Skip to main content
Log in

Examination of microphysical relationships and corresponding microphysical processes in warm fogs

  • Articles
  • Published:
Acta Meteorologica Sinica Aims and scope Submit manuscript

Abstract

In this paper, the microphysical relationships of 8 dense fog events collected from a comprehensive fog observation campaign carried out at Pancheng (32.2°N, 118.7°E) in the Nanjing area, China in the winter of 2007 are investigated. Positive correlations are found among key microphysical properties (cloud droplet number concentration, droplet size, spectral standard deviation, and liquid water content) in each case, suggesting that the dominant processes in these fog events are likely droplet nucleation with subsequent condensational growth and/or droplet deactivation via complete evaporation of some droplets. The abrupt broadening of the fog droplet spectra indicates the occurrence of the collision-coalescence processes as well, although not dominating. The combined effects of the dominant processes and collision-coalescence on microphysical relationships are further analyzed by dividing the dataset according to visibility or autoconversion threshold in each case. The result shows that the specific relationships of number concentration to volume-mean radius and spectral standard deviation depend on the competition between the compensation of small droplets due to nucleation-condensation and the loss of small droplets due to collision-coalescence. Generally, positive correlations are found for different visibility or autoconversion threshold ranges in most cases, although negative correlations sometimes appear with lower visibility or larger autoconversion threshold. Therefore, the compensation of small droplets is generally stronger than the loss, which is likely related to the sufficient fog condensation nuclei in this polluted area.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Achtemeier, G. L., 2008: Effects of moisture released during forest burning on fog formation and implications for visibility. J. Appl. Meteor. Climatol., 47, 1287–1296.

    Google Scholar 

  • Baumgardner, D., B. Baker, and K. Weaver, 1993: A technique for the measurement of cloud structure on centimeter scales. J. Atmos. Oceanic Technol., 10, 557–565.

    Google Scholar 

  • Bergot, T., and D. Guedalia, 1994: Numerical forecasting of radiation fog. Part I: Numerical model and sensitivity tests. Mon. Wea. Rev., 122, 1218–1230.

    Google Scholar 

  • —, E. Terradellas, J. Cuxart, et al., 2007: Intercomparison of single-column numerical models for the prediction of radiation fog. J. Appl. Meteor. Climatol., 46, 504–521.

    Google Scholar 

  • Bott, A., U. Sievers, and W. Zdunkowski, 1990: A radiation fog model with a detailed treatment of the interaction between radiative transfer and fog microphysics. J. Atmos. Sci., 47, 2153–2166.

    Google Scholar 

  • Burnet, F., and J. L. Brenguier, 2007: Observational study of the entrainment-mixing process in warm convective clouds. J. Atmos. Sci., 64, 1995–2011.

    Google Scholar 

  • China Meteorological Administration, 2007: Specifications for surface meteorological observation. Part IV: Observation of weather phenomenon. QX/T 48-2007. (in Chinese)

    Google Scholar 

  • Croft, P. J., R. L. Pfost, J. M. Medlin, et al., 1997: Fog forecasting for the southern region: A conceptual model approach. Wea. Forecasting, 12, 545–556.

    Google Scholar 

  • Duynkerke, P. G., 1991: Observation of a quasi-periodic oscillation due to gravity waves in a shallow radiation fog. Quart. J. Roy. Meteor. Soc., 117, 1207–1224.

    Google Scholar 

  • Eldridge, R. G., 1971: The relationship between visibility and liquid water content in fog. J. Atmos. Sci., 28, 1183–1186.

    Google Scholar 

  • Eugster, W., R. Burkard, F. Holwerda, et al., 2006: Characteristics of fog and fogwater fluxes in a Puerto Rican elfin cloud forest. Agr. Forest Meteorol., 139, 288–306.

    Google Scholar 

  • Fu, G., J. T. Guo, S.-P. Xie, et al., 2006: Analysis and high-resolution modeling of a dense sea fog event over the Yellow Sea. Atmos. Res., 81, 293–303.

    Google Scholar 

  • —, —, A. Pendergrass, et al., 2008: An analysis and modeling study of a sea fog event over the Yellow and Bohai seas. Journal of Ocean University of China, 7, 27–34.

