Compared here are the calculated fields of the Traveling Current Source (TCS), Modified Transmission Line (MTL), and the Diendorfer-Uman (DU) models with a channel base current assumed in Nucci et al. on the one hand and with the channel base current assumed in Diendorfer and Uman on the other hand. The characteristics of the field wave shapes are shown to be very sensitive to the channel base current, especially the field zero crossing at 100 km for the TCS and DU models, and the magnetic hump after the initial peak at close range for the TCS models. Also, the DU model is theoretically extended to include any arbitrarily varying return stroke speed with height. A brief discussion is presented on the effects of an exponentially decreasing speed with height on the calculated fields for the TCS, MTL, and DU models

Diendorfer, Gerhard

Thottappillil, Rajeev

Uman, Martin A.

English

NASA Technical Reports Server

INFLUENCE OF CHANNEL BASE CURRENT AND VARYING RETURN STROKE SPEED ON THE 
CALCULATED FIELDS OF THREE IMPORTANT RETURN STROKE MODELS 
Rajeev Thottappillil Martin A. Uman 
Department of Electrical Engineering 
University of Florida 
Gainesville 
Florida 
Gerhard Diendorfer 
Department of Electrical Power Engineering 
Technical University of Vienna 
Vienna 
Austria 
ABSTRACT 
Recently Nucci et al. [l] compared five return stroke models using an 
identical current at the channel base of each. Diendorfer and Uman [ 2 J introduced 
a new model which reproduces remarkably well the experimentally observed 
characteristics of the fields both close to and far from the return stroke 
channel. Both Nucci et al. [l] and Diendorfer and Uman [2] used a channel base 
current that is typical of measured subsequent stroke current Qf both natural 
lightning and triggered lightning. Though the channel base current adopted in' 
each paper is within the range of measured currents , they differ in the detailed 
wave shape. The first part of this paper compares the calculated fields of the 
Traveling Current Source (TCS), Modified Transmission Line (MTL), and the 
Diendorfer-Uman (DU) models with a channel base current assumed in Nucci et al. 
fl] on the one hand and with the channel base current assumed in Diendorfer and 
Uman [l] on the other hand. The characteristics of the field wave shapes are 
shown to be very sensitive to the channel base current, especially the field zero 
crossing at 100 km for the TCS and DU models, and the magnetic hump after the 
initial peak at close range for the TCS model. In the second part of the paper 
the DU model is theoretically extended to include any arbitrarily varying return 
stroke speed with height and a brief discussion is presented of the effects of 
an exponentially decreasing speed with height on the calculated fields for the 
TCS, MTL, and DU models. 
INTRODUCTION 
There are a number of lightning 
return stroke models that have been 
used to calculate remote electric and 
magnetic fields given an assumed 
current at the base of the channel and 
an assumed speed of the return stroke. 
Nucci et al. [l] compared five of the 
most used models, namely, Bruce-Golde 
(BG), Transmission Line (TL), Master- 
Uman-Lin-Stadler (MULS), Travelling 
Current Source (TCS), and Modified 
Transmission --Line (MTL) models, 
assuming similar currents at the 
channel base. For the assumed channel 
base current, all of the models gave 
reasonable values of fields although 
the charge and current distributions 
along the channel were quite different 
118-1 
https://ntrs.nasa.gov/search.jsp?R=19910023422 2020-03-17T14:59:25+00:00Z
for the different models. Nucci et al. 
(11 also discuss the reasons for the 
differences in the calculated fields 
for the different models and the 
ability of the models to reproduce the 
measured characteristics of the fields. 
Nucci et al. [l] did not deal with the 
influence of the variability of the 
channel base current on the predictions 
of the models, but a general discussion 
on the subject is available in Cooray 
and Orville [ 31 , though not specific to 
the models discussed here. Also, 
Diendorfer and Uman [ 2 ] ,  after 
introducing a new model (henceforth 
called the DU model), discuss the 
influence of the some of the channel 
base current parameters on the 
calculated fields. Although Nucci et 
al. [l] and Diendorfer and Uman [2] 
each assumed a channel base current 
that is typical of the measured 
currents for subsequent strokes inboth 
natural and triggered lightning, the 
two current wave shapes differ in 
detail. In this paper we compare the 
calculated fields for the TCS, MTL, and 
DU models assuming both the current 
adopted by Nucci et al. [l] and the 
current adopted by Diendorfer and Uman 
[2] (henceforth called the Nucci 
current and the DU current, 
respectively) and show that some of the 
characteristics of the fields predicted 
by the models are very sensitive to the 
current waveshape assumed at the 
channel base and, further, that the 
extent of variation in the 
characteristics of the field depends on 
the specific model. Finally, we extend 
the DU model theoretically to include 
return stroke speed variation as an 
arbitrary function of height and 
present calculated fields for the 
