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Seasonal correlations between global radiation and sunshine duration—A case study for eastern Nigeria
Energy Convers. Mgmt Vol. 32, No. 3, pp. 279-282, 1991 Printed in Great Britain. All rights reserved
0196-8904/91 $3.00+ 0.00 Copyright © 1991 Pergamon Press plc
SEASONAL CORRELATIONS BETWEEN GLOBAL RADIATION AND SUNSHINE DURATION--A CASE STUDY FOR EASTERN NIGERIA M. HUSSAIN Physics Department and Renewable Energy Research Centre, University of Dhaka, Dhaka- 1000, Bangladesh (Received 18 December 1989; received for publication 1l October 1990) Al~traet--Regression fits between monthly averaged daily global radiation G and sunshine duration s of four locations in eastern Nigeria having a monsoon climate have been made with a view to look for seasonal correlations. The modified Angstrom equation G/Go = a + b(s/S) has been employed where Go is the extraterrestrial radiation and S is the day length. Fits for individual stations were obtained for the year as a whole and also by dividing the year into rainy and less rainy months. The seasonal correlations produce slightly lower r.m.s, errors in the estimates of G. Collective regressions of data of three inland stations over the year and also over the two seasons show that, again, seasonal fits give better predictions. Collective seasonal values of a and b may be regarded as station independent and used for estimating G at any location over the region in which the stations are situated. Present correlations were found to give smaller errors in estimates than for the individual station fits of Eze and Ododo (Energy Convers. Mgmt 28, 69 (1988): Ref. [1]) who employed the original Angstrom equation G/Gc~ = a + b(s/S) with G , as the clear sky global radiation.
NOMENCLATURE G= G, = GO= n = s = S = 6= ~b = w~=
Monthly averaged daily global irradiation Monthly averaged daily global irradiation for clear day Monthly averaged daily extraterrestrial irradiation on horizontal surface Representative day for which extraterrestrial radiation is closest to average for month Monthly average of daily bright sunshine duration Day length for representative day Solar declination for representative day Geographical latitude Sunset hour angle for representative day
I. INTRODUCTION
Angstrom proposed the classic correlation G/G¢~ = a + b ( s / S )
(1)
where G, is the clear sky global radiation, s is the daily sunshine duration, S is the day length and a, b are regression constants. This relation was modified later by replacing G, by Go, the extraterrestrial radiation on a horizontal surface, which may be easily computed with a high accuracy, and the modified Angstrom relation G/Go = a + b ( s / S )
(2)
has been widely used for estimating G from bright sunshine duration. The relation evidently requires that, for a location, G/Go depends only on siS. Equation (1) has been employed by Eze and Ododo [1] for correlating G with s for four stations in eastern Nigeria--Makurdi, Nsukka, Enugo and Port Harcourt. On the other hand, in this work, an attempt has been made to use equation (2). It is well known that the parameters a and b in equation (2), determined using monthly averaged data of all months of the year, vary from place to place. The surface albedo of the earth is one of the factors responsible for this. Other important contributors are the spatial dependence of 279
280
HUSSAIN:
GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
atmospheric variables like water vapour and ozone which cause changes in the attenuation and scattering of radiation. Attempts have been made by many authors to introduce one or more additional parameters in equation (2) to obtain station independent techniques [2-5] for the estimation of G from s. These, at times, have been found to give errors as large as 30-60% [4] in the estimates. For a monsoon land like eastern Nigeria, there is a considerable variation in the precipitable water amount in the atmosphere for dry and rainy, months, resulting in a difference in the attenuation of beam radiation. As a result of showers, the surface albedo of the earth decreases for the rainy period. Further, the albedo of rain bearing clouds differs from that of thin clouds. These should result in a seasonal variation in the reflected fraction of global radiation. Again, the rains wash down the dust in the atmosphere, lowering its turbidity and decreasing the diffuse radiation. All these might lead to different values of G/Go for the same siS for rainy and dry months and fits with season dependent values of a and b for a station may lead to better estimations than from a fit of data of all months. Here, we investigate the seasonal effect for eastern Nigeria for regression fits using equation (2).
