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Energy Conversion and Management

journal homepage:www.elsevier.com/locate/enconman

Energy Conversion and Management 70 (2013) 139148

General models for estimating daily global solar radiation for differentsolar radiation zones in mainland China

Mao-Fen Li a, Xiao-Ping Tang b, Wei Wu c, Hong-Bin Liu a,d, aCollege of Resources and Environment, Southwest University, Chongqing 400716,China bShapingba Meteorological Bureau, Chongqing 400030, China cCollege of Computer and Information Science, Southwest University, Chongqing 400716, China d

Chongqing Tobacco Science Institute, Southwest University, Chongqing 400716, China

A R T i C L E i N F O ABSTRACT

Article history:Received 22 November 2012Accepted 2 March 2013Available online 2 April 2013

Keywords:General modelSolar radiation zoneTemperature-basedSunshine-based k-Means

Empirical models, proposed to estimate solar radiation (Rs) in various areas, were site-specific in essence.However, it is questionable when they are applied to other stations where there is no record of Rs. Thisstudy aimed to develop general models to estimate daily Rs for different solar radiation zones in main-land China. Daily weather data including Rs, sunsh ine duration, relative humidity, maximum and mini-mum temperatures were collected and analyzed from 83 stations. Two types of simple empiricalequations, namely, temperature- and sunshine-b ased models, were obtained for each site. Five Rs zoneswere determined by k-means clustering algorithm based on long-term mean daily Rs. For each zone, thegeneral model for Rs estimation was developed based on geographical factors (latitude, longitude andaltitude) and site-specific models. Coefficient of residual mass (CRM), mean bias error (MBE), mean per-centage error (MPE), root mean square error (RMSE) and percent root mean square error (%RMSE) wereused to investigate the model performance. The comparative results between measure d and estimateddaily Rs showed that the general models had an acceptable accuracy. It is believed that the general mod-els developed in this work can be reliable and applicable for the locations without available Rs data in

mainland China. 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Solar radiation (Rs), as a vital primary input for crop models11,2], earth eco-envir onment model 13] and building energy effi-ciency codes 14], is measured at limited stations worldwide due tothe cost and techniqu es involved. For instance, there are more than2500 ground meteorological observation stations in mainland China,but only 98 of them have recorded daily Rs 15,6]. Long termmeasured daily global Rs data are not available for most areas inChina, especially in remote rural and mountainou s areas, where

about 80% Chinese inhabited 17]. Hence, methods to estimate Rs forthe locations with no records of solar radiation are of greatsignificance.

By reviewin g the literature, two types of empirical models,namely, temperat ure-base and sunshine-ba sed, are used exten-sivelyto estimate Rs at present 1825]. All of these models have easilyaccessible input parameters (such as temperatures, precipi-tation,relative humidity , dew point temperature, and sunshine

Corresponding author at: College of Resources and Environment, SouthwestUniversity, Chongqing 400716, China. Tel.: +86 23 6825 1069; fax: +86 23 68250444.

E-mail address:[email protected](H.-B. Liu).

0196-8904/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.03.004

hours), reasonable accuracy (root mean square error ranging be-tween 1.0 and 6.0 MJ m-2 d-1) and convenient applications . How-ever, most of them are in essence site-specific. Also, it isquestionable whether they could be applied to other locations wherethere is no record of observed Rs. Besides, some physical-basedmodels for Rs estimation that can be applied generally are usuallyin complex form 119,22].

In China, two zoning were proposed for building designs ther-mal climate zones (GB50176-93) 126] and solar climate zones 127].Based on the average temperatures in the coldest and hottest months

of the year, five thermal climate zones called severe cold (SC), cold(C), hot summer and cold winter (HSCW), mild, and hot summer andwarm winter (HSWW) (GB50176-93) 126] were de-rived. Recently,Lau et al. 127] proposed solar climate zones in terms of monthlymean daily clearness index derived from 123 stations. For Rsestimation at these zones, Lam et al. 128] develope d sun-shine-based models using artificial neural networks (ANNs) to esti-mate dailyRs for 40 cities covering nine major thermal climatic zones and sub-zones. Wan et al. 129] conducted a study of daily Rs estimation forthermal and solar zones using clearness index and sunshine durationextracted from 41 stations. They found that the regressio n modelstended to have slightly smaller mean bias error (MBE) and root meansquare error (RMSE) than ANN approaches.
http://www.elsevier.com/locate/enconmanhttp://www.elsevier.com/locate/enconmanhttp://www.elsevier.com/locate/enconmanmailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.enconman.2013.03.004http://dx.doi.org/10.1016/j.enconman.2013.03.004http://dx.doi.org/10.1016/j.enconman.2013.03.004mailto:[email protected]://www.elsevier.com/locate/enconman


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140 M.-F. Li et al./Energy Conversion and Management 70 (2013) 139148

Then they concluded that there was little to choose between ther-mal and solar climate zone models.

However, both aforementione d zoning were based on measuredmonthly data rather than daily global Rs data. Different data wererequired for identifying different climatic characterist ics with re-spect to the intended application [29]. Consideri ng the simplifica-tion of calculatio n, this study complemented earlier work with the

following objectives : (1) to identify different solar radiation zonesusing observed long-term mean daily Rs, (2) to propose and vali-date site specific daily Rs estimation models based on measuredsunshine hours and temperat ures and relative humidity, respec-tively, and (3) to develop general models based on the best per-formed models and site geographical indicators to estimate dailyglobal Rs for different Rs zones in mainland China.

2. Data and methods

2.1. Data gathering

Daily data, including Rs (MJ m-2 d-1), maximum and minimumtemperature s (Tmax

and Tmin, OC), sunshine hours and relative humidity

(Hum, %), were provided by the Chinese National Cli-matic DataCenter (CDC). There are 98 stations measured and re-corded dailyglobal solar radiation in China [21], while the data of 83 stations(Fig. 1 and Table 1) in mainland China before 2000 were used inthis study. Data quality control is first conducted by the suppliers.For the present study, records with missing data indicated by 32,766were removed from the data set. Missing data were replaced withmeans of the nearby points. A month with more than five continuousmissing or faulty data was eliminated.

2.2. Solar radiation zoning

Zoning would give a better understand ing of the distribution ofRs and an overview of the general solar radiation climatic condi-

tions within a region. There are different ways to classify zonesaccording to different criteria using different climatic variables

and indices in China [30]. This depends largely on the purpose ofestablishi ng such classification. For solar radiation modeling, long-term records of observed solar radiation should be considered forsolar radiation zoning. Measured daily Rs around 40 years of 83stations in China were used in the current study (Table 1). A con-sensus clustering techniquek-means clustering methodwas usedto identify solar radiation zones. The k-means clustering tech-nique

divides the high-dim ensional data space into a number of clusters,each one defined by a prototype and formed by the data for whichthe prototype is the nearest. Existing research showed that k-meansclearly outperform ed classical climate classifications (KppenGeiger approach) [31].

The process of clustering was conducted in SPSS 18.0. Initially,long-term mean daily Rs data for all years of 83 stations were cal-culated and arranged in a data matrix. Five clusters were set in ad-vance in accordance with existing zones in China and maximumiterates (100) were set for the large quantity of data. When theiteration (assign each observati on to the cluster whose mean isclosest to it and calculate the new means to be the centroids of theobservations in the new clusters) stopped until no reclassifica-tionwas necessary, five solar radiation zones were obtained by k-meansclustering methods (Fig. 1). The Rs zoning could be of inter-est forfurther solar radiation estimation.

