Optical Properties of Aerosols and Clouds: The Software Package OPAC

Transcription

1 Optcal Propertes of Aerosols and Clouds: The Software Package OPAC M. Hess,* P. Koepke,* and I. Schult + ABSTRACT The software package OPAC (Optcal Propertes of Aerosols and Clouds) s descrbed. It easly provdes optcal propertes n the solar and terrestral spectral range of atmospherc partculate matter. Mcrophyscal and optcal propertes of sx water clouds, three ce clouds, and 10 aerosol components, whch are consdered as typcal cases, are stored as ASCII fles. The optcal propertes are the extncton, scatterng, and absorpton coeffcents, the sngle scatterng albedo, the asymmetry parameter, and the phase functon. They are calculated on the bass of the mcrophyscal data (sze dstrbuton and spectral refractve ndex) under the assumpton of sphercal partcles n case of aerosols and cloud droplets and assumng hexagonal columns n case of crrus clouds. Data are gven for up to 61 wavelengths between 0.25 and 40 µm and up to eght values of the relatve humdty. The software package also allows calculaton of derved optcal propertes lke mass extncton coeffcents and Ångström coeffcents. Real aerosol n the atmosphere always s a mxture of dfferent components. Thus, n OPAC t s made possble to get optcal propertes of any mxtures of the basc components and to calculate optcal depths on the base of exponental aerosol heght profles. Typcal mxtures of aerosol components as well as typcal heght profles are proposed as default values, but mxtures and profles for the descrpton of ndvdual cases may also be acheved smply. 1. Introducton *Meteorologsches Insttut der Unverstät München, München, Germany. + Max-Planck-Insttut für Meteorologe, Hamburg, Germany. Correspondng author address: Dr. P. Koepke, Meteorologsches Insttut der Unverstät München, Theresenstr. 37, D München, Germany. In fnal form 29 January Amercan Meteorologcal Socety Bulletn of the Amercan Meteorologcal Socety Optcal propertes of partculate atmospherc consttuents, that s, water and ce clouds and aerosol partcles, affect local radatve forcng, the radaton balance of the earth, and thus clmate. Moreover, these propertes are essental for remote sensng, both of the consttuents themselves and wth respect to the maskng effect aganst other quanttes. The effects of aerosol partcles domnate n the solar spectral range but are not neglgble at other wavelengths and the effects of clouds are smlar both n the solar and n the terrestral spectral range. To make such optcal propertes avalable and easy to handle, the software package OPAC (Optcal Propertes of Aerosols and Clouds) was put together, whch on the one hand provdes the optcal propertes of water droplets, ce crystals, and aerosol partcles, both n the solar and terrestral spectral range, and on the other hand ncludes software to handle the data. The propertes of clouds and aerosol partcles are hghly varable, both n tme and space. Ths s vald for the number densty, that s, the amount of partcles per volume, for the mcrophyscal propertes lke sze dstrbuton, refractve ndex and shape, and for the heght dstrbuton. Moreover, n most cases the actual propertes are not known. For ths reason, t s mpossble to model aerosols and clouds n detal. It s necessary to reduce the varablty of naturally occurrng aerosols and clouds to typcal cases, but wthout neglectng possble fluctuatons. In OPAC, ths goal s acheved by the use of a dataset of typcal clouds and nternally mxed aerosol components. The aerosol components can be externally mxed to a wde range of tropospherc aerosols. The propertes of the clouds and aerosol components are gven together wth a FORTRAN program, whch allows the calculaton of optcal parameters for any mxture of clouds and aerosols components. Ths gves the possblty to model clmaterelevant optcal propertes of atmospherc partculate consttuents for ndvdual cases. The optcal proper- 831

2 tes of cloud droplets and aerosol partcles are modeled under the assumpton of sphercty, those of ce crystals under the assumpton of hexagonal columns. Ths concept of separaton of components of mcrophyscal and optcal propertes easly enables future extensons and mprovements. It s possble to add new cloud or aerosol components or to replace exstng data wth mproved data wth changed mcrophyscal nput data or to use propertes of nonsphercal partcles, wthout affectng the remanng parts of OPAC. Secton 2 descrbes the structure of the software package OPAC, and secton 3 the mcrophyscal propertes of all aerosol components and clouds n OPAC. Secton 4 shows whch optcal propertes can be extracted from the dataset or calculated wthn OPAC, and n secton 5 proposed mxtures of aerosol components are presented. Wth respect to global dstrbuton, mxtures of aerosol are presented n the Global Aerosol Data Set (GADS; Koepke et al. 1997). Ths uses the same aerosol components as OPAC but s compled to gve a bass for calculatng global aerosol radatve forcng. 2. The software package OPAC conssts of two parts. The frst part s a dataset of mcrophyscal propertes and the resultng optcal propertes of cloud and aerosol components at dfferent wavelengths and for dfferent humdty condtons. The other part s a FORTRAN program that allows the user to extract data from ths dataset, to calculate addtonal optcal propertes, and to calculate optcal propertes of mxtures of the stored clouds and aerosol components. The dataset gves the mcrophyscal and optcal propertes for sx types of water clouds, three ce clouds, and 10 aerosol components. Data are avalable at 61 wavelengths between 0.25 and 40 µm for aerosols and water clouds, and at 67 wavelengths between 0.28 and 40 µm for ce clouds. The data are gven n each case for 1 partcle cm 3, whch descrbes the effectve propertes of the mxture of all partcles n the sze dstrbuton. For practcal use, the values must be multpled by the total number densty. In the case of those aerosol components that are able to take up water, data for eght values of relatve humdty (0%, 50%, 70%, 80%, 90%, 95%, 98%, 99%) are gven. The data are stored as ASCII fles, one fle for each cloud or aerosol component and each relatve humdty. The total amount of stored data s about 3.2 MB. The computer code serves two purposes. Frst, sngle cloud or aerosol components can be selected, and all or some of ther optcal propertes can be extracted or calculated from the dataset. Second, t s possble to select one of those mxtures of aerosol components, whch are proposed as default values n OPAC (cf. secton 5), or to defne an addtonal mxture and to calculate ts optcal propertes. Heght dstrbuton of aerosol partcles s gven but may also be changed wth data gven by the user. For the sake of portablty, the program s dstrbuted as FORTRAN source code. All necessary nput to the program must be entered as an ASCII text fle. The detals are explaned n an example of such a fle that s dstrbuted wth OPAC. A further fle contans a complete lst of fles belongng to the software package and a descrpton on how to nstall and use OPAC. To run the program, detals to fve topcs must be gven n the nput fle. The frst topc deals wth the desred mxture of cloud or aerosol components. Here, t s possble to select one of the default clouds or aerosol types (cf. secton 5a) or to defne a new mxture of the gven components. The second topc deals wth the heght profle (cf. secton 5b). For the default mxtures the default profles may as well be used as new userdefned profles. For new mxtures, however, new profles have to be ntroduced. The thrd topc s the selecton of the wavelengths for whch optcal parameters shall be calculated from those stored n the database. The fourth topc concerns the selecton of the classes of relatve humdty for whch the calculatons shall be performed. Fnally, the desred optcal parameters (cf. secton 4) have to be selected. The resultng optcal propertes of the cloud or aerosol type are wrtten to an ASCII output fle. 3. Dataset of the mcrophyscal propertes of aerosols and clouds The radatve propertes n OPAC are modeled on the bass of components of aerosols and clouds, from whch weghted sums of these data are used to descrbe radatve propertes of the total amount of aerosol partcles, water droplets, and ce crystals n the atmosphere. Each component s descrbed by an ndvdual partcle sze dstrbuton and spectral refractve ndex. Its radatve propertes are modeled wth Me theory n the case of cloud droplets and aerosol partcles and wth geometrc optcs n the case of ce crystals, whch are assumed to be hexagonal columns for calculatons 832 Vol. 79, No. 5, May 1998