2. D A T A
AND PROCEDURE
We have employed the data of G and s of four stations in eastern Nigeria presented by Eze and Ododo [1]. The global radiation was measured using Gunn-Bellani instruments, and the data were re-standardized with the help of an Eppley pyranometer [1]. The sunshine data were obtained using Campbell-Stokes recorders. The period of measurement varied between 7 and 11 yr for the four stations--Makurdi, Nsukka, Enugo and Port Harcourt. The first three are inland stations at 7°41'N, 6°48'N and 6°28'N lat, respectively, while Port Harcourt at 4°51'N lat is located by the Gulf of Guinea. Regression constants a and b in equation (2) were obtained separately for rainy and dry months and also for the year as a whole for each station. The months from May to October (months 5-10) are taken to form the rainy period and November-April (months 11, 12, 1-4) are considered to be dry months. The monthly averaged day length S was computed from the relation S = 2/15 cos -l ( - t a n ~b tan 6) Table I. Parameters a and b for different fits of the form G/Go = a + b ( s / S ) for data of eastern Nigeria and the correlation coefficient Type of fit
a
b
r
1. Individual station annual
Makurdi Nsukka Enugo Port Harcourt
0.178 0.180 0.207 0.233
0.692 0.611 0.592 0.567
0.98 0.98 0.98 0.95
2. Individual station months 5-10
Makurdi Nsukka Enugo Port Harcourt
0.207 0.187 0.181 0.227
0.623 0.587 0.663 0.571
1.00 1.00 0.97 0.93
Makurdi Nsukka Enugo Port Harcourt
0.213 0.195 0.253 0.334
0.641 0.584 0.504 0.313
0.81 0.84 0.98 0.88
Makurdi Nsukka Enugo
0.163
0.689
0.97
Makurdi Nsukka Enugo
0.164
0.686
0.98
Makurdi Nsukka Enugo
0.102
0.793
0.92
months I1, 12, 1-4
3. Collective annual
4. Collective months 5-10
months 11, 12, 1-4
Station
HUSSAIN:
GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
281
Table 2. Measured and estimated values of G for Makurdi (MJ/m2-day)
Months
Gap
Individual annual fit
January February March April May June July August September October November December
19.36 21.00 21.81 20.80 20.15 17.96 16.22 15.26 17.04 19.32 21.11 19.67
20.08 20.80 20.72 21.08 20.71 18.26 16.38 15.03 16.94 19.32 20.98 19.37
Individual fits, months 5-10 and 11-4
Collective annual fit
Collective fits, months 5-10 and 11-4
Individual fits Ref. [1]
20.19 20.89 20.91 21.27 20.30 18.07 16.38 15.20 16.98 19.03 20.99 19.41
19.52 20.22 20.12 20.48 20.11 17.68 15.82 14.46 16.34 18.74 20.43 18.84
19.63 20.37 20.10 20.47 20.30 17.84 15.95 14.58 16.48 18.91 20.75 19,04
18.76 20.20 20.45 19.31 17.18 15.61 14.86 15.13 17.23 20.33 22.99 22.58
where q~ is the geographical latitude and 6 is the solar declination for the representative day of the month [6]. The daily extraterrestrial radiation was calculated from the equation Go = 24 Io[1 + 0.033 cos(360n /365)] [cos ~b cos 6 sin ws + 2n/360 w~sin ~ sin ~b] 7t where Io is the solar constant which was taken to be 1.367 (kW/m2), n is the representative day number for a month and ws is the sunset hour angle for the day [6]. An attempt was also made to find if satisfactory station independent fits of equation (2) for each of the two seasons for the inland stations Makurdi, Nsukka and Enugo may be obtained using collectively data of these stations. A collective regression fit of data of these locations for all months of the year was also obtained. 