13

Correlations of Electric Potential Gradients at Land Stations and

Their Implication on the Classical Picture of Atmospheric Electricity

By BHARTENDU 1)

Summary- The correlation coefficients of the electric potential gradient of three year annual hourly and monthly hourly means in GMT and LST and monthly means are computed for over one hundred and seventy-five station pairs. In general, low values are found. The validity of the data and analysis are discussed; also the implications of the results on the classical picture of atmospheric electricity.

1. Introduction

The classical global picture of atmospheric electricity envisages the earth and the ionosphere (equalizing layer) as the two conductors of a spherical capacitor separated

by an imperfectly insulating atmosphere. The electric current which flows within this capacitor is controlled and maintained by the terrestrial thunderstorm activity. In

addition to the global generator, local electrical generators also influence the at-

mospheric electric field measurements. The electric field measurements at a station are affected by local generators, the potential difference between the equalizing layer and

the earth, local columnar resistance, and local conductivity. During fair weather when the influence of local generators is assumed to be negligible, the columnar

resistance at globally representative stations is constant and the electric field is governed by the potential difference between the equalizing layer and the ground, and local conductivity. At land stations, the local columnar resistance is not constant and the measurements are further complicated.

Stations on mountain tops, in polar regions, and ocean stations are generally regarded as globally representative but they also suffer f rom deficiencies [1] 2) due to

orographic difficulties, auroral influences, and BLANCHARD'S bubbling effect. M/3HL- EIS~N [2] has reported considerable fluctuations in the electric field at sea even in fair weather and has discussed the difficulties of calculating a suitable reduction factor and minimizing the error due to the ship exhaust. Land stations are easily accessible and a large volume of data has been collected for such stations over the entire globe and many studies comparing the results of various stations using different techniques have been published (for example, MAUCNLY [3]; BROWN [4]; PARAMONOV [5];

1) Meteorological Service of Canada, 315 Bloor Street West, Toronto, Ontario. z) Numbers in brackets refer to References, pages 25/26.

14 Bhartendu (Pageoph,

HATAKEYAMA and KAWANO [6]; ISRAi~L, DOLEZALEK and FRIES [7]; ]MYANITOV and SmFR~N [8]; ANDERSON [9], among others).

ISRAi~L and DE BRUIJN [10] plotted diurnal means of the electric field at two stations with respect to each other and found a large scatter in the graph. They also calculated correlation coefficients of diurnal, monthly and annual means for several station combinations and found that the correlation coefficients in general were low. They concluded that land stations were unable to give global variation. BHARTENDU [11] studied potential gradient variations at twenty land stations for a two-year period and also calculated correlation coefficients of monthly hourly means, annual hourly means, and montly means and found that the correlation coefficients in general were low.

This paper presents the correlation coefficients of the electric potential gradient calculated for a three-year period for over one hundred and seventy-five land station pairs and discusses their implications on the classical concept of atmospheric elec- tricity.

2. Data and Analysis

The potential gradient data used are taken from the monthly publication titled 'Results of Ground Observations of Atmospheric Electricity' published by U.S.S.R. Chief Administration of the Hydrometeorological Service, A. I. Voeikov Main Geophysical Observatory, Leningrad, and are for a three-year period from January 1964 to December 1966. Different definitions of fair weather have been adopted for different stations in these publications. However, it is reasonable to assume that the effect of local generators will be negligible during fair weather for each station and the effect of the global generator will penetrate the troposphere to the ground. This does not, however, mean that the global effect will be immediately recognizable from the records because the influences of local columnar resistance and conductivity are usually large and these will obstruct such recognition. However, it is reasonable to assume that if sufficient data for a long period of time at several stations around the globe were considered, the local columnar resistance and conductivity effects may cancel out and one may obtain a global curve.

Fair weather potentials gradient data for twenty land stations have been analysed and the correlation coefficients between various combinations of mean values and the respective standard errors have been calculated using standard formulae.

3. Results

Monthly hourly means

The monthly hourly means were obtained by averaging the hourly values for each hour of the day separately for each month during January 1964 to December 1966. These are provided in the above-mentioned publication. The correlation coefficients

Vol. 84, 1971/I) Correlations of Electric Potential Gradients at Land Stations 15

of hourly fair weather averages for all months (or months for which data were

available) were calculated for 179 station pairs. Each month had 24 hourly means and a maximum of 36 months of data per station was available. Thus, the maximum nmnber of monthly hourly means for any station was 864.

