Estimation of daily diffuse solar radiation in China

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1.014

Renewable Energy 29 (2004) 1537–1548

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Data bank

Estimation of daily diffuse solar radiationin China

Zhou Jin �, Wu Yezheng, Yan GangSchool of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 21 January 2004; accepted 25 January 2004

Abstract

Applying the measured global and diffuse solar radiation data from 78 meteorologicalstations in China, a countrywide general correlation model for calculating the daily diffuseradiation was derived on the basis of Liu and Jordan method. Two widely used statistics:root mean square error and mean bias error were used to assess the performance of thecorrelation. And the correlation shows good behavior when applied to most of the stations.Subsequently, with the measured data from the 78 stations, an analysis of geographical dis-tribution of solar energy resource in China was also presented in the form of clearness index(the ratio of global solar radiation to extraterrestrial radiation) percentage frequency, andresults show that the solar energy resource in western and northern China is relativelyabundant.# 2003 Elsevier Ltd. All rights reserved.

Keywords: Diffuse radiation; Global solar radiation; Correlation models; Geographical distribution

1. Introduction

China, as a developing country with a population of 1.3 billion, is the second

largest energy consumer in the world, and its energy structure is coal-based, with

coal consumption amounting to about 70% of total energy consumption. In an

environment of a rapidly expanding economy, China’s energy industry is con-

fronted with dual pressures from economic development and environmental protec-

tion. In order to have a sustainable development, renewable energy is being

seriously considered for satisfying part of the energy demand in China, as in the

Nomenclature

f eccentricity correction factor (dimensionless)F distribution frequency (%)H0 daily extraterrestrial radiation (MJ/m2)

H0 monthly average daily extraterrestrial radiation (MJ/m2)

Hd daily diffuse solar radiation (MJ/m2)Ht daily global solar radiation (MJ/m2)

H t monthly average daily global solar radiation (MJ/m2)

I0 solar contant (1367 W/m2)Kd daily global clearnessKt daily diffuse fractionMBE mean bias error (%)n number of day of year starting from the first of JanuaryN number of dataRMSE root mean square error (%)

S monthly average daily sunshine duration (h)

S0 monthly average daily maximum possible sunshine duration (h)

ws sunrise hour angle (v)

Z altitude of site (m)d solar declination (

v)

k latitude of site(v)

Z. Jin et al. / Renewable Energy 29 (2004) 1537–15481538

world. Solar energy, as a clean energy source and one kind of renewable energy, isabundant in China. More than two-thirds of area in China receives an annual solarradiation that exceeds 5.9 GJ/m2 with more than 2200 h sunshine per annum [1].Government targets for solar energy utilization are about 3% of total energy useby 2010 [1]. In this respect, the importance of solar radiation data for the designand efficient operation of solar energy systems and associated energy storage sys-tem has been recognized in recent years.

The global solar radiation can be divided into two components: (1) diffuse solarradiation, which results from scattering caused by gases in the Earth’s atmosphere,dispersed water droplets and particulates; and (2) direct solar radiation, which havenot been scattered. Global solar radiation is the algebraic sum of the two compo-nents. Values of global and diffuse radiations are essential for research and engin-eering applications. For China, horizontal global radiation data have beenrecorded at many meteorological stations, but the corresponding diffuse radiationrecords are scarce at some stations. Thus, the diffuse radiation must be estimatedthrough models and correlations. The first model originally developed by Liu andJordan [2] relates the diffuse solar radiation with global solar radiation based onthe data from 98 localities in the USA and Canada. Following the work by Liuand Jordan, many researchers [3–11] have studied the correlations with data in

1539Z. Jin et al. / Renewable Energy 29 (2004) 1537–1548

other regions. Some researchers have found [9] that the regression parameters inthe correlations determined by linear regression using the daily global and diffusesolar radiation at different sites often show remarkable similarity. However, whenthe monthly average daily global and diffuse radiation is used to form theregression correlations, the regression parameters have been found to vary substan-tially between sites and the accuracy of the correlation reduced [10,11].

The study of correlation between global and diffuse solar radiation is very lim-ited in China. Few attempts to develop models, through which the diffuse solarradiation can be estimated, have been found in China. Wenxian et al. [12,13] havestudied the relationship between direct and global solar radiation with the observeddata for only several stations in the Yunnan Province, China, and suggested a cor-relation to estimate the direct radiation, by which the diffuse radiation can beobtained by subtracting the direct radiation from the global radiation. Obviously,this study is valid only for the locality used in the analysis.

