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Empirical correlation for total and diffuse radiation in Bahrain
0360~S442/89 $3.00 + 0.00 Copyright @ 1989 Pergamon Press plc
Energy Vol. 14, No. 7, pp. 409-414, 1989 Printed in Great Britain. All rights reserved
EMPIRICAL CORRELATION FOR TOTAL AND DIFFUSE RADIATION IN BAHRAIN W. E. Physics Department,
University
(Received
ALNASER
of Bahrain,
P.O. Box 32038, Bahrain
18 July 1988)
total and diffuse irradiation in Bahrain are estimated using meteorological data recorded from 1984 to 1987. Two established models were used in calculating the
Abstract-The
total radiation, Next, an empirical equation was used to estimate monthly means and annual total solar radiation on a horizontal surface. The diffuse solar radiation can be obtained from two empirical parameters, namely, the clearness index K, and the fraction of sunshine S/S,.
INTRODUCTION
The amount of solar energy delivered to the surface of the Earth each minute is greater than the total amount of annually depleted fossil energy. Utilization of solar energy, like that of any other natural resource, requires detailed information concerning its availability. Furthermore, to achieve an optimally-designed solarenergy conversion system, we require knowledge about the solar radiation obtainable at particular locations. The best radiation information is obtained from experimental measurements of the global (total) and diffuse components of the solar insolation at these places. In Bahrain, which is a tiny island in the Arabian Gulf located at a latitude of 27”N and a longitude of 50”E, sunshine is frequently available in all seasons. There are three meteorological stations, viz. the Bahrain International Airport station, the System Control Centre station of the Ministry of Works, Power & Water and the station of the University of Bahrain. The available meteorological data at these stations provide the total components of solar radiation, humidity, temperature (wet and dry bulb), rain level, and wind speed and its direction. Unfortunately, only the first-named station provides a computerized record of the sunshine data. Since the global and diffuse radiation are useful parameters in solar-energy technology and have not been correlated with these meteorological data previously, we have estimated these values. A number of authors have estimated the global and diffuse radiation by relating these parameters to the number of sunshine hours.lm5 On the other hand, Sabbagh et al6 and Gopinathan’ related the solar radiation to the sunshine duration, relative humidity, temperature, latitude, and altitude of the location relative to a water surface. We use both methods to estimate the monthly average of the daily global radiation on a horizontal surface and the diffuse irradiation for the years 1984-1987.
EXPERIMENTAL
DATA
Data obtained from the Bahrain International Airport records were used. Table 1 shows the meteorological information and includes the following: the monthly mean daily number of hours of observed bright sunshine, the monthly mean daily maximum possible number of sunshine hours S,, the monthly average of daily relative humidity R as a percentage, and the monthly average for the daily temperature T (in “C). These parameters represent averages over 4 yr. 409
10.23
6.93
kc
10.20
10.60
10.83
11.65
9.73
10.00
QP
8. JO
10.48
Aug
12.00
Nov
10.25
Jul
12.10
12.05
11.58
10.9
10.7
9.83
S.(hr)
Ott
9.45
10.25
JUII
m
bY
7.03
9.00
nar
7.78
8.18
Feb
S(hr)
Jan
l4onth
0.68
0.23
0.92
0.92
0.90
0.86
0.85
0.78
0.78
0.65
0.76
0.79
S/S,
73.0
71.0
65.5
65.5
63.8
59.3
55.8
56.8
61.3
67.0
71.0
75.0
a(x)
21.40
28.00
33.40
36.70
30.00
38.40
36.20
34.90
29.80
24.60
21.60
20.55
T(OC)
0.2716
0.2758
0.2797
0.3068
0.2925
0.3164
0.3139
0.2869
0.2x%7
0.2881
0.2683
0.2668
A
0.4521
0.4767
0.4489
0.4179
0.4307
0.4177
0.4232
0.4616
0.4766
0.4849
0.4742
0.4744
B
0.579
0.681
0.693
0.691
0.687
0.676
0.674
0.647
0.671
0.603
0.629
0.642
(WH,),
0.573
0.621
0.642
0.638
0.632
0.623
0.627
0.606
0.607
0.594
0.600
0.607
m/a,),
0.346
0.231
0.217
0.219
0.224
0.238
0.238
0.269
0.242
0.319
0.289
0.274
(H~/H:
Table 1. Monthly mean daily values of S, $,, R, T, A, B, and (H/H,), for Page’s model, (Ho/Ho), for Gopinathan’s model, and H,/H for Bahrain during the period 1984-1987. Measurements were taken at a height of 2 m.
