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Measurements of the electrode effect over flat, snow-covered ground
Measurements of the electrode effect over flat, snow-covered ground E. KNUDSEN, S. ISRAELSON and B. H4LLBERG* Department
of Meteorology,
Uppsala
University,
(Received infindform
Box 516. S-751 20 Uppsala,
Sweden
14 April 1989)
Abstract-Space charge density profiles up to 3 m above ground were recorded with the Obolensky-filter method. A measuring technique with two instruments was used, where one reference instrument was p!aced on a fixed level and the other was moved up and down. The space charge difference between the reference and the actual level, and the correlation coefficient were calculated. From the analysis of the recordings, made under very similar atmospheric and ground conditions (snow-covered ground), we found strong evidence for the existence of the electrode effect. Very good agreement between the experimental results and theoretical calculations were observed.
INTRODUCTION
The vertical gradient of space charge density in the lowest layer of the atmosphere is very much dependent on a phenomenon called the electrode effect. This phenomenon has been investigated both experimentally and theoretically. Theoretical calculations have led to the conclusion that such an effect does exist (see HOPPEL, 1967; WILLETT, 1978, 1979, 1981, 1983 ; TUOMI, 1982 and CHALMERS, 1966, 1967). However, the results of numerous experiments are confusing. CHALMERS (1957) reported that “that simple electrode effect does not occur”. M~HLEISEN (1958) reported a well-pronounced effect over water, but none over land. BENT and HUTCHINSON (1966) concluded that “the electrode effect made itself felt in a number of different ways”. CROZIER (1963) found “a strong manifestation of the electrode effect” during night-time periods with a very low wind velocity. This disparity can, in part, be accounted for by the different measuring methods and the varying local meteorological conditions during the measurement periods. Varying surface radioactivity (trapped radon and thoron) and aerosol concentration give differing results as well. Another complication is the large signal fluctuations during the measurement periods, observed by several researchers (ISRAEL, 1970). The only direct method is the filter method, first described by OBOLENSKY(1925) and later developed by MOORE et al. (1Y61), BENT (1964) and ANDERSON (1966). The principle is as follows : air is sucked through a filter and charged particles are collected. The space charge density can be calculated directly by measuring the current from the filter to the ground. An extensive * Presently
at Studsvik
AB, S-61
I 82 Nykiiping.
Sweden. 521
investigation of the expected sources of errors has been done and is reported separate!y, see KNUDSEN et al. (1989). Combinations of the methods described above have also been used. Though scientists agree that the atmospheric electrical parameters are considerably influenced by local meteorological conditions, very little information about those is provided in this type of investigation. A commonly used expression, “fair weather conditions”. is not a very well-defined concept. The stratification of the lowest part of the atmobe expressed by the Richardson sphere can number. defined as : R, = g(aO/&)/T(&i/~?)‘,
(1)
where &/c?z and SO/& are the gradient of wind and potential temperature, respectively, T is the temperature in Kelvin and g is the acceleration due to gravity. The stratification in the lowest part of the atmosphere can be classified in terms of R,. Neutral stratification means only mechanically driven vertical air exchange. Since this situation scarcely exists the expression “near neutral stratification” will be more correct, -0.03 < R, < 0.03. Conditions with other stratifications will be treated in future studies. Preliminary recordings from conditions with stable stratification show a pronounced disparity from the results presented here. Fair weather conditions in night-time (low wind speed and little cloudiness) generally occur under conditions with marked inversion, and hence low vertical air exchange. Trapped radon and thoron gases in the lowest atmospheric layer will then be accumulated and cause considerable ionization. On the other hand, fair weather conditions during day time with a pro-
E. KNUDSENPI al
522
nounced negative temperature gradient and a positive wind gradient, will give rise to a marked vertical air exchange. Although these classifications can, no doubt, be applied to several types of atmospheric electrical investigation, still little attention has been paid to the influence of atmospheric stability, except by WILLETT (1978). The purpose of this investigation was to measure space charge density profiles under neutral atmospheric stratification above an extremely flat ground surface. It showed that strictly neutral stratification occurred very rarely. Therefore, this criterion had to be extended to the weak stable and weak unstable stratification.
No measurements were performed during days with snow drift, since even a very small amount of hydrometeors may cause large amplitude fluctuations. As drifting snow appears at wind speeds of only 4.55 m so- ‘, this meant a considerable reduction in the number of days during which recordings could be made. In order to minimize the effect to strong turbulent mixing. only periods with near neutral stratification were considered. The principle of measurement was based on measuring several vertical profiles, each consisting of a large number of observations under similar conditions, and finally calculating the averages. The rccording period lasted more than 4 months but only 4 days with a total of 13 profiles were considered to meet the necessary criteria. The number of samples on different heights was in the range 240- 390.