3 n the solar spectral range (Hess and Wegner 1994). In the terrestral spectral range, ce crystals are also consdered to be spheres because the geometrc optcs assumpton s only vald for partcles, whch are consderably larger than the wavelength of the ncdent radaton. The components are descrbed n the followng sectons. Default values of aerosol mxtures are gven n secton 5. a. Water clouds Water clouds are descrbed by the modfed Gamma dstrbuton after Dermendjan (1969): dn dr wth α α r = Nar exp r γ mod B = α r γ γ γ mod Nar =, α γ exp( Br ) (3a) where N s the total number densty n partcles per cubc centmeter and r mod the mode radus n mcrometers. The constants α and γ descrbe the slope of the sze dstrbuton, whle a s a normalzaton constant ensurng that the ntegral of the sze dstrbuton over all rad yelds N. From ths sze dstrbuton, as from any sze dstrbuton, an effectve radus r eff may be derved, whch often s used n cloud research: r eff = 3 r dn dr dr r dn. (3b) 2 dr dr The parameters of the sze dstrbutons together wth r eff wth partcle number densty N and the lqud water content L belongng to ths number densty are lsted n Table 1a. For all models used, droplets outsde the sze range between 0.02 and 50 µm would not sgnfcantly contrbute to ether the optcal propertes or the lqud water content of the clouds, and thus they are not taken nto account. The total partcle number densty gven n Table 1a s a typcal value, whch s used as a seperate fgure to make t possble to vary the lqud water content wthout changng the droplet sze dstrbuton. The parameters of the normalzed sze dstrbutons are selected out of those that Tamper and Tomas (1976) ftted to publshed measurements wth respect to r mod and the relatve course of the sze spectrum. From ths collecton, dstrbutons have been selected that ft publshed measurements wth respect to the lqud water content L for typcal values of the number densty N. Fve water-cloud models and one fog model are consdered n OPAC. They are as well chosen to be representatve for average condtons as to reflect TABLE 1a. Mcrophyscal propertes of the water-cloud and fog models. For explanaton see secton 3a. Component Fle r mod α γ a B r eff N L name (µm) (µm) (cm 3 ) (g m 3 ) Stratus STCO E (contnental) Stratus STMA E (martme) Cumulus CUCC E (cont., clean) Cumulus CUCP E (cont., polluted) Cumulus CUMA E (martme) Fog FOGR E Bulletn of the Amercan Meteorologcal Socety 833