    Google Scholar 

  • Fuzzi, S., M. C. Facchini, G. Orsi, et al., 1992: The Po Valley fog experiment 1989. Tellus B, 44, 448–468.

    Google Scholar 

  • Gao, S. H., H. Lin, B. Shen, et al., 2007: A heavy sea fog event over the Yellow Sea in March 2005: Analysis and numerical modeling. Adv. Atmos. Sci., 24, 65–81.

    Google Scholar 

  • Garcá-Garcá, F., and R. A. Montañez, 1991: Warm fog in eastern Mexico: A case study. Atmósfera, 4, 53–64

    Google Scholar 

  • —, U. Virafuentes, and G. Montero-Martínez, 2002: Fine-scale measurements of fog-droplet concentrations: A preliminary assessment. Atmos. Res., 64, 179–189.

    Google Scholar 

  • Gerber, H., 1991: Supersaturation and droplet spectral evolution in fog. J. Atmos. Sci., 48, 2569–2588.

    Google Scholar 

  • Ghosh, S., J. Dávila, J. C. R. Hunt, et al., 2005: How turbulence enhances coalescence of settling particles with applications to rain in clouds. Proceedings of the Royal Society A; Mathematical, Physical and Engineering Sciences, 461, 3059–3088.

    Google Scholar 

  • Gonser, S. G., O. Klemm, F. Griessbaum, et al., 2012: The relation between humidity and liquid water content in fog: An experimental approach. Pure Appl. Geophys., 169(5–6), 821–833.

    Google Scholar 

  • Gultepe, I., M. D. Müller, and Z. Boybeyi, 2006: AA new visibility parameterization for warm-fog applications in numerical weather prediction models. J. Appl. Meteor. Climatol., 45, 1469–1480.

    Google Scholar 

  • —, R. Tardif, S. C. Michaelides, et al., 2007: Fog research: A review of past achievements and future perspectives. Pure Appl. Geophys., 164, 1121–1159.

    Google Scholar 

  • —, B. Hansen, S. G. Cober, et al., 2009: The fog remote sensing and modeling field project. Bull. Amer. Meteor. Soc., 90, 341–359.

    Google Scholar 

  • Haeffelin, M., T. Bergot, T. Elias, et al., 2010: PARISFOG: Shedding new light on fog physical processes. Bull. Amer. Meteor. Soc., 91, 767–783.

    Google Scholar 

  • Haman, K. E., S. P. Malinowski, M. J. Kurowski, et al., 2007: Small scale mixing processes at the top of a marine stratocumulus-A case study. Quart. J. Roy. Meteor. Soc., 133, 213–226.

    Google Scholar 

  • He Youjiang, Zhu Bin, and Ma Li, 2003: The physical process of Chongqing fog’s genesis and dissipation in winter. J. Nanjing Inst. Meteor., 26, 821–828. (in Chinese)

    Google Scholar 

  • Hong Zhongxiang and Huang Meiyuan, 1965: The second maximum and other related characteristics of the southern mountain cloud spectra. The Study on Microphysics of Cloud/Fog Precipitation in China, J. Zhao, Ed., Science Press, 18–29. (in Chinese)

    Google Scholar 

  • Hu Ruijin, Dong Kehui, and Zhou Faxiu, 2006: Numerical experiments with the advection, turbulence and radiation effects in sea fog formation process. Adv. Mar. Sci., 24, 156–165. (in Chinese)

    Google Scholar 

  • Huang, H. J., H. N. Liu, W. M. Jiang, et al., 2011: Characteristics of the boundary layer structure of sea fog on the coast of southern China. Adv. Atmos. Sci., 28, 1377–1389.

    Google Scholar 

  • Huang Yusheng, Huang Yuren, Li Zihua, et al., 2000: The microphysical structure and evolution of winter fog in Xishuangbanna. Acta Meteor. Sinica, 58, 715–725. (in Chinese)

    Google Scholar 

  • Hudson, J. G., 1980: Relationship between fog condensation nuclei and fog microstructure. J. Atmos. Sci., 37, 1854–1867.

    Google Scholar 

  • —, and G. Svensson, 1995: Cloud microphysical relationships in California marine stratus. J. Appl. Meteor., 34, 2655–2666.

