A Model for the Estimation of Global Solar Radiation from Sunshine Duration for Thailand Serm Janjai* and Korntip Tohsing Solar Energy Research Laboratory, Department of Physics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand
Abstract: A model for estimating global solar radiation from a sunshine duration was developed. In developing the model, a 9-year periods of global radiation and sunshine duration measured at Chiang Mai (18.78 oN, 98.98oE), Ubon Ratchathani (15.25 oN, 104.87oE), Bangkok (13.73 oN, 100.57oE) and Songkhla (7.20 oN, 100.60oE) was analyzed. Linear equations relating normalized H / H S / S monthly average daily global radiation ( 0 ) to normalized sunshine duration ( 0 ) for each station were established. It was found that the slope and the intercept of the graphs representing the equations change systematically with the latitude. The equations H / H of the slope and the intercept as functions of the latitude were formulated. These equation and the relation between 0 and S / S 0 were tested to calculate global solar radiation. The accuracy in terms of root mean square difference is found to be 6.1 %.
Keywords: Solar Radiation, Sunshine Duration, Global Radiation, Model, Meteorological Data.
1. INTRODUCTION the pyranometer of Bangkok, it was regularly calibrated by the Department of Meteorology. Solar radiation data are important for the development The sunshine duration used in this work was measured and the applications of solar energy technology. In general, with Stokes-Campbell instrument at the same stations as these data are obtained from network work of monitoring those of global solar radiation. The measurement was stations where solar radiation is routinely measured. carried out by the Department of Meteorology. However, measuring and recording equipment for solar A nine-year period of data (1995-2003) was collected for radiation are costly. Therefore, numbers of stations in the this work. Before using these data, their quality was network especially in developing countries, are very limited controlled. By comparing with extra-terrestrial radiation and insufficient for use. To overcome this problem, some and by the visual inspection. mathematical models relating solar radiation to other For the sunshine duration data, they were visually meteorological parameters have been proposed. Among controlled. Abnormal data were discarded from the data set. these parameters, sunshine duration is considered to be a Approximately, daily global solar radiation and sunshine good predictor of global solar radiation. duration of 3,285 days were used in this work. In the case of Thailand, models for estimating global radiation from sunshine duration have been proposed by 3. DATA ANALYSIS AND RESULTS Exell and Salicali []1 , Kirtikara and Siriprayuk [2] . However, these models are based on old data set collected To develop the model, monthly average of daily global more than twenty years ago. During the last twenty years, radiation for a given month was calculated from the the environment of Thailand is considerably changed. following equation M Therefore, the objective of this work is to develop a new y N d model for the estimation of global solar radiation from H = ∑∑( Hi, j) / Nd / M y sunshine duration based on a new data set. j==1 i 1
(1) 2. DATA where H = monthly average of daily global The data used in this work are global solar radiation and radiation sunshine duration measured at 4 meteorological stations H i, j = daily global radiation namely, Chiang Mai (18.78 oN, 98.98oE), Ubon Ratchathani o o o o (15.25 N, 104.87 E), Bangkok (13.73 N, 100.57 E) and N d = total number of days in the month o o Songkhla (7.20 N, 100.60 E). For Chiang Mai, Ubon M = total number of year of data Ratchathani and Songkhla, global solar radiation was y measured with pyranometers (Kipp & Zonen, model CM i = index representing a day 21) installed by Laboratory of Atmospheric Physics, j = index representing a year Silpakorn University in 1994, at the regional centre of the Department of Meteorology. Global solar radiation data of Bangkok was measured at the office of the Department of Then the monthly average of daily global radiation ( H ) Meteorology with a pyranometer of Kipp & Zonen (model was nomalized by dividing with the monthly average of CM 11). The pyranometers used at Chaing Mai, Ubon daily extra-terrestrial radiation ( H ). The vaules of Ratchathani and Songkhla were calibrated every year. For H o were obtained from
1 H = (24 / π)I E (π /180)ω (sin δ sin φ) o sc o s c (2) Chiang Mai 0.8 + (cos δ c cos φ sin ωs )
0 0.6 where H o = monthly average of daily extra-terrestrial H
radiation H/ 0.4 Isc = solar constant H/H =0.3169 + 0.3465S/S E o = eccentricity correction factor 0.2 0 0 2 ωs = sunset hour angle R = 0.872 δ = solar declination at the middle of the month 0 c 0 0.2 0.4 0.6 0.8 1 φ = latitude of the station For the sunshine durations, their monthly average of S/S0 daily values for a given month were computed by the following equation. Fig. 1 Graph representing statistical relations between the nomalized global radiation ( H / Ho ) and the normalized M y Nd sunshine duration ( S / So ) of Chiang Mai. S = ∑ (∑ Si,j ) / N d / M y (3) j==1 i 1 1 where S = monthly average of daily sunshine duration Ubon Ratchathani 0.8 Si, j = daily sunshine duration
