Presentation By Brody Fuchs and Vandana Jha ATS 780 Prof Steve rutledge. A computational study of the relationships linking lightning frequency and other thundercloud parameters By MARCIA B. BAKER, HUGH J. CHRISTIAN and JOHN LATHAM . Introduction.
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A computational study of the relationships linking lightning frequency and other thundercloud parameters
By MARCIA B. BAKER, HUGH J. CHRISTIAN and JOHN LATHAM
Figure 1. The meteorological sounding pressure p (mb) and temperature T (K) used in the computations.
Crystal growth is given by the usual diffusion equation, neglecting surface latentheating and shape effects:
Dv(m2/s) is the diffusion constant for vapor in air,
(T) the density of vapor saturated with respect to ice,
S(z) the supersaturation of the cloudy air with respect to ice (calculated from the prescribed vertical profiles of temperature and total water),
pi (kg m-3) the density of ice, taken to be 920 kg m-3.
The crystals grow at this rate as they rise in the updraught until they reach the anvil. After this point they cease growing and are mixed evenly throughout the anvil depth~1 km.
Thus, as the calculation proceeds, the ice-crystal concentrations below the anvil do not change in time but those in the anvil continually increase.
The rate of precipitation due to graupel is
where Q, (Dg, z) (C) is the average pellet charge at z.
The electric field at any point in space is that due to precipitation flux, the charged discs and to their images in the earth's surface. The vertical field at z on the cloud axis is :
where the charge density ρQ(C m-3) is
The field gradients in the vicinity of the balance level, where lightning is usually initiated, to depend on whether the local charging rate is large or small compared with the rate of charge removal by vertical motions-that is, it will depend on the ratio
In the H-M case, for a specified value of w, Ni = 0 at temperatures warmer than -3 C, increases steadily within the H-M temperature band (-3 to -8°C) then remains constant at all higher levels (colder temperatures)
In the Fletcher case, we see a rapid increase in Ni with decreasing temperature and pressure within the zone.
For the latter process the ice-crystal size distribution broadens continuously with altitude because offresh activation of crystals.
On the other hand, since the H-M process creates no ice particles at temperatures colder than-8C, the predicted size distributions narrow as ascent proceeds.
Table 1 presents typical values of N iat various levels within the charging zone for
Both the H-M and Fletcher types of glaciation process.
Table 2 presents values of precipitation flux, P (mm h-') at the ground for a range of updraught speeds w and associated balance-pressure, Pbal.
P increases slowly with increasing w. Its values are lower than are normally associated with lightning-producing clouds because the pellet sizes are somewhat higher than might generally be the case.
Fig 3: As precipitation flux, Fig. 2, but for the variation with pressure p (mb) of net charge density, PQ (C km- 3)
*Immediately before the IC flash, E had achieved the break down value of 3KV/cm atpbal and dropped off sharply on either side of this peak.
Fig 4: As precipitation flux, Fig. 2, but for a cloud-to-ground lightning flash.
Fig 5: As Fig. 3, but for a cloud-to-ground lightning flash.
Following breakdown at the balance level, positive charge was deposited just below pbal which reinforced that already existing, which was probably the legacy of the preceding flash.
The location of the region of strongest electric field (about 85% of the breakdown value) was slightly lowered.
All flashes originate from the same level, precipitation flux, Pbal. The intervals between consecutive flashes are seen to diminish steadily while the charge, Qflash, transferred by lightning increases.
The first seven flashes were IC and the final three, for which RQ is seen to exceed the threshold value, were C-G.
Table 3 presents characteristic computed values of various electrical parameters associated with successive lightning flashes from a single storm.
Figure 7 precipitation flux, asFigure 6 ,but for Fletcher glaciation with R=1km, FF=1000, and HF =0.01m-2s-1
Figure 6. The variations of (A) mean flash-interval, t(s), and (B) time of occurrence of first lightning, t(s), with updraught speed w (m s-l). Hallett-Mossop glaciation. Solid lines, Pbal= 403 mb; squares and triangles, bal= 392 mb, tand t1 respectively. R = 1 km, Ni = 2 x l05m-3, and HF= 0.01 m-2 s-l
The difference between the f (and also the t l ) values at the two pressures is much greater for Fletcher than for H-M ice production.
This is probably because, in the former case, additional ice crystals are nucleated as cloudy air ascends between the two pressure levels; and these contribute significantly to dpQ/dtand dE/dt.
Figures 6 and 7 show, for H-M and Fletcher respectively, the sensitivities of t and t1to w when , Pbalwas kept constant by adjusting ql
Ti isindependent of w in both cases, probably because as w increases, the increase in dρQ/dt associated with larger pellets is roughly matched by a decreasing dρQ/dt caused by the smaller size of the ice crystals near Pbal.
t1 decreases slowly as w increases, in both cases becausethe arrangement of charges producing the electric field is more rapidly established at higher values of w.
Figure 10:The variation with cloud radius R (km) of the mean flash-interval,t(s). Hallett-Mossop glaciation.
w = 10 m s-l, P bal= 414 mb, N,= 2 x 105 m-3, and HF= 0.01 m-2s-1
t is roughly linear with precipitation flux, Ni for the higher ice-crystal concentrations and changes more slowly as Ni decreases.
For higher values of Ni the more effective charging causes a larger fraction of the total separated charge to be localized in the vicinity of Zbal (where the field is a maximum and breakdown occurs), than for lower values. This approximate linearity is predicted by the Eq.
Figure 11: The variationof mean flsh-interval,t(s), with ice-crystal concentration N,(m-3 x l0-4).Hallett- Mossopglaciation.w=10ms-l, Pbal=403mb, R=1km, and HF = 0.01m-'s-l
In this situation, with the top of the charging zone at the level of the charge-reversal isotherm, the charge structure in the thundercloud is necessarily non-classical ( i s - /+).
Lightning is found to occur, in this situation, with values of f (and also t l ) several times greater than in the classical (+/-) case (Fig. 10).
The variation with cloud radius R (km) of the mean flash-interval, (s). Hallett-Mossop glaciation. Inverted-polarity cloud.w=7.1ms-l, ha1=488mb, Ni=2x lo6m-3, and HF=0.01m-2s-1
Figure16. precipitation flux, The variation of mean flash-interval, t(s), with the charging parameter CQ (m4x l0^18)
Figure17. The variation of( A)mean flash-interval, i(s), and (B) time of first lightning, Il(s),withthe charging parameter CQ (m4x 10^18) defined by Eq.(20). Fletcher glaciation.
linearity betweenf (and also l/t1) and CQ
f(l/f) increases about ten times faster than CQ over the range of parameter values considered. This is probably because the contribution of freshly created ice crystals (not present in the H-M case) to the charge transfer and associated field-growth is appreciable.