METHOD OF MEASUREMENT The space charge density profile depends on several factors, e.g. the generation of ions of both polarities by cosmic rays and radioactivity close to the ground. An atmospheric electrical field is necessary to implement separation and vertical motion of the ions. The degree of turbulent mixing of the air depends on the stratification and topographic irregularities. There is also an attachment effect, i.e. ions are captured at the ground surface and, finally, the aerosol density in the air also causes an attachment effect. It was intended, in planning the measurements, to keep the number of varying parameters as low as possible in order to make an assessment of whether or not the classical electrode effect exists. All the measurements were performed under the following conditions : the wind direction was within a sector of about 90’ where the flat ground had an extension of 2-3 km. This limitation prevented the effect of topographical irregularities. The local production of aerosols was considered to be very low, since there were only a few farms in the surrounding IO-20 km. As proposed by M~JHLEISEN(1958), the measurements were made in winter-time with l&30 cm of snow on the ground. It turned out that the ground was also covered with a 5-10 mm layer of ice. The latter efficiently prevented ion generation caused by emanation of the radioactive gases Rn222 and Rn220 from the ground. The small remaining ground radioactivity showed a very constant rate, without daily variations, according to ISRLELSSONet al. (1973). Since the snow surface was extremely flat, the attachment effect was neglected except for the lowest few centimeters. The amount of aerosols was considered to be equivalent to that of the Arctic or oceanic regions.
INSTRUMENTATION Measurements of the fine structure of the vertical space charge density profile require an instrument which measures the charge densities in a thin layer. For this purpose the filter method was found to be suitable. Two identical instruments were constructed which, apart from minor modifications, arc copies of the Anderson apparatus, (see ANDERSON, 1966). The instrument is s!lown schematically in Fig. 1. Instrument data : length of outer guarding tube 50 cm, length of inner tube 30 cm, diameter of outer tube 12 cm and the diameter of inner tube 10 cm. The electrometer circuit consisted of an AD31 1 operational amplifier with selection gains of 10, 20, 50 and 100, and a time constant of 12 s. The operational amplifier was placed in a metal box attached to the outer tube. The air flow was 2.9 m s ‘. In order to determine the stratification in the atmospheric surface layer, data were recorded at different heights, i.e. temperature and wind speed at 0.5, 1.5, 4.0, 9.8 and 17.6 m above the ground, wind direction at 9.8 m and humidity at I .5 m. Due to the varying thickness of the snow cover. the given values of the different levels varied from day to day. Print-outs of average, maximum and minimum values were made once per hour. A somewhat modified atmospheric electrical recording station of the Kasemir-Dolezalek construction was continuously recording the atmospheric electrical field, i.e. polar conductivities and space charge density, by the Faraday cage method. These recordings provided valuable background data, and information about the general atmospheric electrical state, e.g. if the actual situation was suitable.
523
The electrode effect over flat, snow-covered ground Insulators
-TO pump r (
f Outer
I
grounded
II
‘To ,
Pcitot tube
IY 34: 10'"n
-=I?
Fig. 1. Schematic diagram of the recording instrument
RECORDING
TECHNIQUE
To obtain a fine structure of the vertical profile, the density has to be measured at several levels, and therefore several instruments of high stability are needed. Instead of having several instruments we decided to keep one instrument at 0.8 m height as reference. The other instrument was moved to the different levels 0.1, 0.2, 0.3, 1.6 and 3.1 m. The reference instrument was closely checked with respect to sensitivity. At the beginning of each recording period both instruments were placed side by side at the reference level and the constant for the movable instrument was adjusted so that both instruments gave identical readings. Re-checks were frequently made during the recordings, but only in exceptional cases was readjustment necessary. Computer recordings were carried out during 5 min intervals at each height. When the recording program was planned, very little was known to what degree fluctuations influenced the results, therefore 1 min print-outs were made for checking. It turned out, however, that in general even large variations of the charge densities had little effect on the relative distribution as a function of height. This was confirmed by the chart recording in Fig. 2. The two instruments were placed at 0.8 m level and the sensitivity was adjusted to be the same for both instruments-part A in the figure. One instrument was then moved to 0.2 m level and part B clearly shows an amplitude difference, but with the fluctuations corresponding very well to each other.