4 cloud-formaton processes (Pruppacher and Klett 1978): the sze dstrbuton of stratus clouds s usually broader than that of cumul but they contan fewer drops per volume than cumulus clouds. Clouds over the oceans tend to have broader dstrbutons than clouds over the contnents, and polluted clouds contan more but smaller drops than clean ones. The followng clouds have been chosen. Stratus (contnental) s descrbed accordng to measurements publshed by Dem (1948) and Hoffmann and Roth (1989). A sze dstrbuton ftted to measurements at the base of a stratus cloud has been selected from Tamper and Tomas (1976). Stratus (martme) contans fewer but larger drops than the contnental stratus, and ts sze dstrbuton s broader. A sze dstrbuton ftted to measurements at the top of a stratus cloud after Tamper and Tomas (1976) has been selected because ths dstrbuton showed the best ft wth regard to N, r mod, and L, measured by Squres (1958), Stephens et al. (1978), Tsay and Jayaweera (1984), and Kng et al. (1993), and the approprate dstncton to the contnental stratus and the cumulus clouds descrbed below. Cumulus (contnental, clean) s descrbed by the dstrbuton parameters for the cumulus model 4 n Tamper and Tomas (1976). They satsfactorly ft measurements publshed by Squres (1958), Leatch et al. (1992), and Ftzgerald and Spyers-Duran (1973). The dstrbuton s smaller than that of the stratus clouds and t contans more drops. Cumulus (contnental, polluted) s descrbed by the dstrbuton parameters for the cumulus model 3 n Tamper and Tomas (1976). It contans more and smaller droplets than a clean cumulus cloud. The values for N, r mod, and L are wthn the range reported from Dem (1948) and Ftzgerald and Spyers-Duran (1973). Ths should be consdered as an example of a cloud developed n a strongly polluted atmosphere. The same sze dstrbuton, but wth a number densty N = 400 partcles cm 3, s also suted to represent a stratocumulus cloud. In ths case the lqud water content s L = g m 3. Cumulus (martme) contans less and larger drops than the contnental cumulus clouds and the sze dstrbuton s broader. As sze dstrbuton parameters, those of the cumulus model 11 n Tamper and Tomas (1976) have been selected. The selected fog sze dstrbuton s radaton fog 3 of Tamper and Tomas (1976) wth a number densty of 15 partcles cm 3, yeldng a lqud water content of Ths s a very broad dstrbuton wth large droplets, thus representng a mature fog wth moderately low vsblty. In all cases, the refractve ndex of pure water after Hale and Querry (1973) s used for the calculatons of optcal propertes. The addtonal absorpton n cloud droplets, whch s caused by the cloud condensaton nucle, should not be neglected, but approprate refractve ndex data are not avalable yet. b. Crrus clouds The sze dstrbuton functons used are analytcal functons after Heymsfeld and Platt (1984), calculated wth help of the parametrzaton after Lou (1992), whch relates the parameters a 1,2, b 1,2, and I to the temperature n the cloud: dn dx dn dx b 1 Nfa x I for x< x 0 = 1 2 Nfa x I for x> x 0, = 2 b (3c) wth x the maxmum dmenson of the ce crystals, that s, the length of the columnar crystals used for calculatng the optcal propertes; N the number densty; and I the ce water content. Here f s an addtonal factor that had to be ntroduced because ntegraton of the sze dstrbutons does not yeld n all cases the expermentally derved ce water content I, f sngle hexagonal columns are assumed as partcle shape (Strauss et al. 1997). The sze dstrbutons are mxtures of eght columnar ce crystals of dfferent sze and correspondngly dfferent aspect rato that are randomly orentated n space (Hess and Wegner 1994). Propertes of three crrus clouds are provded, vald for clouds at dfferent temperatures. Crrus 1 s vald for a temperature of 25 C. The slope of ths sze dstrbuton shows a consderably slower decrease toward large partcles than that of the model crrus 2. Crrus 2 s vald for 50 C. In ths case, the value of f = 3.48 suggests the presence of rosette-lke crystals, whch consst of several arms of columnar crystals. Snce such partcles are more lkely to have larger szes, f s only appled to partcles larger than 90 µm. The models crrus 1 and crrus 2 may be regarded 834 Vol. 79, No. 5, May 1998

5 TABLE 1b. Mcrophyscal propertes of ce cloud models. For explanaton of the sze dstrbuton parameters see Secton 3b. crrus 3 s the same dstrbuton as crrus 2 between 20 and 2000 µm. Addtonally, there are partcles m 3 between 2 and 6 µm and partcles m 3 between 6 and 20 µm. Component Fle a 1 b 1 a 2 b 2 x 0 f r eff N I name (µm) (cm 3 ) (g m 3 ) Crrus 1: 25 C CIR E E Crrus 2: 50 C CIR E Crrus 3: 50 C CIR E (+ small partcles) as lmtng cases for what can be expected n the presence of crrus clouds wth respect to the relatve amount of large partcles. These sze dstrbutons are only vald for ce crystals larger than 20 µm. Smaller partcles are neglected. Ths wll not lead to large errors, as long as the cloud s optcal depth s prescrbed and only phasefunctons n the vsble spectral range are consdered. If the optcal depth, however, shall be calculated from the partcle number densty and the cloud boundares, the small partcles may not be neglected. In ths case, crrus 3 should be appled, whch s the same as crrus 2 but extended wth partcles n the sze range 2 20 µm based on arcraft measurements wth help of an ce crystal replcator. Ths sze dstrbuton s taken after Strauss et al. (1997). The parameters of the dstrbutons together wth total partcle number densty N and ce water content I are lsted n Table 1b. The szes of the smallest and the largest ce crystal used correspond to surface equvalent spheres wth rad of 1.8 and 271 µm, respectvely. Snce the sze dstrbutons do not decrease to larger rad as fast as the gamma dstrbutons used for water clouds, even the larger ce crystals contrbute sgnfcantly to the optcal propertes and the ce water content of the cloud. c. Aerosol components Aerosol partcles result from dfferent sources and processes. At any place n the atmosphere there exsts a mxture of partcles of dfferent orgn. To descrbe the wde range of possble compostons, the aerosol partcles are modeled as components (Deepak and Gerber 1983), each of them meant to be representatve for a certan orgn, that s, an nternal mxture of all chemcal substances that have a smlar orgn. These components may be externally mxed to form aerosol types. External mxture means that there s no physcal or chemcal nteracton between partcles of dfferent components. Useful examples of aerosol types, as typcal external mxtures of the components, are descrbed n secton 5. As sze dstrbutons, lognormal dstrbutons [cf., e.g., Deepak and Gerber (1983)] are appled for each component : dn r N r r () 1 log log = exp dr 2π r log ln10 2 log mod N, 2, (3d) where r modn, s the mode radus, measures the wdth of the dstrbuton, and N s the total partcle number densty of the component n partcles per cubc centmeter. The mcrophyscal propertes of aerosol components are lsted n Table 1c. The upper and lower lmts of the partcle szes taken nto account for Me calculatons are r mn and r max. Here ρ s the densty of the partcles n grams per cubc centmeter. The mass concentraton M* n mcrograms per cubc meter s vald for N = 1 partcle cm 3 and s calculated wth a cutoff radus of 7.5 µm to gve results, whch descrbe usual mpactor measurements. The term r modv s the mode radus of the volume dstrbuton, whch can be calculated from Eq. (3d) usng V nstead of N and r modv, nstead of r modn,. The mode radus s calculated from r modn, wth r modv = r ( ( ) ). (3e) log ln mod N The followng paragraphs descrbe the aerosol components. They are based on older descrptons (e.g., Bulletn of the Amercan Meteorologcal Socety 835