2.3. Solar radiation modeling

Two types of commonly used Rs estimating models, namelytemperat ure-based and sunshine-ba sed models, were adopted. Theindependen t variables were Tmax, Tmin, and Hum for tempera-ture-base d models and sunshine hours for sunshine-base d equa-tions.Table 2 showed the models used in the present study to estimateglobal Rs on a horizontal surface. In view of the practical propertie sand easy to operate of Rs estimating, linear models were constructedwith measured Rs, temperat ures, sunshine duration and relativehumidity to estimate daily global Rs in mainland China. Models 14

were based on temperat ures and relatively humidity while models 5and 6 were based on sunshine hours, respectively .

Fig. 1. Distribution of the studied stations in different solar radiation zones in mainland China.


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M.-F. Li et al./Energy Conversion and Management 70 (2013) 139148

Table 1Meteorological stations and period of daily data records used in this study.

141

Station Longitude (, E) Latitude (, N) Altitude (m) Data period Data No. Solar climatezone [27]

Thermal climatezone [26]

Heihe 127.27 50.15 166.4 19612000 14,478 II SCHailaer 119.45 49.13 610.2 19601968, 19721977, 19822000 12,077 II SCHarbin 126.46 45.45 142.3 19612000 14,610 III SCAltai 88.05 47.44 735.3 19602000 14,911 II SC

Qitai 89.34 44.01 793.5 19871990 1461 II SCYining 81.2 43.57 662.5 19602000 14,941 II SCUrumchi 87.37 43.47 917.9 19592000 15,340 II SCTurpan 89.12 42.56 34.5 19612000 14,548 II MildKuqa 82.54 41.48 1072.5 19571990 12,235 II SCKash 75.59 39.28 1288.7 19572000 15,808 II ColdRuoqiang 88.1 39.02 888.3 19572000 15,918 II ColdHetian 79.56 37.08 1374.6 19572000 15,920 II ColdKumul 93.31 42.49 737.2 19612000 14,570 I SCDunhuang 94.41 40.09 1139.0 19572000 15,769 I Cold

Jiuquan 98.29 39.46 1477.2 19932000 2922 II SCMinqin 103.05 38.38 1367.0 19612000 14,608 II SCGangcha 100.08 37.2 3301.5 19932000 2922 I SCGolmud 94.54 36.25 2807.6 19572000 15,828 I SCXining 101.46 36.37 2261.2 19592000 15,340 II SCLanzhou 103.53 36.03 1517.2 19592000 15,221 III ColdErenhot 111.58 43.39 964.7 19572000 15,917 I SC

Haliut 108.31 41.34 1288.0 19922000 3288 II SCHohhot 111.41 40.49 1063.0 19591966, 19681968 2585 II SCDatong 113.2 40.06 1067.2 19612000 14,609 II SCYinchuan 106.13 38.29 1111.4 19611967, 19732000 12,625 II SCTaiyuan 112.33 37.47 778.3 19612000 14,610 III ColdYanan 109.3 36.36 958.5 19902000 4018 III ColdAnyang 114.22 36.07 75.5 19611990 10,956 III ColdXilinhot 116.04 43.57 989.5 19902000 3987 II SCTongliao 122.16 43.36 178.5 19601992 9799 III SCChangchun 125.13 43.54 236.8 19591981, 19832000 14,945 III SCYenki 129.28 42.53 176.8 19602000 14,915 III SCChaoyang 120.27 41.33 169.2 19632000 13,759 III SCShenyang 123.27 41.44 42.8 19612000 14,607 III SCBeijing 116.17 39.56 54.0 19572000 15,951 III ColdTianjin 117.04 39.05 2.5 19592000 15,339 III ColdLeting 118.54 39.25 10.5 19922000 3288 III ColdDalian 121.38 38.54 91.5 19632000 12,386 III ColdYantai 121.15 37.3 32.6 19952000 2160 III Cold

Jinan 116.59 36.41 51.6 19612000 14,605 III ColdGar 80.05 32.3 4278.0 19712000 10,499 I SCNakchu 92.04 31.29 4507.0 19611968, 19722000 13,025 II ColdLhasa 91.08 29.4 3648.7 19611968, 19712000 13,573 I ColdYushu 97.01 33.01 3681.2 19601973, 19782000 12,871 II ColdGolok 100.15 34.28 3719.0 19932000 2922 II SCChamdo 97.1 31.09 3306.0 19611968 19702000 14,183 II SCGanzi 100 31.37 3393.5 19942000 2557 II ColdChengdu 104.01 30.4 506.1 19612000 14,610 V HSCWEmeishan 103.2 29.31 3047.4 19612000 14,578 III HSCWChaotung 103.45 27.2 1949.5 19611967, 19691990 10,401 III MildLijiang 100.13 26.52 2393.2 19611967, 19691974, 19762000 13,330 II MildPanzhihua 101.43 26.35 1190.1 19922000 3288 III MildTengchong 98.3 25.01 1654.6 19612000 14,577 III MildKunming 102.41 25.01 1891.4 19611967, 19692000 13,848 III Mild

Jinghong 100.48 22 552.7 19612000 14,394 III MildMengzi 103.23 23.23 1300.7 19612000 14,609 III Mild

Tianshui 105.38 34.36 1368.0 19601966 2280 III ColdXian 108.56 34.18 397.5 19612000 14,601 IV ColdZhengzhou 113.39 34.43 110.4 19612000 14,606 III ColdNanchong 106.05 30.48 297.7 19811990 3652 V HSCWWanhsien 108.21 30.48 432.7 19611967, 19681990 10,743 V HSCWYichang 111.18 30.42 133.1 19612000 14,546 IV HSCWWuhan 114.08 30.37 23.3 19612000 14,578 IV HSCWChongqing 106.28 29.35 259.1 19612000 14,426 V HSCWChangsha 112.55 28.13 68.0 19882000 4749 IV HSCWZunyi 106.55 27.41 849.3 19611990 10,954 V HSCWGuiyang 106.43 26.35 1074.3 19612000 14,608 V MildGuilin 110.18 25.19 194.4 19612000 14,457 IV HSCWGanzhou 114.57 28.52 123.8 19612000 14,244 IV HSCWGushi 115.4 32.1 57.1 19612000 14,518 III HSCWNanjing 118.48 32 8.9 19612000 14,610 IV HSCWHefei 117.14 31.52 27.9 19612000 13,929 IV HSCWBaoshan 121.29 31.24 3.5 19912000 3653 IV HSCW


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n1MBE1/4

n i1/41

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Table 1 (continued)


Station Longitude (, E) Latitude (, N) Altitude (m) Data period Data No. Solar climatezone [27]

Thermal climatezone [26]

Shanghai 121.26 31.1 4.5 19611990 10,957 IV HSCWHangzhou 120.1 30.14 41.7 19612000 14,610 IV HSCWCixi 121.1 30.16 7.1 19611990 10,773 IV HSCWLushan 115.59 29.35 1243.3 19611990 10,957 IV HSCWNanchang 115.55 28.36 46.7 19612000 14,543 IV HSCW

Fuzhou 119.17 26.05 84.0 19612000 14,579 IV HSCWShaoguan 113.36 24.48 68.7 19611990 10,957 IV HSWWGuangzhou 113.19 23.08 6.6 19612000 14,549 IV HSWWShantou 116.41 23.24 1.1 19612000 14,606 IV HSWWNanning 108.21 22.49 73.1 19612000 14,580 IV HSWW

Table 2Models proposed in this study. RMSE1/4

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni1/41Oi ~Ei2 1

nModel No. Models

1 Rs =( a~ Tmax+b~ Tmin+c~Hu m)~R0+ m2 Rs =( a~ Tmax+b~ Tmin)~R0+ c~Hu m)+ m

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 Rs 1/4 a ~ Tmax ~ Tmin b ~Hum ~R0 m

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 Rs 1/4 a ~ Tmax ~ Tmin ~R0 b ~Hum m5a Rs/R0 = a ~ n/N+ m6 Rs=a~ n+b ~R0 + m

a, b, c and m were coefficients. n was the daily actual sunshine duration (h), Nwasthe daily maximum possible sunshine duration (h). R0 was daily extraterrestrialradiation on horizontal surface (MJ m~2 d~1).R0 andNwere calculated by Allen et al. [32] and Liu et al. [33], respectively.a ngstrmPrescott model [8,9].