RESULTS
A survey of the results is given in Table 1 and Fig. 3 for the four days which fulfilled the criteria for
measurements. The atmospheric stability was very irregular between 0.3 m and 1.3 m due to the influence of the snow temperature, but the stratification above 1.3 m is near neutral. The meteorological data, here frictional velocity, u *, given in Table 1 are average values during the period of measurements, usually 3-5 h. Due to different depths of the snow cover, the actual measurement heights were not the same on different days. The values given in the tables are average values. Table 1 also shows the results of the measurements of other atmospheric electric parameters, conductivity and electric field. The average of the absolute values of the space charge densities at different levels is plotted in Fig. 3. The standard deviation calculated for all values on each level is also indicated. The individual 13 profiles for the space charge density mostly gave a confusing impression. It must be kept in mind, however, that the time requested for recording one profile was nearly an hour, and during this time both atmospheric electric parameters and meteorological conditions could vary considerably. This is probably the reason for the fairly poor correlation between the space charge density profile and the atmospheric electric parameters. The conductivity was very constant during the measurements. The scattering has therefore not been given in Table 1. The listed conductivity in Table 1 must be considered as normal winter values at our site. The general tendency of the percentage distribution, when looking at the different days of measurements, is a well-pronounced decrease in space charge density with respect to height. The curve gives strong evidence for the existence of the electrode effect. The space charge density is nearly 50% higher at 0.1 m and 25% lower at 3.1 m, compared with the 0.8 m reference level.
524
E.
kbiUDSEN
rt
al.
PC/m3
Fig. 2. Chart recordings of space charge densities at the reference height 0.8 m and the height 0.2 m (A). Present measurements with both instruments at 0.8 m.
The correlation between the reference level and the other heights was found to be very good, 0.77-0.94. Only 16% of the calculated correlation coefficients were less than 0.8. Most of them appeared between the reference and 3.1 m. The chart recording reproduced in Fig. 2 indicates that good correlation could be expected. The space charge density could change by a factor of 1 : 5 within a 5 min period, while the relation between the two levels only changed a few per cent. It should be noted that in spite of the great number of sampled values there were no negative values. Although the influence of the attachment effect was supposed to be minimized, and the curve in Fig. 3 does indicate this, one could not forget that some influence does exist. The 10 cm diameter of the inlet of the instrument could not give a vertical resolution good enough for any definite conditions. In case there
exists an attachment effect it should be weak and limited to the first few centimetres above the snow. In Fig. 4 recordings on the atmospheric electric station are given for the period 10.00-16.00 UTC + 1 h, 17 December 1985. The conductivity was measured with a double Gerdien-aspirator having critical mobility of 2. 10e4 m2 V ’ sm‘, and the space charge density according to the Faraday cage method. For clearness, the parameters have been given in the number of charged particles per m3. As can be seen in the figure there is a low correlation between i, - /, and the space charge density. This indicates that ions with low mobility dominate within the space charge columns. Sources of expected errors for the instruments, e.g. accuracy of measurement, influence of disturbed lines of force and point discharge at the orifice of the instru-
Table 1. Meteorological and electrical data ;h represents height, t temperature and u wind velocity Date 13 Nov. 1985
16 Dec. 1985
h(m)
t (‘Cl
u (m s- ‘)
I (‘C)
17.4 9.6 3.8 1.3 0.3
-2.0 -2.2 -2.1 - 1.9 -1.3
2.4 2.0 1.8 1.7
-4.7 -4.8 -4.9 -5.0 -3.0
Frictional velocity (m s-‘) Electric field (V m- ‘) Conductivity (fs mm ‘)
u(ms-‘)
2.3 2.2 2.0 1.9
17 Dec. 1985 l(C)
u(ms-‘I
-7.4 - 7.4 -7.4 -7.6 -6.4
2.7 2.5 2.2 2.0
13 Feb. 1986 ((0
u (m s
f0.6 +0.7 +0.8 f0.7 +0.3
4.0 3.7 3.4 2.9
0.06
0.07
0.13
0.13
77
122
195
32
32
25
26
28
‘)
The electrode effect over flat, snow-covered ground 3.1-
k'f
h m
I
I
I
I
an effective value of the ionization
I I
I
q<,f = q-@N
t
I I I I
+
= an*,
2 = 2kne.
20
Fig. 3. Space charge
30
40
SO pC
density profile. The standard is indicated.
mm3
deviation
ment have been discussed by KNUDSEN et al. (1989). Although a small influence of point discharge for the fields could be expected measuring at the 3.1 m level, this error is negligible for the final mean values, and has therefore not been considered.