6 TABLE 1c. Mcrophyscal propertes of aerosol components n dry state. Here,, r modn, r modv, r mn, and r max are parameters of the lognormal sze dstrbutons (see secton 3c). The term ρ s the densty of the aerosol partcles and M* s the aerosol mass per cubc meter ar, ntegrated over the sze dstrbuton and normalzed to 1 partcle per cubc centmeter of ar. The term M* [(µg m 3 ) (partcles cm 3 ) 1 ] s calculated wth a cutoff radus of 7.5 µm. M* Fle r modn r modv r mn r max ρ (µg m 3 )/ Component name (µm) (µm) (µm) (µm) (g cm 3 ) (part. cm 3 ) Insoluble INSO E1 Water-soluble WASO E 3 Soot SOOT E 5 Sea salt (acc. mode) SSAM E 1 Sea salt (coa. mode) SSCM E2 Mneral (nuc. mode) MINM E 2 Mneral (acc. mode) MIAM E0 Mneral (coa. mode) MICM E2 Mneral-transported MITR E1 Sulfate droplets SUSO E 2 Shettle and Fenn 1979; Deepak and Gerber 1983; d Almeda et al. 1991) wth slght modfcatons that can be found n GADS (Koepke et al. 1997), where the same aerosol components are used as n OPAC. It must be mentoned that the gven aerosol components are adapted to average condtons, and therefore ther sze dstrbutons and refractve ndces are not necessarly vald for actual condtons. The water-nsoluble part of aerosol partcles conssts mostly of sol partcles wth a certan amount of organc materal. The water-soluble part of aerosol partcles orgnates from gas to partcle converson and conssts of varous knds of sulfates, ntrates, and other, also organc, water-soluble substances. Thus t contans more than only the sulfate aerosol that s often used to descrbe anthropogenc aerosol. The mass densty of sulfate s only about half that of the water-soluble component. Ths component s also used to model the dmethyl sulfde related aerosol produced over the oceans. The soot component s used to represent absorbng black carbon. Carbon s not soluble n water and therefore the partcles are assumed not to grow wth ncreasng relatve humdty. The densty of soot s gven as 1 g cm 3 because the soot partcles sampled on flters and used to determne aerosol weght per volume of ar are fluffy partcles wth space nsde. The optcal propertes, however, neglect the chanlke character of these partcles and are calculated assumng the sze dstrbuton wth many very small partcles (whch would have the densty 2.3 g cm 3 ). Moreover, no coagulaton of soluble aerosol and soot s assumed. Sea-salt partcles consst of the varous knds of salt contaned n seawater. Two sea-salt modes are gven to allow for a dfferent wnd-speed-dependent ncrease of partcle number for partcles of dfferent sze (Koepke et al. 1997). Mneral aerosol or desert dust s produced n ard regons. It conssts of a mxture of quartz and clay mnerals and s modeled wth three modes to allow to consder ncreasng relatve amount of large partcles for ncreasng turbdty. Mneral transported s used to descrbe desert dust that s transported over long dstances wth a reduced amount of large partcles. Mneral aerosol partcles are assumed not to enlarge wth ncreasng relatve humdty. The sulfate component (75% H 2 SO 4 ) s used to descrbe the amount of sulfate found n the Antarctc aerosol. It s also used as the stratospherc background 836 Vol. 79, No. 5, May 1998

7 aerosol, whch s consdered only for calculatng the aerosol optcal depth (cf. secton 5b). It s not suted to descrbe anthropogenc sulfate aerosols that are ncluded n the water-soluble component. For those aerosols that are able to take up water, the mode radus as well as the lmtng rad are ncreased wth ncreasng relatve humdty, whle s assumed to reman unchanged. Eght values of relatve humdty have been appled for the calculatons: 0%, 50%, 70%, 80%, 90%, 95%, 98%, and 99%. The rad for the eght relatve humdtes are calculated wth a program after Hänel and Zankl (1979). The assumpton of a sngle functon relatonshp between relatve humdty and sze of aerosol partcles, wthout consderng the hysteress effect (whereby dryng partcles at the same relatve humdty may have dfferent szes than mostenng partcles), s made wth respect to natural condtons. Partcles have n most cases passed through condtons wth hgh relatve humdty and therefore act on the upper branch of the hysteress curve. The refractve ndex of humd aerosols changes as the dry partculate matter s mxed wth water. Ths change has been calculated by a smple volume weghtng formula after Shettle and Fenn (1979) usng the mode rad of the dry and wet partcles for calculatng an average partcle volume. Water refractve ndces, after Hale and Querry (1973), are used. The refractve ndces of the aerosol components domnantly are from d Almeda et al. (1991), whch partly refer to Shettle and Fenn (1979), n a few cases corrected wth respect to dfferent sources (Koepke et al. 1997). They are avalable n the OPAC fles of optcal propertes of aerosol and cloud components together wth the refractve ndces of water and ce, but are not gven here as a table. To avod repeated Me- or ray-tracng calculatons, optcal propertes of basc aerosol components and clouds are stored n OPAC n separate fles for each component and relatve humdty. These are the extncton coeffcent 1 e (km 1 ), the scatterng coeffcent 1 s (km 1 ), the absorpton coeffcent 1 a (km 1 ), the volume phase functon p 1 (Θ) (km 1 sr 1 ), the sngle scatterng albedo ϖ 0, and the asymmetry parameter g. Here, 1 e, 1 s, 1 a, and p1 are normalzed to a number densty of 1 partcle cm 3. To get the absolute values of e, s, a, and p(θ), the stored data have to be multpled by the total partcle number densty. The followng quanttes may easly be taken from OPAC, where they are calculated from the stored data by use of the equatons gven below. The normalzed extncton coeffcent e,n s normalzed to the value at the wavelength 0.55 µm, en, e = 055. µ m. (4a) e ( ) The ldar rato L(sr) s defned by L = e p ( 180 ). (4b) The aerosol optcal depth τ s calculated from the extncton coeffcent of the chosen aerosol type (cf. secton 5a) n combnaton wth the heght profle N (h) (cf. secton 5b), whch s predefned n OPAC or gven by the user for four dscrete layers: 4. Modeled optcal propertes OPAC allows the calculaton of the optcal propertes of aerosols and water clouds at 61 wavelengths between 0.25 and 40 µm and of crrus clouds at 67 wavelengths between 0.28 and 40 µm. The real and magnary parts of the refractve ndces are gven for these wavelengths. The optcal propertes are calculated wth Me theory (Quenzel and Müller 1978) for water droplets, aerosol partcles, and ce crystals n the terrestral spectral range and wth ray tracng for ce crystals n the solar spectral range (Hess and Wegner 1994). H 1 Zj τ = ej, ( hdh ) = ej, Nj( 0 ) e dh, j H j, max j, mn j H H j, max j, mn h (4c) where 1 s the extncton coeffcent of the aerosol e, or cloud n layer j, normalzed to 1 partcle cm 3. The parameters of the heght profle are explaned n secton 5b. The optcal depth of clouds s calculated assumng one homogeneous layer wth cloud droplet densty ndependent of heght (Z = ). Thus, the formula s reduced to Bulletn of the Amercan Meteorologcal Socety 837