    Google Scholar 

  • Jia Xingcan and Guo Xueliang, 2012: Impacts of anthropogenic atmospheric pollutant on formation and development of a winter heavy fog event. Chinese J. Atmos. Sci., 36, 995–1008. (in Chinese)

    Google Scholar 

  • Jonas, P. R., 1996: Turbulence and cloud microphysics. Atmos. Res., 40, 283–306.

    Google Scholar 

  • Kim, C. K., 2011: An observational and numerical study of sea fog formation off the west coast of the Korean Peninsula. Ph. D. dissertation, Yonsei University, 200 pp.

    Google Scholar 

  • Klemm, O., and T. Wrzesinsky, 2007: Fog deposition fluxes of water and ions to a mountainous site in central Europe. Tellus B, 59, 705–714.

    Google Scholar 

  • Kong, F. Y., 2002: An experimental simulation of a coastal fog-stratus case using COAMPS(tm) model. Atmos. Res., 64, 205–215.

    Google Scholar 

  • Kunkel, B. A., 1984: Parameterization of droplet terminal velocity and extinction coefficient in fog models. J. Climate Appl. Meteor., 23, 34–41.

    Google Scholar 

  • Li, P. F., X. Li, C. Y. Yang, et al., 2011: Fog water chemistry in Shanghai. Atmos. Environ., 45, 4034–4041.

    Google Scholar 

  • Li, P. Y., G. Fu, C. G. Lu, et al., 2012: The formation mechanism of a spring sea fog event over the Yellow Sea associated with a low-level jet. Wea. Forecasting, 27, 1538–1553.

    Google Scholar 

  • Li Zihua, 2001: Studies of fog in China over the past 40 years. Acta Meteor. Sinica, 59, 616–624. (in Chinese)

    Google Scholar 

  • —, Zhang Limin, and Zhang Qinghong, 1994: The physical structure of the winter fog in Chongqing metropolitan area and its formation process. Acta Meteor. Sinica, 8(3), 316–328.

    Google Scholar 

  • —, Shi Chun’e, and Lu Taoshi, 1997: 3D model study on fog over complex terrain. Part II: Numerical experiment. Acta Meteor. Sinica, 11, 88–94.

    Google Scholar 

  • —, Huang Jianping, Huang Yusheng, et al., 1999: Study on the physical process of winter valley fog in Xishuangbanna region. Acta Meteor. Sinica, 13(4), 494–508.

    Google Scholar 

  • Liu Duanyang, Pu Meijuan, Yang Jun, et al., 2010: Microphysical structure and evolution of a four-day persistent fog event in Nanjing in December 2006. Acta Meteor. Sinica, 24, 104–115.

    Google Scholar 

  • —, Yang Jun, Niu Shengjie, et al., 2011: On the evolution and structure of a radiation fog event in Nanjing. Adv. Atmos. Sci., 28, 223–237.

    Google Scholar 

  • Liu, Y. G, P. H. Daum, and R. McGraw, 2004: An analytical expression for predicting the critical radius in the autoconversion parameterization. Geophys. Res. Lett., 31, L06121.

    Google Scholar 

  • —, —, and —, 2005: Size truncation effect, threshold behavior, and a new type of autoconversion parameterization. Geophys. Res. Lett., 32, L11811.

    Google Scholar 

  • —, —, R. McGraw, et al., 2006: Generalized threshold function accounting for effect of relative dispersion on threshold behavior of autoconversion process. Geophys. Res. Lett., 33, L11804.

    Google Scholar 

  • —, —, S. S. Yum, et al., 2008: Use of microphysical relationships to discern growth/decay mechanisms of cloud droplets with focus on Z-LWC relationships. Proc. 15th International Conference on Clouds and Precipitation, Cancun, Mexico, the International Commission on Clouds and Precipitation (ICCP).

    Google Scholar 

  • Lu, C. S., and S. J. Niu, 2008: Study on microphysical characteristics of winter fog in Nanjing area, China. Proc. 2008 International Workshop on Education Technology and Training & 2008 International Workshop on Geoscience and Remote Sensing, IEEE Computer Society, Shanghai, China, 273–276.