COMPARISON WITH THEORETICAL
CALCULATIONS
The electrode effect model of TUOMI (1982) was used to calculate profiles of space charge density. The model, which is valid for cases with snow-covered ground, includes turbulent ion transport, and makes a linearization of the steady state equations that govern the atmospheric electricity parameters near plane ground, see WILLETT (1978). It is assumed that aerosols are uniformly distributed and only affect the order of magnitude of the small-ion densities. The effect of aerosols was taken into consideration by use of
n .106 mm3
400 -
15.00
200 -
rate, q, viz : (2)
where n = n+ z nm is the small-ion density, N the aerosol density, q z 10’ m-3 s- ’ the true ionization rate and a z /j’ z 1.6. lo- ‘* m3 s- ’ are the small-ion recombination and aerosol attachment coefficients, respectively. The small-ion density, n, can be calculated from the conductivity, I, by :
I
I
1.6
525
(3)
This is not true when the turbulence is weak. i.e. when the wind speed is low. The solutions of the linearized equations included modified Bessel functions of the second kind, which were approximated using their asymptotic form for large values, and an equation that exhibits accurate behaviour near the ground. Tuomi found the results of this approximation to agree very well with the results of WILLETT (1978). The parameters used by TUOMI (1982) and WILLETT (1978) were as follows : ionization, q = 10’ mm 3 s ’ ; recombination coefficient, tl = 1.6 * IO- ‘* m3 s ’ ; and mobility of the ions, k = 1.5. 10m4 m2 V ’ SK’. The effective ionization rate is here calculated using the average value of the conductivity, A, at the site (see Table 1). This value was i = 27.8 fs mm ‘, which gives qrf = 0.8 * 10h mm 3 sm‘. Previous studies (ISRAELSSON et al., 1970) gave an average mobility of the ions k = I .25 * lo- 4 m2 V ’ sm’ with modal values in the range 0.6 - 0.9 * 10e4 m* V ’ s- ‘. For the actual conditions we have: atmospheric electric field E = 106 V m- ’ ; roughness parameter (for flat snow cover), z,, = 0.002 m; and friction velocity (h = 1.3 m,u=2ms-’ and z0 = 0.002) u* = 0.1 m s ‘. Figure 5 shows a comparison between calculated and experimental profiles of space charge density for different values of u*, q and k. The meteorological data are comparable, but for the measured profile the mobility of the ions given in the diagram represents data from previous measurements (ISRAELSSONet al., 1970). From the diagrams we note that the experimental profile seems to agree fairly well with calculated profiles for the ionization rates l--6 * 10’ me3 S ’ and the mobilities 0.6-0.9. lo- 4m2V ’ s ‘. The attachment effect close to the ground cannot be seen in the experimental profile due to the diameter of the inlet of the instrument (10 cm).
,A-
400 * -600 L
I
Fig. 4. Simultaneous recordings of the space charge density (p) and the polar conductivities (A+) given in terms of n, number of charged particles per m3.
CONCLUSIONS
By reducing the number of factors which influence the space charge profile, it has been possible to measure profiles which are in good agreement with the
E. KNUDSEN et al
526
“*
9
k
I,,,<').106,+<' .10-4mzv"s~' ProfIle1 2
Measured
0
20
M
0.1 0.2
1 4
0.6 06
0.1
30
40 pC.d3
Fig. 5. Measured and calculated profiles of space charge density
classical electrode effect. Comparison between the measured profile and the theoretical model of TUOMI (1982) and WILLETT (1978) shows a very good agreement. The tendency to high correlation coefficients between the measured values on the reference level and all other levels, in combination with strong fluctuations of the space charge density, shows that the space charge volume consists of very variable space charge densities. Even within such volumes there exists a pronounced gradient. It will be ofconsiderable inter-
est to see to what extent this effect is caused by strong turbulence and other ground conditions. The principle of measurement, using one instrument as a reference and moving another instrument to different levels, has turned out to be very successful. Future measurements under other meteorological and ground conditions are therefore being planned.
Acknowledgement-The research was supported Swedish Natural Science Research Council.
by the
REFERENCES ATKINS C.-J. ANDERSON R. V. BENT R. B. BENT R. B. and HUTCHINSONC. W. A CHALMERS J. A.
19.59 1966 1964 1966 1957
Quart. J. Roy. Met. Sot. 85, 237. J. geophys. Res. 71, 5809. J. atmos. terr. Phys. 26, 3 13. J. atmos. terr. Phys. 28, 53. Atmospheric Electricity, p. 149. Pergamon
Press, Lon-
don. CHALMERS J. A. CHALMERS J. A. CROZIER W. D. HOPPEL W. A. h_AEL
H.
~SRAELSSON S., KNUDSEN E. and UNGETH~~ME. ISRAELSON S., KUDSEN E. and UNGETH~~ME. KNUDSEN E., JAYAKATNE K. P. S. C. and 1sR~E~ss0N S. MOORE C. B., VONNEGUT B. and MALLAHAN F.-J. M~JHLEISENJ. OBOLENSKY W.
