Diffuse solar irradiation at a location in the Balkan Peninsula

Renewable Energy 28 (2003) 2147–2156 www.elsevier.com/locate/renene

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Diffuse solar irradiation at a location in the Balkan Peninsula A.G. Paliatsos a,∗, H.D. Kambezidis b, A. Antoniou c a

c

General Department of Mathematics, Technological and Education Institute of Piraeus, 250 Thivon and P. Ralli, GR-12244 Athens, Greece b Atmospheric Research Team, Institute of Environmental Research and Sustainable Development, National Observatory of Athens, PO Box 20048, GR-11810 Athens, Greece Department of Computer Systems, Technological and Education Institute of Piraeus, 250 Thivon and P. Ralli, GR-12244 Athens, Greece Received 14 February 2003; accepted 27 February 2003

Abstract This study correlates experimental values with modelled values of global (KT) and diffuse (KD) clearness index in Athens, Greece. The experimental values come from measurements of daily global and diffuse solar irradiation on horizontal surface, while the modelled ones are from linear regression expressions fitted to the experimental data. It is found that the correlations give excellent results for nearly all experimental periods considered (1990–2000). The study also tries to correlate KT values with black smoke (BS) concentration. The analysis shows that there is no significant trend in KT, which would reflect an increase or decrease in light scattering by BS.  2003 Elsevier Science Ltd. All rights reserved. Keywords: Global horizontal radiation; Diffuse horizontal irradiance; Clearness index; Regression models; Balkan Peninsula

1. Introduction The amount of solar energy reaching the surface of the earth is a primary source of renewable energy. A pre-requisite for the estimation of the incident solar radiation on horizontal or inclined surface is the inclusion of the sky conditions in the compu∗

Corresponding author. Fax: +30-210-545-0962. E-mail address: [email protected] (A.G. Paliatsos).

0960-1481/03/$ - see front matter  2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0960-1481(03)00077-6

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tations at a locality for design purposes. These conditions can be quantified by the following two dimensionless parameters: (i) the clearness index, KT (=Hg/Hex), and (ii) the cloudiness index, KD (=Hd/Hg). Here, Hg represents the daily total global solar irradiation, Hex the daily extraterrestrial irradiation, and Hd the daily diffuse irradiation, all components being considered on horizontal surface. The clearness index, KT, gives the depletion of the incoming global radiation by the atmosphere and, therefore, indicates both the level of availability of solar irradiance at the surface of the earth and the changes in atmospheric conditions. The cloudiness index, KD, denotes the depletion of the diffuse component due to the concentration of the atmospheric aerosols and the presence of clouds. These two parameters have been used to establish sky conditions at various places [1–13].

2. Data collection The database used corresponds to daily observations of global and diffuse irradiation on a horizontal plane made by Eppley PSP radiometers at the National Observatory of Athens (NOA); NOA is situated on the Hill of Nymphs near the centre of Athens (latitude: 37° 59⬘ N, longitude: 23° 45⬘ E, altitude: 107 m asl). The database covers a period of 11 years, i.e. from January 1990 to December 2000, inclusive.

3. Results and discussion 3.1. Daily clearness index Fig. 1 shows the time series of daily KT values in the urban environment of Athens in the examined period. The dominant feature is the large annual variation of KT,

Fig. 1. Time series of daily KT values in the urban environment of Athens during the period January 1990–December 2000.