3. RESULTS Table 1 presents the parameters a and b for our regression fits. The values of the coefficient of correlation r are also shown for each of the fits. The first type of fits is for data over the year for individual stations. In the second type, data for months generally having a high rainfall, May-October (months 5-10) and those of other months (11, 12, 1-4) are employed separately to find season dependent values of the parameters a and b for each station. The third type is for data over the year of Makurdi, Nsukka and Enugo taken together and is a collective fit. The fourth type consists of collective fits for the three stations for months 5-10 and also for months 11, 12, 1-4. We do not use the data of Port Harcourt for collective fits as this station is situated on the sea coast, unlike the others. In Table 2, we present the computed values of G for our fits for a representative station, Makurdi, along with the measured values, as well as the predictions of Eze and Ododo. The r.m.s, deviations of the computed values from the measured ones for all the fits are shown in Table 3 for the four stations. 4. D I S C U S S I O N The correlation coefficients for all of our fits shown in Table 1 are quite satisfactory. Their values range from 0.81 to 1.00. Table 2 shows that, for a representative station, Makurdi, the different Table 3. Root mean square errors (MJ/m2-day) for different estimates of G
Station Makurdi Nsukka Enugo Port Harcourt
Individual, Collective, Individual, months 5-10 Collective, months 5-10 annual and 11-4 annual and 11-4 0.45 0.42 0.38 0.58
0.40 0.42 0.34 0.48
0.73 0.78 0.50 --
0.63 0.69 0.56 --
Ref. [1] individual 1.69 0.89 0.50 2.49
282
HUSSAIN: GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
fits for equation (2) give smaller errors in the estimates of G as compared to the predictions of Eze and Ododo from correlations using equation (1). Such is generally the case (Table 3) for the other stations. For their correlation, Eze and Ododo used tabulated values of G,, and this procedure may have contributed to the large errors in their estimates. However, it is to be noted that Gcs is hard to measure for rainy months. Columns 2 and 3 of Table 3 show that individual station fits give monthly estimates with a high precision with period dependent fits having r.m.s, deviations between 0.34 and 0.48 MJ/m2-day or 2.0-3.4%, while fits for data over the year give r.m.s, deviations of 0.38-0.58 MJ/m2-day or 2.3--4.1%. Hence, one may partition out data of rainy and less rainy seasons to obtain best estimates for the four stations. However, for any other location in eastern Nigeria, where G is not measured, uncertainty arises in assigning the values of the parameters a and b from their values at the four locations, as one has to take recourse to extrapolation or interpolation techniques. To obviate the problem, one may use collective fits of data for a group of stations having similar climatic features. We find from columns 4 and 5 of Table 3 that the period dependent collective fits give generally lower errors than for the collective annual fits for the three inland stations, Makurdi, Nsukka and Enugo. To make dependable predictions of G from sunshine data for inland locations in eastern Nigeria away from the three stations, one may, therefore, use season dependent parameters of the pair of collective fits (Table 1). The maximum error in the predictions of G from collective fits for a month is found to be 8.8% for three stations for period dependent fits, while for the annual fit, it is 10%. For coastal locations, one could use the season dependent parameters obtained for Port Harcourt (Table 1) till data for other coastal stations are available to find collective fits. It may be mentioned that excellent season dependent correlations have already been found for a large part of India [7]. REFERENCES 1. A. E. Eze and J. C. Ododo, Energy Convers. Mgmt 28, 69 (1988). 2. J. E. Hay, Sol. Energy 23, 301 (1979). 3. A. A. M. Sayigh, Solar energy availability prediction from climatological data. In Solar Energy Engineering. Academic Press, New York (1977). 4. H. P. Garg and S. N. Garg, Energy Convers. Mgmt 23, 113 (1983). 5. M. Hussain, Sol. Energy 33, 217 (1984). 6. J. A. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes. Wiley, New York (1980). 7. M. Hussain, Energy Convers. Mgmt 30, 163 (1990).