The data set were randomly divided into a calibrate d dataset (inthis study, 67% of the whole data) and a validation data set (33% ofthe whole data). The calibrated set was used to develop Rs estimat-ing models and the validation set was used to evaluate the models.

The general model for each zone was then developed using thecoefficients of the best performed models and the site geographical

indicators (altitude, latitude, and longitude). Correlations werebuilt between the coefficients of best performed model and thecorrespondi ng site geographical indicators, because someresearchers found that coefficients of estimating models varyingwith latitude and ngsrm coefficients strongly correlate d to lati-tude (or elevation) [34].

2.4. Statistical evaluation

The performance of the models was evaluated in terms of thefollowing statistical indices: root mean square error (RMSE), meanbias error (MBE), coefficient of residual mass (CRM) mean percent-age error (MPE) and percent root mean square error (%RMSE), anindicator of the overall relative accuracy of a model. MBE is an indi-

cation of the average deviation of the estimated values from thecorrespondi ng measured data. A negative value of MBE indicatesthe amount of overestimat ion in the estimated global Rs and viceversa. RMSE provides informat ion on the short term performanc eand is a measure of the variation of estimate d values around themeasured data. Low value of RMSE indicates that the estimationmodel performs well. MPE can be defined as the percentage devi-ation of the estimate d and measured daily solar radiation. CRM de-notes the overall under- or over-estimati on. A positive value ofCRM indicates the tendency of the model to under estimate the Rs,whereas the negative value of CRM shows a tendency to over-estimate solar radiation. In general, a positive MBE (the tendency ofthe model to underestimati on) coincides with a positive CRM andvice versa. While in the same tendency (under- or over-esti-mation),value of RMSE was the conclusive index on the performance of thestudied models in the current study. The five indicators werecalculated as follows:

Oi ~Ei 2

Pni1/41Oi~ Pni1/41Ei


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n1MPE1/4

n i1/41Ei ~ Oi

CRM 1/4 Pn 3i1/41Oi

4Oi

%RMSE1/4RMSEO 100 5

where n was the number of validatio n data of each site; Oi and Eiwas daily observed and estimated Rs, respective ly. was the meanvalue of observed Rs. The indicators were capable for performanc ecompari son between studied models at each zone. For compar isonof model performanc e between solar radiation zones, CRM and%RMSE were fairer than RMSE and MBE, for CRM and %RMSEwere dimens ionless. In this study, model accuracy was consider edexcel-lent when %RMSE < 10%; good if 10% < %RMSE < 20%; fairif 20% < %RMSE < 30%; and poor if %RMSE P 30% [35,36]. Allcalcula-tions were done in SPSS 18.0.

3. Results and discussion

3.1. Solar radiation zones

Five solar radiation zones (Table 3) were obtained by k-meansclustering and shown in Fig. 1, Stations of zone 1 (eight sites)mainly concentr ated in Yunnan province. A total of 21 stations inzone 2 scattered in the upper basin of Yangtze River and YellowRiver. In zone 3, the seven stations distributed in Sichuan Basin,particular ly, along the borders of Yunnan, Sichuan and Chongqingprovince s. And stations of zone 4 occurred in the SE coastal areain the south of 35N. The rest stations belonged to zone 5 andspread in the NE and NW China.

It was clear in Table 3 that zone 2 had abundan t solar resource swith annual averaged daily Rs of 17.406 MJ m~2 d~1, followed aszone 1 which had annual averaged daily Rs of 15.022 MJ m~2 d~1,zone 5 of 14.246 MJ m~2 d~1, zone 4 of 12.362 MJ m~2 d~1 and zone 3of 9.782 MJ m~2 d~1.

Solar radiation zoning in the present study was slightly differ-entfrom the published solar climatic zones using monthly mean daily

clearness sky index [27] and different from the thermal cli-matezones (GB50176-93) [26] (Fig. 1 and Tables 1 and 3). For in-stance,Rs zone 1 in the current study was largely in line with the solarclimate zone III-B [27] and mild climatic zone (GB50176-93)


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Table 3Summary of the five solar radiation zones derived in current study.

143

Zone Stations Station Average RsNo. (MJ m d )

1 Emeishan, Chaotung, Lijiang, Panzhihua, Tengchong, Kunming, Jinghong, Mengzi 8 15.0222 Kuqa, Ruoqiang, Hetian, Kumul, Dunhuang, Jiuquan, Minqin, Gangcha, Golmud, Xining, Erenhot, Haliut, Hohhot, Yinchuan,

Gar, Nakchu, Lhasa, Yushu, Golok, Chamdo, Ganzi21 17.406

3 Chengdu, Nanchong, Wanhsien, Yichang, Chongqing, Zunyi, Guiyang 7 9.782

4 Xian, Wuhan, Changsha, Guilin, Ganzhou, Gushi, Nanjing, Hefei, Baoshan, Shanghai, Hangzhou, Cixi, Lushan, Nanchang,Fuzhou, Shaoguan, Guangzhou, Shantou, Nanning 19 12.362

5 Heihe, Hailaer, Harbin, Altai, Qitai, Yining, Urumchi, Turpan, Kash, Lanzhou, Datong, Taiyuan, Yanan, Anyang, Xilinhot,Tongliao, Changchun, Yenki, Chaoyang, Shenyang, Beijing, Tianjin, Leting, Dalian, Yantai, Jinan, Tianshui, Zhengzhou

28 14.246

Fig. 2. Comparison of daily global Rs of observed, best modeled and general modeled at representative stations of each zone.


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Table 4

Performance of the proposed solar radiation estimation models for mainland China.