    Google Scholar 

  • —, —, Yang Jun, et al., 2010a: Jump features and causes of macro and microphysical structures of a winter fog in Nanjing. Chinese J. Atmos. Sci., 34, 681–690. (in Chinese)

    Google Scholar 

  • —, —, L. L. Tang, et al., 2010b: Chemical composition of fog water in Nanjing area of China and its related fog microphysics. Atmos. Res., 97, 47–69.

    Google Scholar 

  • —, Y. G. Liu, and S. J. Niu, 2011: Examination of turbulent entrainment-mixing mechanisms using a combined approach. J. Geophys. Res., 116, D20207.

    Google Scholar 

  • Meyer, M. B., J. E. Jiusto, and G. G. Lala, 1980: Measurements of visual range and radiation-fog (haze) microphysics. J. Atmos. Sci., 37, 622–629.

    Google Scholar 

  • —, G. G. Lala, and J. E. Jiusto, 1986: Fog-82: A cooperative field study of radiation fog. Bull. Amer. Meteor. Soc., 67, 825–832.

    Google Scholar 

  • Niu, F., Z. Q. Li, C. Li, et al., 2010a: Increase of wintertime fog in China: Potential impacts of weakening of the East Asian monsoon circulation and increasing aerosol loading. J. Geophys. Res., 115, D00K20.

    Google Scholar 

  • Niu, S. J., C. S. Lu, H. Y. Yu, et al., 2010b: Fog research in China: An overview. Adv. Atmos. Sci., 27, 639–661.

    Google Scholar 

  • —, —, Y. G. Liu, et al., 2010c: Analysis of the microphysical structure of heavy fog using a droplet spectrometer: A case study. Adv. Atmos. Sci., 27, 1259–1275.

    Google Scholar 

  • —, D. Y. Liu, L. J. Zhao, et al., 2012: Summary of a 4-year fog field study in northern Nanjing. Part 2: Fog microphysics. Pure Appl. Geophys., 169(5–6), 1137–1155.

    Google Scholar 

  • Petterssen, S., 1956: Weather Analysis and Forecasting. 2nd ed. Vol. 2, McGraw-Hill, 266 pp.

    Google Scholar 

  • Pilié, R. J., E. J. Mack, W. C. Kocmond, et al., 1975: The life cycle of valley fog. Part II: Fog microphysics. J. Appl. Meteor., 14, 364–374.

    Google Scholar 

  • Pinnick, R. G., D. L. Hoihjelle, G. Fernandez, et al., 1978: Vertical structure in atmospheric fog and haze and its effects on visible and infrared extinction. J. Atmos. Sci., 35, 2020–2032.

    Google Scholar 

  • Porson, A., J. Price, A. Lock, et al., 2011: Radiation fog. Part II: Large-eddy simulations in very stable conditions. Bound.-Lay. Meteor., 139, 193–224.

    Google Scholar 

  • Price, J., 2011: Radiation fog. Part I: Observations of stability and drop size distributions. Bound.-Lay. Meteor., 139, 167–191.

    Google Scholar 

  • Pu, M. J., G. Z. Zhang, W. L. Yan, et al., 2008: Features of a rare advection-radiation fog event. Sci. China (Ser. D), 51, 1044–1052.

    Google Scholar 

  • Quan, J., Q. Zhang, H. He, et al., 2011: Analysis of the formation of fog and haze in North China Plain (NCP). Atmos. Chem. Phys., 11, 8205–8214.

    Google Scholar 

  • Rémy, S., and T. Bergot, 2010: Ensemble Kalman Filter data assimilation in a 1D numerical model used for fog forecasting. Mon. Wea. Rev., 138, 1792–1810.

    Google Scholar 

  • Roach, W. T., 1976: On some quasi-periodic oscillations observed during a field investigation of radiation fog. Quart. J. Roy. Meteor. Soc., 102, 355–359.

    Google Scholar 

  • —, R. Brown, S. J. Caughey, et al., 1976: The physics of radiation fog. I: A field study. Quart. J. Roy. Meteor. Soc., 102, 313–333.

    Google Scholar 

  • Rogers, R. R., and M. K. Yau, 1989: A Short Course in Cloud Physics. 3rd ed. Butterworth Heinemann, 290 pp.