0196-8904/91 $3.00+ 0.00 Copyright © 1991 Pergamon Press plc
SEASONAL CORRELATIONS BETWEEN GLOBAL RADIATION AND SUNSHINE DURATION--A CASE STUDY FOR EASTERN NIGERIA M. HUSSAIN Physics Department and Renewable Energy Research Centre, University of Dhaka, Dhaka- 1000, Bangladesh (Received 18 December 1989; received for publication 1l October 1990) Al~traet--Regression fits between monthly averaged daily global radiation G and sunshine duration s of four locations in eastern Nigeria having a monsoon climate have been made with a view to look for seasonal correlations. The modified Angstrom equation G/Go = a + b(s/S) has been employed where Go is the extraterrestrial radiation and S is the day length. Fits for individual stations were obtained for the year as a whole and also by dividing the year into rainy and less rainy months. The seasonal correlations produce slightly lower r.m.s, errors in the estimates of G. Collective regressions of data of three inland stations over the year and also over the two seasons show that, again, seasonal fits give better predictions. Collective seasonal values of a and b may be regarded as station independent and used for estimating G at any location over the region in which the stations are situated. Present correlations were found to give smaller errors in estimates than for the individual station fits of Eze and Ododo (Energy Convers. Mgmt 28, 69 (1988): Ref. [1]) who employed the original Angstrom equation G/Gc~ = a + b(s/S) with G , as the clear sky global radiation.
NOMENCLATURE G= G, = GO= n = s = S = 6= ~b = w~=
Monthly averaged daily global irradiation Monthly averaged daily global irradiation for clear day Monthly averaged daily extraterrestrial irradiation on horizontal surface Representative day for which extraterrestrial radiation is closest to average for month Monthly average of daily bright sunshine duration Day length for representative day Solar declination for representative day Geographical latitude Sunset hour angle for representative day
I. INTRODUCTION
Angstrom proposed the classic correlation G/G¢~ = a + b ( s / S )
(1)
where G, is the clear sky global radiation, s is the daily sunshine duration, S is the day length and a, b are regression constants. This relation was modified later by replacing G, by Go, the extraterrestrial radiation on a horizontal surface, which may be easily computed with a high accuracy, and the modified Angstrom relation G/Go = a + b ( s / S )
(2)
has been widely used for estimating G from bright sunshine duration. The relation evidently requires that, for a location, G/Go depends only on siS. Equation (1) has been employed by Eze and Ododo [1] for correlating G with s for four stations in eastern Nigeria--Makurdi, Nsukka, Enugo and Port Harcourt. On the other hand, in this work, an attempt has been made to use equation (2). It is well known that the parameters a and b in equation (2), determined using monthly averaged data of all months of the year, vary from place to place. The surface albedo of the earth is one of the factors responsible for this. Other important contributors are the spatial dependence of 279
280
HUSSAIN:
GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
atmospheric variables like water vapour and ozone which cause changes in the attenuation and scattering of radiation. Attempts have been made by many authors to introduce one or more additional parameters in equation (2) to obtain station independent techniques [2-5] for the estimation of G from s. These, at times, have been found to give errors as large as 30-60% [4] in the estimates. For a monsoon land like eastern Nigeria, there is a considerable variation in the precipitable water amount in the atmosphere for dry and rainy, months, resulting in a difference in the attenuation of beam radiation. As a result of showers, the surface albedo of the earth decreases for the rainy period. Further, the albedo of rain bearing clouds differs from that of thin clouds. These should result in a seasonal variation in the reflected fraction of global radiation. Again, the rains wash down the dust in the atmosphere, lowering its turbidity and decreasing the diffuse radiation. All these might lead to different values of G/Go for the same siS for rainy and dry months and fits with season dependent values of a and b for a station may lead to better estimations than from a fit of data of all months. Here, we investigate the seasonal effect for eastern Nigeria for regression fits using equation (2).
