Atmospheric Chemistry and Physics www.atmos-chem-phys.net 1680-7316 1680-7324 7 20 2007 10.5194/acp-7-5447-2007 http://www.atmos-chem-phys.net/7/5447/2007/ http://www.atmos-chem-phys.net/7/5447/2007/acp-7-5447-2007.html http://www.atmos-chem-phys.net/7/5447/2007/acp-7-5447-2007.pdf 5447 5466 2007-10-19 Contribution of primary carbonaceous aerosol to cloud condensation nuclei: processes and uncertainties evaluated with a global aerosol microphysics model J. R. Pierce jrpierce@andrew.cmu.edu K. Chen P. J. Adams Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, USA Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA This paper explores the impacts of primary carbonaceous aerosol on cloud condensation nuclei (CCN) concentrations in a global climate model with size-resolved aerosol microphysics. Organic matter (OM) and elemental carbon (EC) from two emissions inventories were incorporated into a preexisting model with sulfate and sea-salt aerosol. The addition of primary carbonaceous aerosol increased CCN(0.2%) concentrations by 65–90% in the globally averaged surface layer depending on the carbonaceous emissions inventory used. Sensitivity studies were performed to determine the relative importance of organic solubility/hygroscopicity in predicting CCN. In a sensitivity study where carbonaceous aerosol was assumed to be completely insoluble, concentrations of CCN(0.2%) still increased by 40–50% globally over the no carbonaceous simulation because primary carbonaceous emissions were able to become CCN via condensation of sulfuric acid. This shows that approximately half of the contribution of primary carbonaceous particles to CCN in our model comes from the addition of new particles (seeding effect) and half from the contribution of organic solute (solute effect). The solute effect tends to dominate more in areas where there is less inorganic aerosol than organic aerosol and the seeding effect tends to dominate in areas where there is more inorganic aerosol than organic aerosol. It was found that an accurate simulation of the number size distribution is necessary to predict the CCN concentration but assuming an average chemical composition will generally give a CCN concentration within a factor of 2. If a "typical" size distribution is assumed for each species when calculating CCN, such as is done in bulk aerosol models, the mean error relative to a simulation with size resolved microphysics is on the order of 35%. Predicted values of carbonaceous aerosol mass and aerosol number were compared to observations and the model showed average errors of a factor of 3 for carbonaceous mass and a factor of 4 for total aerosol number; however, errors in the accumulation mode concentrations were found to be lower in comparisons with European and marine observations.. The errors in CN and carbonaceous mass may be reduced by improving the emission size distributions of both primary sulfate and primary carbonaceous aerosol. Adams, P. J. and Seinfeld, J. H.: Disproportionate impact of particulate emissions on global cloud condensation nuclei concentrations, Geophys. Res. Lett., 30, ISI:000182151300004, 2003. Adams, P. J. and Seinfeld, J. H.: Predicting global aerosol size distributions in general circulation models, J. Geophys. Res. Atmos., 107, 4370, 2002. Albrecht, B. A.: Aerosols, Cloud Microphysics, and Fractional Cloudiness, Science, 245, 1227–1230, 1989. Andreae, M. O. and Gelencser, A.: Black carbon or brown carbon? The nature of light-absorbing carbonaceous aerosols, Atmos. Chem. Phys., 6, 3131–3148, ISI:000239346600001, 