1. In this work we present results of cloud electrification obtained with the RAMS model that includes the process of charge separation between ice particles in the presence of supercooled water

2. Overview
Motivation
Description of the electrification numerical scheme
Results : (1) single cloud simulations
(2) cloud field simulations
Summary
Conclusions
After the motivation for doing this work we will present the description of the numerical scheme used to calculate charge separation.
Results will be presented for a single cloud and for a cloud system.
After summarizing, some conclusions will be presented.

3. Motivation
Better understanding of differences between lightning activity over land and sea
Focus on the contribution
of geographical factors:
Temperature differences between
land and sea
The coast shape
Topography
There is a strong difference in the number of flash lightning between the land and the sea, as can be seen in the picture.
Former studies show that the number of flashes over the continents are much higher than the oceans. Particularly, the eastern Mediterranean presents a large number of flashes, even larger than over the land. This occurs in the winter when the sea is still relatively warm (>17C)
On a smaller scale, observations show a different number of flashes between
Tel Aviv in central Israel, and Haifa, north of Israel. The distance between them is less than 100km, but there are significant differences in the coastal shape and topography. While Tel Aviv is flat, Haifa is on a hill (~550m height) and on a bay.

4. The RAMS microphysical scheme
Bulk microphysical scheme
Water categories: vapor, cloud droplets, rain, pristine ice, snow, aggregates, graupel and hail.
A generalized gamma function is assumed for the size spectrum of the categories
RAMS version 4.3 was used with standard two moment microphysics in which both the mixing ratio and number concentration of the species are calculated (expect for cloud drops, for them the number concentration is predetermined and was set to 500 #/cc)
Processes: nucleation, condensation, evaporation and melting, collision and coalescence, drops breakup, secondary ice production, shedding, sedimentation.

5. The noninductive charging mechanism
T, LWC
Graupel
Supercooled water
Ice particle
The mechanism for charge separation implemented in the model is the noninductive one which occurs when graupel collides and bounces from an ice particle, in the presence of supercooled water.
The quantification of the process was done according to three different schemes. The last one was recently suggested by Saunders in order to solve a long standing discrepancy between the first two schemes as will be shortly shown.
Free ions (evaporation, sublimation, corona currents), inductive drop-drop, drop-ice requires a strong electric field.
Three parameterizations were implemented into the model:
Saunders et al. (1991).
Takahashi (1978, 2002).
Based on Saunders et al. (2003)

6. The electrification scheme stages
Calculation of the noninductive charging rate of the particles in the cloud. (RAMS)
Interactions of graupel-pristine ice, graupel-snow, graupel-aggregates
Tracking the charge on the particles. (RAMS)
Spatial distribution of charge
3. Calculation of the electric potential from Poisson’s equation. (offline)
The workflow of the cloud electrification process is as follows:
In RAMS the noninductive charging rate is calculated, based on the electrification scheme used, for the interactions between graupel and pristine ice, graupel and snow and graupel and aggregates. The second stage is to calculate an overall charge balance in the cloud due to advection, turbulence, sedimentation and mass transfer between species.
The two next steps were conducted offline from RAMS (now we can calculate them on-line): calculation of electric potential and electric field.
4. Calculation of the electric field from the potential by Gauss’ law. (offline)

7. Saunders’ scheme Charge per separation event
Vg and Vi - terminal fall velocities of the graupel and ice
k - constant ( 3 m s-1 )
G(Di) - a polynomial fit to the experimental data of Keith and Saunders (1989)
In Saunder’s scheme from 1991, the charge separated per event (of charge separation) strongly depends on the difference between terminal velocities of the graupel and ice particles and on a high order polynom of the graupel diameter following data from Keith and Saunders

8. Saunders suggested the following charging zones as a function of the temperature and effective LWC
The charging zones as a function of temperature and effective liquid water content.
Saunders et al. (1991)
EW=LWC x Ecoll,gw

9. Takahashi’s scheme Charge per collision
Charge (in fC) gained by graupel as a function of temperature and liquid water content.
Takahashi (1978)
In the second scheme, Takahashi suggested the following scheme for calculating the charge separated per collision (in Saunders it was per event)

10. Vg and Vi - terminal fall velocities of the graupel and ice
The charge per collision is multiplied by an efficiency factor α (Marshall et al., 1978, Takahashi 1984) that converts it to charge per separation event.
Vg and Vi - terminal fall velocities of the graupel and ice
Di – diameter
V0 and D0 - constants
In order to convert charge per collision to charge per event the following factor is used.

