## Results and Discussion

Calculate the global radiation of four cities (Seoul, Busan, Daejeon, Gwangju), where the global radiation is currently measured, by using the cloud amount data. For this, the coefficient of each location needed for global radiation calculation using the altitude of the sun and the cloud amount data in four cities has to be obtained. The global radiation calculated by applying the coefficient of each area will be compared with the global radiation actually measured.

30.4.1 Function of cloud amount and solar altitude for global radiation

Solar radiation coefficient was estimated using clouds amount and solar altitude from the four cities, of which solar radiation is currently measured. The data were first grouped into four seasons: March, April, May (spring), June, July, August (summer), September, October, November (autumn), and December, January, February (winter).

Within each season, the hourly values were assorted into classes of equal mean hourly solar elevation y by intervals of Ay =10°. The radiation data within each of these classes were then assorted according to total cloud amount N. Since the radiation data are hourly sums whereas the cloud are momentaneous observations at the end of the respective hour, only such cases were admitted when the reported cloud amount at the forgoing hour was identical to the hour under consideration (Kasten and Czeplak, 1979).

The clouds amount and solar radiation changes with the solar altitude are shown in Figs. 30.4- 30.7. For Seoul, G(N)/G(0), the proportion of clouds amount to change of solar radiation in cloudless day was observed increased from clouds amount N=1 octa and then decreased to the point of N= 5 octa. And at the point of N=8 octa it fell to approximately 0.25. In Busan, Gwangju, and Daejeon, G(N)/G(0) increased from the point of N=1 octa and then decreased to 0.23, 0.28, and 0.25 respectively, at the point of N=8 octa, which was similar to that of Seoul.

The overall changes of solar radiation with the clouds amount and the solar altitude over 20 years (1986-2005) were observed as large in y =10°, but in other solar altitude, it showed a gentle decrease. Also, global radiation under cloudless and overcast sky, G(0) and G(8), respectively, is plotted vs. sin r. Multiple reflection between atmosphere and snow covered-ground and less turbidity is supposed to be responsible for the slightly higher winter and spring values. On the yearly average, 20-30% of the incoming global radiation is transmitted through overcast (Kasten and Czeplak, 1979).  o.so

o.so O 1 2 3 5 6

o.so O 1 2 3 4

Fig. 30.4 Global radiation G as a function of total cloud amount N for different solar elevations r in the four seasons (from upper: spring, summer, fall, and winter) in korea.

Fig. 30.4 Global radiation G as a function of total cloud amount N for different solar elevations r in the four seasons (from upper: spring, summer, fall, and winter) in korea.  Fig. 30.5 Global radiation G as a function of total cloud amount N for different solar elevations r in the four seasons (from upper: spring, summer, fall, and Winter) in Busan. --20" ---3D" - -40 - 50 60

700 600 500 J 400 300 200 100 0

SOO SOO 700 600 500 400 300 200 100 0

12 3 4 n

10'

--20"

---3D"

1 .50

- -40-

- 50"

6D"

600 500

g 400 300 200 100 0 O 1 2 3 4 5 6 Ol 2 3 4 5 6 7 S

Fig. 30.6 Global radiation G as a function of total cloud amount N for different solar elevations r in the four seasons (from upper: spring, summer, fall, and winter) in Gwangju.

123 45678 N

S 00 700 600 500 i 400 300 200 100 O

900 SOO 700 600 500 400 300 200 100 O

700 600 500 g 400 300 200 100 O O 1 2 3 4 01234567S 01234567S

0.50

0.50 OI 2 3 4 5 6 7 S

Fig. 30.7 Global radiation G as a function of total cloud amount N for different solar elevations r in the four seasons (from upper: spring, summer, fall, and Winter) in Daejeon. Fig. 30.8 Same as Figs. 30.4-30.7 but for the whole year 1986-2005 (from upper: Seoul, Busan, Gwangju, Daejeon). Fig. 30.9 Global radiation as a function of the sine of solar elevation r under cloudless sky:G(0) and under overcast sky: G(8) (from upper left: Seoul, Busan, Gwangju, Daejeon).

30.4.2 Comparison of measured and calculated data Fig. 30.10 Plot of hourly global solar radiation calculated from CRM model vs. measured data for four cities (left: Original, right: site fitted).

The data calculated applying coefficient of each location as described above will be compared to the data calculated applying the original coefficient. It is to estimate the influence of the coefficient calculated applying geographical climatic factor on the global radiation calculated based on the cloud amount.

A plot of hourly irradiance calculated using CRM (original and site-fitted coefficient) vs. measured values (Krarti and Huang, 2006) is shown in Fig. 30.10 for four cities of South Korea. The original coefficients are used as Hamburg coefficients (Muneer and Gul, 2000). The CRM relies heavily on one variable, the cloud amount, and generally underestimates global solar radiation when original or fitted model coefficients are used as clearly indicated by global solar radiation presented in Fig. 30.10.

As a result of the comparison, in the case of Seoul, when the original coefficient and the site-fitted coefficient were applied, the R2 (coefficient of determination) values were 0.747, and 0.749, respectively, which showed some correlation between the two figures. In case of Busan, the figures were 0.817 and 0.819, respectively, which also showed strong correlation. For Gwangju, like the above two cities, R2 was reported as 0.618 and 0.622, respectively, showing that site-fitted coefficient produced higher determinant coefficient. Meanwhile, Daejeon's R2 was reported as 0.772 and 0.773, meaning both of the two cases are correlated, but the original coefficient produced very slightly higher result.

These figures were re-evaluated through 'MAD.' Statistical evaluation of CRM based on original and site-fitted coefficients is presented in Table 30.3. A new performance indicator, the mean of absolute deviations (MAD), is also introduced herein. MAD is defined as

where C is the calculated and M the measured irradiance; n denotes the number of observations (Gul et al., 1998).

The estimated site-fitted coefficient from this study, as is shown in Table 30.2, was compared with the estimated solar radiation applying original coefficient from Hamburg to reveal the excellence of site-fitted figures, as is indicated in Table 30.3, except that of Daejeon. However, in the other regions, the calculated solar radiation by the Kasten and Czeplak (1979) suggestion was decently satisfactory.

 Region A B C D Seoul 963 106 0.75 2.6 Busan 930 64 0.77 2.9 Gwangju 969 ll 0.72 2.l Daejeon 984 76 0.75 2.6
 Table 30.3 Statistical evaluation of CRM for South Korean sites (2000). Region Hamburg coefficients Site-fitted coefficients MAD(W/m2) MAD(W/m2) Seoul 81 54 Busan 51 51 Gwangju 117 113 Daejeon 66 72 