are photolysisrates and the K's are the two or T•-m MODEL three body reaction rates for the various relevant reactions. The model domain is from -85 ø to + 85 ø in latitude at 10 ø The i, j, k subscriptsrepresentindividual photolysispathways, intervals and from the ground to approximately 60 km in binary reactions,and tertiary reactions,respectively,which altitude, with vertical resolutionof about 2 km as represented contributeto the total production and lossrates for speciesn. by 30 levelsin log pressurecoordinates.At each point in the Tables of these rates are given in the World Meteorological grid the model solvesa set of N speciescontinuityequations Organization[1981, hereafter referred to as WMO 81] report of the form along with the cross sectionsfor the computation of the $ coefficientsfor photolysis.Appendix B presentsthe reactions 8Sn - -V. F n + P.- L.S. (1) usedin this study.In this model, scatteringis neglectedso that 8t a simple Beer's law calculation of the solar flux within the where S. is the concentrationof speciesn, F. is the flux of atmospherecan be used.The effectsof sphericalgeometryin speciesn, P. is the volume production rate, and L. is the the earth's atmosphere are approximated by use of the photochemical loss rate. The numerical technique used is Chapman function [McCartney, 1976]. The solar flux above
GUTHRIE ET AL.' DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
0.1
DIABATIC HEAT DRIVEN ,
,
•
-,
,
•
,
,
VERTICAL VEL (CM/SEC) •
I
I
'
0.1DIABATIC HEAT DRIVEN
'
MER•IDIONAL VEL• (CM/SEC)
B
A
9591
1.o
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100.0 .
ß
-- •.•
- •.•
- 30.00
0.00
30.00
60.00
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0.1DIABATIC HEAT DRIVEN
0.1
!
•
I
[
!
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]
90.00
DAY = 90 0
MERIDIONAL VEL(CM/SEC)
[
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-,
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,,-
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,'__•o.•-•::: • ZoO; •w••' -90,00
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LATITUDE (DEGREES)
60.00
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90.00
--•.•
180.0
-30.0
.'•'
0.00 30.0 LATITUDE (DEGREES)
-30.0 • 2o•o.oj 60.0 DAY = 180.0
•.00
Fig. 2. Vertical and meridionalwindsfor (a), (b), vernalequinoxand (c),(d) summersolstice.Shadingshowsdescending motion.
the atmosphereis taken from Mount and Rottman [1981] for wavelengthsshorter than 165 nm. Between 165 and 400 nm the flux usedis given by D. F. Heath (private communication, 1981,seealso WMO 81), and for wavelengthslongerthan 400
the chemicalreactiontermsare formedby integratinga onedimensionalversion of the chemistryequationsand forming the 24-hour averageof each reaction at each altitude at 30øN latitude for springequinox.The largesterror arisingfrom the nm the flux is taken from WMO 81. Where the flux data sets useof this singleset of diurnal averagereactionratesoccursin are joined the valuesof Heath are usedas the referencevalues the polar regionsin the monthsjust before and after winter for smoothlyjoining the data. night. For the tracersconsideredherethe dominantprocesses The procedurefor assemblingthe terms entering into Pn are photolytic, and the accuracyis essentiallyindependentof and Ln is similar to that describedby Herman [1979]. Each latitude. We approximate the solar spectrum with 39 wavereactionrate and d coefficientis diurnally averaged.The diur- length intervals. nally averagedd coefficientsare obtained by averagingthe Recently, Herman and Mentall [1982] have suggestedthat instantaneous d values over 24 hours for each latitude conabsorptioncross sectionsfor O2 between 200 and 230 nm tained in the grid and for several values of the solar decli- should be smaller than those measuredby Hassonand Nination angle. Linear interpolation is used for the diurnal cholls[1971]. Severalauthors[Froidevauxand Yung, 198•; averagesfor other solar declinations.The diurnal averagesof Brasseuret al., 1983] have comparedthe resultsof the two sets
9592
GUTHRIE ET AL.' DIABAXlC CIRCULATION MODEL WITH PHOTOCHEMISTRY
in comparisonto advectivetransportand may be neglectedor,
180
at most, considered as a "correction" to the basic advective
circulation. Since the approximation must break down at somespatial or temporal scaleof atmosphericbehavior,it is important to determinewhere,if anywhere,the approximation is good, as evidencedby its ability or inability to simulate observedatmospherictracer distributions. The great advantageof the residualmean approachis that transport processesdivide neatly into advection (including that resulting from eddy transport if one goes beyond the diabatic approximation)and diffusivemixing, as represented by the symmetricportion of the eddy diffusion tensor.The flux divergencemay be written [see, for example, Holton,
160
140
120
_
--- thismodel
0 1970
I I I I I I I I I 72
74
76
78
_
1
I I I I I I I I I I 80 1970
S.H.