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which is strongly dependent upon the annual variation of global irradiation (Hg). Furthermore, Fig. 1 shows that the occurrence of clear-sky conditions (K Tⱖ0.65) is fairly frequent in the Athens area, accounting for 74.8% of the period considered, i.e. 2817 days. On the other hand, KT gets lower values under overcast conditions; to find an appropriate threshold value for KT, some (low) KT values are tried, including those suggested by Liu and Jordan [1], Collares-Pereira and Babl [4], Erbs et al. [6], Lalas et al. [9], Newland [10], Jacovides et al. [13] and Udo [14]. The analysis shows that a suitable threshold is 0.10, and that KT varies in the range 0.10–0.80. Day-to-day fluctuations in KT are large; Udo [14] attributes this effect to the changes in atmospheric conditions. The dependence of the clearness index daily values on atmospheric and sky conditions has been well established in previous studies [1,9,15]. In order to provide a quantitative relation between the daily values of KD and KT, the experimental period is divided into different periods. The first period is the whole 11-year one, the second is the cold period (October–March, inclusive), the third is the warm period (April–September, inclusive), and the other four correspond to the calendar seasons of the year (winter, spring, summer and autumn). For each period, a scatter diagram of KD vs. KT values is formed and linear and quadratic regression models are applied to the scatter plots. The obtained results are given in Table 1. It is seen from Table 1 that the differences in R2 between the linear and quadratic models in each experimental sub-period are small. The linear models are preferred for their simplicity. Figs. 2–4 show that 74.2% / 83.5% of KD values can only be explained by the variations in KT in the summer/warm periods. In a similar study, Lalas et al. [9] conclude that such variations are observed in Athens during the summer. The slightly different results in the present study may be attributed to the air pollution problem [9]. Higher aerosol loading in the Athens atmosphere occurred in the period 1990–2000 than during the 3-year period (1983–1985) investigated by those researchers. Moreover, most of the photochemical air pollution episodes occur during the warm period in the urban Athens area [16,17]. From the above analysis, the following conclusions can be drawn. (i) There is no significant difference in R2 between the semester data sets and the data for the warm, cold and the whole experimental periods. (ii) The lowest R2 occurs in the summer for both linear and quadratic models. The observed significant difference between the cold and the warm periods as for the variance in KD can be explained by the variations in KT; this leads to the consideration that the diffuse component can easily be estimated using the corresponding linear model. Moreover, to improve the evaluation, seasonal versions of the linear models are also tested. To compare observed and estimated diffuse radiation values for Athens (1990–2000), Fig. 5a,b is provided. As it appears from these figures, the agreement between the observed and the estimated values is good. For the cold period (Fig. 5a), R 2 = 0.963 (or 96.3%) and for the warm period (Fig. 5b), R 2 = 0.963 (or 96.3%). The root-mean-square-error (RMSE) gives values of 0.666 MJ m–2 for the cold and 1.693 MJ m–2 for the warm period, respectively.

Whole Warm Cold Spring Summer Autumn Winter

Experimental period

KD KD KD KD KD KD KD

= = = = = = =

1.771⫺1.4285KT 1.1582⫺1.3705KT 1.2124⫺1.5088KT 1.1783⫺1.3741KT 1.0522⫺1.2314KT 1.2165⫺1.5380KT 1.2347⫺1.5573KT

Equation

Linear model

(2a) (3a) (4a) (5a) (6a) (7a) (8a)

0.876 0.835 0.882 0.891 0.742 0.884 0.886

R2 KD = 1.0827⫺0.8670KT⫺0.7405K2T KD = 1.0704⫺1.0266KT⫺0.3359K2T KD = 1.0801⫺0.7617KT⫺0.8835K2T KD = 1.0490⫺0.7548KT⫺0.6455K2T KD = 0.7585⫺0.1496KT⫺0.9614K2T KD = 1.0827⫺0.8670KT⫺0.7405K2T KD = 1.0810⫺0.5446KT⫺1.1038K2T

Equation

Quadratic model

Table 1 Linear and quadratic models for KD vs. KT values for Athens in the period 1990–2000. KT varies in the range 0.10–0.80

(2b) (3b) (4b) (5b) (6b) (7b) (8b)

0.889 0.836 0.890 0.896 0.750 0.889 0.897

R2

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Fig. 2. Scatter diagrams of KD vs. KT in Athens (1990–2000) for the whole experimental (a), the cold (b) and the warm (c) periods.

3.2. Monthly clearness index Fig. 6 illustrates the mean monthly KT values in the urban Athens area. The literature reveals a considerable number of contradicting reports regarding KT variability at different locations in the world. The annual step of the mean monthly KT values at the earth’s surface generally follows that of the solar elevation. These values show a winter to summer ratio of about 1:2.2; these results may be caused by excess aerosol loading entry in the urban Athens atmosphere during the cold period [18]. The weather variability conditions may be the reason for the observed scatter of the monthly KT values shown in Fig. 7. Thus, in March, monthly KT values differ as much as 69%, while in August, the corresponding difference is only 16%. The smooth curve is determined by a polynomial of fourth order. From this figure, it is

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Fig. 3.

Fig. 4.

Scatter diagrams of KD vs. KT in Athens (1990–2000) for winter (a) and spring (b).

Scatter diagrams of KD vs. KT in Athens (1990–2000) for summer (a) and autumn (b).

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Fig. 5.

Model evaluation during the cold (a) and warm (b) periods of the year for Athens (1990–2000).

Fig. 6.

Mean monthly values of KT vs. the months in the period 1990–2000 in the urban area of Athens.

noticed that the mean annual values of KT range from a minimum of 0.309 in January 1996 to a maximum of 0.680 in June of the same year. Fig. 8 presents the plot of KT against black smoke (BS) concentration, both expressed as monthly mean daily values over the 11-year period, as well as the bestfit line given by Eq. (1):

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Fig. 7. Mean monthly values of KT vs. the 12 months of the year in the urban Athens area. The data points at each month represent the 11 years in the period 1990–2000.

Fig. 8. Scatter diagram of mean monthly daily values of KT against BS concentration for Athens (1990– 2000). The solid line is the best-fit curve expressed by the equation K T = 0.0049 × BS.