8 τ = 1 e N(0) h, (4d) e (λ) = β λ α, (4j) where h s the geometrcal thckness of the cloud. The default value of h = 1 km may be changed by the user. In both cases, for aerosols and clouds, the optcal depth of ar molecules s not ncluded. The spectral turbdty factor T L s gven as T L = τ + τ τ M M, (4e) where τ M s the spectral optcal depth of the ar molecules, calculated wth a formula after Hansen and Travs (1974). The vsblty (km) s 3.0 vs = 055. µ m 055. µ m, (4f) e ( )+ ( ) wth the constant set to 3.0 to represent real observer vsblty (Gordon 1970). The term M s the extncton coeffcent due to ar molecules at 0.55 µm. In OPAC the value vald for p o = 1013 hpa (sea level) s used: M (0.55µm) = (km 1 ). M (4g) For other alttudes, descrbed by pressure p, t must be adapted by multplcaton wth p/p o. The mass extncton cross secton (specfc extncton coeffcent) e * (m 2 g 1 ) s the rato of extncton coeffcent e (km 1 ) to the aerosol mass M (µg m 3 ): =. (4h) e e M It should be mentoned agan that, for compatblty wth measurements, the extncton coeffcent s calculated for the arborne partcles, that s, for rad up to the value r max, whle the mass s determned under assumpton of an mpactor cutoff radus of 7.5 µm. The mass absorpton cross secton (specfc absorpton coeffcent) * α (m 2 g 1 ) s defned smlar to the extncton rato but usng a : =. (4) a a M The Ångström coeffcent α descrbes the relatve spectral course of the extncton coeffcent n where β s the extncton coeffcent at 1 µm. Ths formula s vald for all wavelengths only f the partcle sze dstrbuton fts a Junge power law functon. For lognormal sze dstrbutons as used n OPAC and for most of natural condtons, α s not constant, but ts value depends on the wavelength range that s used for ts determnaton. Thus, OPAC gves the possblty to calculate α and β for two pars of wavelengths, namely, µm and µm, whch cover the range often used n the descrpton of measured spectral aerosol extncton: [ ( )] ( ) ( ) ( ) [ ] log e λ2 log e λ1 α = log λ log λ 1 2 β = ( λ ). e 1 λ α 1, and (4k) Wth respect to practcal use, n addton to the spectral optcal propertes, spectrally weghted optcal propertes may be calculated. In case of the solar spectral range, the spectral optcal propertes are weghted wth the solar spectrum E o between 0.3 and 3.3 µm: ea,, sol = λ E λ dλ ea, o -1. km, (4l) 33 E λ dλ 03. ( ) ( ) o ( ) the sngle scatterng albedo s ω o = 33. ( ) ( ) ( ) ( ) ω λ λ E λ dλ o e o , (4m). λ E λ dλ 03. e ( ) ( ) and the asymmetry parameter g = g λ λe λdλ s o ( ) ( ) ( ) o. (4n) 33. ( λ) E ( λ) dλ 03. s o 838 Vol. 79, No. 5, May 1998

9 In case of the terrestral spectral range, the terrestral emsson at 300 K between 8 and 15 µm B 300 s used for the weghted absorpton coeffcent: a, ter = 15 ( ) ( ) a λ B300 λ dλ -1 ( km ). (4o) 15 B λ dλ ( ) As already mentoned, optcal propertes of cloud and aerosol components are stored n OPAC as separate ASCII fles, one for each component and relatve humdty. They easly can be accessed wth any textvewng program and thus are not shown here n detal as tables. Only as examples, radatve propertes at 0.5 µm for the cloud types are gven n Table 2 and a few examples of optcal propertes of typcal aerosol mxtures as proposed n the next chapter are shown n Table 3. Basc optcal propertes of the aerosol components are, however, publshed n Koepke et al. (1997). 5. Mxng of atmospherc partcles Optcal propertes of aerosol components are not of drect practcal use, snce aerosol partcles n the atmosphere always exst as mxtures of several components. In OPAC, they are handled n that way wth the possblty to combne them as much as you lke. Frst, the components can be mxed and thus the optcal propertes for an atmospherc layer can be calculated. Second, up to four atmospherc layers can be used for calculatng the aerosol optcal depth. a. Mxtures of dfferent components The capablty of OPAC to mx optcal propertes of components s most nterestng wth respect to aerosol because aerosol usually s a combnaton of partcles of dfferent orgn. Nevertheless, t s also possble to defne external mxtures of clouds and aerosols, thus modelng the effect of ntersttal aerosol partcles n clouds. OPAC allows handlng of mxtures of the gven components, freely defned by the user. Moreover, default values of 10 aerosol types are proposed to span the range of clmatologcally mportant aerosols. They are gven both to represent average condtons and also to consder extreme condtons for senstvty studes, and therefore users should be careful wth respect to use for actual stuatons. The aerosol types and the components that compose them are specfed n Table 4. Number denstes N (partcles cm 3 ) and mass denstes M (µg m 3 ) both belongng to the components and to the total aerosol type are gven, as well as the mxng ratos agan both for number (n ) and mass (m ). Mxng n OPAC s based, however, n any case on the partcle number denstes N, whch are ndependent of relatve humdty. They sum up to the number densty N = N = N n. (5a) The mass, however, depends on relatve humdty h: ( )= ( )= ( ) Mh M h NM h = N nm ( h)= NM ( h) m( h), (5b) where M* s the mass normalzed to one partcle that s, an average value, where the ntegral over the number sze dstrbuton s 1. The mass values gven n TABLE 2. Selected optcal propertes of all clouds at a wavelength of 0.55 µm. Cloud e (0.55 µm) Vs ω o (0.55 µm) g(0.55 µm) (km 1 ) (km) Stratus (contnental) Stratus (martme) Cumulus (cont.,clean) Cumulus (cont., polluted) Cumulus (martme) Fog Crrus Crrus Crrus Bulletn of the Amercan Meteorologcal Socety 839

