ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-12-2823-2012 Inverse modelling of cloud-aerosol interactions – Part 2: Sensitivity tests on liquid phase clouds using a Markov chain Monte Carlo based simulation approach Partridge D. G. 1 2 Vrugt J. A. 3 4 Tunved P. 1 2 Ekman A. M. L. 2 5 Struthers H. 1 2 5 Sorooshian A. 6 7 Department of Applied Environmental Science, Stockholm University, 10691 Stockholm, Sweden Bert Bolin Centre for Climate Research, Stockholm University, 10691 Stockholm, Sweden The Henry Samueli School of Engineering, Department of Civil and Environmental Engineering, University of California, Irvine, USA Computational Geo-Ecology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands Department of Meteorology, Stockholm University, Sweden Department of Chemical and Environmental Engineering, The University of Arizona, Tucson, USA Department of Atmospheric Sciences, The University of Arizona, Tucson, USA 16 03 2012 12 6 2823 2847 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/12/2823/2012/acp-12-2823-2012.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/2823/2012/acp-12-2823-2012.pdf

This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC) algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the global sensitivity of a cloud model to input aerosol physiochemical parameters. Using numerically generated cloud droplet number concentration (CDNC) distributions (i.e. synthetic data) as cloud observations, this inverse modelling framework is shown to successfully estimate the correct calibration parameters, and their underlying posterior probability distribution. <br></br> The employed analysis method provides a new, integrative framework to evaluate the global sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode aerosol and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insights. There is a transition in relative sensitivity from very clean marine Arctic conditions where the lognormal aerosol parameters representing the accumulation mode aerosol number concentration and mean radius and are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm<sup>−3</sup>) where particle chemistry is more important than both number concentration and size of the accumulation mode. <br></br> The competition and compensation between the cloud model input parameters illustrates that if the soluble mass fraction is reduced, the aerosol number concentration, geometric standard deviation and mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution. <br></br> This study demonstrates that inverse modelling provides a flexible, transparent and integrative method for efficiently exploring cloud-aerosol interactions with respect to parameter sensitivity and correlation.

 References Andreae, M. O. and Rosenfeld, D.: Aerosol-cloud-precipitation interactions. Part 1. The nature and sources of cloud-active aerosols, Earth Sci. Rev., 89, 13–41, 2008. Anttila, T. and Kerminen, V.-M.: On the contribution of Aitken mode particles to cloud droplet populations at continental background areas – a parametric sensitivity study, Atmos. Chem. Phys., 7, 4625–4637, http://dx.doi.org/10.5194/acp-7-4625-2007doi:10.5194/acp-7-4625-2007, 2007. Ayers, G. P. and Larson, T. V.: Numerical study of droplet size dependent chemistry in oceanic, wintertime, stratus cloud at southern midlattitudes, J. Atmos. Chem., 11, 143–167, 1990. Benke, K. K., Lowell, K. E., and Hamilton, A. J.: Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model, Math. Comput. Model., 47, 1134–1149, 2008. Bikowski, J., van der Kruk, J., Huisman, J. A., Vereecken, H., and Vrugt, J. A.: Inversion and sensitivity analysis of GPR data with waveguide dispersion using Markov Chain Monte Carlo simulation, Ground Penetrating Radar (GPR), 13th International Conference, 2010. Birmili, W., Wiedensohler, A., Heintzenberg, J., and Lehmann, K.: Atmospheric particle number size distribution in Central Europe: statistical relations to air masses and meteorology, J. Geophys. Res., 106, 32005–32018, http://dx.doi.org/10.1029/2000JD000220doi:10.1029/2000JD000220, 