Relation between cloud thickness-cloud number concentration differences and rain occurrence based on Koren-Feingold model

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1 Journal of Physics: Conference Series PAPER OPEN ACCESS Relation between cloud thickness-cloud number concentration differences and rain occurrence based on Koren-Feingold model Related content - Recent changes in the frequency of freezing precipitation in North America and Northern Eurasia Pavel Ya Groisman, Olga N Bulygina, Xungang Yin et al. To cite this article: R Sulistyowati et al 6 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on //8 at 5:

2 Journal of Physics: Conference Series 77 (6) 47 doi:.88/ /77//47 Relation between cloud thickness-cloud number concentration differences and rain occurrence based on Koren-Feingold model R Sulistyowati,, S Viridi, R Kurniadi and W Srigutomo Physics of Earth and Complex Systems Research Division, Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jal an Ganesha, Bandung 4, Indonesia Physics Education Department, Faculty of Teacher Training and Science Education, Universitas PGRI Palembang, Jalan Ahmad Yani, Lrg. Gotong Royong 9/ Ulu, Palembang, Indonesia Nuclear Physics and Biophysics Research Division, Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha, Bandung 4, Indonesia ritarahman8@gmail.com Abstract. Koren-Feingold (KF) model, a model that relates growth of cloud thickness (H) and cloud number concentration (N) is discussed and analyzed in this work. Two boundary conditions are required by this model, where the first is cloud thickness potential H and the second is aerosol concentration N. The initial conditions are simply H() = and N() =. Several pairs of (H, N ) values are chosen in calculating the precipitation. Three categories of rainfall are used in this work, which are no drizzle D, light drizzle D, and drizzle D. As H evolves in time t, it produces maximum cloud thickness H max and saturation cloud thickness H sat, as also N does N max and N sat. Two kinds of cloud thickness difference, ΔH = H H max and ΔH = H H sat are proposed and also for cloud concentration difference ΔN and ΔN with similar definitions. Pairs of (ΔH, ΔN ) and (ΔH, ΔN ) are used in analyzing simulation results. The first pair can be used as prediction of rainfall occurrence, while the second pair is more for confirmation and understanding the relation between cloud thickness and cloud concentration in producing rainfall. It is observed that H < H and N < N are always fulfilled. Rainfall in category D will have significant differences in H and N, while in category D will not. Typical differences for H are about 8 % and -5 % for both cases. Deeper discussion about (ΔH, ΔN ) and (ΔH, ΔN ) is presented in this work.. Introduction Aerosol-cloud interaction is a very complex process. It is an important key in understanding weather change, including the occurrence of rain [5,, 6]. However, the effect of aerosol particles on clouds and precipitation is still under debate [4, ] and poorly described. Numerous researches, based on observation and numerical, have been intensively carried to improve better understanding about this interaction. One of the numerical model that can explain the phenomenon is a model initiated by Koren- Feingold []. This model consists of equations that describe the coupled interactions between cloud thickness (H) and cloud number concentration (N) at rain occurances. In this study, Koren-Feingold Content from this work may be used under the terms of the Creative Commons Attribution. licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd

3 Journal of Physics: Conference Series 77 (6) 47 doi:.88/ /77//47 (KF) model is used to calculate changes in cloud thickness (ΔH) and aerosol concentrations (ΔN) at different rainfall events. An analysis of the values of ΔH and ΔN are expected to explain the behavior of changes in cloud thickness and aerosol concentrations due to rain.. Methodology KF model will be solved as equation (), () and () below []: dh H H H r ( t T) with H R dt c H c N () dn dt N N N r ( t T) with H r c NR () N d H ( t T' ) R( t) () N( t T' ) First equation described the growth rate of cloud, first term of right side indicates cloud growth before rain falls, while the second term serves the same but after rain falls. c is a constant value as a function of cloud base temperature and pressure; for warm adiabatic cloud c - m - and is a constant related to warm stratocumulus clouds. H shows carrying capacity of cloud, namely potential cloud thickness. So that if there is no rain, after constant time (τ ), maximum amount of cloud growth H could reach asymtotic limit of H. In the equation (), N is assumed to be aerosol background concentration belong to the system (carrying capacity). τ is constant time of aerosol growth characteristic and c - m - []. The used input is H and N. Some input pair H and N are employed to calculate some rain (R) occurences and generate values of rainfall with several categories, namely: No Drizzle (D), Light Drizzle (D), and Drizzle (D). For the initial conditions, H () = and N () = are set. As H evolves in time t, it produces maximum cloud thickness H max and saturation cloud thickness H sat, as also N does N max and N sat. Some parameters were used to analyze cloud thickness change and cloud number concentration (N) change, before and after rain. Those are defined as shown at the table below: Table. Parameter and definition of cloud thickness (ΔH) and cloud number concentration (ΔN) change Parameter Definition ΔH ΔH = H H max ΔH ΔH = H H sat ΔN ΔN = N N max ΔN ΔN = N N sat. Results and discussions From the calculation of the KF model equation, we obtained the relationship between ΔH and ΔN as seen in figures and below