Table I and Table I I show the correlation coefficients for monthly hourly means in G M T and local standard time, respectively. The local standard times for the stations were obtained f rom the 'Rand McNally Commercial Atlas and Marketing Guide'

75th edition, Rand McNally and Company, New York, 1944. As can be seen from

Table I, the correlation coefficient, r, is >0.7 for only four station pairs and >0.8 for only two station pairs. However, the data available for the station pairs exhibiting r >0.8 are only for one month and hence their representativity is in question. Out of

the four station pairs giving r > 0.7, two have data only for one month, one has data for six months, and one for twenty-one months. Thus, if we consider a minimum of

20 months of data to be essential for the establishment of representative averages, only one station pair, Uccle-Dourbes, shows a correlation coefficient higher than 0.7. Figure 1 shows the histogram of the computed correlation coefficients and indicates

that only about 2 ~ are greater than 0.7.

-~.o - 9 - ~ . 7 - . 6 - ~ ~.4 ~ - ~ - i o .i 2 .3 4 �9 . 6 7 .B 9 i o

CORRELATION COEFFICIENT

Figure 1 Histogram of the correlation coefficient of the monthly hourly mean in GMT of the potential gradient

Table II shows the correlation coefficients of monthly hourly means in local standard time and gives similar results. Only 1 station pair yields r >0.8 but the data available are only for 1 month. Of five station pairs exhibiting r > 0.7, three have data for only one month, one for six months, and one for twenty-one months. As with the G M T case, the only station pair with 20 months (or more) of data showing a correla-

~ ~i

~

oo

~o

~"

~ ~

- ~'

~ :.

~ ~,

~;

~ ~.

Z~

t~

~-

~:~

~ o ~

~q

8 %

e,

c~

q~

q~

q

0

�9

~ o

~ ~

~:

, t ~

~ =

~

~ ~

o ~

~ ~

~ ~

~ ~

r~

~ =~

~

~ ~

D ~

~ ~

~ ~L

~ ~

=~

~

~,"

: ~

~ ~

~ ~

~ ~

~ ~

Q

~ �9

c~

18

14

13

12

II

IO

9

a

f_ 6

4 ~

3

2

t o

Bhartendu (Pageoph,

-~ -~ -7 -6 .5 -4 -3 -2 - I 0 r ~ 3

CORRELATION COE~ICIEfVT

Figure 2 Histogram of the correlation coefficient of the monthly hourly mean in LST of the potential gradient

tion coefficient higher than 0.7 is Uccle-Dourbes. Figure 2 presents the histogram

and shows that only about 2~o of the correlation coefficients are greater than 0.7.

Annual hourly means

The annual hourly means were obtained by averaging for each hour of the day

hourly values over a period of three years. The correlation coefficients of these means in G M T and LST were calculated for 190 station pairs as presented in Tables I I I and IV, respectively. The corresponding histograms are illustrated in Figures 3 and 4.

The limiting correlation coefficient for the one percent probability level for these tables is 0.5 [12].

Table I I I shows that out of ten station pairs exhibiting r > 0.9, nine have data for more than twenty months, while the corresponding figures for r >0.8 are 20 out of 22 and for r > 0.7, 25 out of 33 station pairs with more than twenty months of data. In view of the limiting correlation coefficient of 0,5, significantly high correlation coeffi- cients are considered to be 0.8 and higher, provided data for twenty months or more

are available. Thus, it appears that about 11 percent of station pairs give significantly high correlation coefficients of the annual hourly means in GMT. Fig. 3 shows that 6 percent of correlations coefficients fall into the range 0 .9> r >0,8, and 5 percent into 1.0> r >0.9.

Table IV shows that for r >0.9, three out of four station pairs have more than twenty-months of data, while for r > 0 . 8 the figure is 14 out of twenty-two. The limiting correlation coefficient for the one percent probability level is 0.5 here too.

Vol. 84, 1971/I) Correlations of Electric Potential Gradients at Land Stations 19

CORRELATION C~EFFICIENT

Figure 3 Histogram of the correlation coefficient of the annual hourly mean in GMT of the potential gradient

-e - s - 4 - ~ - 2 -, o ~ .s 4 3 ~ ? .e 9 ,o

CORRELATION COEVFICIENT

Figure 4 Histogram of the correlation coefficient of the annual hourly mean of LST of the potential gradient

Thus, abou t seven percent of stat ion pairs are considered to yield significantly high

correlat ion coefficients of the a n n u a l hourly means in LST. Figure 4 exhibits that

abou t n ine percent of the correlat ion coefficients are 0.9 > r > 0.8 and five percent are

1 .0> r >0.9.

C~

~rr

L

jl ~x

c~

0

ii!i ;C

g

~o

~

o~

,' 7

. ,'

..

..

..

..

'

.' .'

7 .

..

..

.

,' F

. .

o

~ o

~ ~

~"

~

~ m

q

~o

~

~ ~

L~

n ~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

~ ~

~

~ ~

~ ~

~ ~

~ I ~

~ t ~

~ ~

~ ~

~ ~

~ i ~

t ~ ~

~ !