Zone Site MBE (MJ m-2d-1) RMSE(MJm-2d-1) CRM MPE %RMSE

M1 M2 M3 M4 M5 M6 GM(T) GM(S) M1 M2 M3 M4 M5 M6 GM(T) GM(S) M1 M2 M3 M4 M5 M6 GM(T) GM(S) M1 M2 M3 M4 M5 M6 GM(T) GM(S) M1 M2 M3 M4 M5 M6 GM(T) GM(S)

1 Emeishan 0.92 1.07 1.19 1.03 0.5 0.65 4.19 0.86 4.56 4.68 4.68 4.91 3.39 3.50 6.11 3.46 0.07 0.08 0.09 0.08 0.0 4 0.05 0 0.07 0.34 0.32 0.3 0.29 0.17 0.18 0.41 0.26 36.02 36.95 36.93 38.78 26.77 27.66 48.22 27.28

Chaotung -0.06 0.11 0.24 0.18 -0.14 -0.2 -0.9 0.31 3.88 3.98 3.89 4.02 2.94 3.02 4.01 3 -0.01 0.01 0.02 0.01 -0.01 -0.02 -0.07 0.02 0.23 0.23 0.19 0.26 0.62 0.68 0.63 0.63 27.9 28.65 28.01 28.92 21.14 21.73 28.84 21.58 Lijiang 0.25 0.18 0.17 0.14 0.41 0.41 -1.26 0.47 3.23 3.27 3.3 3.38 2.26 2.29 3.57 2.29 0.02 0.01 0.01 0.01 0.0 3 0.02 -0.08 0.03 0.44 0.47 0.35 0.42 0 0.01 0.14 -0.01 19.29 19.47 19.67 20.18 13.47 13.66 21.27 13.66 Panzhihua -1.09 -1.01 -0.89 -0.91 -0.72 -0.77 -2.55 -1.38 3.46 3.5 3.5 3.57 1.7 1.78 4.19 2.09 -0.07 -0.07 -0.06 -0.06 -0.05 -0.05 -0.17 -0.09 0.05 0.06 0.0 6 0.07 0.14 0.16 0.44 0.2 22.88 23.19 23.19 23.66 11.24 11.8 27.75 13.81 Tengchong 0.63 1.27 1.05 0.9 0.69 0.68 0.97 0.82 3.51 3.87 3.84 3.92 2.88 2.90 3.67 2.91 0.04 0.08 0.07 0.06 0.0 5 0.05 0.06 0.05 0.29 0.29 0.27 0.29 0.07 0.07 0.25 0.07 23.08 25.46 25.26 25.75 18.95 19.06 24.13 19.1Kunming 0.18 0.47 0.76 0.44 1.35 1.34 -1.17 0.06 3.66 3.91 4.03 4.03 3.02 3.02 3.88 2.69 0.01 0.03 0.05 0.03 0.0 9 0.09 -0.08 0 0.11 0.09 0.0 9 0.12 0.08 0.09 0.73 0.25 24.69 26.38 27.21 27.2 20.38 20.41 26.21 18.13 Jinghong -0.97 -1.11 -0.37 -1.08 0.18 0.23 0.11 0.73 4.61 4.41 5.06 4.53 2.8 2.84 4.69 2.83 -0.06 -0.07 -0.02 -0.07 0.0 1 0.02 0.01 0.05 0.25 0.26 0.23 0.27 0.05 0.06 0.27 0.03 30.4 29.11 33.4 29.89 18.46 18.74 30.93 18.67 Mengzi 0.17 0.16 0.19 0.1 0.31 0.26 -0.47 0.59 3.73 3.8 3.76 3.79 2.68 2.64 3.79 2.78 0.01 0.01 0.01 0.01 0.0 2 0.02 -0.03 0.04 0.3 0.29 0.3 0.28 0.06 0.07 0.25 0.04 24.58 25.04 24.79 24.98 17.65 17.41 25.02 18.32 Mean 0 0.14 0.29 0.1 0.32 0.33 -0.14 0.31 3.83 3.93 4.01 4.02 2.71 2.75 4.24 2.76 0 0.01 0.02 0.01 0.0 2 0.02 -0.05 0.02 0.25 0.25 0.22 0.25 0.15 0.17 0.39 0.18 26.11 26.78 27.31 27.42 18.51 18.81 29.05 18.82

2 Kuqa -1.27 -1.26 -1.11 -1.18 0.13 0.33 -0.16 1.86 3.72 3.71 3.7 3.79 2.21 2.42 3.61 3.06 -0.08 -0.08 -0.07 -0.08 0.0 1 0.02 -0.01 0.12 0.16 0.17 0.15 0.17 0 0.03 0.13 0.01 24.17 24.1 24.02 24.61 14.36 15.68 23.42 19.84

Ruoqiang 0.0 1 0.01 0.11 0.03 -0.01 0.0 9 -0.87 0.51 3.37 3.37 3.45 3.46 2.22 2.36 3.57 2.38 0 0 0.01 0 0 0.01 -0.05 0.03 0.21 0.21 0.2 0.21 0.02 0.03 0.13 0.07 19.86 19.86 20.31 20.38 13.08 13.91 21.07 14.05 Hetian -0.05 0 0.05 -0.05 -1.04 -0.94 0.37 0.1 3.34 3.35 3.35 3.46 2.13 2.22 3.53 2.01 0 0 0 0 -0.07 -0.06 0.02 0.01 0.25 0.26 0.24 0.25 0.38 0.39 0.17 0.12 20.77 20.83 20.87 21.53 13.25 13.82 21.98 12.5Kumul -1 -0.81 -0.66 -0.74 -1.21 -1.10 -0.55 1.27 3.58 3.43 3.21 3.28 3.49 3.45 3.23 2.38 -0.06 -0.05 -0.04 -0.04 -0.07 -0.07 -0.03 0.08 0.09 0.09 0.0 8 0.09 0.19 0.19 0.13 0.03 21.35 20.49 19.2 19.56 20.83 20.6 19.27 14.19 Dunhuang 0.0 1 0.11 0.14 0.1 -0.67 -0.60 -0.51 0.54 3.50 3.49 3.39 3.43 1.99 2.12 3.46 2.10 0 0.01 0.01 0.01 -0.04 -0.03 -0.03 0.03 0.13 0.12 0.12 0.13 0.06 0.07 0.12 0.07 19.94 19.84 19.29 19.52 11.35 12.09 19.71 11.97 Jiuquan -0.28 -0.23 -0.24 -0.25 -0.31 -0.49 -0.70 -0.18 3.38 3.37 3.32 3.41 1.53 1.72 3.53 1.59 -0.02 -0.01 -0.01 -0.02 -0.02 -0.03 -0.04 -0.01 0.18 0.16 0.14 0.15 0.04 0.05 0.14 0.09 20.1 19.99 19.71 20.27 9.09 10.23 20.96 9.42Minqin 1.3 1.23 1.21 1.15 0.37 0.3 -0.65 -0.72 4.26 4.23 4.11 4.16 2.28 2.07 3.98 2.17 0.08 0.07 0.07 0.07 0.0 2 0.02 -0.04 -0.04 0.09 0.08 0.0 8 0.08 0.05 0.05 0.21 0.14 25.16 24.97 24.26 24.58 13.47 12.21 23.48 12.83 Gangcha -1.3 -1.3 -1.13 -1.17 -1.3 -1.34 0.77 -0.11 3.88 3.88 3.86 4.02 2.58 2.54 4.04 2.1 -0.08 -0.08 -0.07 -0.07 -0.08 -0.08 0.04 -0.01 0.09 0.09 0.0 8 0.09 0.19 0.18 0.17 0.16 22.33 22.33 22.24 23.15 14.83 14.62 23.25 12.07

Golmud 2.94 2.7 1.86 1.68 -0.32 -0.29 1 1.09 5.10 5.10 4.03 4.19 1.71 1.85 4.01 2.03 0.17 0.16 0.11 0.10 -0.02 -0.02 0.02 0.06 0.07 0.08 0.0 7 0.08 0.04 0.04 0.05 -0.01 26.55 26.55 20.99 21.79 8.9 9.62 20.85 10.58