10 TABLE 3. Selected optcal propertes of all tropospherc aerosol types at a relatve humdty of 80% and of the background aerosols. The optcal depths of boundary layer aerosols nclude the free troposphere and the stratosphere. Heght profles are gven n Table 5. e * e (0.55 µm) (0.55 µm) τ Vs ω o g α α Aerosol type (km 1 ) (m 2 g 1 ) (0.55 µm) (km) (0.55 µm) (0.55 µm) ( ) ( ) Contnental clean Contnental average Contnental polluted Urban Desert Martme clean Martme polluted Martme tropcal Arctc Antarctc Mneral transported (2 3.5 km) Free troposphere (2 12 km) Stratosphere (12 35 km) Table 4 as examples and dscussed later represent a relatve humdty of 50%. It must be emphaszed that the number mxng ratos gven to descrbe aerosol types may be used only n combnaton wth the sze dstrbutons gven for the components. Mass mxng ratos of the components, whch usually are expected to descrbe the fractons of the components, result from the combnaton of a gven of number mxng ratos and sze dstrbutons of the components, together wth the physcal densty ρ used for the partcles. As to be seen n Table 4, the very low values n number mxng rato of the nsoluble component must not be neglected, and the rather hgh number mxng rato of soot s realstc wth respect to the sze dstrbutons used. The extncton coeffcent s calculated by 1 =, N. e e (5c) The other optcal parameters are calculated accordng to the same prncple. In the followng paragraphs, short descrptons of the aerosol types proposed n OPAC are gven. Contnental aerosol types are dstngushed between desert and nondesert types, and the nondesert types agan are separated wth respect to the amount of soot. Contnental clean aerosol represents remote contnental areas wthout or wth very low anthropogenc nfluences and consequently less than 0.1 µg m -3 soot. The composton that s gven n Table 4 contans no soot at all and thus s a lower benchmark wth respect to absorpton n the solar spectral range. Contnental average aerosol s used to descrbe anthropogencally nfluenced contnental areas. Therefore t contans soot and an ncreased amount of the nsoluble and water-soluble components. 840 Vol. 79, No. 5, May 1998

11 Contnental polluted aerosol s for areas hghly polluted by man-made actvtes. The mass densty of soot s 2 µg m 3, and the mass densty of water-soluble substances s more than double that n contnental average aerosol. Urban aerosol represents strong polluton n urban areas. The mass densty of soot s 7.8 µg m 3, and the mass denstes of both watersoluble substance and nsoluble substance are about twce those of the contnental polluted aerosol as found n center areas of large ctes. Desert aerosol s used to descrbe aerosol over all deserts of the world, and no dstncton wth respect to the local propertes s made. It conssts of the mneral aerosol components n a combnaton that s representatve for average turbdty, together wth a certan part of the water-soluble component. Martme aerosol types contan sea salt partcles whose amount depends on the wnd speed. Here, an amount of 20 partcles m 3 sea salt s assumed. Ths corresponds to a wnd speed of 8.9 m s 1 as a result of an emprcal relaton (Koepke et al. 1997), whch was developed usng data of number and mass concentratons and also fts sze dstrbuton measurements. Martme clean s gven to represent undsturbed remote martme condtons wth no soot, but wth a certan amount of water-soluble aerosol, whch s used to represent the non sea salt sulfate. TABLE 4. Composton of aerosol types. Mass values are gven for a relatve humdty of 50% and for a cutoff radus of 7.5 µm. Number Mass N M mxng mxng Aerosol types Components (cm 3 ) (µg m 3 ) ratos (n j ) ratos (m j ) Contnental total clean water soluble nsoluble E Contnental total average water soluble nsoluble E soot Contnental total polluted water soluble nsoluble E soot Urban total water soluble nsoluble e soot Desert total water soluble mneral (nuc.) mneral (acc.) E mneral (coa.) Martme total clean water soluble sea salt (acc.) E sea salt (coa.) 3.2E E Martme total polluted water soluble sea salt (acc.) E sea salt (coa.) 3.2E E soot Martme total tropcal water soluble sea salt (acc.) E sea salt (coa.) 1.3E E Arctc total water soluble nsoluble E sea salt (acc.) E soot Antarctc total sulfate sea salt (acc.) 0.47E e mneral (tra.) 0.53E E Bulletn of the Amercan Meteorologcal Socety 841