11. The polarity of charge gained by graupel
1) Based on the experimental studies of Saunders et al. (1991). (Black bold dashed lines).
2) Based on the experimental results of Takahashi (1978, 2002). (Black thin lines).
As can be seen in this plot, there is a strong discrepancy between the two schemes with respect to the polarity of the charge gained by the graupel at around -15C and around 1 g/kg of LWC.
Recently, Saunders suggested that his scheme should be modified and the polarity in that area should be negative. In this work we assumed the following changes in Saunders polarity map.
Note that the values for low values of LWC are vaguely know.
3) Based on a modified scheme suggested by Saunders et al. (2003). (Red bold dashed lines).

12. The noninductive charging rate
The rate of change of charge density on graupel particles:
Vg and Vi - terminal fall velocities of the graupel and ice
Dg and Di - diameters
Egi – collision-separation-charging efficiency
δq – charge per separation event
The charging rate is calculated using a similar approach to the one implemented in RAMS to calculate rate of change of densities of the different species due to collision-coalescence processes, with the difference that the charge separated per event is part of the integrand.

13. The electric potential
Using a standard numerical solver (NAG) for the electric potential at all grid points by Poisson equation:
The electric field
Solving for the electric field at all grid points:
Standard procedures with standard libraries to calculate the electrical potential and electric field.

14. Single Cloud Simulation - Setup
Bet Dagan – January 5, 2000
Warm-humid bubble initialization
Vertical wind shear
1 grid X 105 X 27 cells
32 X 32 X 12 Km
The single cloud simulation was run in an homogeneous environment (a single radiosonde) and initialized with a warm-humid bubble.
The wind shear was only vertical without change in the direction.

15. Single Cloud Simulation: Results
1200
Cloud base (m) 4°
Cloud base (°C)
-28°
Cloud top (°C) 14
Max updraft (m/s)
2.5
Max LWC (g/Kg)
0.3
Max Snow Content (g/Kg)
2.7
Max Graupel Content (g/Kg)
1.6
Max Aggregates Content (g/Kg)
@ 25 min of simulation

16. Mass content (g/Kg) at 11 min
Cloud drops
Pristine ice
Snow
Graupel
At this stage the cloud drops and graupel are mainly locted below the -10C level.
The amount of aggregates is too small at this stage.
Note the signature of the wind shear.

17. Mass content (g/Kg) at 21 min
Cloud drops
Snow
Aggregates
Pristine ice
Graupel
At this stage cloud species reach the -20C level (and even higher)

18. Charge density (fC/l) at 11 min with Takahashi’s scheme
Pristine ice
Snow
Graupel
Total
Because of the location of the graupel particles at this stage, they are mainly positively charged and the pristine ice and snow get the negative charge.
The total charge plot shows an inverted dipole.

19. Charge density (fC/l) at 21 min with Takahashi’s scheme
Pristine ice
Snow
Graupel
Aggregates
When the graupel goes higher (colder) into the cloud, the polarity reverses and it accumulates negative charge.
The main carrier of the positive charge is the aggregates.
Total

20. Total Charge density (fC/l) at 21 min with Takahashi’s scheme
+1111
The total charge show a tripole, with a small positive center a the lower part of the cloud.
-2515
+115

21. Charge density (fC/l) at 11 min with Saunders’ scheme
Pristine ice
Snow
Graupel
Total
Similar to Takahashi

22. Charge density (fC/l) at 21 min with Saunders’ scheme
Pristine ice
Snow
Graupel
Aggregates
Total
The two main charge centers form an inverted dipole. The upper charge center is too small.
Lower charges.

23. Total Charge density (fC/l) at 21 min with Saunders’ scheme
+10
-155
+77
Also a tripole but underestimates the upper positive center.
The overall amount of charge are lower than in Takahashi’s scheme,
Probably due to the strong dependence on the ice particle’s radius.
Note that this charge distribution was obtained thru the cloud center in the direction of cloud movement, different cuts may show a different charge distribution.
+72

24. Takahashi’s scheme Saunders’ scheme
Also a tripole but underestimates the upper positive center.
The overall amount of charge are lower than in Takahashi’s scheme,
Probably due to the strong dependence on the ice particle’s radius.
Note that this charge distribution was obtained thru the cloud center in the direction of cloud movement, different cuts may show a different charge distribution.