Empirical correlation for radiation in Bahrain MATHEMATICAL
411
MODELS
Global radiation The relation between the global radiation on a horizontal
sunshine was estimated Page,8 i.e.
surface and the relative duration of by using a linear regression of Angstrom’s equation as developed by H/H,
= A + BSI&,
(1)
where H is the monthly average of the daily global radiation on a horizontal surface in kWh/m* and HO is the corresponding monthly average of the daily extraterrestrial solar radiation on a horizontal surface. The latter may be obtained by following Klein,’ i.e. H,, = (24/n)Z,[l+
0.033 cos(36On/365)][(cos
L)( cos s)(sin 0) + (20/36O)(sin L)(sin S)],
(2)
where Z,, is the solar constant (1353 W/m*), n the day number starting from the first of January, the sunset hour angle is w = cos-l[( - tan L)(tan S)], I is the latitude (in degrees), and the solar declination
(3)
angle is
6 = 23.45 sin[360(284 + n)/365].
(4)
The mean daily number of hours of daylight (&) in a given month between sunset can be calculated from Cooper’s” formula S, = (2/15) cos-‘[(-tan
sunrise and
L)(tan S)].
The regression constants A and B in Eq. (1) are measured follows:
(5) in terms of the latitutde
L as
A=fL+g,
(6)
B=pL+q,
(7)
where the values off, g, p, and q may be obtained from Table 2.’ The values of A and B for Bahrain are shown in Table 1. Table 2. Values off, f
Month
g, p, and (I vs the month of the year. g
P
9
Jan
- 0.00301
0.34507
0.00495
0.34572
Feh
- 0.00255
0.33450
0.00457
0.35533
mar
- 0.00303
O-36690
0.00466
0.36377
&r
- 0.00334
0.38557
0.00456
0.35802
maY
- 0.00245
0.35057
0.00485
0.33550
Jun
- 0.00327
0.39890
0.00578
0.27292
.JUl
- 0.00369
0.41234
0.00568
0.27004
Aug
- 0.00269
0.36243
0.00412
0.33162
Sep
- 0.00338
0.39467
0.00564
0.27125
Ott
- 0.00317
0.36213
0.00504
0.31790
NOV
-
0.00350
0.36680
0.00623
0.31467
Dee
-
0.00350
0.36262
0.00559
0.30676
Year
- 0.00290
0.36239
0.00491
0.31876
lG?SllS
-
0.00313
0.37022
0.00606
0.32029
W. E.
412
ALNASER
Recently, Gopinathan’ proposed a new model for estimating the total solar radiation. He developed a multiple, linear-regression equation for determining the monthly mean daily global radiation as a function of several meteorological parameters in the following form: H/H,, = a + b cos L + ch + d(S/S,J
+ eT +fR,
(8)
where L is the latitude in degrees and h the elevation of the location in km above sea level, T the monthly mean daily maximum temperature, and R the monthly mean relative humidity. The regression coefficients a, b, c, d, e, and f were calculated by using data for four stations in South Africa. The result is H/H, = 0.801-
0.387 cos L + 0.0128h + 0.316(S/Sc,) - 1.215 x 10-3T - 1.049 x 10-3R.
(9)
Diffuse radiation The prediction of the mean daily diffuse solar radiation
Hd may be obtained by applying an empirical equation proposed by Page.8 This relation correlates the estimated monthly mean of the daily diffuse radiation component Hd with the monthly mean daily total radiation as follows: H,/H = 1 - l.l3K,, (10)
where Kt is the mean clearness index, which is equal to H/H,,. Klein’ and Liu and Jordan” have proposed the following correlation equation for the diffuse radiation: H,/H
= 1.39 - 4.027K, + 5.53(Q2
RESULTS
AND
- 3.108(K,).3
(11)
DISCUSSION
Equation (1) was used for the monthly mean of the daily global radiation on a horizontal surface. In Fig. 1, we show (H/H,) for the monthly mean of the fractional daily number of sunshine hours (S/Q in Bahrain, as obtained from the following equation: H/H,
= 0.338(*0.038)
r = 0.938.
