Abstract
This study incorporated the Weather Research and Forecasting (WRF) model double-moment 6-class (WDM6) microphysics scheme into the mesoscale version of the Global/Regional Assimilation and PrEdiction System (GRAPES_Meso). A rainfall event that occurred during 3–5 June 2015 around Beijing was simulated by using the WDM6, the WRF single-moment 6-class scheme (WSM6), and the NCEP 5-class scheme, respectively. The results show that both the distribution and magnitude of the rainfall simulated with WDM6 were more consistent with the observation. Compared with WDM6, WSM6 simulated larger cloud liquid water content, which provided more water vapor for graupel growth, leading to increased precipitation in the cold-rain processes. For areas with the warmrain processes, the sensitivity experiments using WDM6 showed that an increase in cloud condensation nuclei (CCN) number concentration led to enhanced CCN activation ratio and larger cloud droplet number concentration (Nc) but decreased cloud droplet effective diameter. The formation of more small-size cloud droplets resulted in a decrease in raindrop number concentration (Nr), inhibiting the warm-rain processes, thus gradually decreasing the amount of precipitation. For areas mainly with the cold-rain processes, the overall amount of precipitation increased; however, it gradually decreased when the CCN number concentration reached a certain magnitude. Hence, the effect of CCN number concentration on precipitation exhibits significant differences in different rainfall areas of the same precipitation event.
Similar content being viewed by others
References
Bae, S. Y., S.-Y. Hong, and K.-S. S. Lim, 2016: Coupling WRF double-moment 6-class microphysics schemes to RRTMG radiation scheme in weather research forecasting model. Adv. Meteor., 2016, 1–11, doi: 10.1155/2016/5070154.
Baker, M. B., 1997: Cloud microphysics and climate. Science, 276, 1072–1078, doi: 10.1126/science.276.5315.1072.
Chen, D. H., and X. S. Shen, 2006: Recent progress on GRAPES research and application. J. Appl. Meteor. Sci., 17, 773–777, doi: 10.3969/j.issn.1001-7313.2006.06.014. (in Chinese)
Chen, D. H., J. S. Xue, X. S. Yang, et al., 2008: New generation of multi-scale NWP system (GRAPES): General scientific design. Chinese Sci. Bull., 53, 3433–3445, doi: 10.1007/s11434-008-0494-z.
Chen, Y. D., R. Z. Zhang, D. M. Meng, et al., 2016: Variational assimilation of satellite cloud water/ice path and microphysics scheme sensitivity to the assimilation of a rainfall case. Adv. Atmos. Sci., 33, 1158–1170, doi: 10.1007/s00376-016-6004-3.
Clark, T. L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30, 857–878, doi: 10.1175/1520-0469(1973)030<0857:NMOTDA>2.0.CO;2.
Cohard, J.-M., and J.-P. Pinty, 2000a: A comprehensive twomoment warm microphysical bulk scheme. I: Description and tests. Quart. J. Roy. Meteor. Soc., 126, 1815–1842, doi: 10.1002/qj.49712656613.
Cohard, J.-M., and J.-P. Pinty, 2000b: A comprehensive twomoment warm microphysical bulk scheme. II: 2D experiments with a non-hydrostatic model. Quart. J. Roy. Meteor. Soc., 126, 1843–1859, doi: 10.1002/qj.49712656614.
Cotton, W. R., G. J. Tripoli, R. M. Rauber, et al., 1986: Numerical simulation of the effects of varying ice crystal nucleation rates and aggregation processes on orographic snowfall. J. Climate Appl. Meteor., 25, 1658–1680, doi: 10.1175/1520-0450(1986)025<1658:NSOTEO>2.0.CO;2.
Deng, Z. Z., C. S. Zhao, N. Ma, et al., 2013: An examination of parameterizations for the CCN number concentration based on in situ measurements of aerosol activation properties in the North China Plain. Atmos. Chem. Phys., 13, 145–176, doi: 10.5194/acp-13-6227-2013.