1973
J. atmos. ferr. Phys. 28, 565. J. atmos. ferr. Phys. 29, 307. J. geophys. Res. 68,345 1. J. atmos. terr. Phys. 29, 709. Atmospheric Electricity, Vol. II, p. 442. Israel Program for Sci. Trans., Jerusalem. Report No. 16, Dept. of Meteorology, Uppsala University, Uppsala. Tellus 25, 28 1.
1989
J. utmos. terr. Phys. 51, 529
1961
J. geophys. Res. 66,3219.
1958 1925
J. atmos. lerr. Phys. 20, 79 Ann. Physik 77, 644.
1966 1967 1963 1967 1970 1970
The electrode TUOMZT.-J. WILLETT J. WILLETTJ. WILLETTJ. WILLETTJ.
C. C. C. C.
effect over flat, snow-covered 1982 1978 1979 1981 1983
ground
f. afmos. terr. Phys. 44,737. J. geophys. Res. 80,402. J. geophys. Ret MC, 103. NRL Report 8519. J. geophl?s. Res. 88C, 8453.
527
of Meteorology,
Uppsala
University,
(Received infindform
Box 516. S-751 20 Uppsala,
Sweden
14 April 1989)
Abstract-Space charge density profiles up to 3 m above ground were recorded with the Obolensky-filter method. A measuring technique with two instruments was used, where one reference instrument was p!aced on a fixed level and the other was moved up and down. The space charge difference between the reference and the actual level, and the correlation coefficient were calculated. From the analysis of the recordings, made under very similar atmospheric and ground conditions (snow-covered ground), we found strong evidence for the existence of the electrode effect. Very good agreement between the experimental results and theoretical calculations were observed.
INTRODUCTION
The vertical gradient of space charge density in the lowest layer of the atmosphere is very much dependent on a phenomenon called the electrode effect. This phenomenon has been investigated both experimentally and theoretically. Theoretical calculations have led to the conclusion that such an effect does exist (see HOPPEL, 1967; WILLETT, 1978, 1979, 1981, 1983 ; TUOMI, 1982 and CHALMERS, 1966, 1967). However, the results of numerous experiments are confusing. CHALMERS (1957) reported that “that simple electrode effect does not occur”. M~HLEISEN (1958) reported a well-pronounced effect over water, but none over land. BENT and HUTCHINSON (1966) concluded that “the electrode effect made itself felt in a number of different ways”. CROZIER (1963) found “a strong manifestation of the electrode effect” during night-time periods with a very low wind velocity. This disparity can, in part, be accounted for by the different measuring methods and the varying local meteorological conditions during the measurement periods. Varying surface radioactivity (trapped radon and thoron) and aerosol concentration give differing results as well. Another complication is the large signal fluctuations during the measurement periods, observed by several researchers (ISRAEL, 1970). The only direct method is the filter method, first described by OBOLENSKY(1925) and later developed by MOORE et al. (1Y61), BENT (1964) and ANDERSON (1966). The principle is as follows : air is sucked through a filter and charged particles are collected. The space charge density can be calculated directly by measuring the current from the filter to the ground. An extensive * Presently
at Studsvik
AB, S-61
I 82 Nykiiping.
Sweden. 521
investigation of the expected sources of errors has been done and is reported separate!y, see KNUDSEN et al. (1989). Combinations of the methods described above have also been used. Though scientists agree that the atmospheric electrical parameters are considerably influenced by local meteorological conditions, very little information about those is provided in this type of investigation. A commonly used expression, “fair weather conditions”. is not a very well-defined concept. The stratification of the lowest part of the atmobe expressed by the Richardson sphere can number. defined as : R, = g(aO/&)/T(&i/~?)‘,
(1)
where &/c?z and SO/& are the gradient of wind and potential temperature, respectively, T is the temperature in Kelvin and g is the acceleration due to gravity. The stratification in the lowest part of the atmosphere can be classified in terms of R,. Neutral stratification means only mechanically driven vertical air exchange. Since this situation scarcely exists the expression “near neutral stratification” will be more correct, -0.03 < R, < 0.03. Conditions with other stratifications will be treated in future studies. Preliminary recordings from conditions with stable stratification show a pronounced disparity from the results presented here. Fair weather conditions in night-time (low wind speed and little cloudiness) generally occur under conditions with marked inversion, and hence low vertical air exchange. Trapped radon and thoron gases in the lowest atmospheric layer will then be accumulated and cause considerable ionization. On the other hand, fair weather conditions during day time with a pro-
E. KNUDSENPI al
522
nounced negative temperature gradient and a positive wind gradient, will give rise to a marked vertical air exchange. Although these classifications can, no doubt, be applied to several types of atmospheric electrical investigation, still little attention has been paid to the influence of atmospheric stability, except by WILLETT (1978). The purpose of this investigation was to measure space charge density profiles under neutral atmospheric stratification above an extremely flat ground surface. It showed that strictly neutral stratification occurred very rarely. Therefore, this criterion had to be extended to the weak stable and weak unstable stratification.