The objective of this paper are the follows: (1) to develop and test method toestimate the diffused solar radiation using global solar radiation based on the datain 78 locations in China, and (2) to analyze the geographical distribution of solarenergy resource in China.

2. Data used and methods of analysis

2.1. Database

In this study, a database containing daily measured value of global and diffusesolar radiation, covering 78 meteorological stations in China was obtained fromChina Meteorological administration. Information for the meteorological stationsand the periods of the data considered are given in Table 1. These stations cover alatitudinal range from 15.9

vto 53.5

vand a longitudinal range from 76.0

vto 130.3

v,

and have largely varied altitude from 1 to 4507 m. All the major biomes withinChina are represented.

Valid measurements were extracted from the database from those days withcomplete records based on the following criteria: (1) Ht=H0 � 1:0 and (2)Hd=Ht � 1:0, where Ht is the daily global radiation, Hd is the daily diffuse radi-ation, and H0 is extraterrestrial radiation. These two criteria were used to removeobvious errors in the database.

2.2. Method

Based on the individual daily global and diffuse solar radiation data, the dailyglobal clearness Kt and the daily diffuse fraction Kd were calculated by

Kt ¼Ht

H0ð1Þ

Kd ¼ Hd

Htð2Þ


Table 1

The general information of the 78 meteorological stations

# L
ocation L at. (vN) L ong. (
vE) A
lt. (m) Record time
(year)

1 M
ohe 5 3.5 1 22.4 296 8
2 H
eihe 5 0.3 1 27.5 166 31
3 J
iamusi 4 6.8 1 30.3 81 31
4 H
aerbin 4 5.8 1 26.8 142 40
5 A
letai 4 7.7 88.1 735 33
6 Q
itai 4 4.0 89.6 794 4
7 Y
ining 4 4.0 81.3 663 33
8 W
ulumuqi 4 3.8 87.6 918 42
9 T
ulufan 4 2.9 89.2 35 30
10 K
uche 4 1.8 82.9 1 073 34
11 K
ashi 3 9.5 76 1 289 44
12 R
uoqiang 3 9.0 88.2 888 36
13 H
etian 3 7.1 79.9 1 375 36
14 H
ami 4 2.8 93.5 737 32
15 E
jinaqi 4 2.0 1 01.1 941 9
16 D
unhuang 4 0.2 94.7 1 139 36
17 M
inqin 3 8.6 1 03.1 1 367 32
18 G
eermu 3 6.4 94.9 2 808 44
19 X
ining 3 6.6 1 01.8 2 261 33
20 L
anzhou 3 6.1 1 03.9 1 517 42
21 E
rlianhaote 4 3.7 1 12 965 35
22 H
uhehaote 4 0.8 1 11.7 1 063 10
23 T
umotezuoqi 4 0.7 1 11.2 1 021 22
24 D
atong 4 0.1 1 13.3 1 067 31
25 Y
ijinhuoluoqi 3 9.4 1 09.8 1 310 31
26 Y
inchuan 3 8.5 1 06.2 1 111 32
27 T
aiyuan 3 7.8 1 12.6 778 31
28 G
uyuan 3 6.0 1 06.3 1 753 8
29 H
ouma 3 5.7 1 11.4 434 31
30 C
hangchum 4 3.9 1 25.2 237 33
31 S
henyang 4 1.7 1 23.5 43 40
32 B
eijing 3 9.9 1 16.3 54 44
33 T
ianjin 3 9.1 1 17.1 3 31
34 Y
antai 3 7.5 1 21.4 47 31
35 J
inan 3 6.7 1 17 52 31
36 N
aqu 3 1.5 92.1 4 507 32
37 L
asa 2 9.7 91.1 3 649 40
38 Y
ushu 3 3.0 97 3 681 33
39 C
hangdu 3 1.2 97.2 3 306 32
40 M
ianyang 3 1.5 1 04.7 471 14
41 C
hengdu 3 0.7 1 04 506 40
42 E
mcishan 2 9.5 1 03.3 3 047 31
43 L
eshan 2 9.5 1 03.8 424 18
44 W
eining 2 6.9 1 04.3 2 235 30
45 T
engchong 2 5 98.5 1 655 31
46 K
unming 2 5 1 02.7 1 891 40
47 J
inghong 2 2 1 00.8 553 32
48 M
engzi 2 3.4 1 03.4 1 301 10


where H0 is the daily extraterrestrial radiation and can be calculated by the follow-ing equations [14]:

H0 ¼24� 3600

pI0f coskcosdsinws þ

p180

wssinksind� �

ð3Þ

f ¼ 1 þ 0:33 cos360n

365

� �ð4Þ

d ¼ 23:45sin360ð284þ nÞ

365

� �ð5Þ

ws ¼ cos�1 �tanktandð Þ ð6Þ

where I0 is the solar constant (1367 W/m2), f is the eccentricity correction factor,d is the solar declination, k is the latitude of the site, ws is the sunrise hour angle,and n is number of day of the year starting from first of January.

Table 1 (continued )

#
Location L at. (vN) Long. (
vE)
Alt. (m) Record time
(year)

49
Xian 3 4.3 108.9 398 32
50
Zhengzhou 3 4.7 113.7 110 40
51
Nanchong 3 0.8 106.1 298 18
52
Wanxian 3 0.8 108.4 433 30
53
Yichang 3 0.7 111.3 133 31
54
Wuhan 3 0.6 114.1 23 40
55
Chongqing-1 2 9.9 106.4 242 27
56
Chongqing-2 2 9.6 106.5 259 4
57
Luzhou 2 8.9 105.4 335 8
58
Changsha-1 2 8.2 113.1 36 27
59
Changsha-2 2 8.2 112.9 68 5
60
Zunyi 2 7.7 106.9 849 30
61
Guiyang 2 6.6 106.7 1074 32
62
Guilin 2 5.3 110.3 194 31
63
Ganzhou 1 5.9 115 124 31
64
Nanjing 3 2 118.8 9 29
65
Hefei 3 1.9 117.2 28 31
66
Shanghai-1 3 1.4 121.5 4 10
67
Shanghai-2 3 1.2 121.4 5 30
68
Hangzhou 3 0.2 120.2 42 29
69
Cixi 3 0.3 121.2 7 30
70
Nanchang 2 8.6 115.9 47 31
71
Fuzhou 2 6.1 119.3 84 31
72
Shaoguan 2 4.8 113.6 69 30
73
Guangzhou 2 3.1 113.3 7 40
74
Shantou 2 3.4 116.7 1 31
75
Nanning 2 2.8 108.4 73 31
76
Zhongshan 2 2.6 113.4 1 26
77
Haikou 2 0 110.4 14 31
78
Sanya 1 8.2 109.5 6 9


To analyze the correlations between daily diffuse radiation and correspondingglobal radiation, constant or linear expressions depending on the daily clearnessindex are generally used:

Kd ¼ a0 for Kt � d0 ð7ÞKd ¼ b0 þ b1Kt for d0 < Kt � d1 ð8ÞKd ¼ c0 for Kt > d1 ð9Þ

where d0 and d1 are the range limits of the daily clearness index, a0, b0, b1 and c0are empirical coefficients.

In order to study the site dependence on the daily diffuse radiaion with datafrom the 78 stations, the following correlation was also used in this study when Kt

lies between d0 and d1:

Kd ¼ b2 þ b3k þ b4Zð Þ þ b5 þ b6k þ b7Zð ÞKt for d0 < kt � d1 ð10Þwhere k is the latitude, Z is the altitude in kilometer, and b2–b7 are empirical coeffi-cients.

2.3. Methods of model evaluation

The accuracy of the correlations was assessed by means of two widely used stat-istics: root mean square error (RMSE) and mean bias error (MBE). The followingexpressions for RMSE and MBE, as a percentage of the average value, were used:

RMSE ¼ 100

D

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXNi¼1

Die �Dimð Þ2=N

vuut ð11Þ

MBE ¼ 100

D

XNi¼1

Die �Dimð Þ=N" #

ð12Þ

where N is the number of data, Die is the ith estimated value, Dim is the ith mea-sured value and D is the mean of the measured values.

3. Results and discussion

3.1. Correlations between the daily diffuse radiation and the corresponding globalradiation

In order to obtain the general correlation between daily diffuse and global solarradiation, the daily data for all stations were pooled across all years and were ana-lyzed. The value of d0 and d1 was set to 0.20 and 0.75, respectively. The value of a0

was determined by averaging Kd for days when Kt was less than 0.20, and the valueof c0 was determined by averaging Kd for days when Kt was higher than 0.75. Thenempirical coefficients in Eqs. (8) and (10) were estimated by linear regression usingall data where Kt lies between 0.20 and 0.75.