Dong, H., H. M. Xu, and Y. L. Luo, 2012: Effects of cloud condensation nuclei concentration on precipitation in convection permitting simulations of a squall line using WRF model: Sensitivity to cloud microphysical schemes. Chinese J. Atmos. Sci., 36, 145–169, doi: 10.3878/j.issn.1006-9895.2012.01.12. (in Chinese)
Duda, J. D., X. G. Wang, F. Y. Kong, et al., 2014: Using varied microphysics to account for uncertainty in warm-season QPF in a convection-allowing ensemble. Mon. Wea. Rev., 142, 2198–2219, doi: 10.1175/MWR-D-13-00297.1.
Feng, Q. J., P. R. Li, M. Y. Fan, et al., 2012: Observational analysis of cloud condensation nuclei in some regions of North China. Trans. Atmos. Sci., 35, 533–540, doi: 10.3969/j.issn.1674-7097.2012.05.003. (in Chinese)
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249–280,doi:10.1175/1520-0469(1994)051<0249:ADMMPF> 2.0.CO;2.
Guo, X. L., M. Y. Huang, H. Y. Xu, et al., 1999: Rain category numerical simulations of microphysical processes of precipitation formation in stratiform clouds. Chinese J. Atmos. Sci., 23, 745–752, doi: 10.3878/j.issn.1006-9895.1999.06.11. (in Chinese)
Gao, W. H., F. S. Zhao, Z. J. Hu, et al., 2012: Improved CAMS cloud microphysics scheme and numerical experiment coupled with WRF model. Chinese J. Geophys., 55, 396–405, doi: 10.6038/j.issn.0001-5733.2012.02.004. (in Chinese)
Guo, X. L., D. H. Fu, X. Guo, et al., 2014: A case study of aerosol impacts on summer convective clouds and precipitation over northern China. Atmos. Res., 142, 142–157, doi: 10.1016/j.atmosres.2013.10.006.
Hall, W. D., 1980: A detailed microphysical model within a twodimensional dynamic framework: Model description and preliminary results. J. Atmos. Sci., 37, 2486–2507, doi: 10.1175/1520-0469(1980)037<2486:ADMMWA>2.0.CO;2.
Hartmann, D. L., M. E. Ockert-Bell, and M. L. Michelsen, 1992: The effect of cloud type on earth’s energy balance: Global analysis. J. Climate, 5, 1281–1304, doi: 10.1175/1520-0442(1992)005<1281:TEOCTO>2.0.CO;2.
He, H., X. L. Guo, X. E. Liu, et al., 2016: Mesoscale numerical simulation study of warm fog dissipation by salt particles seeding. Adv. Atmos. Sci., 33, 579–592, doi: 10.1007/s00376-015-5151-2.
Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF single-moment 6- class microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129–151.
Hong, S.-Y, K.-S. S. Lim, Y.-H. Lee, et al., 2010: Evaluation of the WRF double-moment 6-class microphysics scheme for precipitating convection. Adv. Meteor., 707253, doi: 10.1155/2010/707253.
Hong, Y. C., and H. Y. Li, 2011: Cloud structure, precipitation mechanism and artificial enhancement precipitation condition for a frontal stratiform cloud system. Plateau Meteor., 30, 1308–1323. (in Chinese)
Hou, T.-J., H.-C. Lei, Z.-X. Hu, et al., 2013: Observations and modeling of ice water content in a mixed-phase cloud system. Atmos. Oceanic Sci. Lett., 6, 210–215, doi: 10.3878/j.issn.1674-2834.13.0020.
Hou, T. J., H. C. Lei, J. F. Yang, et al., 2016: Investigation of riming within mixed-phase stratiform clouds using weather research and forecasting (WRF) model. Atmos. Res., 178–179, 291–303, doi: 10.1016/j.atmosres.2016.04.007.
Hu, Z. J., and G. F. He, 1988: Numerical simulation of microphysical processes in cumulonimbus. Part I: Microphysical model. Acta Meteor. Sinica, 2, 471–489.
