Implementation of three sets of electric charge transfer parameterization in a one-dimensional cloud model

 Results of numerical simulation of intra-cloud electrification depend on a mechanism that determines the sign and magnitude of charge transferred to hydrometeors (including graupels and ice crystals), through their collision (Mansell et al., 2005). Some of the microphysical processes play an important role in the above mechanism. In order to estimate the amount and sign of the transmitted charge per collision for numerical purpose, the results of laboratory researches are commonly used. Two kinds of inductive and non-inductive (used in the current paper) mechanisms could be applied. The research studies conducted for the non-inductive one can be determined based on the liquid water content (LWC), temperature (T), ice accretion rate and the particle size spectrum (Takahashi, 1978; Jayaratne et al., 1983; Gardiner et al., 1985; Saunders et al., 1991; Ziegler et al., 1991; Saunders and Peck, 1998; Pereyra and Avila, 2002).
According to the importance of this issue, in this research three sets of relations resulted from laboratory studies have been used. These sets were proposed by Takahashi (TAK, 1978 and 1984), Jayaratne / Gardiner / Ziegler (JGZ, Jayaratne and colleagues 1983; Gardiner et al. 1985; Ziegler et al. 1991) and Sanders et al. (SAN, Sanders et al. 1991). These parameterizations relate the mean charge transferred per collision to liquid water content and temperature. Following these studies, the prepared schemes of three sets have been implemented in an explicit time-dependent one-dimensional cloud model (ETM), based on Chen and Sun (2002). In the 1-D cloud model entrainment-detrainment and eddy diffusion processes have been considered. Also microphysical processes have been parameterized using Lin et al. (1983) and Rutledge and Hobbs (1984) schemes. The convection is initiated using potential temperature perturbation, defined by Chen and Sun (2004). The input data for the simulation of vertical cloud is from an idealized sounding including pressure, temperature and water vapor mixing ratio. This cloud model simulates vertical velocity (w), equivalent ice potential temperature (θ_ei), water vapor mixing ratio (q_v), cloud water mixing ratio (q_c), ice mixing ratio (q_i), rain water mixing ratio (q_r), snow mixing ratio (q_s) and graupel mixing ratio (q_g). The cloud model was set up with 1 second time step, 70-minutes simulation duration and 250 m spatial resolution in the vertical direction up to a height of 15 km.  The initial radius for the cloud column was considered as 3000 m.
The results of simulated mean charge transferred per collision using three sets of parameterizations (TAK, JGZ and SAN) show that their dipole pattern outputs are not the same. Simulations based on TAK and JGZ relations produced positive dipole (positive charge distribution lies over negative charge one), while simulation using SAN parameterization produced negative dipole pattern (the negative charge distribution on the top of the positive charge one). The simulation results show that the electric field was produced between 25-56, 19-34 and 27-57 minutes using TAK, JGZ and SAN parametric relations, respectively. It is noteworthy that the maximum values of positive and negative intra-cloud electric fields were obtained when applying TAK relations in the charge-transfer simulations. While, simulations using JGZ and SAN parameterizations led to the minimum values for positive and negative intra-cloud electric fields.      
The time and height of positive and negative electric field occurrences based on three sets of applied parameterizations were also compared. The results of comparisons demonstrated that the values acquired from TAK and SAN parameterizations were close. However, the values for simulation using JGZ indicated three minutes time discrepancy and 12.5 km height difference.
Finally, the simulated intra-cloud electric fields using three TAK, JGZ and SAN parameterization sets were compared with the threshold electric field, defined by Marshall et al. (1995), to extract the number of lightning occurrences. Our findings show that the maximum and minimum values of lightning events were seen in simulations using TAK and JGZ parametric relations, respectively. The number of lightning occurrences was 40, 12 and 30 for simulations using TAK, JGZ and SAN parameterizations respectively.