2001. Brenguier, J. L. and Wood, R.: Observational strategies from the micro- to mesoscale, in: Clouds in the Perturbed Climate System: There relationship to Energy Balance, Atmospheric Dynamics and Precipitation, edited by: Heintzenberg, J. and Charlson, R. J., pp. 487–510, MIT Press, Cambridge, Mass, 2009. Chuang, P. Y.: Sensitivity of cloud condensation nuclei activation processes to kinetic parameters, J. Geophys. Res., 111, D09201, http://dx.doi.org/10.1029/2005JD006529doi:10.1029/2005JD006529, 2006. Conant, W. C., VanReken, T. M., Rissman, T. A., Varutbangkul, V., Jonsson, H. H., Nenes, A., Jimenez, J. L., Delia, A. E., Bahreini, R., Roberts, G. C., Flagan, R. C., and Seinfeld, J. H.: Aerosol, cloud drop concentration closure in warm cumulus, J. Geophys. Res., 109, D13204, http://dx.doi.org/10.1029/2003JD004324doi:10.1029/2003JD004324, 2004. Dekker, S. C., Vrugt, J. A., and Elkington, R. J.: Significant variation in vegetation characteristics and dynamics from ecohydrologic optimality of net carbon profit, Ecohydrology, 5, 1–18, http://dx.doi.org/10.1002/eco.17doi:10.1002/eco.17, 2010. Duan, Q. Y., Sorooshian, S., and Gupta, V.: Effective and Efficient Global Optimization for Conceptual Rainfall-Runoff Models, Water Resour. Res., 28, 1015–1031, 1992. 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, 2006. Ervens, B., Feingold, G., and Kreidenweis, S. M.: The influence of water-soluble organic carbon on cloud drop number concentration, J. Geophys. Res., 110, D18211, http://dx.doi.org/10.1029/2004JD005634doi:10.1029/2004JD005634, 2005. Facchini, M. C., Mircea, M., Fuzzi, S., and Charlson, R. J.: Cloud albedo enhancement by surface-active organic solutes in growing droplets, Nature, 410, 257–259, 1999. Feingold, G.: Modelling of the first indirect effect: Analysis of measurement requirements, Geophys. Res. Let., 30, 1997, http://dx.doi.org/10.1029/2003GL017967doi:10.1029/2003GL017967, 2003. Fitzgerald, J. W.: Effect of aerosol composition on cloud droplet size distribution – numerical study, J. Atmos. Sci., 31, 1358–1367, 1974. Gautam, K. K. and Tyagi, V. K.: Microbial surfactants: a review, J Oleo Sci., 55, 155–166, 2006. Gelfand, A. E. and Smith, A. F.: Sampling based approaches to calculating marginal densities, J. Amer. Stat. Assoc., 85, 398–409, 1990. Gelman, A. and Rubin, D. B.: Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457–511, 1992. Hegg, D. A. and Larson, T. V.: The effects of microphysical parameterisation on model predictions of sulfate production in clouds, Tellus, 42B, 272–284, 1990. Heintzenberg, J., Covert, D. C., and Van Dingenen, R.: Size distribution and chemical composition of marine aerosols: a compilation and review, Tellus B, 52, 1104–1122, 2000. Hsieh, W. C., Nenes, A., Flagan, R. C., Seinfeld, J. H., Buzorius, G., and Jonsson, H.: Parameterization of cloud droplet size distributions: Comparison with parcel models and observations, J. Geophys. Res., 114, D11205, http://dx.doi.org/10.1029/2008JD011387doi:10.1029/2008JD011387, 2009. Hudson, J. G.: Variability of the relationship between particle size and cloud nucleating ability, Geophys. Res. Lett., 34, L08801, http://dx.doi.org/10.1029/2006GL028850doi:10.1029/2006GL028850, 2007. Jackson, C., Sen, M. K., and Stoffa, P. L.: An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions, J. Climate, 17, 2828–2841, 2004. Järvinen, H., Räisänen, P., Laine, M., Tamminen, J., Ilin, A., Oja, E., Solonen, A., and Haario, H.: Estimation of ECHAM5 climate model closure parameters with adaptive MCMC, Atmos. Chem. Phys., 10, 9993–10002, http://dx.doi.org/10.5194/acp-10-9993-2010doi:10.5194/acp-10-9993-2010, 2010. 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, http://dx.doi.org/10.5194/acp-5-1053-2005doi:10.5194/acp-5-1053-2005, 2005. Kanso, A., Ghebbo, G., and Tassin, B.: Application of MCMC–GSA model calibration method to urban runoff quality modelling, Reliability Engineering and System Safety, 91, 1398–1405, 2006. Kivekäs, N., Kerminen, V.