2006. Andreae, M. O., Jones, C. D., and Cox, P. M.: Strong present-day aerosol cooling implies a hot future, Nature, 435, 1187–1190, ISI:000230140500033, 2005. Benkovitz, C. M., Scholtz, M. T., Pacyna, J., Tarrason, L., Dignon, J., Voldner, E. C., Spiro, P. A., Logan, J. A., and Graedel, T. E.: Global gridded inventories of anthropogenic emissions of sulfur and nitrogen, J. Geophys. Res. Atmos., 101, 29 239–29 253, ISI:A1996VZ78800050, 1996. Bond, T. C., Streets, D. G., Yarber, K. F., Nelson, S. M., Woo, J. H., and Klimont, Z.: A technology-based global inventory of black and organic carbon emissions from combustion, J. Geophys. Res. Atmos., 109, ISI:000222916600001, 2004. Chuang, C. C., Penner, J. E., Prospero, J. M., Grant, K. E., Rau, G. H., and Kawamoto, K.: Cloud susceptibility and the first aerosol indirect forcing: Sensitivity to black carbon and aerosol concentrations, J. Geophys. Res. Atmos., 107, ISI:000180860300016, 2002. Chung, S. H. and Seinfeld, J. H.: Global distribution and climate forcing of carbonaceous aerosols, J. Geophys. Res. Atmos., 107, ISI:000180860300016,, 2002. Clarke, A. D., Owens, S., and Zhou, J.: An ultrafine sea-salt flux from breaking waves: Implications for CCN in the remote marine atmosphere, J. Geophys. Res. Atmos., 111, ISI:000236332000004, 2006. Cooke, W. F., Liousse, C., Cachier, H., and Feichter, J.: Construction of a 1 degrees × 1 degrees fossil fuel emission data set for carbonaceous aerosol and implementation and radiative impact in the ECHAM4 model, J. Geophys. Res.-Atmos., 104, 22 137–22 162, ISI:000082789200006, 1999. Cooke, W. F. and Wilson, J. J. N.: A global black carbon aerosol model, J. Geophys. Res.-Atmos., 101, 19 395–19 409, ISI:A1996VE25800041, 1996. Dusek, U., Frank, G. P., Hildebrandt, L., Curtius, J., Schneider, J., Walter, S., Chand, D., Drewnick, F., Hings, S., Jung, D., Borrmann, S., and Andreae, M. O.: Size matters more than chemistry for cloud-nucleating ability of aerosol particles, Science, 312, 1375–1378, ISI:000237961600054, 2006. Easter, R. C., Ghan, S. J., Zhang, Y., Saylor, R. D., Chapman, E. G., Laulainen, N. S., Abdul-Razzak, H., Leung, L. R., Bian, X. D., and Zaveri, R. A.: MIRAGE: Model description and evaluation of aerosols and trace gases, J. Geophys. Res.-Atmos., 109, ISI:000224882100001, 2004. Eliason, T. L., Aloisio, S., Donaldson, D. J., Cziczo, D. J., and Vaida, V.: Processing of unsaturated organic acid films and aerosols by ozone, Atmos. Environ., 37, 2207–2219, ISI:000182778900004, 2003. Eliason, T. L., Gilman, J. B., and Vaida, V.: Oxidation of organic films relevant to atmospheric aerosols, Atmos. Environ., 38, 1367–1378, ISI:000189102000013, 2004. El-Zanan, H. S., Lowenthal, D. H., Zielinska, B., Chow, J. C., and Kumar, N.: Determination of the organic aerosol mass to organic carbon ratio in IMPROVE samples, Chemosphere, 60, 485–496, ISI:000231038200006, 2005. FassiFihri, A., Suhre, K., and Rosset, R.: Internal and external mixing in atmospheric aerosols by coagulation: Impact on the optical and hygroscopic properties of the sulphate-soot system, Atmos. Environ., 31, 1393–1402, ISI:A1997WR16000002, 1997. Forster, P., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fahey, D. W., Haywood, J., Lean, J., Lowe, D. C., Myhre, G., Nganga, J., Prinn, R., Raga, G., Schulz, M., and Dorland, R. V.: Changes in Atmospheric Constituents and in Radiative Forcing, in Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: S Solomon, D Qin, M Manning, Z Chen, M Marquis, K B Averyt, M Tignor, and H L Miller, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 2007. Ghan, S., Easter, R., Hudson, J., and Breon, F. M.: Evaluation of aerosol indirect radiative forcing in MIRAGE, J. Geophys. Res.