Z

i ~ I~

�9

�9

~ ~

I ~

~ i~

~

6~

~ ~

tt t

t ~

~ o

g

~ o

~

~ ~

t~

~t

~ ~

! t

~t

t ~

~ ~

~ ~

~ o

ft

~ ~

~ ~l

~ ~

~ ~

~ ~

~ ~

~ t

~ ~

~ ~

~ ~

~ t ~

t~

~

~ ~

~ ~

~ ~

~ ~

~ ~

~l ~

�9

~

~ ~

~ ~

~ ~

~i

~ ~

~ ~

~ ~

~J

~ ~

~ ~

~

~ ~

i ~ ~

..

..

~

~ I I

..

..

~ ~

i I p~

�9

�9

Vol. 84, 1971/I) Correlations of Electric Potential Gradients at Land Stations 23

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2, ...... o; ...... &, o . . . . . . . . . . . . . . . .

Figure 5 Histogram of the correlation coefficient of the monthly mean of the potential gradient

Both Tables I I I and IV show that for the station pair Uccle-Dourbes, the high

correlation coefficient value, 0.98, is observed.

Monthly means

Table V presents the correlation coefficients of the monthly means and Fig. 5 exhibits the corresponding histogram. The limiting correlation coefficient for the one percent probability level is 0.4 in this case. Thus, the significantly high correlation

coefficient is considered to be 0.7 or higher where data are available for at least

twenty months. All the station pairs which yield r >0.8 have only one year of data or less and

hence their significance is doubtful. Out of 21 station pairs showing r >0.7, only 6 have more than twenty months of data. Only these six station pairs are considered to

give significantly high correlation coefficients. These include the Uccle-Dourbes station pair. Thus about 4 percent of station pairs may be considered as giving

significantly high correlation coefficient values. Fig. 5 shows that about 6 percent of the correlation coefficients are 0.8 > r >0.7,

3 percent are 0 .9> r >0.8, and 2 percent are 1.0> r >0.9.

4. Discussion

Validity of the data and analysis

It has been reported [13] that the data to be compared should be taken in open

24 Bhartendu (Pageoph,

plains. The aforesaid publications from which the data used in this paper are taken state that the data for most of the stations have been reduced to flat country. Probably this was done by calculating a suitable reduction factor by comparing simultaneous values at the station and at an open flat terrain. However, the reduction factor itself is variable ([13], [14]) and this procedure suffers from ambiguities. Descriptions of stations do not accompany the published data in the above-referred publications and hence it is impossible to estimate its effect.

It has also been suggested ([13], [15J) that the fulfillment of Ohm's taw should be accepted as a criterion of the suitability of the data for comparison. Ohm's law behaviour in the atmosphere has been studied in detail ([16], [17]) and is found to be complicated. It is also reported ([18], [19]) that Ohm's law is satisfied better if one considers only the positive conductivity and not the sum of the positive and negative conductivities. Various speculative explanations for the non-fulfillment of Ohm's law in the atmospheric have been advanced (e.g. [15], [16], [17]) but still no definite cause or causes expIaining this anomaly has been established. It is also argued that the non-fulfillment of Ohm's law is due to error in the measurements of one or more quantities and hence comparison of data is inaccurate. It is well known that the degree

i/E of fulfillment measured by the quantity Q 2+ +2 _ ' is variable and approaches 1 for

some short periods even when it is much different from 1 for long periods. In this case, is it acceptable to compare short term values and ignore the long term values or the reverse if the fulfillment is better for long periods than short periods? The cause of this variability should first be determined before it is used as a yardstick to measure the suitability of data for comparison. It is also difficult to justitify study of the varia- tions over the globe of the ohm's law parameters from which we derive our knowledge of the electrical state of the lower atmosphere and at the same time discard them for comparison, stating that the measurements are inaccurate. In any case, until the behaviour of ohm's law in the atmosphere is understood completely, its effect on the comparison because of non-fulfillment will not be known.

The determination of the correlation coefficient assumes that the data at 2 stations are linearly related. Low values of correlation coefficients may be due to a non- linear relationship between data at two stations. In this case, cross spectral analysis ([20]), which gives the relationship of the phase and amplitude of various frequency components, should be performed. Future investigations may take this into considera- tion.

Implication of low correlation coefficients on the classical picture

Subject to the assumptions made in this paper, the low correlation coefficient values suggest that either three years of data are not enough to significantly reduce the variations in the electric potential gradient caused by the local columnar resistance and conductivity changes, or the mechanism of the spherical capacitor being charged

Vol. 84, 1971/I) Correlations of Electric Potential Gradients at Land Stations 25

by thunderstorms on a global scale is not an effective cause of the potential gradient

variations at land stations. It may be mentioned that recent observations of M/JHLEISEN

[2] reveal larger local fluctuations on sea than on land. If this were to be true over all

oceans, the global variation may not be easily detected there, and correlation coeffi-

cients for various oceanic stations may be low. This would cast even further doubt on

the classical picture.