+ 0.392(fO.O46)S/&,
(12)
An estimate for the monthly mean of the daily diffuse radiation in Bahrain was calculated from the following equation, which was obtained from Fig. 2 by plotting H,+/H vs S/&: H,/H
= 0.618(f0.042)
r = 0.938.
- 0.442(fO.O52)S/S,,,
The ratio H,/H can also be calculated by using the following equation, plotting H,/H vs K, as in Fig. 3: H,/H
= 0.999(fO.O03)
which is obtained by
r = 0.999.
- 1.1283(f0.003)Kt,
(13)
(14)
Gopinathan’s model7 in Eq. (9), which was used to correlate (H/H,,) with meteorological data such as R, T, S/&, and h, is of interest since these data are routinely recorded and widely available. We show a comparison of Gopinathan’s model with that of Page in Fig. 4. It may be seen that the two curves are similar, viz. there are similar maxima and minima for (H/H,) throughout the year. However, the ratio (H/H,) is always less for Gopinathan’s model than for Page’s model. This difference is the result of using the regression coefficients a, b, c, d, e, and f
-,
0,
1
0.75
0.85
Fig. 1. Plot of HIHO vs S/h.
S/%
I
413
Empirical correlation for radiation in Bahrain
0.26-
Fig. 2. Plot of &II-l Vs S/&J.
Fig. 3. Plot of H,IH vs K,.
0.69-
- 0.68 I J
I
I
I
I
I
I
M
I
I
I
I
I
s
Month Fig. 4. Variations of H/H, (Cl, Page’s model; C2, Gopinathan’s model), S/S,, month of the year.
and H,,H with the
in Eq. (8), which had been obtained for a different latitude in South Africa. For Bahrain, we therefore propose the following equation for the monthly mean global solar radiation as a function of meteorological data: H/H,, = [0.801-
0.378 cos L + 0.0128h + 0.316(S/&) - 1.215 x 10-33T - 1.049 x 10-3R] x W, (15)
where W is a constant and has different values for each month of the year, as listed in Table 3. The corrected annual global radiation in Bahrain (H/H,) can be found by using the following
414
W. E. ALNASER Table 3. Values of W corresponding Month
W
J
I .058
empirical equation,
F
1.046
n
1.015
A
I. 105
I4
1.068
to each month of the average year. J
1.075
J
l.oB5
A
l.cl67
S
0
N
D
1.083
1.079
1.097
1.010
which is based on the use of both models:
(H/H,,), = 0.854 - 0.403 cos L + 0.0136h + 0.337@/&) - 1.297 x 10-3T - 1.119 x 1O-38 f 0.028,
(16)
where .I?, $,, i?, and I? represent the annual mean values of S, S,, T, and R, respectively. The curves for (H/H,) in Fig. 4 (identified as Cl and C2) and for (S/S,,) (identified as C3) vs the month of the year have behavior opposite to that of H,/H vs the month of the year (C4). The trough in April for curve C4 may be attributed to thick cirrus cloud at that time. The other and more evident trough in the September-October period may be related to the effect of ambient temperature, which seems to contribute to scattering and dispersion of the solar radiation. Furthermore, according to Shettle and Fenn,” the relative proportion of the direct to the diffuse radiation is primarily controlled by the concentrations of aerosols, which vary in a random manner geographically and temporally. This point requires further studies. Acknowledgemen&s-The author is thankful to Y. A. Abdulla of the University of Bahrain for many valuable discussions. The author would also like to thank Y. E. Alnaser and A. A. Agab for analyses and calculations and E. Eves for help with typing the manuscript.