Khain, A. P., and I. Sednev, 1996: Simulation of precipitation formation in the eastern Mediterranean coastal zone using a spectral microphysics cloud ensemble model. Atmos. Res., 43, 77–110, doi: 10.1016/S0169-8095(96)00005-1.
Khain, A., A. Pokrovsky, M. Pinsky, et al., 2004: Simulation of effects of atmospheric aerosols on deep turbulent convective clouds using a spectral microphysics mixed-phase cumulus cloud model. Part I: Model description and possible applications. J. Atmos. Sci., 61, 2963–2982, doi: 10.1175/JAS-3350.1.
Khain, A., D. Rosenfeld, and A. Pokrovsky, 2005: Aerosol impact on the dynamics and microphysics of deep convective clouds. Quart. J. Roy. Meteor. Soc., 131, 2639–2663, doi: 10.1256/qj.04.62.
Kovačević, N., and M. Ćurić, 2015: Precipitation sensitivity to the mean radius of drop spectra: Comparison of single- and double-moment bulk microphysical schemes. Atmosphere, 6, 451–473, doi: 10.3390/atmos6040451.
Kogan, Y. L., 1991: The simulation of a convective cloud in a 3-D model with explicit microphysics. Part I: Model description and sensitivity experiments. J. Atmos. Sci., 48, 1160–1189, doi: 10.1175/1520-0469(1991)048<1160:TSOACC>2.0.CO;2.
Li, L., Y. Yin, X. S. Gu, et al., 2014: Observational study of cloud condensation nuclei properties at various altitudes of Huangshan mountains. Chinese J. Atmos. Sci., 38, 410–420, doi: 10.3878/j.issn.1006-9895.2013.13149. (in Chinese)
Li, J. X., Y. Yin, G. Ren, et al., 2015: Observational study of the spatial–temporal distribution of cloud condensation nuclei in Shanxi Province, China. China Environ. Sci., 35, 2261–2271, doi: 10.3969/j.issn.1000-6923.2015.08.003. (in Chinese)
Lim, K.-S. S., and S.-Y. Hong, 2010: Development of an effective double-moment cloud microphysics scheme with prognostic cloud condensation nuclei (CCN) for weather and climate models. Mon. Wea. Rev., 138, 1587–1612, doi: 10.1175/2009MWR2968.1.
Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065–1092, doi: 10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.
Liu, P. F., C. S. Zhao, T. Göbel, et al., 2011: Hygroscopic properties of aerosol particles at high relative humidity and their diurnal variations in the North China Plain. Atmos. Chem. Phys., 11, 3479–3494, doi: 10.5194/acp-11-3479-2011.
Lu, G. X., and X. L. Guo, 2012: Distribution and origin of aerosol and its transform relationship with CCN derived from the spring multi-aircraft measurements of Beijing cloud experiment (BCE). Chinese Sci. Bull., 57, 2460–2469, doi: 10.1007/s11434-012-5136-9.
Ma, N., C. S. Zhao, T. Müller, et al., 2012: A new method to determine the mixing state of light absorbing carbonaceous using the measured aerosol optical properties and number size distributions. Atmos. Chem. Phys., 12, 2381–2397, doi: 10.5194/acp-12-2381-2012.
Meyers, M. P., R. L. Walko, J. Y. Harrington, et al., 1997: New RAMS cloud microphysics parameterization. Part II: The two-moment scheme. Atmos. Res., 45, 3–39, doi: 10.1016/<1065:BPOTSF>S0169-8095(97)00018-5.
Molthan, A. L., and B. A. Colle, 2012: Comparisons of single-and double-moment microphysics schemes in the simulation of a synoptic-scale snowfall event. Mon. Wea. Rev., 140, 2982–3002, doi: 10.1175/MWR-D-11-00292.1.
Morrison, H., and J. O. Pinto, 2005: Mesoscale modeling of springtime arctic mixed-phase stratiform clouds using a new two-moment bulk microphysics scheme. J. Atmos. Sci., 62, 3683–3704, doi: 10.1175/JAS3564.1.
Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of oneand two-moment schemes. Mon. Wea. Rev., 137, 991–1007, doi: 10.1175/2008MWR2556.1.