25. Total Charge density (fC/l) at 21 min with Saunders’ schemes
According to original charging zones
Saunders original scheme leads to an inverted dipole prior to flash and this is not according to measurements.
The changes in polarity lead to positive charge on aggregates, snow and PI and negative on graupel. Then, the aggr, snow and pi that at the top of the cloud carry the positive upper charge center.
According to modified charging zones

26. Maximal electric field in the cloud
29 min
The electric field development was similar in both Saunder’s schemes but remarkably slower than in Takahashi’s scheme. In the last, first flash occurs 21min from cloud development, in Saunders it takes another 8 min.
The time is from the beginning of the electric field buildup (or charge separation).

27. Cloud Field Simulation Cloud water content at 2616 m
19:22 UTC
In the cloud field simulation a post frontal synoptic situation was simulated and focused around the Carmel Mountain and Haifa Bay.
The electrification process was simulated for 4 cells as shown in the figures.
Clouds over the land
Clouds over the sea
Cloud water content at 2616 m

28. Clouds over the sea Clouds over the land ag ag gr gr ag ag gr gr
Charge density (fC/l) with Takahashi’s scheme before first flash.
Sea 1
Sea 2 ag ag gr gr
Land 1
Land 3 ag ag
The two cells over the land and over the sea present a similar charge distribution, respectively.
In all the cases the positive charge is mainly on the aggregates while the negative charge on the graupel.
Over the land it occurs at a larger stage so graupel appear lower in the cloud and so is the charge.
In all the cases there are dipoles.
Different from single cloud maybe because of microphysics. gr gr
Clouds over the land

29. The maximal electric field in the clouds in the Haifa simulation (Takahashi’s scheme)
The most striking difference between the clouds over the land and sea is the rate of buildup of the electric field.
Over the sea it begins at a later stage since the ice development begins later (warmer low levels) but then it develops faster so the charge separation is faster leading to a faster buildup of electric field.
As a results of this the time to first flash lightning is shorter over the sea.
The beginning of the cell’s tracking is determined when LWC is larger than 0.1g/kg.

30. Summary
A new electrification scheme was implemented into the mesoscale RAMS model
Simulations of the electrification of a single cloud and a cloud field thunderstorm were performed.
Three parameterizations of the charge separation mechanism were implemented.

31. Conclusions
* Takahashi’s scheme predicts charge distribution (tripole/ dipole) and charging rate that compares well with measurements.
* Saunders’ original scheme predicts an inverted dipole (in contrast to observations) until close to first flash. Then, a small upper charge center appears.
* Assuming our modification to Saunders’ charging zones, the model predicts a tripole that develops at an earlier stage but with main charge centers in disagreement with observations.

32. Conclusions
* Takahashi’s scheme predicts charge distribution (tripole/ dipole) and charging rate that compares well with measurements.
* Saunders’ original scheme predicts an inverted dipole (in contrast to observations) until close to first flash. Then, a small upper charge center appears.
* Assuming our modification to Saunders’ charging zones, the model predicts a tripole that develops at an earlier stage but with main charge centers in disagreement with observations.

33. Conclusions
* Takahashi’s scheme predicts charge distribution (tripole/ dipole) and charging rate that compares well with measurements.
* Saunders’ original scheme predicts an inverted dipole (in contrast to observations) until close to first flash. Then, a small upper charge center appears.
* Assuming our modification to Saunders’ charging zones, the model predicts a tripole that develops at an earlier stage but with main charge centers in disagreement with observations.

34. Conclusions (cont.)
* The stronger dependence of the charging rate on the size of the particles in Saunders’ scheme leads to a lower charging rate than in Takahashi’s.
* In clouds that develop over the sea, charging begins later but with a higher rate in comparison to clouds over the land.
* The time to the first lightning flash is shorter for clouds that develop over the sea. This could explain the higher frequency of flashes over the Mediterranean Sea.

35. Conclusions (cont.)
* The stronger dependence of the charging rate on the size of the particles in Saunders’ scheme leads to a lower charging rate than in Takahashi’s.
* In clouds that develop over the sea, charging begins later but with a higher rate in comparison to clouds over the land.
* The time to the first lightning flash is shorter for clouds that develop over the sea. This could explain the higher frequency of flashes over the Mediterranean Sea.

36. Conclusions (cont.)
* The stronger dependence of the charging rate on the size of the particles in Saunders’ scheme leads to a lower charging rate than in Takahashi’s.
* In clouds that develop over the sea, charging begins later but with a higher rate in comparison to clouds over the land.
* The time to the first lightning flash is shorter for clouds that develop over the sea. This could explain the higher frequency of flashes over the Mediterranean Sea.