72
74
76
78
1981] as
80
•
•P
N.H.
81 for data references.
of cross sections in 1-D models and found substantial
(3)
or after expanding, rearranging, and neglecting the offdiagonaltermsin the eddydiffusiontensor'
differ-
2qpK=]
ences.Below 200 nm, we have used02 crosssectionsbasedon Allen and Frederick [1982]; between200 and 230 nm, Herman and Mentall [1982]; and above 230 nm, Hasson and Nicholls [1971]. The model is run in a time-dependentmode with a time step of three days. The declination and fraction of day and night [after Rundel,1977] are changedevery time step. TRANSPORT
(pXw) + V. Epg'VX]
Fig. 3. Time history of F-11 (after WMO 81). The points are troposphericmeasurements,the solid line is the 1-D model result of Logan et al. [1981], and the dashedline is the result of this model lbr 45øN and 45øS at ~ 500 mbar. See WMO
•
v.r = cos (Xpcos +
(pKyy) + Re
+X.Iq•8(pw) +2•-• +• cos (pv cos pw
The transport term in (1) must be expressedin terms of some set of parametersthat are determined by the physical where X is mixing ratio, p is atmosphericnumber density processesof interest.Clearly, a model of this type cannot in(m-3), p is In (pressure/1013 mbar),•bis latitude,q is •P/SZ dude exact treatment of sub-grid-scalephysics,nor can it inand Z is altitude(m-• and m), Re is the radiusof the earth clude the physicsof the planetary wave phenomenanoted in (northward) the real atmosphere.In practice the parameterizationusually (m),w is verticalvelocity(m-s-•),v is meridional comes down to only two types of processes:advection by winds, which preservesair parcel properties,and eddy diffusion, which representsatmosphericmotions that mix air par45 ' x ..... •1 ' ' ' celsand thus relax concentrationgradients. \ • N20 The first generation of specified-transport,2-D photochemical models [Widhopf, 1975; Crutzen, 1975; Whitten et al., 1977] was based on the use of locally measured(i.e., Eu35 ß lerian) winds and the eddy diffusion treatment of Reed and German[1965]. The componentsof the eddy diffusion tensor • 30 ---this model must then be obtained through some inversion procedure • ---- Miller et.al. o•, based on tracer measurementsin the real atmosphere.This •, 25- -----Garcia &Solomon approach producesmean and eddy motions that are nearly •: o NO• 19•-• o• cancelling, not necessarilyself-consistent[Mahlman, 1975], 9øN, 5øS • and whosenet effectis the small residualof two nearly equal • - ß NCAR 1979 • but opposite fluxes, neither of which is well determinedby measurements.Attempts to improve the situations are re2øS_9øN Tropopause viewed in chapter 2 of WMO 81. One suggestedalternative is to base the model on the "re10 ......... I , , , 10 1• • sidual mean" circulation as outlined by Pyle and Rogers [1980] and Holton [1981] and in particular to identify that MIXING RATIO (ppbv) circulation with that driven by diabatic heating [Dunkerton, FiB. 4. ComputedcguatorialN•O proQlcsand measurements. In 1978]. A questionremainsas to the adequacyof the approxi- FJSurcs4 throush ½the data pointsare taken from W•O 8], which mation that, in sucha model, diffusivetransport will be small see fo• references.