-Atmos., 106, 5317–5334, ISI:000167635900016, 2001. Gong, S. L., Barrie, L. A., Blanchet, J. P., von Salzen, K., Lohmann, U., Lesins, G., Spacek, L., Zhang, L. M., Girard, E., Lin, H., Leaitch, R., Leighton, H., Chylek, P., and Huang, P.: Canadian Aerosol Module: A size-segregated simulation of atmospheric aerosol processes for climate and air quality models – 1. Module development, J. Geophys. Res.-Atmos., 108, ISI:000181553400003, 2003. Hanel, G.: Single-Scattering Albedo of Atmospheric Aerosol-Particles as a Function of Relative Humidity, J. Atmos. Sci., 33, 1120–1124, ISI:A1976BV24200020, 1976. Hansen, J., Russell, G., Rind, D., Stone, P., Lacis, A., Lebedeff, S., Ruedy, R., and Travis, L.: Efficient 3-Dimensional Global-Models for Climate Studies – Model-I and Model-II, Mon. Wea. Rev., 111, 609–662, ISI:A1983QU10600001, 1983. Heintzenberg, J., Covert, D. C., and Van Dingenen, R. V.: Size distribution and chemical composition of marine aerosols: A compilation and review, Tellus B, 52, 1104–1122, 2000. Heintzenberg, J., Leck, C., Birmili, W., Wehner, B., Tjernstrom, M., and Wiedensohler, A.: Aerosol number-size distributions during clear and fog periods in the summer high Arctic: 1991, 1996 and 2001, Tellus B, 58, 41–50, ISI:000235520500005, 2006. Herzog, M., Weisenstein, D. K., and Penner, J. E.: A dynamic aerosol module for global chemical transport models: Model description, J. Geophys. Res.-Atmos., 109, 18 202–18 213, 2004. Hitzenberger, R., Berner, A., Giebl, H., Kromp, R., Larson, S. M., Rouc, A., Koch, A., Marischka, S., and Puxbaum, H.: Contribution of carbonaceous material to cloud condensation nuclei concentrations in European background (Mt. Sonnblick) and urban (Vienna) aerosols, Atmos. Environ., 33, 2647–2659, ISI:000080975600005, 1999. IPCC: Intergovernmental Panel on Climate Change 2001: The Scientific Basis – Technical Summary, 2001. Jacobson, M. Z.: Analysis of aerosol interactions with numerical techniques for solving coagulation, nucleation, condensation, dissolution, and reversible chemistry among multiple size distributions, J. Geophys. Res. Atmos., 107, ISI:000180428300033, 2002. Jacobson, M. Z.: Strong radiative heating due to the mixing state of black carbon in atmospheric aerosols, Nature, 409, 695–697, ISI:000166816400037, 2001. Janhall, S., Jonsson, A. M., Molnar, P., Svensson, E. A., and Hallquist, M.: Size resolved traffic emission factors of submicrometer particles, Atmos. Environ., 38, 4331–4340, ISI:000223019500006, 2004. Jung, C. H., Kim, Y. P., and Lee, K. W.: Multicomponent aerosol dynamics model with gas/particle transport and modal approach, Environ. Eng. Sci., 21, 437–450, ISI:000222488300003, 2004. Kanakidou, M., Seinfeld, J. H., Pandis, S. N., Barnes, I., Dentener, F. J., Facchini, M. C., Van Dingenen, R., Ervens, B., Nenes, A., Nielsen, C. J., Swietlicki, E., Putaud, J. P., Balkanski, Y., Fuzzi, S., Horth, J., Moortgat, G. K., Winterhalter, R., Myhre, C. E. L., Tsigaridis, K., Vignati, E., Stephanou, E. G., and Wilson, J.: Organic aerosol and global climate modelling: a review, Atmos. Chem. Phys., 5, 1053–1123, ISI:000228024100001, 2005. Kinne, S., Lohmann, U., Feichter, J., Schulz, M., Timmreck, C., Ghan, S., Easter, R., Chin, M., Ginoux, P., Takemura, T., Tegen, I., Koch, D., Herzog, M., Penner, J., Pitari, G., Holben, B., Eck, T., Smirnov, A., Dubovik, O., Slutsker, I., Tanre, D., Torres, O., Mishchenko, M., Geogdzhayev, I., Chu, D. A., and Kaufman, Y.: Monthly averages of aerosol properties: A global comparison among models, satellite data, and AERONET ground data, J. Geophys. Res.