Abstract
An efficient and stable computational scheme for parameterization of atmospheric chemistry is described. The 24‐hour‐average concentration of OH is represented as a set of high‐order polynomials in variables such as temperature, densities of H2O, CO, O3, and NOt (defined as NO + NO2 + NO3 + 2N2O5 + HNO2 + HNO4) as well as variables determining solar irradiance: cloud cover, density of the overhead ozone column, surface albedo, latitude, and solar declination. This parameterization of OH chemistry was used in the three‐dimensional study of global distribution of CH3CCl3 (Spivakovsky et al., this issue). The proposed computational scheme can be used for parameterization of rates of chemical production and loss or of any other output of a full chemical model. Coefficients for the polynomials are computed to provide the least squares fit to results of the full chemical model. Highly overdetermined systems are used with the sets of independent variables selected randomly in accordance with the distributions expected in the atmosphere. The least squares problem is solved using the Householder method of triangularization (by orthogonal transformations). The method allows detection and rectification of ill‐defined conditions (i.e., linear dependence among terms), as well as evaluation of the individual contribution of each term of the polynomial in reducing the residual vector. On the basis of that information the terms that have little bearing on the residual norm are discarded. Once the domain and the statistical distributions of independent variables are chosen, the entire parameterization procedure is implemented as a complete sequence of computer programs requiring no subjective analysis. The output of the procedure includes estimates of accuracy of the approximation against an independent sample of points, and computer written FORTRAN subroutines to compute the polynomials.
Highlights
Directcalculationof theseratesrequiressolutionof a nonlinear in -dimensionaslpacemayleadto astronomicanlumbersof systemof kinetic equationsrelatingthe unknownratesto tracer grid cells and thusto impracticacl ost in computertime and concentrations
Theprocedurereliesheavilyonalgorithmsdescribedby Lawhvolvesreplacingthe nonlinearsystemwith a set of explicit sonandHanson[1974]
Diagonael lementsmallerthana certainthreshold(andassociated Selectionof appropriatermsforthepolynomiaisl anessential termsof the polynomial)canbe discardede, liminatingill condi- partof theparameterizariopnrocedureT. he goalis to composea tions. Inherent to this method is an immediate evaluation of the set that results in a well-conditioned matrix A and contains those role thateachcolumnof matrix A
Summary
The24-hour-averagceoncentratioonf OH is representeadsa setof high-ordeprolynomialisn variablesuchas temperaturdee, nsitieosf H20, CO,, andNOt (definedasNO + NO2+ NO3+ 2N20$+ HNO2+ }INO4)as well asvariablesdetermininsgolarirradiancec:loudcover,densityof theoverheadozonecolumns, urfacealbedo,latitudea, ndsolardeclination.'hisparameterizationf OH chemistrywasusedin thethree-dimensional studyof globaldistributioonf CH3CCI3(Spivakovskeyt al.,thisissue).Theproposecdomputationsacl heme canbeusedforparameterizationf ratesof chemicaplroductioanndlossorof anyotheroutputof a full chemicalmodel.Coefficientfsor thepolynomialasrecomputedto providetheleastsquarefsit to resultsof thefull chemicalmodel. Overdeterminesdystemsareusedwith the setsof independenvtariablesselectedrandomlyin accordancweiththedistributionesxpectedin theatmosphereT.heleastsquarepsroblemis solvedusingtheHouseholdemr ethodof triangularizatio(nbyorthogonatlransformationsT).hemethodallowsdetection andrectificationof ill-definedconditions(i.e.,lineardependencaemongterms),aswell asevaluationof theindividualcontributioonf eachtermof thepolynomiailn reducingtheresiduavl ector.Onthebasisof thatinformationthetermsthathavelitfiebearingontheresiduanl ormarediscardedO. Ncethedomainandthestatistical distributionsof independenvtariablesare chosent,he entireparameterizafiopnrocedureis implementedas a completesequencoef computepr rogramsrequitingno subjectiveanalysis.The outputof the procedureineludesestimatesof accuracyof theapproximatioangainstanindependenstampleof points,andcomputewr rittenFORTRAN subroutinetos computethepolynomials Overdeterminesdystemsareusedwith the setsof independenvtariablesselectedrandomlyin accordancweiththedistributionesxpectedin theatmosphereT.heleastsquarepsroblemis solvedusingtheHouseholdemr ethodof triangularizatio(nbyorthogonatlransformationsT).hemethodallowsdetection andrectificationof ill-definedconditions(i.e.,lineardependencaemongterms),aswell asevaluationof theindividualcontributioonf eachtermof thepolynomiailn reducingtheresiduavl ector.Onthebasisof thatinformationthetermsthathavelitfiebearingontheresiduanl ormarediscardedO. ncethedomainandthestatistical distributionsof independenvtariablesare chosent,he entireparameterizafiopnrocedureis implementedas a completesequencoef computepr rogramsrequitingno subjectiveanalysis.The outputof the procedureineludesestimatesof accuracyof theapproximatioangainstanindependenstampleof points,andcomputewr rittenFORTRAN subroutinetos computethepolynomials
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