40-
x\\
,•Equatorial _
15 - +•ES 197•Mean• 6øS •
GUTHRIE ET AL.' DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
9593
velocity(m-s- •), F-11
40 -
øl
Equatorial -
-'-• •
Kzz
•
thismodel -
• •" • ....
is the eddydiffusiontensor,and Kyy,K==are eddydiffusion coefficients (m2-s- •). Note that the wind velocities and diffu-
----- 25
8 ß
Miller et.al. o o
9ON, 5•s
sion coefficientsare in standard spatial coordinates(rather than latitude-InP) in order to facilitatecomparisonwith other
•
_
oo+•.,• •,
- ß NCAR 1979
_•
15-+ AMoEoS e12o7•,t77 Mea• '' •,'"•
work. TI4E MODEL
EXPERIMENT
The basicprocedureof this modelexperimentis to simulate tracegasprofilesby usingthe diabaticcirculationin a realistic photolysisenvironment.Our intent is to evaluatethe contention that the diabatic circulationprovidesa "good" first approximation of transport in a 2-D model [Holton and Wehrbein, 1980] without substantialeddy diffusion.The required data for this experimentare total diabatic heating rates and temperaturesthroughoutthe model domain at monthly intervals.Although one could usethe zonallyaveragedoutput of a GeM, for our purposewe would prefer heating rates based primarily on atmosphericmeasurements rather than on a particular model computation.No suchself-consistent data base exists,but reasonableapproximationscan be constructed.Solstice and equinox heating rates above 20 km are available from Murgatroyd and Singleton[1961], and seasonalaverage heating rates from 30 km to the ground are available in
5
10
50
100
500
MIXING RATIO (pptv)
Fig. 6. ComputedequatorialF-! ! profilesand measurements.
level. However, the lower level heating rates are the more recent and are based on a more detailed treatment
than are
those of Murgatroyd and Singleton.More importantly, using the specifiedrates in the troposphereand lower stratosphere producesgood agreementwith tropical mixing ratio profiles of all three tracers consideredhere. These profiles depend on the strengthof the upward drive in the tropical lower stratosphere.Adjusting these heating rates upward, rather than those in the upper stratospheredownward, will displacethe tropicalprofilesupwardwith respectto the measurements. The characteristicfeaturesof the diabatic circulation are (1) rising motion in the tropics and descendingmotion at high
Newell et al. [1974]. The low-aItitude values contain latent
latitudesin the lower stratosphere and troposphere, and (2)
heat release as well as radiative effects. The net radiative heat-
the single pole-to-pole cell in the upper stratosphereat sol-
ing usedby Newell et al. was that of Dopplick[1974]. We
stice. The altitude of transition from two cells to one and the
have corrected the radiative
latitude of transitionfrom risingmotion to descendingmotion are uncertain and depend on the details of the heating rate
contribution
in accordance with
Dopplick[1979] whereverthe correctionwas greater than 1%. Unfortunately, the different sets of data do not match in the regionof overlap.An approachtaken by Miller et al. [1981] is to scale the Murgatroyd and Singletonrates uniformly by a factor of 0.4. Although adopting this procedureleaves large mismatchesin variousplacesat variousseasons,it is probably as good as any other arbitrary modification and allows comparison with the Miller et al. model results. The resultant heating rates are shown in Figure 1 for northern hemisphere vernal equinox and summer solstice.Seasonal temperatures
distributions.
The heating rates are convertedto wind fields through the relation derived by Dunkerton[1978]' w-
(4)
F-FA
wherew is verticalwind(m s-•), Q is the heating(K-s-•), F is the temperaturelapserate (K-m-•), and I•A is the adiabatic lapserate (K-m-•). The meridionalwind v is obtainedby
havebeentakenfromMurgatroyd[1969].The gridwasfilled integrating the mass continuity equation from pole to pole out for four seasonsby using spatial interpolation, and the interveningmonths filled in by usingpoint-by-point temporal interpolation. As noted above, this version of the diabatic
circulationis not definitive.One couldmergethe heatingrates in other ways, perhapsadjustingthe values below the merge level instead of, or in addition to, adjustingthem above that
'
' ' •,L"I
I'
•
F-12
-
"
Equatorial
35
---
this model •""--...•'x ß øNø
- -•- Miller et. al. __
25 2O
-_ oNOAA 1977-79 •øø• ø 9øN, 5øS + -
ß NCAR 1979
6øs
- +AMES 197_6-77
2øS -9øNI 1
10
Mean'•
Tropopause 100
MIXING RATIO (pptv)
with v = 0 at the boundaries,i.e.,
v(•,P)= -- p(•,P) 90 øRe cos 1cos•bfv aP aE,o(•b', P)w(&',P)] ß-&Z
(5)
&P
In order to conservemasswithin the model and satisfycontinuity the w field was adjusted to yield zero net mass flux through each pressurelevel. The resultingwind fields rigorously conservemass at each point in the grid for our finite
differencing scheme.The verticaland meridionalvelocityfields for solsticeand equino•½ are shown in Figure 2. Comparison with other results[e.g., Dunkerton,1978; Garcia and Solomon, 1983] showsthe samegeneralpattern,exceptat the top of the
model. Thestrongmeridional je'tassolstice appears• much lower (• 55 vs.75 kin) becauseof the "cap"at •60 kin, with a zero-vertical-velocityboundary condition. In effect the meridional jet has been displaceddownward by the selectionof modeldomain.For presentpurposesthis hasno effecton our ,
Fig. 5. Computed equatorial F-12 profilesand measurements.