specific case of an exponentially 
decreasing return stroke speed with 
height for the TCS , MTL, and DU models. 
RESULTS 
The Nucci current and the DU 
current are compared in Fig.1. The DU 
current has a narrower peak, a small 
hump after the peak, and a faster decay 
than the Nucci current. The small 
differences in peak currents and front 
rise times influence mostly the field 
rise times and peaks and do not 
influence significantly the overall 
wave shape of the fields. For field 
calculation with the MTL model a 
current decay constant of 2000 m is 
assumed which is the same as in Nucci 
et al. [l]. When fields are calculated 
with the DU model, two time constants, 
0.6 ps and 5.0 p s ,  are adopted just as 
in Diendorfer and Uman [ 21 . Fig. 2 shows 
the electric fields at a distance of 
100 km for the DU current and the Nucci 
current and a constant return stroke 
speed of 1.3e08 m/s. From Fig.2a it is 
seen that with the DU current at the 
channel base the TCS model field (line 
2) crosses zero around 50 ps while it 
does not cross zero within 100 ps with 
the Nucci current (curve 5). Similarly, 
the DU model field crosses zero around 
55 ps with the DU current at the 
channel base (curve 3) while it does 
not do so within 100 ps with the Nucci 
current (curve 6 ) .  The choice of base 
current does not appreciably affect the 
zero crossing time (around 30 p s )  of 
the MTL model fields (curves 1 and 4 ) .  
Also note that for the given channel 
base current the TCS and DU model 
fields are different only for the first 
30 ps or so, and after that they are 
almost the same with the DU fields 
being slightly higher. Fig. 2b shows the 
same fields as in Fig.2a for the first 
5 p s .  The initial peak fields are 
higher with the DU channel base current 
for all the models. The initial peak 
fields are the smallest for the DU 
model, less than half of the TCS model 
values and slightly greater than half 
of the MTL model values. Figs. 3a and 3b 
show, respectively, the electric and 
magnetic fields at a distance of 5 km 
for the models with a constant return 
stroke speed of 1.3e08 m/s and with DU 
and Nucci currents at the channel base, 
For a given model the fields produced 
by the DU current at the channel base 
are larger for the first tens of 
microseconds, but becomes less than the 
fields produced by the Nucci current at 
the channel base at later times. For a 
given base current the electric fields 
produced by the TCS and DU models are 
very similar (see the pairs 2, 3 and 5, 
6 of Fig.3a) after about 20 p s ,  with 
the electric fields of the TCS model 
always being larger than the 
corresponding DU model electric fields. 
The magnetic fields for the TCS and the 
DU models are roughly equal after about 
40 us for the given channel base 
currents (see Fig. 3b). Also for the 
fields at 5 km, the magnetic hump after 
the initial peak of the TCS model is 
more prominent with the DU current than 
with the Nucci current (see Fig.3b). 
The DU model was derived for a 
constant return stroke speed in 
Diendorfer and Uman [ 2 ] .  The DU model 
can be generalized to include a 
variable return stroke speed that is an 
arbitrary function of height. It can be 
shown mathematically [ 41 that the 
return stroke channel current i(z',t), 
where z '  is the height above the 
ground, is given by 
i(z',t) - i(O,t+z'/c) 
- i (0, z '/Vav( z ' )+z ' /c) 
where Yav(z') is the return stroke 
speed averaged over a height z' defined 
by 
dz" j' V(Z") 
0 
c, the speed of light, and 7 ,  the time 
constant for discharging the charge on 
the leader. An exponential decrease in 
speed given by 
V ( z ' )  = V*exp[-(z'/A)] (3 )  
where V is the speed at ground level. 
The factor X in equation (3)  is a 
constant whose value is chosen as 2000 
m. The speed at ground level is taken 
as 1.3e08 m/s for all three models. The 
DU current is assumed at the channel 
base for the purpose of comparing the 
fields produced from the constant speed 
case with the variable speed case. The 
other parameters of the three models 
are the same as previously given. 
Fig.4 shows the effect of an 
exponentially decreasing speed on the 
electric fields produced by TCS, MTL, 
and DU models at 100 km. The zero 
crossing time of the TCS and DU models 
are earlier by about 15 ps (compare 
curves 2, 3 with 5 ,  6 respectively), 
but the zero crossing time of the MTL 
model is not affected very much. Also 
the hump after the peak of the TCS and 
DU model fields are less prominent with 
a decreasing speed. 
DISCUSSION 
After a time of about 35 ,us the DU 
channel base current amplitude is 
smaller than the corresponding Nucci 
current and at 100 ps the DU current is 
only about half of the Nucci current. 
The lower channel base currents at 
later times results in lower currents 
along the channel at later times for 
all the models. Hence the fields 
produced at 5 km by a given model for 
the DU current at the channel base are 
smaller than the fields produced by the 
Nucci current at the channel base after 
the first few tens of microseconds. The 
fields at 100 km are dominated by the 
radiation term caused by the time rate 
of change of current all along the 