2. D A T A
AND PROCEDURE
We have employed the data of G and s of four stations in eastern Nigeria presented by Eze and Ododo [1]. The global radiation was measured using Gunn-Bellani instruments, and the data were re-standardized with the help of an Eppley pyranometer [1]. The sunshine data were obtained using Campbell-Stokes recorders. The period of measurement varied between 7 and 11 yr for the four stations--Makurdi, Nsukka, Enugo and Port Harcourt. The first three are inland stations at 7°41'N, 6°48'N and 6°28'N lat, respectively, while Port Harcourt at 4°51'N lat is located by the Gulf of Guinea. Regression constants a and b in equation (2) were obtained separately for rainy and dry months and also for the year as a whole for each station. The months from May to October (months 5-10) are taken to form the rainy period and November-April (months 11, 12, 1-4) are considered to be dry months. The monthly averaged day length S was computed from the relation S = 2/15 cos -l ( - t a n ~b tan 6) Table I. Parameters a and b for different fits of the form G/Go = a + b ( s / S ) for data of eastern Nigeria and the correlation coefficient Type of fit
a
b
r
1. Individual station annual
Makurdi Nsukka Enugo Port Harcourt
0.178 0.180 0.207 0.233
0.692 0.611 0.592 0.567
0.98 0.98 0.98 0.95
2. Individual station months 5-10
Makurdi Nsukka Enugo Port Harcourt
0.207 0.187 0.181 0.227
0.623 0.587 0.663 0.571
1.00 1.00 0.97 0.93
Makurdi Nsukka Enugo Port Harcourt
0.213 0.195 0.253 0.334
0.641 0.584 0.504 0.313
0.81 0.84 0.98 0.88
Makurdi Nsukka Enugo
0.163
0.689
0.97
Makurdi Nsukka Enugo
0.164
0.686
0.98
Makurdi Nsukka Enugo
0.102
0.793
0.92
months I1, 12, 1-4
3. Collective annual
4. Collective months 5-10
months 11, 12, 1-4
Station
HUSSAIN:
GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
281
Table 2. Measured and estimated values of G for Makurdi (MJ/m2-day)
Months
Gap
Individual annual fit
January February March April May June July August September October November December
19.36 21.00 21.81 20.80 20.15 17.96 16.22 15.26 17.04 19.32 21.11 19.67
20.08 20.80 20.72 21.08 20.71 18.26 16.38 15.03 16.94 19.32 20.98 19.37
Individual fits, months 5-10 and 11-4
Collective annual fit
Collective fits, months 5-10 and 11-4
Individual fits Ref. [1]
20.19 20.89 20.91 21.27 20.30 18.07 16.38 15.20 16.98 19.03 20.99 19.41
19.52 20.22 20.12 20.48 20.11 17.68 15.82 14.46 16.34 18.74 20.43 18.84
19.63 20.37 20.10 20.47 20.30 17.84 15.95 14.58 16.48 18.91 20.75 19,04
18.76 20.20 20.45 19.31 17.18 15.61 14.86 15.13 17.23 20.33 22.99 22.58
where q~ is the geographical latitude and 6 is the solar declination for the representative day of the month [6]. The daily extraterrestrial radiation was calculated from the equation Go = 24 Io[1 + 0.033 cos(360n /365)] [cos ~b cos 6 sin ws + 2n/360 w~sin ~ sin ~b] 7t where Io is the solar constant which was taken to be 1.367 (kW/m2), n is the representative day number for a month and ws is the sunset hour angle for the day [6]. An attempt was also made to find if satisfactory station independent fits of equation (2) for each of the two seasons for the inland stations Makurdi, Nsukka and Enugo may be obtained using collectively data of these stations. A collective regression fit of data of these locations for all months of the year was also obtained. 