Xining-1.26 -1.32 -1.17 -1.20 -0.48 -0.42 -1.43 -1.17 4.19 4.21 4.01 4.11 2.31 2.53 4.22 2.56 -0.08 -0.09 -0.08 -0.08 -0.03 -0.03 -0.09 -0.08 0.03 0.3 0.28 0.31 0.14 0.15 0.44 0.25 27.43 27.57 26.27 26.93 15.16 16.61 27.67 16.8Erenhot -0.59 -0.41 0.01 0.06 -0.56 -0.32 -0.06 0.85 4.69 4.36 6.01 5.26 2.23 2.30 5.84 2.29 -0.03 -0.02 0 0 -0.03 -0.02 0.04 0.05 -0.04 -0.05 0.0 3 0.02 0.07 0.08 0.12 0.05 27.65 25.73 35.48 31.05 13.14 13.58 34.46 13.5

Haliut -0.84 -0.81 -0.66 -0.66 -0.86 -0.8 -0.31 -0.27 3.98 3.94 3.77 3.76 1.85 2.03 3.77 1.66 -0.05 -0.05 -0.04 -0.04 -0.05 -0.05 -0.02 -0.02 0.39 0.4 0.36 0.39 0.08 0.09 0.12 0.08 24.41 24.15 23.11 23.08 11.32 12.44 23.13 10.19

Hohhot -0.56 -0.71 -0.65 -0.68 -0.41 -0.45 -0.04 -0.32 4.24 4.19 4 4.02 2.46 2.57 3.89 2.49 -0.03 -0.04 -0.04 -0.04 -0.02 -0.03 0 -0.02 0.24 0.2 0.28 0.19 0.22 0.21 0.45 0.28 25.23 24.97 23.84 23.93 14.67 15.32 23.16 14.85

Yinchuan -0.58 -0.6 -0.52 -0.51 -0.09 0.0 3 0.18 -0.74 4.02 3.99 3.85 3.93 1.85 2.12 3.96 2.08 -0.04 -0.04 -0.03 -0.03 -0.01 0 0.01 -0.05 0.18 0.16 0.15 0.14 0.18 0.19 0.39 0.3 24.82 24.64 23.81 24.28 11.46 13.08 24.47 12.87 Gar 3.15 3.15 2.93 2.87 1.68 1.87 2.45 0.73 6.69 6.67 6.37 6.31 5.22 5.42 6.13 4.97 0.14 0.14 0.13 0.13 0.0 8 0.09 0.11 0.03 0.46 0.46 0.48 0.5 0.01 0 0.07 0.11 30.48 30.38 29.02 28.74 23.75 24.7 27.89 22.61 Nakchu -1.52 -1.26 -0.87 -0.75 -0.63 -0.48 -1.76 -1.98 6.25 6.18 6.41 6.31 5.36 5.30 6.68 5.79 -0.09 -0.08 -0.05 -0.05 -0.04 -0.03 -0.11 -0.12 0.55 0.58 0.55 0.59 0.17 0.17 0.35 0.24 38.92 38.46 39.91 39.3 33.35 33 41.55 36.02 Lhasa -1.98 -1.92 -1.67 -1.67 -1.73 -1.67 1.02 -1.08 4.26 4.23 4.14 4.15 3.53 3.47 3.94 3.39 -0.10 -0.10 -0.09 -0.09 -0.09 -0.09 0.05 -0.06 -0.04 -0.04 -0.04 -0.04 0.12 0.12 -0.01 0.05 22.21 22.06 21.62 21.65 18.41 18.13 20.56 17.67

Yushu -0.52 -0.39 -0.13 -0.03 -0.55 -0.31 -1.28 -0.48 5.22 5.12 5.64 5.44 2.60 2.58 5.72 2.58 -0.03 -0.02 -0.01 0 -0.03 -0.02 -0.08 -0.03 0.16 0.16 0.14 0.14 0.06 0.06 0.23 0.03 31.48 30.88 33.99 32.84 15.71 15.54 34.48 15.58

Golok -1.17 -1.12 -0.83 -0.8 -0.27 -0.29 -0.41 0.23 3.97 3.86 3.72 3.72 1.78 1.93 3.65 1.89 -0.07 -0.07 -0.05 -0.05 -0.02 -0.02 -0.02 0.01 0.18 0.17 0.18 0.16 0.03 0.03 0.08 -0.01 23.25 22.6 21.77 21.81 10.43 11.29 21.37 11.07 Chamdo -1.69 -1.6 -1.52 -1.51 -1.73 -1.63 -3.17 -1.73 4.35 4.32 4.34 4.38 3.65 3.55 5.19 3.64 -0.11 -0.1 -0.1 -0.1 -0.11 -0.11 -0.20 -0.11 0.13 0.13 0.1 0.1 0.17 0.17 0.33 0.13 28.03 27.83 27.93 28.19 23.5 22.85 33.39 23.46 Ganzi -0.67 -0.67 -0.42 -0.38 0 0 0.37 0.40 3.23 3.23 3.06 3.11 1.64 1.77 3.17 1.97 -0.04 -0.04 -0.02 -0.02 0 0 0.02 0.02 0.21 0.21 0.2 0.2 0.01 0.02 0.03 -0.06 18.3 18.3 17.36 17.62 9.3 10.03 17.94 11.16 Mean -0.37 -0.34 -0.25 -0.27 -0.48 -0.41 -0.27 -0.06 4.25 4.20 4.18 4.18 2.60 2.68 4.24 2.63 -0.02 -0.02 -0.02 -0.02 -0.03 -0.03 -0.02 -0.01 0.19 0.19 0.18 0.19 0.11 0.11 0.18 0.1 24.88 24.6 24.52 24.51 15.21 15.68 24.96 15.39

3 Chengdu -1.33 -1.37 -1.26 -1.40 -0.71 -0.75 -1.32 -0.50 3.34 3.37 3.35 3.57 2.41 2.49 3.56 2.37 -0.16 -0.16 -0.15 -0.16 -0.08 -0.09 -0.15 -0.06 0.09 0.09 0.0 7 0.07 0.62 0.68 0.67 0.8 38.86 39.25 39 41.58 28.06 29 41.48 27.63