-M., Anttila, T., Hakola, H., Komppula, M., and Lihavainen, H.: Using Aerosol Number to Volume Ratio in Predicting Cloud Droplet Number Concentration, in: Nucleation and Atmospheric Aerosols, edited by: O'Dowd, C. D. and Wagner, P. E., pp. 551–555, Springer Netherlands, 2007. Koda, M. and Seinfeld, J. H.: Estimation of Urban Air-Pollution, Automatica, 14, 583–595, 1978. Laaksonen, A., Korhonen, P., Kulmala, M., and Charlson, R. J.: Modification of the Köhler equation to include soluble trace gases and slightly soluble substances, J. Atmos. Sci., 55, 853–862, 1998. Laine, M. and Tamminen, J.: Aerosol model selection and uncertainty modelling by adaptive MCMC technique, Atmos. Chem. Phys., 8, 7697–7707, http://dx.doi.org/10.5194/acp-8-7697-2008doi:10.5194/acp-8-7697-2008, 2008. Lance, S., Nenes, A., and Rissman T. A.: Chemical and dynamical effects on cloud droplet number: Implications for estimates of the aerosol indirect effect, J. Geophys. Res., 109, D22208, http://dx.doi.org/10.1029/2004JD004596doi:10.1029/2004JD004596, 2004. Loridan, T., Grimmond, C. S. B., Grossman-Clarke, S., Chen, F., Tewari, M., Manning, K., Martilli, A., Kusaka, H., and Best, M.: Trade-offs and responsiveness of the single-layer urban canopy parameterization in WRF: an offline evaluation using the MOSCEM optimization algorithm and field observations, Q. J. Roy. Meteorol. Soc., 136, 997–1019. http://dx.doi.org/10.1002/qj.614doi:10.1002/qj.614, 2010. McFiggans, G., Artaxo, P., Baltensperger, U., Coe, H., Facchini, M. C., Feingold, G., Fuzzi, S., Gysel, M., Laaksonen, A., Lohmann, U., Mentel, T. F., Murphy, D. M., O'Dowd, C. D., Snider, J. R., and Weingartner, E.: The effect of physical and chemical aerosol properties on warm cloud droplet activation, Atmos. Chem. Phys., 6, 2593–2649, http://dx.doi.org/10.5194/acp-6-2593-2006doi:10.5194/acp-6-2593-2006, 2006. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E.: Equation of state calculations by fast computing machines, J. Chem. Phys., 21, 1087–1092, 1953. Nenes, A., Charlson, R. J., Facchini, M. C., Kulmala, M., Laaksonen, A., and Seinfeld, J. H.: Can chemical effects on cloud droplet number rival the first indirect effect?, Geophys. Res. Lett., 29, 1848, http://dx.doi.org/10.1029/2002GL015295doi:10.1029/2002GL015295, 2002. Partridge, D. G., Vrugt, J. A., Tunved, P., Ekman, A. M. L., Gorea, D., and Sorooshian, A.: Inverse modelling of cloud-aerosol interactions – Part 1: Detailed response surface analysis, Atmos. Chem. Phys., 11, 7269–7287, http://dx.doi.org/10.5194/acp-11-7269-2011doi:10.5194/acp-11-7269-2011, 2011. Pérez, C. J., Martín, J., and Rufo, M. F.: Sensitivity estimations for Bayesian inference models solved by MCMC methods, Reliability Engineering and System Safety, 91, 1310–1314, 2006. Platnick, S. and Twomey, S.: Determining the susceptibility of cloud albedo to changes in droplet concentration with the Advanced Very High Resolution Radiometer. J. Appl. Meteor., 33, 334–347, 1994. Quinn, P. K., Bates, T. S., Coffman, D. J., and Covert, D. S.: Influence of particle size and chemistry on the cloud nucleating properties of aerosols, Atmos. Chem. Phys., 8, 1029–1042, http://dx.doi.org/10.5194/acp-8-1029-2008doi:10.5194/acp-8-1029-2008, 2008. Rissman, T., Nenes, A., and Seinfeld, J. H.: Chemical amplification (or dampening) of the Twomey effect: Conditions derived from droplet activation theory, J. Atmos. Sci., 61, 919–930, 2004. Roelofs, G. J. and Jongen, S.: A model study of the influence of aerosol size and chemical properties on precipitation formation in warm clouds, J. Geophys. Res., 109, D22201, http://dx.doi.org/10.1029/2004JD004779doi:10.1029/2004JD004779, 2004. San Martini, F. M., Dunlea, E. J., Grutter, M., Onasch, T. B., Jayne, J. T., Canagaratna, M. R., Worsnop, D. R., Kolb, C. E., Shorter, J. H., Herndon, S. C., Zahniser, M. S., Ortega, J. M., McRae, G. J., Molina, L. T., and Molina, M. J.: Implementation of a Markov Chain Monte Carlo method to inorganic aerosol modelling of observations from the MCMA-2003 campaign – Part I: Model description and application to the La Merced site, Atmos. Chem. Phys., 6, 4867–4888, http://dx.doi.org/10.5194/acp-6-4867-2006doi:10.5194/acp-6-4867-2006, 2006. Schoups, G. and Vrugt, J. A.: A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-Gaussian errors, Water Resour. Res., 46, W10531, http://dx.doi.org/10.1029/2009WR008933doi:10.1029/2009WR008933, 2010. Snider, J. R. and Brenguier, J.