3. RESULTS Table 1 presents the parameters a and b for our regression fits. The values of the coefficient of correlation r are also shown for each of the fits. The first type of fits is for data over the year for individual stations. In the second type, data for months generally having a high rainfall, May-October (months 5-10) and those of other months (11, 12, 1-4) are employed separately to find season dependent values of the parameters a and b for each station. The third type is for data over the year of Makurdi, Nsukka and Enugo taken together and is a collective fit. The fourth type consists of collective fits for the three stations for months 5-10 and also for months 11, 12, 1-4. We do not use the data of Port Harcourt for collective fits as this station is situated on the sea coast, unlike the others. In Table 2, we present the computed values of G for our fits for a representative station, Makurdi, along with the measured values, as well as the predictions of Eze and Ododo. The r.m.s, deviations of the computed values from the measured ones for all the fits are shown in Table 3 for the four stations. 4. D I S C U S S I O N The correlation coefficients for all of our fits shown in Table 1 are quite satisfactory. Their values range from 0.81 to 1.00. Table 2 shows that, for a representative station, Makurdi, the different Table 3. Root mean square errors (MJ/m2-day) for different estimates of G
Station Makurdi Nsukka Enugo Port Harcourt
Individual, Collective, Individual, months 5-10 Collective, months 5-10 annual and 11-4 annual and 11-4 0.45 0.42 0.38 0.58
0.40 0.42 0.34 0.48
0.73 0.78 0.50 --
0.63 0.69 0.56 --
Ref. [1] individual 1.69 0.89 0.50 2.49
282
HUSSAIN: GLOBAL RADIATION AND SUNSHINE DURATION--EASTERN NIGERIA
fits for equation (2) give smaller errors in the estimates of G as compared to the predictions of Eze and Ododo from correlations using equation (1). Such is generally the case (Table 3) for the other stations. For their correlation, Eze and Ododo used tabulated values of G,, and this procedure may have contributed to the large errors in their estimates. However, it is to be noted that Gcs is hard to measure for rainy months. Columns 2 and 3 of Table 3 show that individual station fits give monthly estimates with a high precision with period dependent fits having r.m.s, deviations between 0.34 and 0.48 MJ/m2-day or 2.0-3.4%, while fits for data over the year give r.m.s, deviations of 0.38-0.58 MJ/m2-day or 2.3--4.1%. Hence, one may partition out data of rainy and less rainy seasons to obtain best estimates for the four stations. However, for any other location in eastern Nigeria, where G is not measured, uncertainty arises in assigning the values of the parameters a and b from their values at the four locations, as one has to take recourse to extrapolation or interpolation techniques. To obviate the problem, one may use collective fits of data for a group of stations having similar climatic features. We find from columns 4 and 5 of Table 3 that the period dependent collective fits give generally lower errors than for the collective annual fits for the three inland stations, Makurdi, Nsukka and Enugo. To make dependable predictions of G from sunshine data for inland locations in eastern Nigeria away from the three stations, one may, therefore, use season dependent parameters of the pair of collective fits (Table 1). The maximum error in the predictions of G from collective fits for a month is found to be 8.8% for three stations for period dependent fits, while for the annual fit, it is 10%. For coastal locations, one could use the season dependent parameters obtained for Port Harcourt (Table 1) till data for other coastal stations are available to find collective fits. It may be mentioned that excellent season dependent correlations have already been found for a large part of India [7]. REFERENCES 1. A. E. Eze and J. C. Ododo, Energy Convers. Mgmt 28, 69 (1988). 2. J. E. Hay, Sol. Energy 23, 301 (1979). 3. A. A. M. Sayigh, Solar energy availability prediction from climatological data. In Solar Energy Engineering. Academic Press, New York (1977). 4. H. P. Garg and S. N. Garg, Energy Convers. Mgmt 23, 113 (1983). 5. M. Hussain, Sol. Energy 33, 217 (1984). 6. J. A. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes. Wiley, New York (1980). 7. M. Hussain, Energy Convers. Mgmt 30, 163 (1990).