results, sincethetracermixingratiosbecomeessentially inde-
9594
GUTHRIE ET AL.: DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
-
ßJLilich MidLat • • •\ ', -s(P .•e '•. oNOAA Laramie •'•:; 1•,"',•x
ß o•ø '
-_
10 5
o
-
!5
necessarilythe most illuminating approach to a test of the transporttreatment.Instead,we have fixed ozone(the primary photochemicalabsorber in the near ultraviolet) at monthly intervals (basedon Nimbus 7 BUV data from McPeters et al. [1983]) and injected tracers at the ground for which stratosphericphotolysisis the predominant or sole destructionprocess.We specifya constantmixing ratio of 300 ppbv for N20 at the ground. The chlorofluoromethanesF-11 and F-12 are specifiedas time-dependentand latitude-dependentfluxes according to historical releaserates from Bauer [1979] for 1960 through 1974 and from WMO 81 for 1975 through 1980.The
--
•is
•
m
---- Miller etal.
.... G•'• •o1•o•
model is run to 1980; the time evolution of F-11 and F-12 is
10
shown in Figure 3. The resulting distributions of the three tracers arc compared with atmospheric measurements.One reasonfor selectingthis test is that it has alwaysbeendifficult to defineeddy diffusioncoefficientsthat would fit N20, F-11, and F-12 simultaneously [-see,for example, Hunten, 1983; Miller et al., 1981]. As will be seen,this parameterizationdoes an almostequallygoodjob for all three.
N20 MIXINGRATIO(ppbv)
• •øN '•Winmr
o.o• '
_
Aretic Airma•
•o• • o
RESULTS AND DISCUSSION
. me, Miller et. al.
10
51
....
Gamia & Solomon
o
i i i i i ii,l i i , , ,1111i 10 N20 MIXING RATIO (ppbv)
Fig. 7. Computed mid-latitude N20 profiles vs. measurementsfor (a) summer,(b) winter.
tectable at altitudes below the jet. For problems involving photochemicallyactive specieswith sourcesin the upper stratosphereor mesospherethe treatment of the upper boundary would need to be reconsidered. A primary goal of an advectivetransport model is to determine the degreeto which the observeddistribution of tracers can be explainedby advectiveprocesses. Accordingly,we have attempted to minimize the dependence on eddy-diffusive transport. In this experiment the symmetric parts of the K
Figure 4 showsthe equatorial altitude profile for N•.O obtained from measurements(WMO 81), Miller et al. [19811, Garcia and Solomon[19831, and this study. While the model resultsare nearly identical below 30 km, they diverge in the upper stratosphere,where the more diffusive transport treatments produce a larger upward flux. A similar effect appears for F-12, as shown in Figure 5. Preliminary analysisof this model, using the previously accepted O2 cross sectionsof Allen and Frederick [1982], indicates that the differencesbetween this experimentand the Miller et al. resultsare more probably due to the differencein transport treatment than to the differencesin crosssections[Jackman and Guthrie, 1983].
40I A ........
I •.;
'•L.......•
35•
-- •
' ' ' .... I
I
40-45øN F-12 Summer I
•
tensor, KyyandKzz,aresetto 2 x 109cm2 s-• and2 x 103 cm2 s-•, respectively, everywhere above100mbar.Thereis no latitudinalvariation,andKyz = Kzy= 0 everywhere. Thesymmetric componentsare increasedby a factor of 5 in the lowest
four layers to provide enhancedtroposphericmixing (thus avoiding a buildup of chlorofluoromethanes near the ground where the diabatic circulation is a very poor approximation) and tapered down to the above values over the intervening five layers.Thesevaluesare large enoughto provide damping of wavesproducedby irregularitiesin the velocity fields but small in the sensethat in the stratospherethe advectiveterms in the flux divergenceequation (equation (3)) are generally
25-
o•
moe,
•'•
10 - ----Miller e[ al. 5
........
terization
in a model there must be some well-&fined
stan-
dard or figure of merit with which the results can be compared.While the eventualgoal in most photochemicalmodels is a self-consistent calculationof all active species,this is not
.........