The statistical approach of the present paper may be justified on the ground that

the main evidence of the classical concept of atmospheric electricity itself is based on a

statistical relationship.

5. Conclusion

The important conclusions of this paper are as below:

1. The correlation coefficients of the electric potential gradient of the monthly

hourly means in GMT and LST for 36 months were calculated for 179 station pairs.

A significantly high correlation coefficient based on a sufficiently long period of data

(> 20 months) was found for only one station pair, Uccle-Dourbes.

2. The correlation coefficients of the electric potential gradient of the three year

annual hourly means in GMT and LST were computed for 190 station pairs. Signi-

ficantly high correlation coefficients based on 20 months or more data were gound

for eleven percent of station pairs in GMT and for six percent in LST. These station

pairs included the Uccle-Dourbes station pari. 3. The correlation coefficients of the electric potential gradient of the montly

means of three-year data were calculated for 147 station pairs. Significantly high

correlation coefficients based on a minimum of 20 months of data were found for

four percent of station pairs, including Uccle-Dourbes.

REFERENCES

[1] H. DOLEZALEK, Discussion o f a n atmospheric electricity ten-year program, Tech. Rep. No. D-2, Contract No. N00014-66-CO303, Boston College, Mass. (1967).

[2] R. MOHLHSEN, Atmospheric electricity measurements at sea, Results from the Atlantic expedition of the research vessel "Meteor' 1965, Part 1: Measurements o f field strength and ions, Meteor Forschungsergebnisse [Series B], No. 2 (Gebriider Borntraeger, Berlin 1968).

[3] S. J. MAUCHLY, On the diurnal variation of the potential gradient of atmospheric electricity, Terr. Magn. Atmosph. Elect. 28 (1923), 61-81.

[4] J. G. BROWN, The local variation of the earth's electric field, Terr. Magn. Atmosph. Elect. 40 (1935), 413-424.

[5] N. m. PARAMONOV, On the unitary variation of the atmospheric electric potential gradient, Dokl. Akad. Nauk. USSR. 70 (1950), 37-38.

[6] H. HATAKEYAMA and M. KAWANO, On the dirnal variation of atmospheric potential gradient in the Japan Archipelago, Pap. Meteor. Geophys. 4 (1953), 55-60.

[71 H. ISRAEL, H. DOLEZALEK and G. FRIES, The atmospheric electric climate at four selected stations in the Swiss Alps, Tech. Note No. 13, Contract AF61(5t4) 640. (t957).

[8] I. M. IMYANITOV and K. S. SHIFRIN, Present state of research on atmospheric electricity, Soviet Phys. USPEKHI 5 (1962), 292-322.

26 Bhartendu

[9] R. V. ANDERSON, Measurement of world-wide diurnal atmospheric electricity variation, Monthly Weath. Rev. 95 (1967), 899-904.

[10] H. ISRAEL and P. DE BRUIJN, The present status of atmospheric eleetric researeh, Arch. Met. Geoph. Biokl. [A] 26 (1967), 281-299.

[11] BHARTENDU, The atmospheric electric potential gradient variation at land stations, Arch. Met. Geoph, Biokl. [A] 18 (1969), 345-363.

[12] R. A. FISHER and F. YATES, Statistical tables for biological, agricultural and medical research (Oliver and Boyd, Ltd., Edinburgh 1963).

[13] H. ISRAEL and H. DOLEZALEK, On the problem of comparing measurements of atmospheric electricity, Zeits. Geophys. 26 (1960), 77-86.

[14] H. ISRAgL, The comparison of atmospheric results, J. Atmos. Terr. Phys. 24 (1962), 65-66. [15] H. DOLEZALEK, On the eorrelation between atmospheric electricity measurements, J. Applied

Meteor. 8 (1969), 462-463. [16] H. DOLEZALEK, On the calculation of the electric circuit of the atmosphere II: On the validity of

Ohm's law in the atmosphere, Geofisica pura e applicata 45 (1960/I), 273-297. [17] H. DOLEZALEK, On the calculation of the atmospheric electricity circuit Ill: Investigation of the

Ohm's law by measurement. Geofisica pura e appticata 46 (1960/II), 125-144. [18] W. E COBB, The atmospheric electric climate at Mauna Loa Observatory, Hawaii, J. Atmos. Sci.

25 (1968), 470480. [19] P. M. Buls, Current density measurements in atmospheric eleetricity, Nature 216 (1967), 360-361. [20] BHARTENDU, Electric Potential Gradient Measurements' from a radioactive Collector at Meteoro-

logical Research Station, Canadian Meteorological Research Report 5/69 (1969).

Discussion of this paper was conducted together with the discussion of the follo-

wing paper by KOEN~GSFELD, see after that one.