REFERENCES 1. Y. A. Abdulla
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
and G. M. Feregh, Energy Cowers. Mgmt 28, 63 (1988). Y. A. Abdulla and M. K. Bagdady, Sol. Wind Technol. 2, 209 (1985). K. K. Gopinathan, Sol. Wind-Technol. 5, 103 (1987). S. M. B. Sukhera and M. A. Pasha, Sol. Wind Technol. 4, 229 (1987). H. P. Garg and S. M. Garg, Sol. Wind Technof. 4, 113 (1987). J. A. Sabbagh, A. A. Sayigh, and E. M. El Salam, Sol. Energy 19, 307 (1977). K. K. Gopinathan, Sol. Wind Technol. 5, 107 (1988). J. K. Page, “Methods for the Estimation of Solar Energy on Vertical and Inclined Surfaces”, in Solar Energy Conversion, pp. 37-99, L. E. Dixon and J. D. Leslie eds., Pergamon Press, Canada (1979). A. S. A. Klein, Sol. Energy 9,327 (1977). P. I. Cooper, Sol. Energy 12, 333 (1969). B. T. Liu and R. C. Jordon, Sol. Energy 4, 1 (1960). E. P. Shettle and R. W. Fenn, “Models of Aerosols in the Lower Atmosphere and the Effect of Humidity Variations on Their Optical Properties,” Report AFGL-TR-79-0214, Hanscom Air Force Base, MA 01731 (1979).
Energy Vol. 14, No. 7, pp. 409-414, 1989 Printed in Great Britain. All rights reserved
EMPIRICAL CORRELATION FOR TOTAL AND DIFFUSE RADIATION IN BAHRAIN W. E. Physics Department,
University
(Received
ALNASER
of Bahrain,
P.O. Box 32038, Bahrain
18 July 1988)
total and diffuse irradiation in Bahrain are estimated using meteorological data recorded from 1984 to 1987. Two established models were used in calculating the
Abstract-The
total radiation, Next, an empirical equation was used to estimate monthly means and annual total solar radiation on a horizontal surface. The diffuse solar radiation can be obtained from two empirical parameters, namely, the clearness index K, and the fraction of sunshine S/S,.
INTRODUCTION
The amount of solar energy delivered to the surface of the Earth each minute is greater than the total amount of annually depleted fossil energy. Utilization of solar energy, like that of any other natural resource, requires detailed information concerning its availability. Furthermore, to achieve an optimally-designed solarenergy conversion system, we require knowledge about the solar radiation obtainable at particular locations. The best radiation information is obtained from experimental measurements of the global (total) and diffuse components of the solar insolation at these places. In Bahrain, which is a tiny island in the Arabian Gulf located at a latitude of 27”N and a longitude of 50”E, sunshine is frequently available in all seasons. There are three meteorological stations, viz. the Bahrain International Airport station, the System Control Centre station of the Ministry of Works, Power & Water and the station of the University of Bahrain. The available meteorological data at these stations provide the total components of solar radiation, humidity, temperature (wet and dry bulb), rain level, and wind speed and its direction. Unfortunately, only the first-named station provides a computerized record of the sunshine data. Since the global and diffuse radiation are useful parameters in solar-energy technology and have not been correlated with these meteorological data previously, we have estimated these values. A number of authors have estimated the global and diffuse radiation by relating these parameters to the number of sunshine hours.lm5 On the other hand, Sabbagh et al6 and Gopinathan’ related the solar radiation to the sunshine duration, relative humidity, temperature, latitude, and altitude of the location relative to a water surface. We use both methods to estimate the monthly average of the daily global radiation on a horizontal surface and the diffuse irradiation for the years 1984-1987.
EXPERIMENTAL
DATA
Data obtained from the Bahrain International Airport records were used. Table 1 shows the meteorological information and includes the following: the monthly mean daily number of hours of observed bright sunshine, the monthly mean daily maximum possible number of sunshine hours S,, the monthly average of daily relative humidity R as a percentage, and the monthly average for the daily temperature T (in “C). These parameters represent averages over 4 yr. 409
10.23
6.93
kc
10.20
10.60
10.83
11.65
9.73
10.00
QP
8. JO
10.48
Aug
12.00
Nov
10.25
Jul
12.10
12.05
11.58
10.9
10.7
9.83
S.(hr)
Ott
9.45
10.25
JUII
m
bY
7.03
9.00
nar
7.78
8.18
Feb
S(hr)
Jan
l4onth
0.68
0.23
0.92
0.92
0.90
0.86
0.85
0.78
0.78
0.65
0.76
0.79
S/S,
73.0
71.0
65.5
65.5
63.8
59.3
55.8
56.8
61.3
67.0
71.0
75.0
a(x)
21.40
28.00
33.40
36.70
30.00
38.40
36.20
34.90
29.80
24.60
21.60
20.55
T(OC)
0.2716
0.2758
0.2797
0.3068
0.2925
0.3164
0.3139
0.2869
0.2x%7
0.2881
0.2683
0.2668
A
0.4521
0.4767
0.4489
0.4179
0.4307
0.4177
0.4232
0.4616
0.4766
0.4849
0.4742
0.4744
B
0.579
0.681
0.693
0.691
0.687
0.676
0.674
0.647
0.671
0.603
0.629
0.642
(WH,),
0.573
0.621
0.642
0.638
0.632
0.623
0.627
0.606
0.607
0.594
0.600
0.607
m/a,),
0.346
0.231
0.217
0.219
0.224
0.238
0.238
0.269
0.242
0.319
0.289
0.274
(H~/H:
Table 1. Monthly mean daily values of S, $,, R, T, A, B, and (H/H,), for Page’s model, (Ho/Ho), for Gopinathan’s model, and H,/H for Bahrain during the period 1984-1987. Measurements were taken at a height of 2 m.