I
,
• .....
CCI2F2 MIXING RATIO (ppN)
• B
'P•% F-12Win•r •øN J o
largerthanthe diffusiveterms.The valuesof KyyandK:: are factorsof ~ 20 and ~ 2 larger, respectively,than the numerical diffusionobtained in a squarewave test for this grid spacing and time step. These values are an order of magnitude or more below the stratosphericdiffusion coefficientsused in most other models [Whitten et al., 1977; Vupputuri, 1978; Miller et al., 1981] and quite close to the values recently derived by Kida [1983]. In order to evaluate the use of a given transport parame-
•
10
•
•%
•'
oøø
25
15-
•
•ism•el
10 - -----Miller elal. 5
ß AreticAir Ma•l
........
I
1
10
CCl2F2 MIXING RATIO (ppN)
Fig. 8. Computed mid-latitude F-]• profiles rs. measurementsfor (•) summer,(h) winter.
GUTHRIE ET AL.: DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
The profile for equatorial F-11 (Figure 6) clearly fits the
A
measurements lesswell, indicatingthat fbr this species,even with the revisedO2 crosssections,there is possiblystill a problem with the photolysisrate. It is, of course,possibleto
9595
i
i
F- 1 1
•
40-45øN
Summer
"'"'""--.-..
-
. JUlich MidLat
- 0_•... oNOAA Laramie
specifyother combinationsof winds and eddy diffusion coefficients that will produce profiles in good agreement with measurements. Recentwork by Gidel et al. [1983] usinglarge eddy diffusioncoefficientsand extremelysmall vertical winds in the lower stratosphereillustratesthis. The point here is that
-
oO.O .oo
\
,
-- this model , ......
about as well in simulating tracer profiles as tuned eddy diffusion parameterizations,but with a simple physicalmechanism
".•
oo 'o .g.N N xx
_ ---Miller et. al.
the diabaticcirculationmodel,with very little diffusion,does
-•.
-,- © oV,.,oo o•
_
_
ß
1
,I
%"•
;•
, , , , ,,,,I
10
I I
.....
100
CClaF MIXING RATIO (pptv)
as its basis.Whether this simple treatment is adequatefor more complexproblemsremainsto be seen. At mid-latitudes the fit for all three tracers is substantially poorer (Figures7, 8, 9) with a consistentoverestimateof concentrationsin the lower stratosphere.We considerthis to be most probably due to the limitations of the circulation, as
]__
40-45øN F'11 Winter _]
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discussed below.
Several characteristic
features of the diabatic circulation
are
evident in Figure 10, which shows seasonalcontour plots of mixing ratio for N20. Starting at about 200 mbar, there is a "bubble" which representsthe effect of upward flowing tropical air (refer to Figure 2). As the upward flow slowsand turns poleward, this structure develops anvils that produce larger mixing ratios at mid-latitudesin the lower stratospherethan thosefound in the real atmosphere.This resultsin the "shoulder" between 20 and 30 km on the profiles in Figures 7-9.
Similarstructureshavebeenreportedby Ko et al. [1983] (for
•
20 15
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1
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/
lOO
pptv
Fig. 9. Computed mid-latitude F-11 profiles vs. measurementsfor (a) summer,(b) winter.
a model with the lower boundary at the tropopause)and are suggestedby the data of Krey et al. [1977]. However, as the positionthan doesthe actual atmosphere.A similar interpreprofiles indicate, any such structure in the real atmosphere tation was suggestedby Garcia and Solomon[1983] on the must be confined to lower latitudes. The shoulder in the midbasisof both upwardand downwardflowingconstituents. latitudeprofilesoccurswherethe flow (againreferto Figure2) It is, of course,still possiblethat the mid-latitude mismatch is primarilymeridional, thatis,highmixingratioair is flowing is due to inherentlimitationsin the applicabilityof thi• diabaupwardin the tropicsand thenpolewardin the mid-latitudes tic circulation or to our use of latitude-invariant eddy diffubetween50 and 10 mbar. This flow doesnot begin to descend sion coefficients. However, the mismatchis not substantially until it reaches •
+ 50 ø in latitude.