Murakami, M., 1990: Numerical Modeling of dynamical and microphysical evolution of an isolated convective cloud: The 19 July 1981 CCOPE cloud. J. Metor. Soc. Japan, 68, 107–128, doi: 10.2151/jmsj1965.68.2_107.
Ovtchinnikov, M., and Y. L. Kogan, 2000: An investigation of ice production mechanisms in small cumuliform clouds using a 3D model with explicit microphysics. Part I: Model description. J. Atmos. Sci., 57, 2989–3003, doi: 10.1175/1520-0469(2000)057<2989:AIOIPM>2.0.CO;2.
Pinsky, M. B., and A. P. Khain, 2002: Effects of in-cloud nucleation and turbulence on droplet spectrum formation in cumulus clouds. Quart. J. Roy. Meteor. Soc., 128, 501–533, doi: 10.1256/003590002321042072.
Ramanathan, V., P. J. Crutzen, J. T, Kiehl, et al., 2001: Aerosols, climate, and the hydrological cycle. Science, 294, 2119–2124, doi: 10.1126/science.1064034.
Reisin, T., Z. Levin, and S. Tzivion, 1996: Rain production in convective clouds as simulated in an axisymmetric model with detailed microphysics. Part I: Description of the model. J. Atmos. Sci., 53, 497–519, doi: 10.1175/1520-0469(1996)053<0497:RPICCA>2.0.CO;2.
Reisner, J., R. M. Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124, 1071–1107, doi: 10.1002/qj.49712454804.
Rong, Y. M., and Y. Yin, 2010: The response of convective clouds to aerosol and relative humidity: A numerical study. Chinese J. Atmos. Sci., 34, 815–826, doi: 10.3878/j.issn.1006-9895.2010.04.13. (in Chinese)
Seifert, A., and K. D. Beheng, 2001: A double-moment parameterization for simulating autoconversion, accretion and selfcollection. Atmos. Res., 59–60, 265–281, doi: 10.1016/S0169-8095(01)00126-0.
Seifert, A., and K. D. Beheng, 2006: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Atmos. Phys., 92, 45–66, doi: 10.1007/s00703-005-0112-4.
Shen, X. Y., H. X. Mei, W. G. Wang, et al., 2015: Numerical simulation of ice-phase processes using a double-moment microphysical scheme and a sensitivity test of ice nuclei concentra-tion. Chinese J. Atmos. Sci., 39, 83–99, doi: 10.3878/j.issn.1006-9895.1405.13310. (in Chinese)
Shi, L. X., and Y. Duan, 2007: Observations of cloud condensation nuclei in North China. Acta Meteor. Sinica, 75, 644–652, doi: 10.3321/j.issn:0577-6619.2007.04.016.(in Chinese)
Shi, R. G., Q. J. Liu, and Z. S. Ma, 2015: Numerical simulation of aerosol effects on cloud and precipitation using GRAPES model. Meteor. Mon., 41, 272–285, doi: 10.7519/j.issn.1000-0526.2015.03.002. (in Chinese)
Soong, S.-T, 1974: Numerical simulation of warm rain development in an axisymmetric cloud model. J. Atmos. Sci., 31, 1262–1285, doi: 10.1175/1520-0469(1974)031<1262:NSOWRD>2.0.CO;2.
Stephens, G. L., 2005: Cloud feedbacks in the climate system: A critical review. J. Climate, 18, 237–273, doi: 10.1175/JCLI-3243.1.
Stevens, B., G. Feingold, W. R. Cotton, et al., 1996: Elements of the microphysical structure of numerically simulated nonprecipitating stratocumulus. J. Atmos. Sci., 53, 980–1006, doi: 10.1175/1520-0469(1996)053<0980:EOTMSO>2.0.CO;2.