KT ⫽ 0.0049 ⫻ BS

(1)

where R = 0.901 (or 90.1%), BS is expressed in µg m and the multiplier has dimensions of m3 µg–1. The BS concentration values used in Eq. (1) come from a central station that is the most representative station of the air quality network in Athens [18]. An attempt to provide a quantitative relation between monthly means of KT and KD is made (Fig. 9). Similar efforts have been presented in the literature [9,13,19]. For this purpose, a scatter diagram is constructed for Athens and a linear model is fitted. The mathematical expression of the linear model is: K¯ D = 1.18505⫺ 1.43983K¯ T, with a corresponding R 2 = 0.903 (or 90.3%) and an RMSE = 0.00176 MJ m–2. Further efforts to improve fitting by higher-order polynomials did not give any better results (higher R2). 2

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Fig. 9. Scatter diagram of mean monthly mean values of KD vs. KT for Athens in the period 1990–2000. The solid line is the best-fit curve expressed by the equation KD = 1.18505⫺1.43983 KT.

4. Conclusions This work demonstrated the efficient computation of the diffuse component from an estimation of KD vs. KT using data from Athens. The data set covers a period of 11 years. The analysis performed on the data showed that there is a significant difference in the correlation of KD vs. KT between the cold and the warm periods. Linear and quadratic models were tried to estimate KD from KT. It was found that the diffuse component can easily be estimated using the linear models. Correlation between mean KT values and BS concentration showed that there is no significant trend in KT in the examined period 1990–2000 due to the scattering of light by BS. This is so because BS levels have had a decreasing trend in the urban Athens area during the examined experimental period.

References [1] Liu BYU, Jordan RC. The inter-relationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 1960;4:1–19. [2] Page JK. The estimation of the monthly mean values of daily total shortwave radiation on vertical and inclined surfaces from sunshine records for latitudes 40° N–40° S. In: Proceedings of the United Nations Conference on New Sources of Energy. 1961. [paper no. 35/5/98]. [3] Choudhury NKD. Solar radiation at New Delhi. Solar Energy 1963;7:44. [4] Collares-Pereira M, Rabl A. The average distribution of solar radiation-correlation between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy 1979;22:155–64. [5] Barbado S, Cannata G, Coppilino S, Leone C, Sinagra E. Diffuse radiation statistics for Italy. Solar Energy 1981;26:429–35. [6] Erbs DG, Klein SA, Duffie JA. Estimation of the diffuse radiation fraction for hourly, daily and monthly average global radiation. Solar Energy 1982;28:293–302. [7] Iberiah FJK. On the relation between diffuse and global radiation. Solar Energy 1983;31:119–24.

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[8] Rao NCR, Bradley WA, Young LT. The diffuse component of the daily global solar irradiation at Corvallis, Oregon (USA). Solar Energy 1984;32:637–41. [9] Lalas DP, Petrakis M, Papadopoulos C. Correlations for the estimation of the diffuse radiation component in Greece. Solar Energy 1987;39:455–8. [10] Newland FJ. A study of solar radiation models for the coastal region of south China. Solar Energy 1989;43:227–35. [11] Al-Riahi M, Al-Handami N, Taxir T. Contribution to the study of solar radiation climate of Baghdad environment. Solar Energy 1990;44:7–12. [12] Akuffo FO, Breu-Hammond A. The frequency distribution of global solar irradiation at Kumasi. Solar Energy 1993;50:145–54. [13] Jacovides CP, Hadjioannou L, Pashiardis S, Stefanou L. On the diffuse fraction of daily and monthly global radiation for the island of Cyprus. Solar Energy 1996;56:565–72. [14] Udo SO. Sky conditions at Ilorin as characterized by clearness index and relative sunshine. Solar Energy 2000;69:45–53. [15] Badescu V. Verifications of some very simple clear and cloudy sky models to evaluate global solar irradiance. Solar Energy 1997;61:251–4. [16] Lalas DP, Asimakopoulos DN, Deligiorgi DG, Helmis CG. Seabreeze circulation and photochemical pollution in Athens, Greece. Atmospheric Environment 1983;17:1621–32. [17] Ziomas IC, Melas D, Zerefos CS, Bais AF, Paliatsos AG. Forecasting peak pollutant levels from meteorological variables. Atmospheric Environment 1995;29:3703–11. [18] Paliatsos AG, Kaldellis JK, Koronakis PS, Garofalakis JE. Fifteen year air quality trends associated with the vehicle traffic in Athens, Greece. Fresenius Environmental Bulletin 2002;11:1119–26. [19] Koronakis PS. On the choice of the angle of tilt for south facing solar collectors in the Athens basin area. Solar Energy 1986;36:217–25.