-Atmos., 108, ISI:000186198500001, 2003. Koch, D.: Transport and direct radiative forcing of carbonaceous and sulfate aerosols in the GISS GCM, J. Geophys. Res.-Atmos., 106, 20 311–20 332, ISI:000171044200023, 2001. Koch, D., Jacob, D., Tegen, I., Rind, D., and Chin, M.: Tropospheric sulfur simulation and sulfate direct radiative forcing in the Goddard Institute for Space Studies general circulation model, J. Geophys. Res.-Atmos., 104, 23 799–23 822, 1999. Laaksonen, A., Korhonen, P., Kulmala, M., and Charlson, R. J.: Modification of the Kuhler equation to include soluble trace gases and slightly soluble substances, J. Atmos. Sci., 55, 853–862, ISI:000072288400011, 1998. Liousse, C., Penner, J. E., Chuang, C., Walton, J. J., Eddleman, H., and Cachier, H.: A global three-dimensional model study of carbonaceous aerosols, J. Geophys. Res.-Atmos., 101, 19 411–19 432, ISI:A1996VE25800042, 1996. Lohmann, U., Feichter, J., Penner, J., and Leaitch, R.: Indirect effect of sulfate and carbonaceous aerosols: A mechanistic treatment, J. Geophys. Res.-Atmos., 105, 12 193–12 206, ISI:000087366600008, 2000. Malm, W. C., Pitchford, M. L., Scruggs, M., Sisler, J. F., Ames, R., Copeland, S., Gebhart, K. A., and Day, D. E.: Spational and Seasonal Patterns and Temporal Variability of Haze and its Constituents in the United States: Report III, 2000. Moise, T. and Rudich, Y.: Reactive uptake of ozone by aerosol-associated unsaturated fatty acids: Kinetics, mechanism, and products, J. Phys. Chem. Atmos., 106, 6469–6476, ISI:000176600600005, 2002. Novakov, T. and Penner, J. E.: Large Contribution of Organic Aerosols to Cloud-Condensation-Nuclei Concentrations, Nature, 365, 823–826, ISI:A1993MD95100045, 1993. Park, R. J., Jacob, D. J., Palmer, P. I., Clarke, A. D., Weber, R. J., Zondlo, M. A., Eisele, F. L., Bandy, A. R., Thornton, D. C., Sachse, G. W., and Bond, T. C.: Export efficiency of black carbon aerosol in continental outflow: Global implications, J. Geophys. Res.-Atmos., 110, ISI:000229829100006, 2005. Penner, J. E., Chuang, C. C., and Grant, K.: Climate forcing by carbonaceous and sulfate aerosols, Clim. Dynamm., 14, 839–851, ISI:000076963400001, 1998. Penner, J. E., Eddleman, H., and Novakov, T.: Towards the Development of a Global Inventory for Black Carbon Emissions, Atmos. Environ., 27, 1277–1295, ISI:A1993LJ39000013, 1993. Petters, M. D. and Kreidenweis, S. M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity, Atmos Chem Phys., 7, 1961–1971, 2007. Pierce, J. R. and Adams, P. J.: Global evaluation of CCN formation by direct emission of sea salt and growth of ultrafine sea salt, J. Geophys. Res.-Atmos., 111, ISI:000236332000002, 2006. Prather, M. J.: Numerical advection by conservation of second-order moments, J. Geophys. Res.-Atmos., 91, 6671–6681, 1986. Putaud, J. P.: A European aerosol phenomenology; physical and chemical characteristics of particulate matter at kerbside, urban, rural and background sites in Europe, 2003, European Commission, EUR 20411 EN., http://ies.jrc.cec.eu.int/Download/cc Raymond, T. M. and Pandis, S. N.: Cloud activation of single-component organic aerosols, J. Geophys. Res.-Atmos., 107, 4787–4784, 2002. Raymond, T. M. and Pandis, S. N.: Formation of cloud droplets by multicomponent organic particles, J. Geophys. Res. Atmos., 108, 4469–4476, 2003. Reddy, M. S. and Boucher, O.: A study of the global cycle of carbonaceous aerosols in the LMDZT general circulation model, J. Geophys. Res.