Nanchong -0.56 -0.26 -0.34 -0.07 -0.13 -0.12 0.21 0.09 3.51 3.54 3.53 3.74 2.60 2.63 3.53 2.6 -0.06 -0.03 -0.04 -0.01 -0.02 -0.01 0.02 0.01 0.61 0.63 0.48 0.57 0.57 0.64 0.67 0.69 38.44 38.77 38.7 40.98 28.48 28.87 38.74 28.45 Wanh sien -0.7 -0.67 -0.63 -0.7 -0.03 0.0 3 -1.01 -0.51 3.49 3.63 3.58 3.92 2.48 2.51 3.73 2.53 -0.08 -0.07 -0.07 -0.08 0 0 -0.11 -0.05 0.62 0.49 0.49 0.42 0.61 0.71 0.83 0.79 37.36 38.86 38.35 41.98 26.59 26.93 39.97 27.16 Yichang -0.84 -0.85 -0.69 -0.8 -0.03 -0.04 -0.64 0.24 6.64 5.93 6.9 6.06 2.78 2.94 5.97 2.8 -0.08 -0.08 -0.07 -0.08 0 0 -0.06 0.02 0.69 0.72 0.4 0.75 0.69 0.77 0.9 0.68 63.82 56.98 66.33 58.24 26.72 28.26 57.41 26.95 Chongqing 0.0 2 0 0.05 -0.02 0.41 0.36 -0.52 0.04 2.98 3.04 3.13 3.26 2.53 2.5 3.09 2.48 0 0 0.01 0 0.0 5 0.04 -0.06 0.01 0.85 0.61 0.67 0.75 0.66 0.75 0.76 0.81 35.12 35.77 36.84 38.39 29.8 29.47 36.38 29.22 Zunyi -0.73 -0.84 -0.73 -0.97 -0.83 -0.87 -0.89 -0.67 3.11 3.14 3.16 3.43 2.84 2.82 3.21 2.75 -0.09 -0.1 -0.09 -0.11 -0.1 -0.1 -0.11 -0.08 0.49 0.26 0.2 0.09 0.85 0.88 0.63 0.77 36.63 36.96 37.15 40.35 33.39 33.15 37.73 32.32 Guiyang 0.0 9 -0.02 0.12 -0.01 0.78 0.73 0.12 0.73 3.62 3.60 3.86 3.76 3.21 3.21 3.61 3.21 0.01 0 0.01 0 0.0 8 0.08 0.01 0.08 0.34 0.15 0.21 0.09 0.4 0.41 0.48 0.41 37.12 36.95 39.62 38.58 32.96 32.91 37.08 32.95 Mean -0.58 -0.57 -0.5 -0.57 -0.08 -0.09 -0.58 -0.08 3.81 3.75 3.93 3.96 2.69 2.73 3.81 2.68 -0.07 -0.06 -0.06 -0.06 -0.01 -0.01 -0.07 -0.01 0.53 0.42 0.36 0.39 0.63 0.69 0.71 0.71 41.05 40.51 42.28 42.87 29.43 29.8 41.26 29.24

4 Xian -0.67 -0.67 -0.73 -0.83 1 1.19 -1.09 1.15 3.66 3.67 3.68 3.80 3.56 3.75 4.08 3.70 -0.06 -0.06 -0.06 -0.07 0.0 9 0.10 -0.09 0.10 0.5 0.49 0.31 0.38 0.39 0.51 0.88 0.32 31.44 31.49 31.59 32.62 30.55 32.22 35 31.75

Wuha n -1.43 -1.49 -0.98 -1.35 -1.06 -1.02 -0.76 -1.15 4.11 4.23 4.33 4.41 3.02 3.1 4.1 3.05 -0.13 -0.14 -0.09 -0.12 -0.1 -0.09 -0.07 -0.11 0.42 0.4 0.38 0.37 0.64 0.73 0.91 0.76 37.48 38.65 39.51 40.22 27.53 28.31 37.44 27.82

Changsha -0.19 0.20 0.23 0.36 0.50 0.43 0.62 0. 24 3.5 3.61 4.02 3.88 2.94 2.99 3.69 2.90 -0.02 0.02 0.02 0.03 0.0 5 0.04 0.06 0.02 0.68 0.69 0.6 0.68 0.36 0.45 0.45 0.45 32.7 33.75 37.52 36.28 27.43 27.92 34.45 27.06

Guilin -1.04 -0.98 -0.7 -0.88 -0.6 -0.58 -1.65 -0.75 3.97 4.01 4.06 4.12 2.93 2.95 4.20 2.95 -0.10 -0.09 -0.07 -0.08 -0.06 -0.06 -0.16 -0.07 0.77 0.77 0.68 0.72 0.63 0.67 0.83 0.75 37.68 37.99 38.49 39.02 27.76 27.97 39.86 28.01 Ganzhou -0.16 -0.23 -0.05 -0.18 -0.06 0.0 4 -1.08 0.12 3.47 3.45 3.78 3.62 2.26 2.36 3.59 2.26 -0.01 -0.02 0 -0.01 -0.01 0 -0.09 0.01 0.44 0.38 0.39 0.35 0.32 0.34 0.52 0.31 28.51 28.34 31.12 29.79 18.59 19.39 29.54 18.63 Gushi -1.36 -1.74 -0.74 -1.36 -0.31 -0.35 -0.38 0.07 6.64 5.98 7.36 6.78 2.93 3.05 7.02 2.85 -0.11 -0.14 -0.06 -0.11 -0.03 -0.03 -0.03 0.01 0.35 0.23 0.24 0.15 0.25 0.37 0.91 0.31 53.78 48.46 59.66 54.97 23.72 24.71 56.88 23.09 Nanjing -0.89 -0.98 -0.69 -0.85 -0.63 -0.58 -1.43 -0.58 3.81 3.73 3.93 3.86 2.23 2.38 3.87 2.2 -0.08 -0.08 -0.06 -0.07 -0.05 -0.05 -0.12 -0.05 0.97 0.7 1.11 0.82 0.47 0.57 0.84 0.6 32.26 31.58 33.24 32.61 18.87 20.16 32.72 18.57

Hefei -1.03 -1.35 -0.45 -1.07 0.16 0.16 -2.02 -0.37 6.46 5.52 7.27 6.15 2.66 2.79 7.20 2.67 -0.09 -0.12 -0.04 -0.09 0.0 1 0.01 -0.18 -0.03 0.75 0.67 0.69 0.65 0.61 0.8 0.94 0.72 55.91 47.73 62.84 53.16 23.01 24.15 62.31 23.07