The latitudinal
extent of
the lower stratosphericcirculationcell and the position of the descendingportion are determined by the location of the change from net heating to net cooling in the atmosphere. Sincethe heatingratesin the lower stratosphereare small and dependon somewhatuncertainmeasurementsof water vapor concentrations [Dopplick, 1974, 1979] as well as other trace
reducedin summer,whenwave dissipationand transienceeffectsare usuallyreducedin the real atmosphereand the diabatic approximationis likely to be very good.As for the uniform diffusion, while real atmosphericmixing processesare un-
doubtedly variablein bothtimeandspace, the appropriate distribution
for use with a residual mean circulation
is still an
open question. gasdistributions, it is quitepossible that the actualtransition In consideringthe transport characteristicsof different from net heating to net coolingin the lower stratosphere modelsit must be rememberedthat the values of eddy diffuoccurs at lower latitudes
than the transition
shown in our
heating rates. If so the position of the descendingside of the cell should be farther equatorward, which would tend to reducethe mismatchin the mid-latitude profiles. The altitude of the heating rate transition that generates this cell (see Figure l a) is between about 100 and 50 mbar, correspondingto the centerof the circulationcell.This is well below the region of mergingthe two heatingrate data setsand thus unlikely to be affectedby the merging procedure.Doubling or halving the heating rates everywhereproducesthe expectedincreaseand decrease,respectively,in the wind velocitiesbut doesnot changethe locationof the cellcenter.It is the signChangein the heatingratesthat determinesthe latitude of the descent.Comparisonwith measurements and the presence of the shoulder in our calculated mid-latitude profiles are taken to indicate that the lower stratosphericheating rates usedhave a heating-to-coolingtransition at a more poleward
sioncoefficients maynot be directlycomparable. The values chosenfor the K's in a givenmodel will dependon the formulation of that model and the physicsbeing parameterized within the K theory approach.It is incorrectto useK values derived from Eulerian
formulation
mean winds and wind variances in a
based on the residual mean circulation or the
diabatic approximation thereto. Within the diabatic circulation approximation,eddy diffusionis presumedto represent only irreversiblemixingprocesses, suchas turbulentdiffusion. Within the Eulerian formulation, the eddy coefficientsmust
also representsystematic motionsthat are nearlyequalin magnitudeto thoserepresented by the Eulerianmeanwinds. The K valuesusedhere,while small comparedto thoseused in most other 2-D models, may not be small compared to those appropriate to the residual mean formulation. Kida [1983], for example, derived values very similar to these in attempting to model trajectoriesin the lower stratosphere.
9596
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Fig. 10. Height-latitudedistributionsof N20 for (a) winter,(b) spring,(c) summer,(d) fall. The time is 1 month after the relevantequinoxor solstice.
They are small in the sensethat, for tracer studies,the flux divergencetermsresultingfrom eddy diffusionare much less than thoseresultingfrom advectioneverywherein the stratosphere,as requiredfor a test of the ability of the diabatic
perhapsa factor of 5 is sufficientto reducethe mid-latitude gradientsand remove the anvils on the contours.This, how-
ever, increasesthe mixing ratios in the middle and upper stratosphere to valuesimplyinga substantiallylesssteepde-
circulation to simulate tracer distributions.
creasewith height than seen in the data. It also violates the
In the real atmosphere the locationand intensityof mixing motionswill clearly vary with time, and the use of spatially and temporallyinvarianteddycoefficients in the modelstratosphereis not intendedto be a good modelof actualphysical
diabaticcirculationapproximationin the lower stratosphere by making the diffusivetermsas large as the advectiveterms.
If this is indeedthe case,a detailedtreatmentof the eddy mixing consistentwith the residual mean circulation is remixing processes. It is rather a fairly severetest of the conten- quired. tion that such variations may be neglectedin the diabatic Another characteristicfeature of the contour plots is the approximation.Experimentsbasedon increasingthe value of transition from the bubble to more nearly flat contours.In K•z throughout the stratosphereindicate that an increaseof thisregion(above5 mbarespecially) theinfluence of thedirect
GUTHRIE ET AL.' DIABATIC CIRCULATION MODEL WITH PHOTOCHEMISTRY
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