No measurements were performed during days with snow drift, since even a very small amount of hydrometeors may cause large amplitude fluctuations. As drifting snow appears at wind speeds of only 4.55 m so- ‘, this meant a considerable reduction in the number of days during which recordings could be made. In order to minimize the effect to strong turbulent mixing. only periods with near neutral stratification were considered. The principle of measurement was based on measuring several vertical profiles, each consisting of a large number of observations under similar conditions, and finally calculating the averages. The rccording period lasted more than 4 months but only 4 days with a total of 13 profiles were considered to meet the necessary criteria. The number of samples on different heights was in the range 240- 390.
METHOD OF MEASUREMENT The space charge density profile depends on several factors, e.g. the generation of ions of both polarities by cosmic rays and radioactivity close to the ground. An atmospheric electrical field is necessary to implement separation and vertical motion of the ions. The degree of turbulent mixing of the air depends on the stratification and topographic irregularities. There is also an attachment effect, i.e. ions are captured at the ground surface and, finally, the aerosol density in the air also causes an attachment effect. It was intended, in planning the measurements, to keep the number of varying parameters as low as possible in order to make an assessment of whether or not the classical electrode effect exists. All the measurements were performed under the following conditions : the wind direction was within a sector of about 90’ where the flat ground had an extension of 2-3 km. This limitation prevented the effect of topographical irregularities. The local production of aerosols was considered to be very low, since there were only a few farms in the surrounding IO-20 km. As proposed by M~JHLEISEN(1958), the measurements were made in winter-time with l&30 cm of snow on the ground. It turned out that the ground was also covered with a 5-10 mm layer of ice. The latter efficiently prevented ion generation caused by emanation of the radioactive gases Rn222 and Rn220 from the ground. The small remaining ground radioactivity showed a very constant rate, without daily variations, according to ISRLELSSONet al. (1973). Since the snow surface was extremely flat, the attachment effect was neglected except for the lowest few centimeters. The amount of aerosols was considered to be equivalent to that of the Arctic or oceanic regions.
INSTRUMENTATION Measurements of the fine structure of the vertical space charge density profile require an instrument which measures the charge densities in a thin layer. For this purpose the filter method was found to be suitable. Two identical instruments were constructed which, apart from minor modifications, arc copies of the Anderson apparatus, (see ANDERSON, 1966). The instrument is s!lown schematically in Fig. 1. Instrument data : length of outer guarding tube 50 cm, length of inner tube 30 cm, diameter of outer tube 12 cm and the diameter of inner tube 10 cm. The electrometer circuit consisted of an AD31 1 operational amplifier with selection gains of 10, 20, 50 and 100, and a time constant of 12 s. The operational amplifier was placed in a metal box attached to the outer tube. The air flow was 2.9 m s ‘. In order to determine the stratification in the atmospheric surface layer, data were recorded at different heights, i.e. temperature and wind speed at 0.5, 1.5, 4.0, 9.8 and 17.6 m above the ground, wind direction at 9.8 m and humidity at I .5 m. Due to the varying thickness of the snow cover. the given values of the different levels varied from day to day. Print-outs of average, maximum and minimum values were made once per hour. A somewhat modified atmospheric electrical recording station of the Kasemir-Dolezalek construction was continuously recording the atmospheric electrical field, i.e. polar conductivities and space charge density, by the Faraday cage method. These recordings provided valuable background data, and information about the general atmospheric electrical state, e.g. if the actual situation was suitable.
523
The electrode effect over flat, snow-covered ground Insulators
-TO pump r (
f Outer
I
grounded
II
‘To ,
Pcitot tube
IY 34: 10'"n
-=I?
