ACPD Atmospheric Chemistry and Physics Discussions ACPD 1680-7375 Copernicus GmbH Göttingen, Germany 10.5194/acpd-11-4749-2011 Towards inverse modeling of cloud-aerosol interactions – Part 1: A detailed response surface analysis Partridge D. G. 1 Vrugt J. A. 2 3 4 Tunved P. 1 Ekman A. M. L. 5 Gorea D. 4 Sorooshian A. 6 7 Dept. of Applied Environmental Science, Stockholm University, Sweden The Henry Samueli School of Engineering, Department of Civil and Environmental Engineering, University of California, Irvine, USA Earth and Environmental Sciences Division, Los Alamos National Laboratory, Mail Stop T003, Los Alamos, NM, 87545, USA Computational Geo-Ecology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands Dept. of Meteorology, Stockholm University, Sweden Dept. of Chemical and Environmental Engineering, The University of Arizona, Tucson, USA Dept. of Atmospheric Sciences, The University of Arizona, Tucson, USA 09 02 2011 11 2 4749 4806 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-discuss.net/11/4749/2011/acpd-11-4749-2011.html The full text article is available as a PDF file from http://www.atmos-chem-phys-discuss.net/11/4749/2011/acpd-11-4749-2011.pdf

This paper explores the feasibility of inverse modeling to determine cloud-aerosol interactions using a pseudo-adiabatic cloud-parcel model. Two-dimensional plots of the objective function, containing the difference between the measured and model predicted droplet size distribution, are presented for selected pairs of cloud parcel model parameters. From these response surfaces it is shown that the "cloud-aerosol" inverse problem is particularly difficult to solve due to significant parameter interaction, presence of multiple regions of attractions, numerous local optima, and considerable parameter insensitivity. Sensitivity analysis is performed to help select an appropriate objective function that maximizes information retrieval from the measured droplet size distribution to help identify the unknown model parameters. The identifiability of the model parameters will be dependent on the choice of the objective function; including the interstitial aerosol will aid the calibration of parameters describing the smaller aerosol mode. Cloud parcel models that employ a moving-centre based calculation of the droplet size distribution require both the <i>X</i> and <i>Y</i> components of the <i>dN/d</i>log<i>d<sub>p</sub></i> size distribution function to be explicitly included in the objective function. Other possible improvements identified include an improved representation of the resolution of the region of the size spectrum associated with droplet activation within cloud parcel models, and further development of fixed-sectional cloud models that minimize numerical diffusion. Despite these developments, powerful search algorithms remain necessary to efficiently explore the parameter space and successfully solve the cloud-aerosol inverse problem.

 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(1–2), 143–167, 1990. Arabas, S. and Pawlowska, H.: Adaptive method of lines for multi-component aerosol condensational growth and CCN activation, Geosci. Model Dev., 4, 15–31, http://dx.doi.org/10.5194/gmd-4-15-2011doi:10.5194/gmd-4-15-2011, 2011. Beven, K.: A manifesto for the equifinality thesis, J. Hydrol., 320(1–2), 18–36, 2006. 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. Cochran, R. N. and Horne, F. H.: Statistically weighted principle component analysis of rapid scanning wavelength kinetics experiments, Anal. Chem., 49(6), 846–853, 1977. 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(D13), D13204, http://dx.doi:10.1029/2003JD004324doi:10.1029/2003JD004324, 2004. Cressie, N., Calder, C. A., Clark, J. S., Hoef, J. M. V., and Wikle, C. K.: Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling, Ecol. Appl., 19(3), 553–570, 2009. Crump, J. G. and Seinfeld, J. H.: A New Algorithm for Inversion of Aerosol Size Distribution Data, Aerosol. Sci. Technol., 1(1), 15–34, 1982. Duan, Q. Y., Sorooshian, S., and Gupta, V.: Effective and Efficient Global Optimization for Conceptual Rainfall-Runoff Models, Water Resour. Res., 28(4), 1015–1031, 1992. Duan, Q. Y., Gupta, V. K., and Sorooshian, S.: Shuffled Complex Evolution Approach for Effective and Efficient Global Minimization, J. Optimiz. Theory App., 76(3), 501–521, 1993. 