    Google Scholar 

  • Roquelaure, S., and T. Bergot, 2008: A local ensemble prediction system for fog and low clouds: Construction, bayesian model averaging calibration, and validation. J. Appl. Meteor. Climatol., 47, 3072–3088.

    Google Scholar 

  • Shi Chun’e, Sun Xuejin, Yang Jun, et al., 1996: 3D model study on fog over complex terrain. Part I: Numerical study. Acta Meteor. Sinica, 10, 493–506.

    Google Scholar 

  • —, J. Yang, M. Y. Qiu, et al., 2010: Analysis of an extremely dense regional fog event in eastern China using a mesoscale model. Atmos. Res., 95, 428–440.

    Google Scholar 

  • —, L. Wang, H. Zhang, et al., 2012: Fog simulations based on multi-model system: A feasibility study. Pure Appl. Geophys., 169(5–6), 941–960.

    Google Scholar 

  • Stoelinga, M. T., and T. T. Warner, 1999: Nonhydrostatic, mesobeta-scale model simulations of cloud ceiling and visibility for an east coast winter precipitation event. J. Appl. Meteor., 38, 385–404.

    Google Scholar 

  • Stolaki, S., I. Pytharoulis, and T. Karacostas, 2012: A study of fog characteristics using a coupled WRFCOBEL model over Thessaloniki airport, Greece. Pure Appl. Geophys., 169(5–6), 961–981.

    Google Scholar 

  • Tardif, R., and R. M. Rasmussen, 2007: Event-based climatology and typology of fog in the New York City region. J. Appl. Meteor. Climatol., 46, 1141–1168.

    Google Scholar 

  • Thalmann, E., R. Burkard, T. Wrzesinsky, et al., 2002: Ion fluxes from fog and rain to an agricultural and a forest ecosystem in Europe. Atmos. Res., 64, 147–158.

    Google Scholar 

  • Thoma, C., W. Schneider, M. Masbou, et al., 2012: Integration of local observations into the one dimensional fog model PAFOG. Pure Appl. Geophys., 169(5–6), 881–893.

    Google Scholar 

  • Tomasi, C., and F. Tampieri, 1976: Features of the proportionality coefficient in the relationship between visibility and liquid water content in haze and fog. Atmosphere, 14, 61–76.

    Google Scholar 

  • Wang, G. L., L. M. Huang, S. X. Gao, et al., 2002: Characterization of water-soluble species of PM10 and PM2.5 aerosols in urban area in Nanjing, China. Atmos. Environ., 36, 1299–1307.

    Google Scholar 

  • —, H. Wang, Y. J. Yu, et al., 2003: Chemical characterization of water-soluble components of PM10 and PM2.5 atmospheric aerosols in five locations of Nanjing, China. Atmos. Environ., 37, 2893–2902.

    Google Scholar 

  • Wang, J., P. H. Daum, S. S. Yum, et al., 2009: Observations of marine stratocumulus microphysics and implications for processes controlling droplet spectra: Results from the Marine Stratus/Stratocumulus Experiment. J. Geophys. Res., 114, D18210.

    Google Scholar 

  • Welch, R. M., M. G. Ravichandran, and S. K. Cox, 1986: Prediction of quasi-periodic oscillations in radiation fogs. Part I: Comparison of simple similarity approaches. J. Atmos. Sci., 43, 633–651.

    Google Scholar 

  • Wendisch, M., S. Mertes, J. Heintzenberg, et al., 1998: Drop size distribution and LWC in Po Valley fog. Contrib. Atmos. Phys., 71, 87–100.

    Google Scholar 

  • Wobrock, W., D. Schell, R. Maser, et al., 1992: Meteorological characteristics of the Po Valley fog. Tellus B, 44, 469–488.

    Google Scholar 

  • Xue, Y., L.-P. Wang, and W. W. Grabowski, 2008: Growth of cloud droplets by turbulent collisioncoalescence. J. Atmos. Sci., 65, 331–356.

    Google Scholar 

  • Yang, D., H. Ritchie, S. Desjardins, et al., 2010: Highresolution GEM-LAM application in marine fog prediction: Evaluation and diagnosis. Wea. Forecasting, 25, 727–748.