Empirical correlation for radiation in Bahrain MATHEMATICAL
411
MODELS
Global radiation The relation between the global radiation on a horizontal
sunshine was estimated Page,8 i.e.
surface and the relative duration of by using a linear regression of Angstrom’s equation as developed by H/H,
= A + BSI&,
(1)
where H is the monthly average of the daily global radiation on a horizontal surface in kWh/m* and HO is the corresponding monthly average of the daily extraterrestrial solar radiation on a horizontal surface. The latter may be obtained by following Klein,’ i.e. H,, = (24/n)Z,[l+
0.033 cos(36On/365)][(cos
L)( cos s)(sin 0) + (20/36O)(sin L)(sin S)],
(2)
where Z,, is the solar constant (1353 W/m*), n the day number starting from the first of January, the sunset hour angle is w = cos-l[( - tan L)(tan S)], I is the latitude (in degrees), and the solar declination
(3)
angle is
6 = 23.45 sin[360(284 + n)/365].
(4)
The mean daily number of hours of daylight (&) in a given month between sunset can be calculated from Cooper’s” formula S, = (2/15) cos-‘[(-tan
sunrise and
L)(tan S)].
The regression constants A and B in Eq. (1) are measured follows:
(5) in terms of the latitutde
L as
A=fL+g,
(6)
B=pL+q,
(7)
where the values off, g, p, and q may be obtained from Table 2.’ The values of A and B for Bahrain are shown in Table 1. Table 2. Values off, f
Month
g, p, and (I vs the month of the year. g
P
9
Jan
- 0.00301
0.34507
0.00495
0.34572
Feh
- 0.00255
0.33450
0.00457
0.35533
mar
- 0.00303
O-36690
0.00466
0.36377
&r
- 0.00334
0.38557
0.00456
0.35802
maY
- 0.00245
0.35057
0.00485
0.33550
Jun
- 0.00327
0.39890
0.00578
0.27292
.JUl
- 0.00369
0.41234
0.00568
0.27004
Aug
- 0.00269
0.36243
0.00412
0.33162
Sep
- 0.00338
0.39467
0.00564
0.27125
Ott
- 0.00317
0.36213
0.00504
0.31790
NOV
-
0.00350
0.36680
0.00623
0.31467
Dee
-
0.00350
0.36262
0.00559
0.30676
Year
- 0.00290
0.36239
0.00491
0.31876
lG?SllS
-
0.00313
0.37022
0.00606
0.32029
W. E.
412
ALNASER
Recently, Gopinathan’ proposed a new model for estimating the total solar radiation. He developed a multiple, linear-regression equation for determining the monthly mean daily global radiation as a function of several meteorological parameters in the following form: H/H,, = a + b cos L + ch + d(S/S,J
+ eT +fR,
(8)
where L is the latitude in degrees and h the elevation of the location in km above sea level, T the monthly mean daily maximum temperature, and R the monthly mean relative humidity. The regression coefficients a, b, c, d, e, and f were calculated by using data for four stations in South Africa. The result is H/H, = 0.801-
0.387 cos L + 0.0128h + 0.316(S/Sc,) - 1.215 x 10-3T - 1.049 x 10-3R.