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(5778), 1375–1378, 2006. Feingold, G.: Modeling of the first indirect effect: Analysis of measurement requirements, Geophys. Res. Lett., 130(19), ASC7.1–ASC7.4, 2003. Fitzgerald, J. W.: Effect of aerosol composition on cloud droplet size distribution – numerical study, J. Atmos. Sci., 31, 1358–1367, 1974. Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information, Water Resour. Res., 34(4), 751–763, 1998. Hänel, G.: The role of aerosol properties during the condensational stage of cloud: a reinvestigation of numerics and microphysics, Beitr. Phys. Atmosph., 60, 321–339, 1987. Hegg, D. A. and Larson, T. V.: The effects of microphysical parameterisation on model predictions of sulfate production in clouds, Tellus B, 42, 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(4), 1104–1122, 2000. Helsper, C., Fissan, H., Kapadia, A., and Liu, B. Y. H.: Data Inversion by simplex minimization for the electrical aerosol analyzer, Aerosol Sci. Technol., 1, 135–146, 1982. Hsieh, W. C., Nenes, A., Flagan, R. C., Seinfeld, J. H., Buzorius, G., and H., Jonsson.: 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. IPCC 2007: Climate Change: Summary for Policymakers, in: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K. B., Tignor M., and Miller, H. L., New York: Cambridge Univ. Press, 2007. Jacobson, M. Z.: Development and application of a new air pollution modeling system-II, Aerosol model structure and design, Atmos. Environ., 31, 131–144, 1997. 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. Kandlikar, M. and Ramachandran, G.: Inverse methods for analysing aerosol spectrometer measurements: A critical review, J. Aerosol. Sci., 30(4), 413–437, 1999. Köhler, H.: The nucleus in and the growth of hygroscopic droplets, Trans. Faraday Soc., 32, 1152–1161, 1936. Korhonen, H., Kerminen, V.-M., Lehtinen, K. E. J., and Kulmala, M.: CCN activation and cloud processing in sectional aerosol models with low size resolution, Atmos. Chem. Phys., 5, 2561–2570, http://dx.doi.org/10.5194/acp-5-2561-2005doi:10.5194/acp-5-2561-2005, 2005. Kuczera, G.: On the Relationship between the Reliability of Parameter Estimates and Hydrologic Time-Series Data Used in Calibration, Water Resour. Res., 18(1), 146–154, 1982. 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(5), 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. Lehtinen, K. E. J. and Kulmala, M.: A model for particle formation and growth in the atmosphere with molecular resolution in size, Atmos. Chem. Phys., 3, 251–257, http://dx.doi.org/10.5194/acp-3-251-2003doi:10.5194/acp-3-251-2003, 2003. 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. Lu, M. L., Conant, W. C., Jonsson, H. H., Varutbangkul, V., Flagan, R. C., and Seinfeld, J. H.: The Marine Stratus/Stratocumulus Experiment (MASE): Aerosol-cloud relationships in marine stratocumulus, J. Geophys. Res., 112, D10209, http://dx.doi:10.1029/2006JD007985doi:10.1029/2006JD007985, 2007. Luo, Y. Weng, Q., E. S., Wu, X. W., Gao, C., Zhou, X. H., and Zhang, L.: Parameter identifiability, constraint, and equifinality in data assimilation with ecosystem models, Ecol. Appl., 19(3), 571–574, 2009. 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. Nenes, A., Ghan, S., Abdul-Razzak, H., Chuang, P. Y., and Seinfeld, J. H.: Kinetic limitations on cloud droplet formation and impact on cloud albedo, Tellus, 53, 133–149, 2001. 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(17), 1848, http://dx.doi:10.1029/2002GL015295doi:10.1029/2002GL015295, 2002. Pérez, C. J., Martín, J., and Rufo, M. F.: Sensitivity estimations for Bayesian inference models solved by MCMC methods, Reliab. Eng. Sys. Safe., 91, 1310–1314, 2006. Pollacco, J. A. P. and Angulo-Jaramilo, R.: A Linking Test that investigates the feasibility of inverse modeling: application to a simple rainfall interception model for Mt Gambier, southeast South Australia, Hydrol. Process., 23(14), 2023–2032, 2009. Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation (Atmospheric and Oceanographic Sciences Library), 976~pp., Springer, 1996. 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. Reutter, P., Su, H., Trentmann, J., Simmel, M., Rose, D., Gunthe, S. S., Wernli, H., Andreae, M. O., and Pöschl, U.: Aerosol- and updraft-limited regimes of cloud droplet formation: influence of particle number, size and hygroscopicity on the activation of cloud condensation nuclei (CCN), Atmos. Chem. Phys., 9, 7067–7080, http://dx.doi.org/10.5194/acp-9-7067-2009doi:10.5194/acp-9-7067-2009, 2009. Roelofs, G. J.: On the drop and aerosol size dependence of aqueous sulfate formation in a continental cumulus cloud, Atmos. Environ., 26A, 2309–2321, 1992. 