-Atmos., 109, ISI:000222916300002, 2004. Riemer, N., Vogel, H., and Vogel, B.: Soot aging time scales in polluted regions during day and night, Atmos. Chem. Phys., 4, 1885–1893, ISI:000223866600001, 2004. Rissler, J., Swietlicki, E., Zhou, J., Roberts, G., Andreae, M. O., Gatti, L. V., and Artaxo, P.: Physical properties of the sub-micrometer aerosol over the Amazon rain forest during the wet-to-dry season transition - comparison of modeled and measured CCN concentrations, Atmos. Chem. Phys., 4, 2119–2143, ISI:000224840800001, 2004. Rissler, J., Vestin, A., Swietlicki, E., Fisch, G., Zhou, J., Artaxo, P., and Andreae, M. O.: Size distribution and hygroscopic properties of aerosol particles from dry-season biomass burning in Amazonia, Atmos. Chem. Phys., 6, 471–491, ISI:000235230500001, 2006. Rodriguez, M. A. and Dabdub, D.: A modeling study of size- and chemically resolved aerosol thermodynamics in a global chemical transport model, J. Geophys. Res.-Atmos., 109, ISI:000188672100002, 2004. Schnell, R. C.: Chapter 3: Aerosols and Radiation, in: Climate Monitoring and Diagnostics Laboratory Summary Report No. 27, edited by: A McComisky, 2002–2003, 2003. Schwartz, S. E.: Uncertainty requirements in radiative forcing of climate change, J. Air Waste Ma., 54, 1351–1359, ISI:000224972400002, 2004. Seinfeld, J. H. and Pandis, S. N.: Atmospheric Chemistry and Physics, John Wiley and Sons., New York, 784–790, 1998. Spracklen, D. V., Carslaw, K. S., Kulmala, M., Kerminen, V. M., Mann, G. W., and Sihto, S. L.: The contribution of boundary layer nucleation events to total particle concentrations on regional and global scales, Atmos. Chem. Phys., 6, 5631–5648, ISI:000242944600002, 2006. Spracklen, D. V., Pringle, K. J., Carslaw, K. S., Chipperfield, M. P., and Mann, G. W.: A global off-line model of size-resolved aerosol microphysics: I. Model development and prediction of aerosol properties, Atmos. Chem. Phys., 5, 2227–2252, ISI:000231363700002, 2005a. Spracklen, D. V., Pringle, K. J., Carslaw, K. S., Chipperfield, M. P., and Mann, G. W.: A global off-line model of size-resolved aerosol microphysics: II. Identification of key uncertainties, Atmos. Chem. Phys., 5, 3233–3250, ISI:000233951200001, 2005b. Stanier, C. O., Khlystov, A. Y., and Pandis, S. N.: Ambient aerosol size distributions and number concentrations measured during the Pittsburgh Air Quality Study (PAQS), Atmos. Environ., 38, 3275–3284, ISI:000221838500015, 2004. Stevens, B., Feingold, G., Cotton, W. R., and Walko, R. L.: Elements of the microphysical structure of numerically simulated nonprecipitating stratocumulus, J. Atmos. Sci., 53, 980–1006, ISI:A1996UD08500005, 1996. Stier, P., Feichter, J., Kinne, S., Kloster, S., Vignati, E., Wilson, J., Ganzeveld, L., Tegen, I., Werner, M., Balkanski, Y., Schulz, M., Boucher, O., Minikin, A., and Petzold, A.: The aerosol-climate model ECHAM5-HAM, Atmos. Chem. Phys., 5, 1125–1156, ISI:000228059900001, 2005. Strom, J., Okada, K., and Heintzenberg, J.: On the State of Mixing of Particles Due to Brownian Coagulation, J. Aerosol Sci., 23, 467–480, ISI:A1992JK55400006, 1992. Subramanian, R., Khlystov, A. Y., and Robinson, A. L.: Effect of peak inert-mode temperature on elemental carbon measured using thermal-optical analysis, Aerosol Sci. Tech., 40, 763–780, ISI:000239954300005, 2006. Tegen, I. and Lacis, A. A.: Modeling of particle size distribution and its influence on the radiative properties of mineral dust aerosol, J. Geophys. Res.