4 Journal of Physics: Conference Series 77 (6) 47 doi:.88/ /77//47 From 4 the calculation of the equation model KF, we obtained the relationship between and ΔN as seen 5in figures and below N (cm - ) 5 No Drizzle Light Drizzle Drizzle N (cm - ) 4 No Drizzle Light Drizzle Drizzle H (m) 4 6 H (m) Figure. Relation between H and N Figure. Relation between H and N Figure shows the coupled relationship between ΔH and ΔN in different rain events. The condition of No Drizzle (D) generally occurred in ΔH, both ΔH and ΔH, less than m. Light Drizzle (D) condition occurs in ΔH between - m; while Drizzle (D) condition occurs in ΔH> m. While, for all condition of the same H, either D, D or D generally occure at all range of ΔN. Based on this analysis, it can be stated that in prediction of the presence/absence of rain, ΔH and ΔH value have contribution more than the value ΔN and ΔN. Further, the change of cloud thickness and cloud number concentration at numerous rain occurences could be analyzed from percentage of N sat decrease to N max D D H (m) 4 Hmax Hsat N (cm - ) 4 Nmax Nsat D 5 5 H (m) Figure. Plot of H max and H sat for some rain occurences D 5 N (cm - ) Figure 4. Plot of N max and N sat for some rain occurences D D

5 Journal of Physics: Conference Series 77 (6) 47 doi:.88/ /77//47 In the condition of No Drizzle (D), there are no significant differences between the value ΔH and ΔH, as well as between ΔN and ΔN. Conversely, for the condition of Light Drizzle (D) and Drizzle (D), the difference in value ΔH and ΔH, ΔN and ΔN, increased. At conditions of Light Drizzle, the concentration of cloud number saturation (N sat) due to rain occurences may decrease as much as -5% of the value N max. While the condition of Drizzle, N sat value may decrease until it reaches 8% of the value N max that can be achieved. 4. Conclusion KF models can be used to identify some rain occurences through the analysis of the value of ΔH and ΔN. For various categories of rain occurences, both value (ΔH, ΔN ) or (ΔH, ΔN ) showed the same pattern that increases linearly. Rain occurences are more likely to be influenced by ΔH than ΔN. Parameter ΔH more relevant for the prediction of the presence/absence of rain (before the rain occurs) while ΔH more relevant to investigate the character/kind of rain because the calculation of ΔH requires H sat value that can only be known after the rain. Acknowledgments This research is funded by Institut Teknologi Bandung Research Program 6 (Division Research B). References [] Houghton J T et al IPCC Third Assessment Report Climate change : The scientific basis (Cambridge: Cambridge Univ. Press) p 994 [] Koren I and Feingold G Aerosol cloud precipitation system as a predator-prey problem Proceedings of the National Academy of Sciences 8 7- [] NASA planning document. Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) OCT.pdf. [4] National Research Council (NRC) 5 Radiative forcing of climate change: Expanding the concept and addressing uncertainties (Washington DC: The National Academies Press) [5] Ramanathan V et al Science [6] Tao W K et al Impact of aerosols on convective clouds and precipitation Rev. Geophys. 5 4