The performance of the regression model was evaluated on the basis of RMSE

and MBE. Table 2 shows the value of RMSE and MBE for the two models used.

It can be seen that the difference between the errors value of two models is less.This means that the accuracy of the correlation was increased little by the addition

of the latitude and altitude into correlation, and the first model (Eqs. (7)–(9)) isrecommended to estimate the diffuse solar radiation in China. The resulting corre-

lations are given by the following correlations for three different ranges of Kt value:

Kd ¼ 0:987 for Kt < 0:20 ð13Þ

Kd ¼ 1:292� 1:447Kt for 0:20 � Kt < 0:75 ð14Þ

Kd ¼ 0:209 for Kt > 0:75 ð15Þ

The performance of the above correlations was also evaluated for each of the 78

stations on the basis of RMSE and MBE. The value of RMSE and MBE for each

station is given in Table 3. The RMSE does not exceed 30% at 90% of the stationand has a maximum of 44.18%, the MBE ranges from �21.19% to 17.16%.

Fig. 1 shows the relationship between Kd and Kt with nine stations in Table 1 as

example, the correlations Eqs. (13)–(15) are also plotted in Fig. 1.

3.2. Geographical distribution of solar energy resource in China

As can be seen in Fig. 1, although the relationship between Kd and Kt shows

similarity at different stations and can be described by Eqs. (13) and (15), the dis-

tribution pattern of Kt varies substantially between stations. In order to analyzethe difference of distribution pattern of Kt its range (from 0 to 1) was divided into

regular intervals, and then the distribution frequency of Kt was calculated for eachinterval by the following equation:

Fi ¼ 100Ni=N ð16Þ

where Fi is the distribution frequency of Kt for the ith interval, Ni is the number of

Kt data in the ith interval and N is the total number of Kt data.For each interval in Kt at a step of 0.05, the distribution frequency of Kt was cal-

culated for five stations selected from Table 1 and plotted against the mid-point

value of Kt in that interval. As shown in Fig. 2, the distribution pattern of Kt var-ies substantially between stations, and a high value of distribution frequency with

high Kt value indicates the high proportion of sunshine days (see stations 32 and38 in Fig. 2). This is consistent with the well known relationship between sunshine

Table 2

Comparison of RMSE and MBE errors of two daily diffuse correlations

Correlations R
MSE (%) M BE (%)
Eqs. (7)–(9) 2
1.769 0 .000
Eqs. (7), (9) and (10) 2
0.356 0 .000


Table 3

RMSE and MBE errors for each of the 78 stations for daily diffuse radiation correlations (Eqs.

(13)– (15))

#
Locations RMSE M BE
1
Mohe 27.38 �4.38
2
Heibe 29.47 0.33
3
Jiamusi 28.22 7.29
4
Haerbin 25.81 8.07
5
Aletai 35.55 �5.10
6
Qitai 30.40 6.18
7
Yining 33.48 1.05
8
Wulumuqi 26.78 7.94
9
Tulufan 24.72 �7.78
10
Kuche 31.84 � 21.19
11
Kashi 27.22 � 10.78
12
Ruoqiang 32.25 � 20.95
13
Hetian 29.83 � 20.61
14
Hami 31.79 � 12.58
15
Ejinaqi 28.30 �0.89
16
Dunhuang 32.48 � 17.00
17
Minqin 29.96 �5.32
18
Geermu 33.72 � 15.67
19
Xining 24.95 �6.58
20
Lanzhou 19.46 �4.59
21
Erlianhaote 36.53 �4.35
22
Huhehaote 29.91 � 11.21
23
Tumotezuoqi 35.52 17.16
24
Datong 23.63 0.19
25
Yijnhuoluoqi 32.75 7.21
26
Yinchuan 24.53 � 10.70
27
Taiyunn 19.90 �1.29
28
Guyuan 19.16 �5.04
29
Houma 17.85 �1.98
30
Changchun 24.89 1.95
31
Shenyang 21.86 5.90
32
Beijing 19.59 �2.80
33
Tianjin 21.97 3.16
34
Yantai 29.45 14.17
35
Jinan 20.34 7.29
36
Naqu 44.18 8.24
37
Lasa 35.95 8.66
38
Yushu 29.66 0.15
39
Changdu 32.15 9.95
40
Mianyang 10.33 �3.41
41
Chengdu 10.52 �3.04
42
Emcishan 19.31 �5.01
43
Leshan 9.99 �1.19
44
Weining 17.96 3.15
45
Tengchong 21.01 5.91
46
Kunming 21.18 6.52
47
Jinghong 26.27 9.11
48
Mengzi 22.19 6.81