-Atmos., 101, 19 237–19 244, ISI:A1996VE25800026, 1996. Twomey, S.: Pollution and the Planetary Albedo, Atmos. Environ., 8, 1251–1256, 1974. Tzivion, S., Feingold, G., and Levin, Z.: The evolution of raindrop spectra. Part II: Collisional collection/breakup and evaporation in a rainshaft, J. Atmos. Sci., 46, 3312–3327, 1989. Tzivion, S., Fiengold, G., and Levin, Z.: An Efficient Numerical Solution to the Stochastic Collection Equation, J. Atmos. Sci., 44, 3139–3149, 1987. Van Dingenen, R., Raes, F., Putaud, J. P., Baltensperger, U., Charron, A., Facchini, M. C., Decesari, S., Fuzzi, S., Gehrig, R., Hansson, H. C., Harrison, R. M., Huglin, C., Jones, A. M., Laj, P., Lorbeer, G., Maenhaut, W., Palmgren, F., Querol, X., Rodriguez, S., Schneider, J., ten Brink, H., Tunved, P., Torseth, K., Wehner, B., Weingartner, E., Wiedensohler, A., and Wahlin, P.: A European aerosol phenomenology-1: physical characteristics of particulate matter at kerbside, urban, rural and background sites in Europe, Atmos. Environ., 38, 2561–2577, ISI:000221265500011, 2004. Vignati, E., Wilson, J., and Stier, P.: M7: An efficient size-resolved aerosol microphysics module for large-scale aerosol transport models, J. Geophys. Res. Atmos., 109, ISI:000225400100001, 2004. Volkamer, R., Jimenez, J. L., San Martini, F., Dzepina, K., Zhang, Q., Salcedo, D., Molina, L. T., Worsnop, D. R., and Molina, M. J.: Secondary organic aerosol formation from anthropogenic air pollution: Rapid and higher than expected, Geophys. Res. Lett., 33, ISI:000240642100006, 2006. Weingartner, E., Burtscher, H., and Baltensperger, U.: Hygroscopic properties of carbon and diesel soot particles, Atmos. Environ., 31, 2311–2327, ISI:A1997XE53100014, 1997. Wesely, M. L. and Hicks, B. B.: Some Factors That Affect Deposition Rates of Sulfur-Dioxide and Similar Gases on Vegetation, J. Air Waste Ma., 27, 1110–1116, ISI:A1977EA08300011, 1977. Wexler, A. S., Lurmann, F. W., and Seinfeld, J. H.: Modeling Urban and Regional Aerosols .1. Model Development, Atmos. Environ., 28, 531–546, ISI:A1994NR21300012, 1994. Wilson, J., Cuvelier, C., and Raes, F.: A modeling study of global mixed aerosol fields, J. Geophys. Res.-Atmos., 106, 34 081–34 108, ISI:000173879800053, 2001. Yu, L. E., Shulman, M. L., Kopperud, R., and Hildemann, L. M.: Fine organic aerosols collected in a humid, rural location (Great Smoky Mountains, Tennessee, USA): Chemical and temporal characteristics, Atmos. Environ., 39, 6037–6050, ISI:000232762600003, 2005. Yu, S. C., Kasibhatla, P. S., Wright, D. L., Schwartz, S. E., McGraw, R., and Deng, A. J.: Moment-based simulation of microphysical properties of sulfate aerosols in the eastern United States: Model description, evaluation, and regional analysis, J. Geophys. Res.-Atmos., 108, ISI:000183746000002, 2003. Zhang, Q., Worsnop, D. R., Canagaratna, M. R., and Jimenez, J. L.: Hydrocarbon-like and oxygenated organic aerosols in Pittsburgh: insights into sources and processes of organic aerosols, Atmos. Chem. Phys., 5, 3289–3311, 2005. Zhang, Y., Easter, R. C., Ghan, S. J., and Abdul-Razzak, H.: Impact of aerosol size representation on modeling aerosol-cloud interactions, J. Geophys. Res.-Atmos., 107, ISI:000180860300010, 2002. Zhang, Y., Seigneur, C., Seinfeld, J. H., Jacobson, M. Z., and Binkowski, F. S.: Simulation of aerosol dynamics: A comparative review of algorithms used in air quality models, Aerosol Sci. Tech., 31, 487–514, ISI:000083886600008, 1999. Zuberi, B., Johnson, K. S., Aleks, G. K., Molina, L. T., and Laskin, A.: Hydrophilic properties of aged soot, Geophys. Res. Lett., 32, ISI:000226510800003, 2005.