Sun, J., X. F. Lou, Z. J. Hu, et al., 2008: Numerical experiment of the coupling of CAMS complex microphysical scheme and GRAPES model. J. Appl. Meteor. Sci., 19, 315–325, doi: 10.3969/j.issn.1001-7313.2008.03.007. (in Chinese)
Sun, J., X. F. Lou, and Y. Q. Shi, 2011: The effects of different microphysical schemes on the simulation of a meiyu front heavy rainfall. Acta Meteor. Sinica, 69, 799–809. (in Chinese)
Takahashi, T., 1975: Tropical showers in an axisymmetric cloud model. J. Atmos. Sci., 32, 1318–1330, doi: 10.1175/1520-0469(1975)032<1318:TSIAAC>2.0.CO;2.
Tao, Y., H. Y. Li, and Y. C. Hong, 2013: Numerical studies on cloud physics characteristic and influence of the graupel/hail category on cloud and precipitation during a heavy rainstorm over North China. Plateau Meteor., 32, 166–178, doi: 10.7522/j.issn.1000-0534.2012.00017. (in Chinese)
Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Wea. Rev., 132, 519–542, doi: 10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2.
Thompson, G., P. R. Field, R. M. Rasmussen, et al., 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095–5115, doi: 10.1175/2008MWR2387.1.
Van Weverberg, K., E. Goudenhoofdt, U. Blahak, et al., 2014: Comparison of one-moment and two-moment bulk microphysics for high-resolution climate simulations of intense precipitation. Atmos. Res., 147–148, 145–161, doi: 10.1016/j.atmosres.2014.05.012.
Wang, C., and J. S. Chang, 1993: A three-dimensional numerical model of cloud dynamics, microphysics, and chemistry. 1: Concepts and formulation. J. Geophys. Res., 98, 14827–14844, doi: 10.1029/92JD01393.
Wang, H., J. F. Yin, and D. H. Wang, 2014: Comparative analysis of single-moment and double-moment microphysics schemes on a local heavy rainfall in South China. Plateau Meteor., 33, 1341–1351, doi: 10.7522/j.issn.1000-0534.2013.00119. (in Chinese)
Wang, H., G. Y. Shi, X. Y. Zhang, et al., 2015: Mesoscale modelling study of the interactions between aerosols and PBL meteorology during a haze episode in China Jing–Jin–Ji and its near surrounding region—Part 2: Aerosols’ radiative feedback effects. Atmos. Chem. Phys., 15, 3277–3287, doi: 10.5194/acp-15-3277-2015.
Wu, X. J., Z. Y. Jin, L. P. Huang, et al., 2005: The software framework and application of GRAPES model. J. Appl. Meteor. Sci., 16, 539–546, doi: 10.3969/j.issn.1001-7313.2005.04.015. (in Chinese)
Wu, H. Y., D. H. Chen, and G. Q. Xu, 2007: Sensitive experiments of various parameterization schemes in different physical processes on Guizhou precipitation. Meteor. Mon., 33, 23–28, doi: 10.3969/j.issn.1000-0526.2007.04.004. (in Chinese)
Xiao, H., and Y. Yin, 2011: A numerical study of polluted aerosol effects on precipitation in Shanxi Province. Chinese J. Atmos. Sci., 35, 235–246, doi: 10.3878/j.issn.1006-9895.2011.02.04. (in Chinese)
Xiao, H., Y. Yin, L. J. Jin, et al., 2015: Simulation of the effects of aerosol on mixed-phase orographic clouds using the WRF model with a detailed bin microphysics scheme. J. Geophys. Res., 120, 8345–8358, doi: 10.1002/2014JD022988.
Xu, G. Q., X. D. Liang, H. Yu, et al., 2007: Precipitation simulation using different cloud–precipitation schemes for a landfall typhoon. Plateau Meteor., 26, 891–900. (in Chinese)
Xu, G. Q., D. H. Chen, J. S. Xue, et al., 2008: The program structure designing and optimizing tests of GRAPES physics. Chinese Sci. Bull., 53, 3470–3476, doi: 10.1007/s11434-008-0418-y.