12 Martme polluted refers to a martme envronment under anthropogenc nfluence wth hghly varable amounts of soot and also of anthropogenc watersoluble partcles. Here 0.3 and 7.6 µg m 3 are assumed, respectvely. The sea salt components are kept unchanged compared to clean martme. Martme tropcal aerosol has a low densty of water-soluble substance. We also assume a lower wnd speed (5 m s 1 ) and hence a correspondngly lower number densty of sea salt. Arctc aerosol can be found n the whole Arctc regon north of 70 N. The type modeled here descrbes condtons wth a large amount of soot partcles transported from the mdlattude contnental areas to the Arctc. Snce these condtons are vald manly durng sprngtme, one should be careful wth the applcaton of ths aerosol type for other seasons. Antarctc aerosol can be found over the Antarctc contnent. It conssts mostly of sulfate droplets but also of mneral and sea salt partcles. The composton provded here s vald for summer condtons. All aerosol types defned here may have addtonal components wth varyng number denstes accordng to the actual locaton for whch they are assumed to be vald. In coastal areas, for example, they all may have an addtonal sea salt component. Near deserts, urban aerosol may be nfluenced by mneral aerosols. As long as one s nterested only n average condtons at a certan place or on aerosol varablty, the predefned aerosol types wll be suffcent. In other cases the user hmself should defne approprate mxtures of aerosol types. The aerosol types descrbed above are vald for the mxng layer that s, the frst atmospherc layer above the ground that s assumed to be well mxed. Above ths layer up to three addtonal layers of background aerosols may be placed for calculatons of the optcal depth. A possble second aerosol layer above the boundary layer aerosol types s mneral transported. Ths s present f mneral aerosol s lfted by convecton to heghts where t can be transported over long dstances, for nstance, from the Sahara over the Atlantc or from the Gob to Chna. In the Saharan dust layer over the Atlantc, the partcle number densty of mneral aerosol vares from about 100 partcles cm 3 near the Afrcan coast to less than 1 partcle cm 3 near the Amercan coast. For the aerosol type mneral transported, the component mneral transported s used wth 175 µg m 3 correspondng to 11 partcles cm 3. To allow calculaton of total optcal depth, data are ncluded to descrbe aerosol extncton n the free troposphere and the stratosphere. The aerosol n the free troposphere s modeled by the contnental components at a relatve humdty of 50%, wth a domnant part of the water-soluble component (n = 0.6 and m = 0.949), a certan part of soot (n = 0.4 and m = ), and some nsoluble partcles (n = and m = 0.032), whch can be assumed for the Northern Hemsphere. A hypothetcal number densty of 730 partcles cm 3 at sea level s assumed, allowng the use of (5d) for the descrpton of heght dstrbutons, resultng, for example, n a number densty of 390 partcles cm 3 (M = 0.49 µg m 3 ) at a heght of 5 km. The aerosol n the stratosphere s gven only for background condtons wth 3 partcles cm 3, whch yelds an optcal depth of about The treatment of stratospherc aerosol s not comprehensve, but only used to nfer spectral optcal depths. As mentoned, the goal of OPAC s an easy provson of optcal propertes between 0.3 and 40 µm wavelengths for as many combnatons of the components as you lke. Thus, only an example can be gven here. In Table 3, the most relevant optcal propertes at 550 nm are shown for all aerosol types proposed above. They are vald for a relatve humdty of 80% n the case of the boundary aerosols and of 50% for the free troposphere. The optcal depth of the boundary layer aerosols s calculated wth the heght profles descrbed below that s, ncludng the free troposphere and the stratospherc layer but wthout mneral transported aerosol. The optcal depth of the background layers s gven separately n Table 3 usng the ndcated layer boundares and the scale heghts gven n Table 5. b. Vertcal dstrbuton To provde optcal depths of aerosols or of cloud layers n OPAC [cf. Eqs. (4c) and (4d)], heght profles of the partcle number densty are gven. For all clouds, a unform heght dstrbuton wthn the cloud s assumed and a thckness of 1 km s gven as a default value, whch may be changed by the user. The dstrbuton of aerosol partcles wth heght s descrbed by means of exponental profles gven by h ( )= ( ) Z Nh N0 e, (5d) wth h the alttude above ground n klometers and Z 842 Vol. 79, No. 5, May 1998

13 TABLE 5. Heght profles of all aerosol types. H Z H ft Aerosol type (km) (km) (km) Contnental clean Contnental average Contnental polluted Urban Desert Martme clean Martme polluted Martme tropcal Arctc Antarctc Mneral transported (2 3.5 km) Free troposphere 8 (H ft varable) Stratosphere (12 35 km) the scale heght n klometers, whch descrbes the slope of the profle. Wth Z = 8 km, the value vald for ar molecules, a constant mxng of ar and aerosol s descrbed. Here Z = 99 km represents a homogeneous layer wthout dependence on heght; N(0) s the number densty of the aerosol type at sea level (N n Table 4). The atmosphere s comprsed of up to four dscrete layers. For each layer j the thckness H = (H j,max H j,mn ) of the aerosol layer and the scale heght Z are shown n Table 5. The layer boundares H j,mn and H j,max of all layers may be changed by the user. In the frst layer, aerosol s assumed wth the mxtures descrbed n secton 5a. The scale heght Z for the proposed aerosol types s gven n Table 5, but t may also be changed by the user. On top of ths frst layer a desert dust layer may be placed, consstng of the type of mneral transported. The default value for the thckness of ths layer s 0. Here (H 2,mn = H 2,max ), that s, no dust s assumed, but t may be changed by the user. A layer thckness of 1.5 km and a partcle number densty of 11 partcles cm 3 (default) yeld an addtonal optcal thckness of 0.1. The term N may be changed by the user and s assumed to be ndependent of heght (Z = 99 km). The thrd and fourth layers represent the free troposphere and the stratosphere. The aerosol n the free troposphere s assumed for the regon above the aerosol near ground or above the layer wth mneral-transported aerosol f present. For the proposed aerosol types, the upper boundary of ths layer s always stuated at 12 km. Therefore, ts thckness depends on the thckness of the frst layer and the presence of the mneral-transported layer. The resultng values are gven as H ft n Table 5. The composton of the background aerosol types [.e., e,j 1 and N j (0) n Eq. (4c)] cannot be changed by the user, but the background optcal depth can be vared by changng the layer boundares and the scale heghts. The stratospherc aerosol always s assumed between 12 and 35 km wth no varatons wth respect to volcanc actvty. 6. Conclusons The software package OPAC s ntended to serve as a tool to scentsts who need to descrbe the optcal propertes of the atmosphere for clmate-modelng purposes. It therefore conssts of datasets of optcal propertes of cloud and aerosol components that descrbe average condtons n combnaton wth easyto-use software, whch allows calculaton of any mxtures of these components. Varous user-defned aerosol mxtures are possble, and a set of typcal mxtures s also provded. Combnaton of dfferent ndvdual radatve datasets n OPAC has the advantage of convenent use and also easy mprovements. Ths can be done by smply changng or addng sngle components or ther propertes. For example, t wll be possble to nclude optcal propertes of nonsphercal aerosol partcles nstead of the results of Me calculatons, whch are used now even for the nsoluble and mneral aerosol components. The software package OPAC s freely avalable on the World Wde Web at aerosol/aerosol.html. Acknowledgments. OPAC was desgned and planned by G. A. d Almeda as a PC-based aerosol database to contan the aerosol data that are descrbed n the global aerosol clmatology by d Almeda et al. (1991). He also compled the aerosol-related data Bulletn of the Amercan Meteorologcal Socety 843