Fig. 1. Schematic diagram of the recording instrument
RECORDING
TECHNIQUE
To obtain a fine structure of the vertical profile, the density has to be measured at several levels, and therefore several instruments of high stability are needed. Instead of having several instruments we decided to keep one instrument at 0.8 m height as reference. The other instrument was moved to the different levels 0.1, 0.2, 0.3, 1.6 and 3.1 m. The reference instrument was closely checked with respect to sensitivity. At the beginning of each recording period both instruments were placed side by side at the reference level and the constant for the movable instrument was adjusted so that both instruments gave identical readings. Re-checks were frequently made during the recordings, but only in exceptional cases was readjustment necessary. Computer recordings were carried out during 5 min intervals at each height. When the recording program was planned, very little was known to what degree fluctuations influenced the results, therefore 1 min print-outs were made for checking. It turned out, however, that in general even large variations of the charge densities had little effect on the relative distribution as a function of height. This was confirmed by the chart recording in Fig. 2. The two instruments were placed at 0.8 m level and the sensitivity was adjusted to be the same for both instruments-part A in the figure. One instrument was then moved to 0.2 m level and part B clearly shows an amplitude difference, but with the fluctuations corresponding very well to each other.
RESULTS
A survey of the results is given in Table 1 and Fig. 3 for the four days which fulfilled the criteria for
measurements. The atmospheric stability was very irregular between 0.3 m and 1.3 m due to the influence of the snow temperature, but the stratification above 1.3 m is near neutral. The meteorological data, here frictional velocity, u *, given in Table 1 are average values during the period of measurements, usually 3-5 h. Due to different depths of the snow cover, the actual measurement heights were not the same on different days. The values given in the tables are average values. Table 1 also shows the results of the measurements of other atmospheric electric parameters, conductivity and electric field. The average of the absolute values of the space charge densities at different levels is plotted in Fig. 3. The standard deviation calculated for all values on each level is also indicated. The individual 13 profiles for the space charge density mostly gave a confusing impression. It must be kept in mind, however, that the time requested for recording one profile was nearly an hour, and during this time both atmospheric electric parameters and meteorological conditions could vary considerably. This is probably the reason for the fairly poor correlation between the space charge density profile and the atmospheric electric parameters. The conductivity was very constant during the measurements. The scattering has therefore not been given in Table 1. The listed conductivity in Table 1 must be considered as normal winter values at our site. The general tendency of the percentage distribution, when looking at the different days of measurements, is a well-pronounced decrease in space charge density with respect to height. The curve gives strong evidence for the existence of the electrode effect. The space charge density is nearly 50% higher at 0.1 m and 25% lower at 3.1 m, compared with the 0.8 m reference level.
524
E.
kbiUDSEN
rt
al.
PC/m3
Fig. 2. Chart recordings of space charge densities at the reference height 0.8 m and the height 0.2 m (A). Present measurements with both instruments at 0.8 m.
The correlation between the reference level and the other heights was found to be very good, 0.77-0.94. Only 16% of the calculated correlation coefficients were less than 0.8. Most of them appeared between the reference and 3.1 m. The chart recording reproduced in Fig. 2 indicates that good correlation could be expected. The space charge density could change by a factor of 1 : 5 within a 5 min period, while the relation between the two levels only changed a few per cent. It should be noted that in spite of the great number of sampled values there were no negative values. Although the influence of the attachment effect was supposed to be minimized, and the curve in Fig. 3 does indicate this, one could not forget that some influence does exist. The 10 cm diameter of the inlet of the instrument could not give a vertical resolution good enough for any definite conditions. In case there
exists an attachment effect it should be weak and limited to the first few centimetres above the snow. In Fig. 4 recordings on the atmospheric electric station are given for the period 10.00-16.00 UTC + 1 h, 17 December 1985. The conductivity was measured with a double Gerdien-aspirator having critical mobility of 2. 10e4 m2 V ’ sm‘, and the space charge density according to the Faraday cage method. For clearness, the parameters have been given in the number of charged particles per m3. As can be seen in the figure there is a low correlation between i, - /, and the space charge density. This indicates that ions with low mobility dominate within the space charge columns. Sources of expected errors for the instruments, e.g. accuracy of measurement, influence of disturbed lines of force and point discharge at the orifice of the instru-
Table 1. Meteorological and electrical data ;h represents height, t temperature and u wind velocity Date 13 Nov. 1985
16 Dec. 1985
h(m)
t (‘Cl
u (m s- ‘)
I (‘C)
17.4 9.6 3.8 1.3 0.3
-2.0 -2.2 -2.1 - 1.9 -1.3
2.4 2.0 1.8 1.7
-4.7 -4.8 -4.9 -5.0 -3.0
Frictional velocity (m s-‘) Electric field (V m- ‘) Conductivity (fs mm ‘)
u(ms-‘)
2.3 2.2 2.0 1.9
17 Dec. 1985 l(C)
u(ms-‘I
-7.4 - 7.4 -7.4 -7.6 -6.4
2.7 2.5 2.2 2.0
13 Feb. 1986 ((0
u (m s
f0.6 +0.7 +0.8 f0.7 +0.3
4.0 3.7 3.4 2.9
0.06
0.07
0.13
0.13
77
122
195
32
32
25
26
28
‘)
The electrode effect over flat, snow-covered ground 3.1-
k'f
h m
I
I
I
I
an effective value of the ionization
I I
I
q<,f = q-@N
t
I I I I
+
= an*,
2 = 2kne.