hours and global solar radiation [15,16], which is usually expressed as

Ht

H0

¼ Aþ B SS0

ð17Þ

where Ht is the monthly average daily global radiation, H0 is the monthly average

daily extraterrestrial radiation, S is the monthly average daily sunshine duration S0is the monthly average daily maximum possible sunshine duration, and A and Bare empirical coefficient. Although the monthly average daily value of sunshineduration and global solar radiation were involved in Eq. (17), it can be concludedthat high value of Kt indicates long sunshine duration and high distributionfrequency of Kt with high value indicates relatively abundant solar energy resource.So Kt can be used to analyze the geographical distribution of solar energy resource.

In order to analyze the distribution of solar energy resource in China, the distri-bution frequency of Kt for the 78 stations in this study was calculated for threeintervals of Kt: 0–1/3, 1/3–2/3 and 2/3–1. The combined influence of latitude and

Table 3 (continued )

# L
ocations RMSE MBE
49 X
ian 15.22 �2.40
50 Z
hengzhou 17.54 �0.58
51 N
anchong 10.30 �1.10
52 W
anxian 11.52 1.53
53 Y
ichang 14.56 0.49
54 W
uhan 16.64 0.68
55 C
hongqing-1 10.89 0.33
56 C
hongqing-2 8.61 0.06
57 L
uzhou 8.94 �0.68
58 C
hangsha-1 15.01 0.95
59 C
hangsha-2 11.33 �2.69
60 Z
unyi 10.79 �1.87
61 G
uiyang 12.85 1.11
62 G
uilin 15.68 1.64
63 G
anzhou 19.27 7.55
64 N
anjing 16.50 3.24
65 H
efei 17.22 3.27
66 S
hanghai-1 12.38 2.35
67 S
hanghai-2 13.74 0.80
68 H
angzhou 16.68 5.08
69 C
ixi 17.22 4.21
70 N
anchang 15.55 0.49
71 F
uzhou 17.12 4.79
72 S
haoguan 18.45 3.26
73 G
uangzhou 16.40 4.29
74 S
hantou 21.84 7.35
75 N
anning 16.75 �1.03
76 Z
hongshan 19.29 4.79
77 H
aikou 24.69 9.38
78 S
anya 21.65 13.23


longitude on the distribution frequency in the three intervals for China is shown in

the form of three-dimensional graphs in Fig. 3. For intervals 0–1/3 and 1/3–2/3, F

has high values in inner and southeastern China, whereas for the interval with high

Kt value, high F values were observed in northern and western China. This means

that there was a high proportion of cloudy days and relatively low solar energy

resource in inner and southeastern China, and there was high proportion of sun-

shine days and relatively abundant solar energy resource in northern and western

China. This agrees with the study by Li Junfeng et al. [1], in which China has been

Fig. 1. Relationship between Kd and Kt with nine stations in Table 1 as example.


divided into five regions according to the annual sunshine hours and total solarradiation.

4. Conclusions

Solar radiation data are essential for the work of energy planners, engineers andagricultural scientists. Applying the measured global and diffuse solar radiationdata form 78 stations in China, a countrywide general correlation model for calcu-lating the daily diffuse radiation was derived on the basis of Liu and Jordanmethod. The statistical estimators RMSE and MBE were used to indicate howclosely the correlation agrees with the data. For the 78 stations in the study, theRMSE does not go beyond 30% at 80% of the station, the MBE ranges from

Fig. 2. Distribution frequency of Kt values for five stations selected.

Fig. 3. Distribution frequency of Kt values with latitude and longitude for different intervals of Kt (inter-

vals of Kt are (a) 0–1/3; (b) 1/3–2/3; (c) 2/3–1).


�21.19% to 17.16%. The geographical distribution of solar energy resource inChina was demonstrated in the form of clearness index percentage frequency. It isfound that the solar energy resource in northern and western China is abundant,whereas it is relative low in inner and southeastern China.

Acknowledgements

This work was financially supported by the Doctoral Foundation of X’ian Jiao-tong University.

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Documents

Estimation of daily diffuse solar radiation in China