Correlations to estimate the monthly average daily diffuse radiation on horizontal surfaces in Yunnan Province, China

Energy Convers. Mgmt Vol. 39, No. 5/6, pp. 505-510, 1998

Pergamon PII: S0196-8904(96)00049-0

CORRELATIONS

TO ESTIMATE

DAILY DIFFUSE SURFACES

THE MONTHLY

RADIATION

IN YUNNAN

© 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain 0196-8904/98 $19.00 + 0.00

AVERAGE

ON HORIZONTAL

PROVINCE,

CHINA

LIN WENXIAN, GAO WENFENG, PU SHAOXUAN, LIU TAO and LU ENRONG Solar Energy Research Institute, Yunnan Teachers University, Kunming, Yunnan 650092, People's Republic of China

(Received 28 July 1995) Abstract--Yunnan Province, China, has its unique "cubic climates" which means that the climates in the region vary greatly. There are seven meteorological stations in the province which have measured data of global solar radiation on horizontal surfaces, and only four of them (Kunming, Tengchong, Hekou and Jinhong) have measured data of diffuse radiation on horizontal surfaces. With these data and the relevant data of the geographic and meteorological parameters of these four stations, we develop, in this study, two kinds of correlations to estimate the monthly average daily diffuse radiation on horizontal surfaces in Yunnan Province. It is believed that these correlations are applicable at any site in Yunnan Province. © 1997 Elsevier Science Ltd. Correlations

Diffuse radiation

Cubic climates

Yunnan Province, China

1. INTRODUCTION To determine the feasibility of building a solar energy system, it is necessary to know how much solar radiation is available. The amount of global radiation arriving on horizontal surfaces is the minimum information needed. Most solar energy applications require the estimation of the amount of insolation received on an inclined plane. The quantity of diffuse radiation incident on horizontal surfaces is also needed for this estimation. There are many stations in the world where horizontal global and diffuse radiation data are recorded, but their distribution is far too sparse to provide useful input for the estimation of inclined radiation for every specified location. Many researchers have presented correlations to estimate horizontal diffuse radiation [1-26]. Situated on the Yunnan-Guizhou Plateau, Yunnan Province, China, covers an area of 380,000 km 2 (latitude 21-29°N, longitude 97.5-106°E). Within a tropical-subtropical area, the province has its unique "cubic climates". Its western part is the Dianxi Lengthwise Valley Area, and the eastern part is the main body of the Yunnan-Guizhou Plateau. The entire region has low latitudes, largely varied heights, and complex climatic and meteorological conditions. Due to the block of mountains to cold waves, most parts have high average daily temperatures and winter temperatures. The fresher and thinner plateau air, larger transmittance of sunlight, longer hours of bright sunshine, and better climatic and meteorological conditions in the province result in larger global solar radiation than that in the other regions in China. Yunnan Province has rich resources of solar energy, and the application of solar water heaters is very popular at present. It is expected that other applications of solar energy engineering will also find their popular roles in this province in the near future. Nevertheless, there are seven meteorological stations (Kunming, Tengchong, Hekou, Jinhong, Zhaotong, Lijiang, and Mengzi) in the province which have measured data of global solar radiation on horizontal surfaces, and only four stations (Kunming, Tengchong, Hekou, and Jinhong) that have measured data of diffuse radiation. It is imperative to develop correlations to estimate the desired data of global and diffuse radiation on horizontal surfaces at sites other than the seven stations in the province, based on the measured data of the seven stations. Changhan and Duming have conducted studies on diffuse radiation on horizontal surfaces in China [27-29] and Wenxian developed correlations to estimating monthly global and direct radiation on horizontal surfaces at sites in Yunnan Province in the dry season (Nov.-Apr.) and in the wet season 505

506

LIN WENXIAN et al.: MONTHLY AVERAGE DAILY DIFFUSE RADIATION Table 1. The general information of sevenstations in Yunnan Province, China Location L a t i t u d e Longitude Altitude Data record period Kunming 2 5 ° 0 1 ' N 102°41'E 1891.4m 1971-1975, 1977 Tengchong 25°07'N 9 8 ° 2 9 ' E 1647.8m 1971-1975 Hekou 22°30'N 103°57'E 136.7 m 1971-1977 Jinhong 21°52'N 101°04'E 552.7 m 1971-1973, 1977