    Google Scholar 

  • Yang, J., Y.-J. Xie, C.-E. Shi, et al., 2012: Ion composition of fog water and its relation to air pollutants during winter fog events in Nanjing, China. Pure Appl. Geophys., 169(5–6), 1037–1052.

    Google Scholar 

  • Yuan Jinnan and Huang Jian, 2011: An observational analysis and 3-dimensional numerical simulation of a sea fog event near the Pearl River Mouth in boreal spring. Acta Meteor. Sinica, 69, 847–859. (in Chinese)

    Google Scholar 

  • Yue, Y. Y., S. J. Niu, L. J. Zhao, et al., 2012: Chemical composition of sea fog water along the South China Sea. Pure Appl. Geophys., 169, 2231–2249.

    Google Scholar 

  • —, —, —, et al., 2013: Study on the synoptic system and macro-micro characteristics of sea fog along the Zhanjiang coastal area. Chinese J. Atmos. Sci., 37, 609–622. (in Chinese)

    Google Scholar 

  • Yum, S., 1998: Cloud droplet spectral broadening in warm clouds: An observational and model study. Ph. D. dissertation, University of Nevada, 191 pp.

    Google Scholar 

  • Zhang, S. P., 2012: Recent observations and modeling study about sea fog over the Yellow Sea and East China Sea. Journal of Ocean University of China, 11, 465–472.

    Google Scholar 

  • Zhang Shuting, Niu Shengjie, and Zhao Lijuan, 2013: The microphysical structure of fog droplets in a sea fog event in the South China Sea. Chinese J. Atmos. Sci., 37, 552–562. (in Chinese)

    Google Scholar 

  • Zhang, Q., J. N. Quan, X. X. Tie, et al., 2011: Impact of aerosol particles on cloud formation: Aircraft measurements in China. Atmos. Environ., 45, 665–672.

    Google Scholar 

  • Zhao, L. J., S. J. Niu, Y. Zhang, et al., 2013: Microphysical characteristics of sea fog over the east coast of Leizhou Peninsula, China. Adv. Atmos. Sci., 30, 1154–1172.

    Google Scholar 

  • Zhou, B. B., and B. S. Ferrier, 2008: Asymptotic analysis of equilibrium in radiation fog. J. Appl. Meteor. Climatol., 47, 1704–1722.

    Google Scholar 

  • —, and J. Du, 2010: Fog prediction from a multimodel mesoscale ensemble prediction system. Wea. Forecasting, 25, 303–322.

    Google Scholar 

  • —, J. Du, I. Gultepe, et al., 2012: Forecast of low visibility and fog from NCEP: Current status and efforts. Pure Appl. Geophys., 169(5–6), 895–909.

    Google Scholar 

  • Zhou, Y., S. J. Niu, and J. J. Lu, 2013: The influence of freezing drizzle on wire icing during freezing fog events. Adv. Atmos. Sci., 30, 1053–1069.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chunsong Lu  (陆春松).

Additional information

Supported by National Natural Science Foundation of China (41305120, 41030962, 41275151, 41375138, 41375137, and 41305034), Natural Science Foundation of Jiangsu Province (BK20130988, SK201220841), Specialized Research Fund for the Doctoral Program of Higher Education (20133228120002), China Meteorological Administration Special Public Welfare Research Fund (GYHY201406007), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (13KJB170014), Open Funding from Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration (KDW1201, KDW1102), Open Funding from Key Laboratory of Meteorological Disaster of Ministry of Education (KLME1205, KLME1107), Open Funding from State Key Laboratory of Severe Weather (2013LASW-B06), Qing-Lan Project for Cloud-Fog-Precipitation-Aerosol Study in Jiangsu Province, Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and U.S. Department of Energy’s (DOE) Earth System Modeling (ESM) program via the FASTER project (www.bnl.gov/faster) and Atmospheric System Research (ASR) program.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, C., Liu, Y., Niu, S. et al. Examination of microphysical relationships and corresponding microphysical processes in warm fogs. Acta Meteorol Sin 27, 832–848 (2013). https://doi.org/10.1007/s13351-013-0610-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13351-013-0610-0

Key words

Navigation