Baoshan-

0.37-

0.11

0.28 0.27 0.53 0.54-

0.20

1.03 4.93 4.53 5.01 4.67 2.64 2.71 4.57 2.78-

0.03-

0.01

0.02 0.02 0.0 4 0.05-

0.02

0.09 0.88 0.85 0.7 0.98 0.38 0.48 0.87 0.27 41.08 37.68 41.69 38.9 21.99 22.54 38.03 23.13 Shanghai -1.07 -1.45 -0.84 -1.21 -0.4 -0.37 -1.09 -0.14 4.27 4.16 4.35 4.26 2.34 2.45 4.06 2.3 -0.09 -0.12 -0.07 -0.1 -0.03 -0.03 -0.09 -0.01 0.77 0.56 0.69 0.55 0.34 0.39 0.91 0.37 35.48 34.57 36.16 35.42 19.46 20.36 33.79 19.12 Hangzhou -0.48 -0.6 -0.29 -0.48 0.56 0.57 -2.15 -0.12 4.15 4.06 4.21 4.17 2.95 3.11 4.6 2.89 -0.04 -0.05 -0.03 -0.04 0.0 5 0.05 -0.19 -0.01 0.5 0.49 0.54 0.54 0.39 0.51 0.85 0.49 36 35.23 36.52 36.15 25.62 26.99 39.86 25.07 Cixi -1.18 -1.12 -1.02 -1.1 -0.5 -0.49 -0.34 -0.66 4.86 4.57 4.68 4.56 2.93 2.99 4.44 2.91 -0.1 -0.10 -0.09 -0.09 -0.04 -0.04 -0.03 -0.06 0.54 0.63 0.41 0.57 0.65 0.76 0.9 0.77 40.88 38.42 39.38 38.35 24.64 25.17 37.36 24.48 Lushan -2.17 -2.08 -2.07 -2.09 -1.06 -1 -1.47 -1.07 5.93 5.97 6.4 6.21 3.67 3.73 5.73 3.65 -0.19 -0.18 -0.18 -0.18 -0.09 -0.09 -0.13 -0.09 0.84 0.66 0.72 0.64 0.63 0.68 0.91 0.77 50.51 50.85 54.58 52.95 31.29 31.8 48.89 31.12 Nanchang -1.12 -1.04 -0.89 -0.92 -0.67 -0.67 -0.29 -0.35 4.34 4.36 4.57 4.51 3.35 3.47 4.27 3.29 -0.1 -0.09 -0.08 -0.08 -0.06 -0.06 -0.03 -0.03 0.78 0.79 0.83 0.82 0.65 0.7 0.93 0.81 37.77 37.93 39.71 39.26 29.13 30.15 37.14 28.61 Fuzhou -0.63 -0.59 -0.4 -0.46 0.72 0.73 -3.26 0.59 4.06 4.1 4.32 4.3 3.54 3.56 5.22 3.50 -0.05 -0.05 -0.03 -0.04 0.0 6 0.06 -0.28 0.05 0.74 0.75 0.64 0.66 0.16 0.21 0.73 0.2 34.64 35 36.82 36.67 30.15 30.32 44.55 29.83 Shaoguan -2.26 -2.15 -1.82 -2.01 -1.76 -1.76 -3.47 -1.40 4.29 4.27 4.36 4.37 3.48 3.54 5.03 3.29 -0.21 -0.20 -0.17 -0.19 -0.17 -0.17 -0.33 -0.13 0.25 0.2 0.22 0.18 0.63 0.68 0.85 0.8 40.47 40.24 41.1 41.2 32.83 33.39 47.37 31.03 Guangzhou -1.76 -1.82 -1.3 -1.61 -0.22 -0.14 -2.66 -0.56 5.49 5.09 5.52 5.05 2.61 2.65 6.11 2.68 -0.16 -0.17 -0.12 -0.15 -0.02 -0.01 -0.25 -0.05 0.61 0.71 0.82 0.78 0.42 0.43 0.92 0.45 50.62 46.9 50.84 46.59 24.06 24.4 56.28 24.71 Shantou -1.35 -1.16 -0.51 -0.86 0.04 0.1 1.09 0.26 3.96 4.05 4.24 4.25 2.21 2.3 4.11 2.27 -0.1 -0.08 -0.04 -0.06 0 0.01 1.06 0.02 0.68 0.5 0.65 0.47 0.16 0.16 0.86 0.11 28.66 29.31 30.7 30.74 15.99 16.64 29.73 16.45 Nanning -0.13 -0.06 0.44 0.18 1.1 1.10 0.72 1.11 3.59 3.67 4.06 3.92 3.26 3.32 3.81 3.28 -0.01 0 0.04 0.02 0.0 9 0.09 0.06 0.09 0.33 0.35 0.32 0.35 0.39 0.41 0.49 0.43 28.8 29.42 32.57 31.46 26.14 26.64 30.62 26.3Mean -1.02 -1.02 -0.66 -0.87 -0.14 -0.11 -1.1 -0.14 4.50 4.37 4.74 4.57 2.92 3.01 4.72 2.92 -0.09 -0.09 -0.06 -0.07 -0.01 -0.01 -0.05 -0.01 0.62 0.57 0.58 0.56 0.45 0.52 0.82 0.51 38.67 37.55 40.74 39.28 25.2 25.96 40.62 25.15

5 Heihe -0.34 -0.59 -0.39 -0.55 -0.41 -0.5 -0.74 -0.47 4.01 3.8 3.69 3.68 2.01 2.47 3.70 1.95 -0.03 -0.05 -0.03 -0.05 -0.03 -0.04 -0.06 -0.04 0.03 0.21 0.28 0.28 0.18 0.24 0.63 0.16 33.05 31.28 30.44 30.35 16.6 20.37 30.51 16.09

Hailaer -0.44 -0.41 -0.46 -0.47 -0.63 -0.26 0.42 0.10 4.02 3.89 3.67 3.66 2.15 2.32 3.61 1.96 -0.03 -0.03 -0.03 -0.04 -0.05 -0.02 0.03 0.01 0.56 0.54 0.44 0.51 0.05 0.12 0.35 -0.02 29.97 28.99 27.35 27.31 16.05 17.29 26.94 14.58 Harbin 0.53 0.42 0.62 0.49 0.69 0.92 -0.19 0.37 4.46 4.24 4.21 4.12 2.83 3.18 4.05 2.77 0.04 0.03 0.05 0.04 0.0 5 0.07 -0.01 0.03 0.27 0.25 0.24 0.23 -0.06 0.01 0.37 -0.06 33.97 32.31 32.1 31.35 21.54 24.24 30.85 21.11 Altai -0.53 -0.33 -0.36 -0.38 -0.92 -0.64 0.30 -0.77 4.15 4.03 3.89 3.93 2.24 2.40 4.09 2.19 -0.04 -0.02 -0.03 -0.03 -0.06 -0.04 0.02 -0.05 0.25 0.24 0.21 0.21 0.09 0.16 0.84 0.1 28.05 27.28 26.33 26.58 15.18 16.25 27.64 14.8Qitai -1.52 -1.82 -1.54 -1.66 -1.5 -1.42 -1.39 -1.52 3.77 3.88 3.58 3.7 2.48 2.73 3.60 2.47 -0.12 -0.14 -0.12 -0.13 -0.12 -0.11 -0.11 -0.12 0.36 0.3 0.33 0.32 0.07 0.16 0.86 0.2 29.54 30.39 28.06 28.99 19.41 21.4 28.17 19.31 Yining 0.21 0.15 0.11 0.03 -0.84 -0.8 -0.17 -0.75 4.11 4.01 3.84 3.88 2.37 2.5 3.92 2.34 0.01 0.01 0.01 0 -0.06 -0.05 -0.01 -0.05 0.41 0.39 0.38 0.36 0.06 0.09 0.64 0.26 27.19 26.56 25.4 25.69 15.67 16.54 25.92 15.5Urumchi -0.52 -0.57 -0.53 -0.67 0 0 -0.26 -0.85 4.69 4.38 4.24 4.17 2.14 2.47 4.22 2.31 -0.04 -0.04 -0.04 -0.05 0 0 -0.02 -0.06 0.13 0.13 0.12 0.12 0.11 0.23 0.89 0.12 34.44 32.11 31.1 30.58 15.67 18.11 30.96 16.93 Turpan -0.43 -0.38 -0.31 -0.42 -0.58 -0.45 -2.29 -0.03 5.06 4.93 4.64 4.54 1.89 2.15 5.19 1.79 -0.03 -0.03 -0.02 -0.03 -0.04 -0.03 -0.15 0 0.66 0.53 0.55 0.52 0.03 0.09 0.35 0 33.69 32.81 30.9 30.21 12.57 14.28 34.52 11.91 Kash -1.3 -1.38 -1.17 -1.31 -0.97 -0.98 -0.94 -0.99 4.05 4.08 4 4.11 2.87 3.01 4.02 2.93 -0.09 -0.09 -0.08 -0.09 -0.06 -0.07 -0.06 -0.07 0.30 0.24 0.24 0.22 0.12 0.15 0.22 0.11 26.87 27.09 26.54 27.26 19.02 19.99 26.69 19.45

Lanzhou -1 -0.95 -0.95 -1.03 -0.34 -0.39 -1.59 -1.11 4.3 4.28 4.26 4.4 2.09 2.48 4.55 2.33 -0.07 -0.07 -0.07 -0.07 -0.02 -0.03 -0.11 -0.08 0.57 0.57 0.55 0.6 0.28 0.3 0.75 0.41 30.92 30.76 30.56 31.61 15.01 17.83 32.7 16.71

Datong -1.46 -1.49 -1.41 -1.43 -1.17 -1.02 -1.51 -0.46 4.37 4.3 4.09 4.09 2.44 2.67 4.14 2.12 -0.10 -0.1 -0.1 -0.1 -0.08 -0.07 -0.11 -0.03 0.53 0.51 0.5 0.5 0.21 0.25 0.49 0.11 30.33 29.86 28.42 28.4 16.92 18.51 28.78 14.72


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Lg: longitude (E); La: latitude (N); AL: altitude (m).