(May-Oct) [30-32]. In this work, we develop correlations to estimate the monthly average daily diffuse radiation on horizontal surfaces in Yunnan Province. 2. C A L C U L A T I O N M E T H O D O L O G Y On a cloudy day, the global radiation received is an indication of the extent of cloudiness and should be an indication of the extent of diffuse radiation. Liu and Jordan [1] first developed the following polynomial correlation between H/Ho and Hd/H: Hd/H = 1.39 - 4.027 K, + 5.531 K~t - 3.108 K~ (0.3 < KI < 0.7),

(1)

where H , Hd, and H0 are the monthly average daily global, diffuse and extraterrestrial radiation on horizontal surfaces (MJ/m2/day), respectively, and Kt (where K~ = H/Ho) is the monthly average daily clearness index (dimensionless). Page [7] proposed to develop a correlation based on direct regression analysis of data. Using data from ten locations situated between 40°N and 40°S latitudes, he recommended the following linear equation: Hd/H = 1 . 0 0 - 1.13/ft.

(2)

When the sky is completely covered by clouds, the number of bright sunshine hours recorded will be nil. Under such conditions, all radiation received on earth will be of a diffuse nature. On the other hand, on a completely cloudless day, a certain number of bright sunshine hours will be recorded, and diffuse radiation will be quite minimal. Therefore, we can find a correlation between the diffuse radiation and the number of bright sunshine hours. Based on data from three Canadian

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LIN WENXIAN et al.:

MONTHLY AVERAGE DAILY DIFFUSE RADIATION

507

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stations, Iqbal [8] developed the following correlation: H a / H = 0.791 - 0.635n/Nd,

(3)

where n and Nd are the monthly average daily bright sunshine hours and day length, respectively. In this work, we develop the following two polynomial types of correlations to estimate the monthly average daily diffuse radiation on horizontal surfaces in Yunnan Province: H~/H = ao + a~K, + a2K~t + . . .

(4)

H d / H = bo + b~n/N~ + b2(n/N~)2 + . . . .

(5)

and

where N~ is the modified day length calculated by using the formula given in Ref. [7]. The general information about the four meteorological stations in Yunnan Province is listed in Table 1. With the measured data of monthly average global and diffuse radiation on horizontal surfaces and hours of sunshine at these four stations in the province [33, 34], we present, in Figs 1 and 2, the plots between H a / H and K, and, in Figs 3 and 4, the plots between H d / H and n/N~ in the following two cases: Case 1: All measured values of H, Ha and n in each month during the corresponding years of records for every station are presented, but the average values of H, Ha and n in each month during the corresponding years of records for every station are not presented (the number of observations is 264); Case 2: Only the average values of H, Ha and n in each month during the corresponding years of records for every station are presented (the number of observations is 48). 3. CORRELATIONS AND DISCUSSIONS With the measured data of global and diffuse radiation on horizontal surfaces and the hours of bright sunshine, as well as the data of the geographic and meteorological parameters, at four stations in Yunnan Province, we conduct the auto-correlation method of polynomials, which automatically correlates the best expression of the polynomial based on the given data. The results are listed in Table 2 (in the form of equation (4)) and Table 3 (in the form of equation (5)). From Table 2 and Table 3, we can make the following conclusions:

508

LIN WENXIAN et al.: MONTHLY AVERAGE DAILY DIFFUSE RADIATION

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Fig. 3. The plot between Ha/H and n/N~ in Case 1.

(a) The relationships between Hd/H and K, and between Hd/H and n/N~ are generally linear, except for two correlations which have quadratic forms. (b) The correlations in the form of equation (5) are slightly better than the correlations in the form of equation (4), except for the correlations at Jinhong, but the differences are very small and therefore the correlations in these two forms have the same performance. (c) The obtained correlations are valid when Kt is in the range 0.2 to 0.7 and when n/N~ is in the range 0.1 to 0.95. In addition, the four stations are located in different regions of the Yunnan Province, which have greatly varied geographic and meteorological conditions and

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I

et al.:

LIN WENXIAN

MONTHLY

AVERAGE

DAILY

DIFFUSE

RADIATION

509

T a b l e 2. T h e a u t o - c o r r e l a t i o n results w i t h the c o r r e l a t i o n s in the f o r m o f e q u a t i o n (4) Location

Case

Stations*

Correlations

Ha/H = Hd/H = Hd/H = Hd/H = Hd/H = Hd/H = Ha/H = Hd/H = Ha/H = Hd/H =

1

2 Kunming

1

2 Tengchong

1

2 Hekou

1

2 Jinhong

1

2

1.03931.16301.05921.1628 1.2283 1.20521.06371.07660.9411 1.1731 -

1.2642/<, 1.5214K, 1.4164K, 1.6166/<, 1.5194Kt 1.5430/<, 1.3190K, 1.2700K, 1.0890/<, 1.5489/<,

r-'

No. of observations

sgm

0.7177 0.9125 0.7702 0.9380 0.9179 0.9851 0.5673 0.8665 0.6890 0.8817

264 48 72 12 60 12 84 12 48 12

0.0762 0.0399 0.0735 0.0387 0.0509 0.0213 0.0674 0.0227 0.0576 0.0322

sgm = standard error of residual errors *All f o u r s t a t i o n s t o g e t h e r

T a b l e 3. T h e a u t o - c o r r e l a t i o n results w i t h the c o r r e l a t i o n s in the f o r m o f e q u a t i o n (5) Location

Case

Stations*

1 2 1 2 1 2 1 2 1 2

Kunming Tengchong Hekou Jinhong

Correlations

Hd/H Hd/H Hd/H Hd/H Hd/H Ho/H Hd/H Hd/H Ha/H Hd/H

= = = = = = = = = =

0.9474 0.8767 0.9152 0.9312 0.9884 0.8838 0.8905 0.8501 0.7708 0.8485

-

-

1.0252n/N~ + 0.2728(n/N~) 2 0.7370n/N~ 0.7557n/NA 0.7860n/N~ : 1.1910n/N~ + 0.3963(niNe) 2 0.7612n/N~ 0.7613n/N~ 0.6703n/NA 0.5943n/N~ 0.7194n/N~

r:

No. of observations

sgm

264 48 72 12 60 12 84 12 48 12

0.0591 0.0367 0.0653 0.0387 0.0402 0.0224 0.0522 0.0226 0.0639 0.0487

0.8264 0.8235 0.9495 0.9835 0.7407 0.8679 0.6171 0.7295

sgm = standard error of residual errors *All f o u r s t a t i o n s t o g e t h e r

t h e r e f o r e the c o r r e l a t i o n s (all s t a t i o n s t o g e t h e r ) are r e c o m m e n d e d for use to e s t i m a t e the m o n t h l y a v e r a g e daily diffuse r a d i a t i o n o n h o r i z o n t a l surfaces at a n y site in Y u n n a n Province.

4.

CONCLUSIONS

With the measured data of global and diffuse radiation on horizontal surfaces and the hours of bright sunshine, as well as the relevant data of the geographic and meteorological parameters, at four meteorological stations in Yunnan Province, we develop various correlations between the monthly average daily diffuse radiation on horizontal surfaces and the relative duration of bright sunshine as well as the clearness index. We recommend the following two kinds of correlations to be used to estimate the monthly average daily diffuse radiation on horizontal surfaces at any site in Yunnan Province (see Tables 2 and 3):

Hd/H = 1.0393 - 1.2642 K, (0.2 < Kt < 0.7)

(6)

H~/H = 1.1630 - 1.5214 K, (0.2 < K, < 0.7),

(7)

Hd/H = 0.9474 - 1.0252n/N~ + 0.2728(niNe) 2 (0.1 < n/N~ < 0.95)

(8)

Hd/H = 0.8767 - 0.7370n/NS (0.1 < n/N~ < 0.95).

(9)

or

and

or

Acknowledgements--The a u t h o r s w o u l d like to t h a n k the Y u n n a n P r o v i n c i a l C o m m i t t e e o f Science a n d T e c h n o l o g y f o r the financial s u p p o r t o f this w o r k .

510

LIN WENXIAN et al.: MONTHLY AVERAGE DAILY DIFFUSE RADIATION

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