20
Fig. 3. Space charge
30
40
SO pC
density profile. The standard is indicated.
mm3
deviation
ment have been discussed by KNUDSEN et al. (1989). Although a small influence of point discharge for the fields could be expected measuring at the 3.1 m level, this error is negligible for the final mean values, and has therefore not been considered.
COMPARISON WITH THEORETICAL
CALCULATIONS
The electrode effect model of TUOMI (1982) was used to calculate profiles of space charge density. The model, which is valid for cases with snow-covered ground, includes turbulent ion transport, and makes a linearization of the steady state equations that govern the atmospheric electricity parameters near plane ground, see WILLETT (1978). It is assumed that aerosols are uniformly distributed and only affect the order of magnitude of the small-ion densities. The effect of aerosols was taken into consideration by use of
n .106 mm3
400 -
15.00
200 -
rate, q, viz : (2)
where n = n+ z nm is the small-ion density, N the aerosol density, q z 10’ m-3 s- ’ the true ionization rate and a z /j’ z 1.6. lo- ‘* m3 s- ’ are the small-ion recombination and aerosol attachment coefficients, respectively. The small-ion density, n, can be calculated from the conductivity, I, by :
I
I
1.6
525
(3)
This is not true when the turbulence is weak. i.e. when the wind speed is low. The solutions of the linearized equations included modified Bessel functions of the second kind, which were approximated using their asymptotic form for large values, and an equation that exhibits accurate behaviour near the ground. Tuomi found the results of this approximation to agree very well with the results of WILLETT (1978). The parameters used by TUOMI (1982) and WILLETT (1978) were as follows : ionization, q = 10’ mm 3 s ’ ; recombination coefficient, tl = 1.6 * IO- ‘* m3 s ’ ; and mobility of the ions, k = 1.5. 10m4 m2 V ’ SK’. The effective ionization rate is here calculated using the average value of the conductivity, A, at the site (see Table 1). This value was i = 27.8 fs mm ‘, which gives qrf = 0.8 * 10h mm 3 sm‘. Previous studies (ISRAELSSON et al., 1970) gave an average mobility of the ions k = I .25 * lo- 4 m2 V ’ sm’ with modal values in the range 0.6 - 0.9 * 10e4 m* V ’ s- ‘. For the actual conditions we have: atmospheric electric field E = 106 V m- ’ ; roughness parameter (for flat snow cover), z,, = 0.002 m; and friction velocity (h = 1.3 m,u=2ms-’ and z0 = 0.002) u* = 0.1 m s ‘. Figure 5 shows a comparison between calculated and experimental profiles of space charge density for different values of u*, q and k. The meteorological data are comparable, but for the measured profile the mobility of the ions given in the diagram represents data from previous measurements (ISRAELSSONet al., 1970). From the diagrams we note that the experimental profile seems to agree fairly well with calculated profiles for the ionization rates l--6 * 10’ me3 S ’ and the mobilities 0.6-0.9. lo- 4m2V ’ s ‘. The attachment effect close to the ground cannot be seen in the experimental profile due to the diameter of the inlet of the instrument (10 cm).
,A-
400 * -600 L
I
Fig. 4. Simultaneous recordings of the space charge density (p) and the polar conductivities (A+) given in terms of n, number of charged particles per m3.
CONCLUSIONS
By reducing the number of factors which influence the space charge profile, it has been possible to measure profiles which are in good agreement with the
E. KNUDSEN et al
526
“*
9
k
I,,,<').106,+<' .10-4mzv"s~' ProfIle1 2
Measured
0
20
M
0.1 0.2
1 4
0.6 06
0.1
30
40 pC.d3
Fig. 5. Measured and calculated profiles of space charge density
classical electrode effect. Comparison between the measured profile and the theoretical model of TUOMI (1982) and WILLETT (1978) shows a very good agreement. The tendency to high correlation coefficients between the measured values on the reference level and all other levels, in combination with strong fluctuations of the space charge density, shows that the space charge volume consists of very variable space charge densities. Even within such volumes there exists a pronounced gradient. It will be ofconsiderable inter-
est to see to what extent this effect is caused by strong turbulence and other ground conditions. The principle of measurement, using one instrument as a reference and moving another instrument to different levels, has turned out to be very successful. Future measurements under other meteorological and ground conditions are therefore being planned.
Acknowledgement-The research was supported Swedish Natural Science Research Council.
by the
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527