Author(s): Yan Diran; Huang Hao; Chen Guoxin

Linked Author(s): Guangqian Wang

Keywords: Droplet size spectrum; Kinetic Collection Equation; Bin-based method; Lagrangian super-particle method; Hybrid model; Numerical Simulation

Abstract: It has been discussed extensively but remains many questions how droplet size spectrum (DSP) develops and finally evolves into rainfall in warm clouds. Collision-coalescence is proven a major mechanism of droplet growth and DSP development, and much research has been conducted through solving the Kinetic Collection Equation (KCE), which is an ordinary differential equation without analytical solutions in most conditions. The bin-based method (BM) and the Lagrangian super-particle method (LSM) are the two most popular methods for the approximate solutions. BM is to divide the droplet size into several bins and calculate the gain and loss of droplet concentration in each bin by integrating KCE, and LSM is to trace the growth of droplets. However, BM cannot clearly reflect the behavior of big droplets when the kernel function in KCE is large, and cannot reveal the fluctuation of KCE making for sparse but important large ‘lucky droplets’; while LSM faces the contradiction between accuracy and efficiency if there are too many droplets. Considering the concerns of how big droplets absorb water from small ones in cloud studies and the scope of application of each method, we create a hybrid model (HM) that applies BM to small droplets and LSM to big ones, with the radius of 20 μm as the threshold. The bins are equally divided by mass in BM and the method by Shima et al. (2009) is adopted in LSM. Treatments are developed for the emergence of new big droplets from continuous DSP, the interaction between small and larger ones and mass conservation. The program is realized by Python and techniques of parallel computing are introduced to improve the efficiency. We evaluate our model by comparing it with a classical BM by Bott (1998) using two kernels that have analytic solutions for KCE. We take 3 or 4 different values for all the 7 variables in the 24 groups of simulations, and the average of 50 simulations is used in each group. The DSP including big droplets is drawn by moving average, and the cumulative distributions of mass are also calculated to evaluate the mass conservation. We find that HM can provide relatively accurate DSPs after one hour’s collision with higher efficiency and stability. We also explore the DSP evolution in the turbulence or gravity kernels. The real initial DSP of lognormal distribution for both continental and marine clouds are introduced, and the big droplets will leave the simulation bulk after growing over the gravity settling radius. These analysis indicates that HM has great potential in the computations for real clouds.

DOI: https://doi.org/10.3850/iahr-hic2483430201-303

Year: 2024