-L.: Cloud condensation nuclei and cloud droplet measurements during ACE-2, Tellus B, 53, 828–842, 2000. Sorooshian, A., Murphy, S. M., Hersey, S., Bahreini, R., Jonsson, H., Flagan, R. C., and Seinfeld, J. H.: Constraining the contribution of organic acids and AMS \emphm/z 44 to the organic aerosol budget: On the importance of meteorology, aerosol hygroscopicity, and region, Geophys. Res. Lett., 37, L21807, http://dx.doi.org/10.1029/2010GL044951doi:10.1029/2010GL044951, 2010. Stevens, B. and Feingold, G.: Untangling aerosol effects on clouds and precipitation in a buffered system, Nature, 461, 607–613, 2009. Tamminen, J. and Kyrölä, E.: Bayesian solution for nonlinear and non-Gaussian inverse problems by Markov chain Monte Carlo method, J. Geophys. Res., 106, 14377–14390, http://dx.doi.org/10.1029/2001JD900007doi:10.1029/2001JD900007, 2001. Tomassini, L., Reichert, P., Knutti, R., Stocker, T. F., and Borsuk, M. E.: Robust Bayesian uncertainty analysis of climate system properties using Markov chain Monte Carlo methods, J. Climate, 20, 1239–1254, 2007. Tunved, P., Nilsson, E. D., Hansson, H. C., Strom, J., Kulmala, M., Aalto, P., and Viisanen, Y.: Aerosol characteristics of air masses in northern Europe: Influences of location, transport, sinks, and sources, J. Geophys. Res.-Atmos., 110, D07201, http://dx.doi.org/10.1029/2004JD005085doi:10.1029/2004JD005085, 2005. Twohy, C. H. and Anderson, J. R.: Droplet nuclei in non-precipitating clouds: composition and size matter, Environ. Res. Lett., 3, 045002, http://dx.doi.org/10.1088/1748-9326/3/4/045002doi:10.1088/1748-9326/3/4/045002, 2008. Villagran, A., Huerta, G., Jackson, C. S., and Sen, M. K.: Computational Methods for Parameter Estimation in Climate Models, Bayesian Anal, 3, 823–850, 2008. Voutilainen, A. and Kaipio, J. P.: Sequential Monte Carlo estimation of aerosol size distributions, Comput. Stat Data An, 48, 887–908, 2005. Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39, 1201, http://dx.doi.org/10.1029/2002WR001642doi:10.1029/2002WR001642, 2003. Vrugt, J. A., Clark, M. P., Diks, C. G. H., Duan, Q., and Robinson, B. A.: Multi-objective calibration of forecast ensembles using Bayesian model averaging, Geophys. Res. Lett., 33, L19817, http://dx.doi.org/10.1029/2006GL027126doi:10.1029/2006GL027126, 2006. Vrugt, J.A., Braak, C. J. F. Ter., Clark, M. P., Hyman, J. M., and Robinson, B. A.: Treatment of input uncertainty in hydrologic modelling: Doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44, W00B09, http://dx.doi.org/10.1029/2007WR006720doi:10.1029/2007WR006720, 2008a. Vrugt, J. A., Stauffer, P. H., Wohling, T., Robinson, B. A., and Vesselinov, V. V.: Inverse modelling of subsurface flow and transport properties: A review with new developments, Vadose Zone J., 7, 843–864, 2008b. Vrugt, J. A., Robinson, B. A., and Hyman, J. M.: Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces, IEEE Transactions on Evolutionary Computation, 13, 243–259, 2009a. Vrugt, J. A., Ter Braak, C. J. F., Diks, C. G. H., Robinson, B. A., Hyman, J. M., and Higdon, D.: Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlin. Sci. Num., 10, 273–290, 2009b. Vuollekoski, H., Boy, M., Kerminen, V. M., Lehtinen, K. E. J., and Kulmala, M.: MECCO: A method to estimate concentrations of condensing organics – Description and evaluation of a Markov chain Monte Carlo application, J. Aerosol Sci., 41, 1080–1089, 2010. Wraith, D., Alston, C., Mengersen, K., and Hussein, T.: Bayesian mixture model estimation of aerosol particle size distributions, Environmetrics, 22, 23–34, http://dx.doi.org/10.1002/env.1020doi:10.1002/env.1020, 2009. Xue, H. and Feingold, G.: A modelling study of the effect of nitric acid on cloud properties, J. Geophys. Res., 109, D18204, http://dx.doi.org/10.1029/2004JD004750doi:10.1029/2004JD004750, 2004.