0.6
Like the case of the global radiation, the monthly 0 H
average of daily sunshine duration ( S ) was divided by the 0.4 monthly average of daily day length ( S ). The values of H/ o H/H0 = 0.3129 + 0.3846S/S0 So were computed from the following equation []3 . 0.2 2 R = 0.936 S = (2 /15) cos −1 (− tan φ tan δ ) 0 o c 0 0.2 0.4 0.6 0.8 1 (4) S/S where So = monthly average of daily day length 0 δ c = solar declination at the middle of the month Fig. 2 Graph representing statistical relations between the φ = latitude of the station nomalized global radiation ( H / Ho ) and the normalized sunshine duration ( S / S ) of Ubon Ratchathani. To investigate a statistical relation between global o 1 radiation and sunshine duration, the values H / Ho were Bangkok plotted against S / So . The results of each stations are 0.8 shown in Figs. 1-4
0
H 0.6
H/
0.4
H/H0 = 0.2905 + 0.3783 S/S0 0.2 2 R = 0.950 0 0 0.2 0.4 0.6 0.8 1
S/S0
Fig. 3 Graph representing statistical relations between the nomalized global radiation ( H / H o ) and the
normalized sunshine duration ( S / S ) of Bangkok. o
1 0.6 Songkhla 0.8 0.4
0 0.6 H intercept, a 0.2 a = 0.2296+0.0049ϕ H/ 0.4 2 R = 0.9337 H/H0 = 0.2638 + 0.4912S/S0 0.2 2 0 R = 0.936 0 5 10 15 20 0 Latitude,ϕ (degree) 0 0.2 0.4 0.6 0.8 1
S/S0 Fig. 5 Variation of the y-intercept (a) and the latitude. Fig. 4 Graph representing statistical relations between the 0.6 nomalized global radiation ( H / H o ) and the normalized
sunshine duration ( S / So ) of Songkhla. 0.4
From Figs. 1-4, it is observed that H / H o correlates slope, b linearly with S / So . This correlation can be represented 0.2 b = 0.5709-0.0125° with a general model as follows R2 = 0.9275
H S 0 = a + b (5) 0 5 10 15 20 Ho So Latitude,ϕ (degree)
where a is the y-intercept and b is the slope of the graphs representing the correlation. The value of a and b and the
square of the correlation coefficient R2 are shown in Table 1. Fig. 6 Variation of the slope (b) and the latitude.
Table 1 The values of the latitude of the station ( φ ), the y- It is found that both a and b correlates well with the intercept (a), the slope (b) and the square of the correlation latitude (ϕ) . The best-fitted equations are as follows: coefficient (R2) of the correlation between H / H and o
S / So a = 0.2296 + 0.0049ϕ (6) b = 0.5709 + 0.0125ϕ (7) 2 Station a b R φ Chiang Mai 0.3169 0.3465 0.87 18.78oN Therefore, with the value of a and b computed by the latitude, the model in equation (5) can be used to calculate Ubon Ratchathani 0.3129 0.3846 0.94 15.25oN the global radiation from the sunshine duration. Bangkok 0.2905 0.3783 0.95 13.73oN To valid its performance, the model was used to calculate the global radiation at Chiang Mai, Chiang Rai, Songkhla 0.2638 0.4912 0.94 7.20oN Phitsanulok, Phetchabun, Nakhonsawan, Nakhonpanom, Khonkean, Ubon Ratchathani, Chanthaburi and Phuket where the sunshine duration and global radiation were simultaneously measured. The results are shown in Fig.7. It From Table 1, it is noticed that a and b vary with the was found that global radiation from the model is in good latitude. To investigate this variation, the values of a and b agreement with that obtained from the measurement, with are plotted against the values of the latitude. The results are relative mean bias difference of –0.76 % and the relative shown in Figs. 5 and 6. root mean square difference of 6.1%.
25 Chiang Mai Chiang Rai 20 Phitsanulok Phetchabun
-day)
2 15 Nakhonsawan
Nakhonpanom
(MJ/m Khonkean 10
model Ubon Ratchathani
H Chanthaburi 5 Phuket
0 0 5 10 15 2 0 2 5 Hmeas (MJ/m2-day)
Fig. 7 Comparison between global radiation calculated from the model (H ) and that obtained from the measurement model (H ). meas
4. CONCLUSIONS
A model for calculating the monthly average of daily global radiation from the sunshine duration has been developed. The model is expressed as a linear relation between the normalized global radiation and the normalized sunshine duration. The coefficients of the model are stated as functions of the latitude. The performance of the model was investigated. It was found that global radiation calculated from the model is in good agreement with that obtained from the measurement.
ACKNOWLEDGEMENTS
The authors would like to thank the National Science and Technology Development Agency for the financial support to this research work. The authors also thank the Department of Meteorology for providing the sunshine duration data.
REFERENCES
[1] Exell, R. H. B. and Salicali., (1975) Solar radiation table for Thailand, J. Sci. Soc. Thailand [2] Kirtikara, K. and Siriprayuk, T., (1980) Relationships between some meteorological data of Thailand, Proc. Of the Symposium on Solar Science and Technology, Bangkok, Thailand. [3] Iqbal, M. (1983) Introduction to solar radiation, Academic Press, New York.