14 as descrbed n the above-mentoned book for a prevous verson of ths database. We are grateful to W. Sedel for hs suggestons regardng the behavor of aerosols wth changng relatve humdty and the selecton of water-cloud and fog-sze dstrbutons. The work was partly supported by the German Mnster of Educaton and Research (BMBF). References d Almeda, G. A., P. Koepke, and E. P. Shettle, 1991: Atmospherc Aerosols: Global Clmatology and Radatve Characterstcs. A. Deepak Publshng, 561 pp. Deepak, A., and H. E. Gerber, Eds., 1983: Report of the experts meetng on aerosols and ther clmatc effects. WCP-55, 107 pp. [Avalable from World Meteorologcal Organzaton, Case Postale No. 5, CH-1211 Geneva, Swtzerland.] Dermendjan, D., 1969: Electromagnetc Scatterng on Sphercal Polydspersons. Elsever, 290 pp. Dem, M., 1948: Messungen der gröβe von wolkenelementen II. Meteor. Rundsch., 1, Ftzgerald, J. W., and P. A. Spyers-Duran, 1973: Changes n cloud nucleus concentraton and cloud droplet sze dstrbuton assocated wth polluton from St. Lous. J. Appl. Meteor., 12, Gordon, J. F., 1970: Daytme vsblty. A conceptual revew. AFGL-TR Hale, G. M., and M. R. Querry, 1973: Optcal constants of water n the 200-nm to 200-mm wavelength regon. Appl. Opt., 12, Hänel, G., and B. Zankl, 1979: Aerosol sze and relatve humdty: Water uptake by mxtures of salts. Tellus, 31, Hansen, J. E., and I. D. Travs, 1974: Lght scatterng n planetary atmospheres. Space Sc. Rev., 16, Hess, M., and M. Wegner, 1994: COP: A data lbrary of optcal propertes of hexagonal ce crystals. Appl. Opt., 33, Heymsfeld, A. J., and C. M. R. Platt, 1984: A parameterzaton of the partcle sze spectrum of ce clouds n terms of the ambent temperature and the ce water content. J. Atmos. Sc., 41, Hoffmann, H.-E., and R. Roth, 1989: Cloud physcal parameters n dependence on heght above cloud base n dfferent clouds. Meteor. Atmos. Phys., 41, Kng, M. D., L. F. Radke, and P. V. Hobbs, 1993: Optcal propertes of marne stratocumulus clouds modfed by shps. J. Geophys. Res., 98 (D2), Koepke, P., M. Hess, I. Schult, and E. P. Shettle, 1997: Global Aerosol Data Set. MPI Meteorologe Hamburg Report No. 243, 44 pp. Leatch, W. R., G. A. Isaac, J. W. Strapp, C. M. Bane, and H. A. Webe, 1992: The relatonshp between cloud droplet number concentratons and anthropogenc polluton: Observatons and clmatc mplcatons. J. Geophys. Res., 97 (D2), Lou, K. N., 1992: Radaton and Cloud Processes n the Atmosphere. Oxford Unversty Press, 473 pp. Pruppacher, H. R., and J. D. Klett, 1978: Mcrophyscs of Clouds and Precptaton. D. Redel Publshng Company, 714 pp. Quenzel, H., and H. Müller, 1978: Optcal propertes of sngle Me partcles: Dagrams of ntensty-, extncton-, scatterng-, and absorpton effcences. Unverstät München, Meteorologsches Insttut, Wss. Mt. Nr. 34, 59 pp. [Avalable from Meteorologsches Insttut, Theresenstraße 37, D München, Germany.] Shettle, E. P., and R. W. Fenn, 1979: Models for the aerosols of the lower atmosphere and the effects of humdty varatons on ther optcal propertes. AFGL-TR , 94 pp. [Avalable from AFCRL, Hanscom Feld, Bedford, MA ] Squres, P., 1958: The mcrostructure and collodal stablty of warm clouds. Tellus, 10, Stephens, G. L., C. W. Paltrdge, and C. M. R. Platt, 1978: Radaton profles n extended water clouds III: Observatons. J. Atmos. Sc., 35, Strauss, B., R. Meerkoetter, B. Wssnger, P. Wendlng, and M. Hess, 1997: On the regonal clmatc mpact of contrals: Mcrophyscal and radatve propertes of contrals and natural crrus clouds. Ann. Geophys., 15, Tamper, F., and C. Tomas, 1976: Sze dstrbuton models of fog and cloud droplets n terms of the modfed gamma functon. Tellus, 28, Tsay, S., and K. Jayaweera, 1984: Physcal characterstcs of Arctc stratus clouds. J. Clmate Appl. Meteor., 23, Vol. 79, No. 5, May 1998