Xu, G. Q., D. H. Chen, H. L. Zhang, et al., 2010: The impacts of time-level computation precision of physics in the GRAPES model on precipitation prediction. Chinese J. Atmos. Sci., 34, 875–881, doi: 10.3878/j.issn.1006-9895.2010.05.03. (in Chinese)
Yang, X. S., J. L. Hu, D. H. Chen, et al., 2008: Verification of GRAPES unified global and regional numerical weather prediction model dynamic core. Chinese Sci. Bull., 53, 3458–3464, doi: 10.1007/s11434-008-0417-z.
Yang, J. F., H. C. Lei, Z. X. Hu, et al., 2014: Particle size spectra and possible mechanisms of high ice concentration in nimbostratus over Hebei Province, China. Atmos. Res., 142, 79–90, doi: 10.1016/j.atmosres.2013.12.018.
Yin, Y., Z. Levin, T. Reisin, et al., 2000: Seeding convective clouds with hygroscopic flares: Numerical simulations using a cloud model with detailed microphysics. J. Appl. Meteor., 39, 1460–1472, doi: 10.1175/1520-0450(2000)039<1460:SCCWHF>2.0.CO;2.
Yin, Y., C. Chen, K. Chen, et al., 2010: An observational study of the microphysical properties of atmospheric aerosol at Mt Huang. Trans. Atmos. Sci., 33, 129–136, doi: 10.3969/j.issn.1674-7097.2010.02.001. (in Chinese)
Yin, Y., Q. Chen, L. J. Jin, et al., 2012: The effects of deep convection on the concentration and size distribution of aerosol particles within the upper troposphere: A case study. J. Geophys. Res. Atmos., 117, D22202, doi: 10.1029/2012JD017827.
Yuan, L., Y. Yin, H. Xiao, et al., 2016: A closure study of aerosol optical properties at a regional background mountainous site in eastern China. Sci. Total Environ., 550, 950–960, doi: 10.1016/j.scitotenv.2016.01.205.
Zhao, C. S., X. X. Tie, G. Brasseur, et al., 2006: Aircraft measurements of cloud droplet spectral dispersion and implications for indirect aerosol radiative forcing. Geophys. Res. Lett., 33, L16809, doi: 10.1029/2006GL026653.
Zhao, Z., and H. C. Lei, 2008: A numerical simulation of cloud physical structure and microphysical processes associated with stratiform precipitation in Northwest China. Chinese J. Atmos. Sci., 32, 323–334, doi: 10.3878/j.issn.1006-9895.2008.02.11. (in Chinese)
Zhao, Z., and H. C. Lei, 2014: Aircraft observations of liquid and ice in midlatitude mixed-phase clouds. Adv. Atmos. Sci., 31, 604–610, doi: 10.1007/s00376-013-3083-2.
Zhao, P. G., Y. Yin, and H. Xiao, 2015: The effects of aerosol on development of thunderstorm electrification: A numerical study. Atmos. Res., 153, 376–391, doi: 10.1016/j.atmosres.2014.09.011.
Zhou, C., X. Zhang, S. Gong, et al., 2016: Improving aerosol interaction with clouds and precipitation in a regional chemical weather modeling system. Atmos. Chem. Phys., 16, 145–160, doi: 10.5194/acp-16-145-2016.
Zhu, G. L., W. T. Lin, and Y. H. Cao, 2014: Numerical simulation of a rainstorm event over South China by using various cloud microphysics parameterization schemes in WRF model and its performance analysis. Chinese J. Atmos. Sci., 38, 513–523, doi: 10.3878/j.issn.1006-9895.2013.13202. (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Key Project (2016YFC0203306), National Natural Science Foundation of China (41590874), National (Key) 973 Program (2014CB441201), Chinese Academy of Meteorological Sciences’ Project (2017Z001), and Key Project of Air Pollution Cause and Control (DQGG0104).
Rights and permissions
About this article
Cite this article
Zhang, M., Wang, H., Zhang, X. et al. Applying the WRF Double-Moment Six-Class Microphysics Scheme in the GRAPES_Meso Model: A Case Study. J Meteorol Res 32, 246–264 (2018). https://doi.org/10.1007/s13351-018-7066-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13351-018-7066-1