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:0.1029/2004JD004779doi:0.1029/2004JD004779, 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 modeling 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. Šimúnek, J., Wendroth, O., and van Genuchten, M. T.: Parameter estimation analysis of the evaporation method for determining soil hydraulic properties, Soil Sci. Soc. Am. J., 62(4), 894–905, 1998. Smith, P. L., Kliche, D. V., and Johnson, R. W.: The Bias and Error in Moment Estimators for Parameters of Drop Size Distribution Functions: Sampling from Gamma Distributions, J. Appl. Meteorol. Clim., 48(10), 2118–2126, 2009. Sorooshian, S. and Gupta, V. K.: The Analysis of Structural Identifiability – Theory and Application to Conceptual Rainfall-Runoff Models, Water Resour. Res., 21(4), 487–495, 1985. Sorooshian, S. and Arfi, F.: Response-Surface Parameter Sensitivity Analysis-Methods for Post-Calibration Studies, Water Resour. Res., 18(5), 1531–1538, 1982. Sorooshian, S., Gupta, V. K., and Fulton, J. L.: Evaluation of Maximum-Likelihood Parameter-Estimation Techniques for Conceptual Rainfall-Runoff Models – Influence of Calibration Data Variability and Length on Model Credibility, Water Resour. Res., 19(1), 251–259, 1983. Takeda, T. and Kuba, N.: Numerical Study of the Effect of CCN on the Size Distribution of Cloud Droplets .1. Cloud Droplets in the Stage of Condensation Growth, J. Meteorol. Soc. Jpn., 60(4), 978–993, 1982. Tao, T., Golovitchev, V. I., and Chomiak, J.: A phenomenological model for the prediction of soot formation in diesel spray combustion, Combust. Flame, 136(3), 270– 282, 2004. 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(7), 1239–1254, 2007. Toorman, A. F., Wierenga, P. J., and Hills, R. G.: Parameter-Estimation of Hydraulic-Properties from One-Step Outflow Data, Water Resour. Res., 28(11), 3021–3028, 1992. 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(D7), D07201, http://dx.doi:10.1029/2004JD005085doi:10.1029/2004JD005085, 2005. Twomey, S.: Comparison of Constrained Linear Inversion and an Iterative Nonlinear Algorithm Applied to Indirect Estimation of Particle-Size Distributions, J. Comput. Phys., 18(2), 188–200, 1975. Voutilainen, A. and Kaipio, J. P.: Sequential Monte Carlo estimation of aerosol size distributions, Comput. Stat. Data An., 48(4), 887–908, 2005. Voutilainen, A., Stratmann, F., and Kaipio, J. P.: A non-homogeneous regularization method for the estimation of narrow aerosol size distributions, J. Aerosol. Sci., 31(12), 1433–1445, 2000. Vrugt, J. A., Bouten, W., and Weerts, A. H.: Information content of data for identifying soil hydraulic parameters from outflow experiments, Soil Sci. Soc. Am. J., 65(1), 19–27, 2001. Vrugt, J. A., Schoups, G., Hopmans, J. W., Young, C., Wallender, W. W., Harter, T., and Bouten, W.: Inverse modeling of large-scale spatially distributed vadose zone properties using global optimization, Water Resour. Res., 40(6), W06503, http://dx.doi:10.1029/2003WR002706doi:10.1029/2003WR002706, 2004. Vrugt, J. A., Diks, C. G. H., Gupta, H. V., Bouten, W., and Verstraten, J. M.: Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour. Res., 41(1), W01017, http://dx.doi:10.1029/2004WR003059doi:10.1029/2004WR003059, 2005. Vrugt, J. A., Nualláin, B., Ó. B., Robinson, A., Bouten, W., Dekker, S. C., and Sloot, P. M. A.: Application of parallel computing to stochastic parameter estimation in environmental models, Comput.Geosci., 32(8), 1139–1155, 2006. Vrugt, J. A., Stauffer, P. H., Wohling, T., Robinson, B. A., and Vesselinov, V. V.: Inverse modeling of subsurface flow and transport properties: A review with new developments, Vadose Zone J., 7(2), 843–864, 2008. Vrugt, J. A., Braak Ter., 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, 2009. 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, 2010. Yapo, P. O., Gupta, H. V., and Sorooshian, S.: Automatic calibration of conceptual rainfall-runoff models: Sensitivity to calibration data, J. Hydrol., 181(1–4), 23–48, 2006. 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. Technol., 31, 487–514, 1999.