(9)
Diffuse radiation The prediction of the mean daily diffuse solar radiation
Hd may be obtained by applying an empirical equation proposed by Page.8 This relation correlates the estimated monthly mean of the daily diffuse radiation component Hd with the monthly mean daily total radiation as follows: H,/H = 1 - l.l3K,, (10)
where Kt is the mean clearness index, which is equal to H/H,,. Klein’ and Liu and Jordan” have proposed the following correlation equation for the diffuse radiation: H,/H
= 1.39 - 4.027K, + 5.53(Q2
RESULTS
AND
- 3.108(K,).3
(11)
DISCUSSION
Equation (1) was used for the monthly mean of the daily global radiation on a horizontal surface. In Fig. 1, we show (H/H,) for the monthly mean of the fractional daily number of sunshine hours (S/Q in Bahrain, as obtained from the following equation: H/H,
= 0.338(*0.038)
r = 0.938.
+ 0.392(fO.O46)S/&,
(12)
An estimate for the monthly mean of the daily diffuse radiation in Bahrain was calculated from the following equation, which was obtained from Fig. 2 by plotting H,+/H vs S/&: H,/H
= 0.618(f0.042)
r = 0.938.
- 0.442(fO.O52)S/S,,,
The ratio H,/H can also be calculated by using the following equation, plotting H,/H vs K, as in Fig. 3: H,/H
= 0.999(fO.O03)
which is obtained by
r = 0.999.
- 1.1283(f0.003)Kt,
(13)
(14)
Gopinathan’s model7 in Eq. (9), which was used to correlate (H/H,,) with meteorological data such as R, T, S/&, and h, is of interest since these data are routinely recorded and widely available. We show a comparison of Gopinathan’s model with that of Page in Fig. 4. It may be seen that the two curves are similar, viz. there are similar maxima and minima for (H/H,) throughout the year. However, the ratio (H/H,) is always less for Gopinathan’s model than for Page’s model. This difference is the result of using the regression coefficients a, b, c, d, e, and f
-,
0,
1
0.75
0.85
Fig. 1. Plot of HIHO vs S/h.
S/%
I
413
Empirical correlation for radiation in Bahrain
0.26-
Fig. 2. Plot of &II-l Vs S/&J.
Fig. 3. Plot of H,IH vs K,.
0.69-
- 0.68 I J
I
I
I
I
I
I
M
I
I
I
I
I
s
Month Fig. 4. Variations of H/H, (Cl, Page’s model; C2, Gopinathan’s model), S/S,, month of the year.
and H,,H with the
in Eq. (8), which had been obtained for a different latitude in South Africa. For Bahrain, we therefore propose the following equation for the monthly mean global solar radiation as a function of meteorological data: H/H,, = [0.801-
0.378 cos L + 0.0128h + 0.316(S/&) - 1.215 x 10-33T - 1.049 x 10-3R] x W, (15)
where W is a constant and has different values for each month of the year, as listed in Table 3. The corrected annual global radiation in Bahrain (H/H,) can be found by using the following
414
W. E. ALNASER Table 3. Values of W corresponding Month
W
J
I .058
empirical equation,
F
1.046
n
1.015
A
I. 105
I4
1.068
to each month of the average year. J
1.075
J
l.oB5
A
l.cl67
S
0
N
D
1.083
1.079
1.097
1.010
which is based on the use of both models:
(H/H,,), = 0.854 - 0.403 cos L + 0.0136h + 0.337@/&) - 1.297 x 10-3T - 1.119 x 1O-38 f 0.028,
(16)
where .I?, $,, i?, and I? represent the annual mean values of S, S,, T, and R, respectively. The curves for (H/H,) in Fig. 4 (identified as Cl and C2) and for (S/S,,) (identified as C3) vs the month of the year have behavior opposite to that of H,/H vs the month of the year (C4). The trough in April for curve C4 may be attributed to thick cirrus cloud at that time. The other and more evident trough in the September-October period may be related to the effect of ambient temperature, which seems to contribute to scattering and dispersion of the solar radiation. Furthermore, according to Shettle and Fenn,” the relative proportion of the direct to the diffuse radiation is primarily controlled by the concentrations of aerosols, which vary in a random manner geographically and temporally. This point requires further studies. Acknowledgemen&s-The author is thankful to Y. A. Abdulla of the University of Bahrain for many valuable discussions. The author would also like to thank Y. E. Alnaser and A. A. Agab for analyses and calculations and E. Eves for help with typing the manuscript.
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