channel. As discussed in Nucci et al. 
[l] , the time derivative of the current 
is positive at the return stroke wave 
front for the TCS and MTL models and 
negative at all points below the wave 
front for the TCS model and a few 
meters below the wave front (because of 
the finite rise time of the current) 
for the MTL model. For the DU model the 
time derivative of the current is 
positive at the wave front and a few 
meters below it and negative at all 
other points. The fields at 100 km 
cross zero at the time that the 
contribution to the fields from the 
negative current derivatives become 
dominant. The amplitude of the 
derivative of the current is determined 
by the amplitude, rate of rise, and 
rate of decay of the current. With the 
DU current at the channel base, the 
amplitude of the currents at later 
times along the channel are smaller for 
all the models, and hence there are 
earlier zero crossing times (by more 
than 50 p s )  for the TCS and DU models. 
The zero crossing time of the MTL model 
is not very sensitive to the channel 
base current because in the MTL model, 
as the current from ground travels up 
the channel, it decays exponentially 
and the current value and its 
derivative at the top sections of the 
channel are only a small fraction of 
their values at the bottom sections, 
irrespective of the current at ground. 
For the same return stroke speed at 
ground, a decreasing speed with height 
delays the time at which the return 
stroke wave front reaches a given 
height, which in turn causes the 
smaller currents at the tail of the 
channel base current to appear at 
lesser height when compared to the 
constant speed case. This also causes 
the field at 100 km to cross zero 
earlier (by about 15 ps for an 
exponential speed decay constant of 
2000 m) for the TCS and the DU models. 
The zero crossing of the MTL model is 
not very sensitive to the assumed 
variation in speed for same reason 
mentioned above. 
CONCLUSION 
The fields calculated by the three 
return stroke models studied are 
sensitive to the channel base current 
characteristics and to the return 
stroke speed, but the different models 
respond in varying degrees to the above 
parameters. The differences in the 
predictions may be experimentally 
measurable. In that case, design of an 
experiment for the simultaneous 
measurement of the return stroke speed, 
the channel base current for long 
duration, and the fields, both close 
and far from the channel might allow a 
determination of the best existing 
model or could make possible the 
development of a better model. 
ACKNOWLEDGEMENT 
This research was supported in 
part by NSF grant ATM 8807449 and by 
the U.S. Department of Energy, Office 
of Energy Management, under contract 
No. DE-AC05-840R21400 with Martin 
Marietta Energy Systems. 
REFERENCES 
[l] Nucci C. A., G. Diendorfer, M. A. 
Uman, F. Rachidi, N. Ianoz, and C. 
Mazzetti, Lightning return stroke 
current models with specified channel- 
base current: a review and comparison, 
J .  Geophys. Res., 95, 20395-20408, 
1990. 
[2] Diendorfer G. and M. A. Uman, An 
improved return stroke model with 
specified channel-base current, J. 
Geophys. Res., 95, 13621-13644, 1990. 
[3] Cooray V. and R. E. Orville, The 
effects of variation of current 
amplitude, current rise time, and 
return stroke velocity along the return 
stroke channel on the electromagnetic 
fields generated by return strokes, J. 
Geophys. Res., 95, 18617-18630, 1990. 
[4] Thottappillil R., G. Diendorfer, 
and M. A. Uman, Extension of the 
Diendorfer-Uman lightning return stroke 
model to the case of a variable return 
stroke speed, Submitted Nov. 1990 to 
the J .  Geophys. Res.. 
118-4 
a 
x 
c 
-r-l 
+J 
c 
a_, 
L 
L 
3 
0 
14 
12 
10 
8 
.6 
4 
2 
0 0 
Channel base c u r r e n t  
Nucci 
20 40 60 80 
Time in m i c r o s e c o n d s  
100 
Fig.1 Channel base currents 
118-5 
5 
4 
3 
2 
1 
0 
- 1  
I = 100 km Cur ren t  DU NUCCI 
/2 
DU 3 . 6  
I 1 I I 
L O  20 * 40 60 . 80 100 
T i m e  i n  m i c r o s e c o n d s  
Fig.2a Electric f ie lds  at 100 km of the MTL, TCS, and DU models 
with currents shown in Fig.1 at the channel base. Note 
the difference in time at which the fields cross zero. 
118-6 
5 
E 
\ 
> 
4 c 
-d 
0 0 
2 T 1 MTL TCS DU NUCCI  -1 2 4 5 
DU 3 6 
D = 100 km 
V = 1.3e08 in/: 
= 2000 m 
1 2 3 4 
T i m e  in microseconds 
5 
Fig.2b Electric fields at 100 km of the MTL, TCS, and DU models 
with currents shown in Fig.1 at the channel base. Note 
the difference in the initial peaks. 
118-7 
I 
Vertical E f i e l d  i n  V /m 
w 
Tu n a, 03 0 
0 0 0 0 0 0 
0 
0 
Horizontal 6 f i e l d  i n  UT 
CI 
0 
0 
118-8 
5 
4 
3 
2 
1 
0 
- 1  
D = 100 km DU Current 
V = 1.3e08 m/s 
), i n f i n i t y  2000 
MTL 1 4 
TCS 2 5 
DU 3 6 
I I I I 
20 40 60 80 100 
T i m e  in m i c r o s e c o n d s  
Fig.4 Electric fields at 100 km'of the MTL, TCS, and DU models 
with DU channel base current for the cases of constant 
return stroke speed and decreasing return stroke speed , 
with height. 
118-9 


Influence of channel base current and varying return stroke speed on the calculated fields of three important return stroke models

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