(zone 1). Similar to temperat ure-based models, the studied sun-shine-based models underestimate d daily Rs in zone 1 whereasoverestimat ed Rs in zones 25.

In terms of RMSE, model 5 (ngstrmPrescott model) per-formed better than model 6 in all the five zones. Based on %RMSE,models of sunshine based were classified as good (model 5) andfair (model 6). And there were about 75 stations showed fair per-

formances and over half of the studied stations displayed good per-formances. So it could be reasonable to develop sunshine-ba sedgeneral model from model 5. The comparison between measuredand estimated daily Rs from best site-specific model (sunshinebased) at representat ive stations of five Rs zones was also shown inFig. 2.

3.3. General models for different solar radiation zones

3.3.1. General models based on temperaturesModels performed well at individual stations according to the

statistic indicators (Table 4). But these models were site-spec ificin nature. It was questionable when the site-depend ent modelswere applied to locations with different Rs conditions [37]. Sodeveloping a general model for each Rs zone would make asignif-icant sense.

In the present work, a general model for each zone was ob-tained using geographical factors (latitude, longitude and elevationof the stations) and the proposed equation which performed best atthe correspondi ng zone. According to RMSE, MBE, %RMSE andMPE, the proposed model 1 was used to develop the general modelfor zone 1, model 4 for zones 2 and 5, and model 2 for zones 3 and4. The coefficients of the general models were shown in Table 5.The performance of the general models based on temperature s foreach zone was given in Table 4.

Obviously, for the present solar radiation zone, estimated error fromgeneral model (based on temperature s) of zone 2 got lowest errors withmean CRM of-0.02, mean MPE of 0.18 and mean RMSE of 4.24 MJm-2 d-1. Whereas general model of zone 3 yielded high-est errors with

mean CRM of-0.07, mean MPE of 0.71, mean %RMSE of 41.26%,and mean RMSE of 3.81 MJ m-2 d-1.

It was not surprising that the general models, which developed tocater for all the stations within the correspond ing solar radiationzones, had higher values of mean RMSE than the best performedmodel at individua l station (Table 4). This was consisten t with thefinding reported by Lam et al. [28]. In terms of RMSE, the dif-

ferences in the two models (temperature-based) were smaller inzones 2 and 3; best site-specific model had only 1.58% and 1.78% ofRMSE improvem ent to generalized model, respectively. While thedifferences were larger in zones 4 and 1, RMSE of site-spec ificmodel had 8.06% and 10.69% improvement, respectivel y. Theselarge divergences mainly occurred at Emeishan and Panzhihu a sta-tions in zone 1 and Hefei, Fuzhou, Shaoguan and Guangzhou sta-

tions in zone 4. However, there were 21 stations where generalmodels performed better than best site-depend ent models in termsof RMSE. These stations included Kuqa, Kumul, Minqin, Gol-mud,Hohhot, Gar, Lhasa and Golok of zone 2, Nanchong of zone 3,Wuhan, Shanghai, Cixi, Lushan and Nanchang of zone 4, Hailaer,Harbin, Kash, Qitai, Shenyang , Beijing and Tianjin of zone 5.

General model of zone 2 performed best with mean %RMSE of24.96% (fair) and there were 36 stations had fair performances. Bycomparison with published work on daily Rs estimating usingtemperat ures in China, the present general model had satisfactoryaccuracy (RMSE varied between 3.81 and 4.72 MJ m-2 d-1 for Rszones). The RMSE of 16 evaluated temperat ure-based models inChina was 3.55.5 MJ m-2 d-1 [23], and RMSE of daily Rs estimat-ing in Nanchang station was 4.325.16 MJ m-2 d-1 [38].

Fig. 2 showed the correlations between observed and estimated daily Rs from the temperature -based generaliz ed models at therepresentat ive stations of the five zones. Similar fluctuationbehav-iors were also observed between the measured and estimated daily Rs using the best site-depend ent and general models atthese sta-tions. These results indicated that the performanc e ofthe general models should be appreciated.

3.3.2. General models based on sunshine hoursGeneral models based on sunshine hours for all zones, shown in

Table 6, were developed from model 5 and correspond ing site geo-graphic informat ion. Validation results of sunshine-ba sed generalmodels were presented in Table 3. In terms of RMSE, the accuracyof general models for zones 35 had a little advanced (about 0.010.06%) to the best site-specific model (model 5), though the

improvem ent did not show statistic significant. However , general-ized models for zones 1 and 2 did not perform as well as the bestmodel, which was not surprising.

There were 43 stations that generalized model performed as wellas or even better than the best site-specific models: Hetian, Kumul,Minqin, Gangcha, Haliut, Gar, Lhasa, Yushu, Chamdo in zone 2;Chengdu , Nanchong, Chongqing, Zunyi, Guiyang in zone

Table 5

General model and its coefficients based on temperatures for each Rs zone.

Zone Best model Coefficient

1 1 a = 1.1096 x 10-3 xLg+ 1.0339 x 10-3 xLa + 1.1745 x 10-5 xAL - 0.1283b = -2.3259 x 10-3 xLg- 1.6079 x 10-3 x La - 9.9444 x 10-6 xAL + 0.2758

c = 3.0347x

10-4x

Lg+ 4.0910x

10-4x

La-

1.0983x

10-6x

AL-

4.3121x

10-2

m = -0.59 x Lg- 1.3393 xLa + 1.4215 x 10-3 x AL + 100.9627

2 4 a = -2.1810 x 10-4 xLg- 1.9361 x 10-3 x La - 5.0589 x 10-6 xAL + 0.2412b = -1.9195 x 10-3 x Lg- 9.7064 x 10-3 x La - 3.7620 x 10-5 x AL + 0.5739m = 0.1454 x Lg+ 0.8317 xLa + 2.8742 x 10-3 x AL - 45.7067

3 2 a = -3.8086 x 10-3 xLg+ 4.4710 x 10-3 xLa + 2.0595 x 10-5 xAL + 0.2986b = 4.6372 x 10-3 xLg- 4.4339 x 10-3 xLa - 1.8163 x 10-5 xAL - 0.3857c = -1.4080 x 10-2 x Lg+ 5.8467 x 10-2 x La + 2.4218 x 10-4 x AL - 0.5158m = 1.5245 x Lg- 5.3492 x La - 2.4812 x 10-5 xAL + 21.4445

4 2 a = 1.3868 x 10-3 xLg- 1.8841 x 10-3 xLa + 1.3931 x 10-5 x AL - 7.1953 x 10-2b = -1.1416 x 10-3 xLg+ 1.3806 x 10-3 x La - 9.7985 x 10-6 xAL + 7.0315 x 10-2c = -1.1771 x 10-4 x Lg+ 2.4810 x 10-4 x La - 1.1716 x 10-6 x AL + 1.5744 x 10-3m = 0.1741 x Lg+ 4.7798 x 10-2 x La + 2.5133 x 10-3 x AL-11.7621

5 4 a = 2.3949 x 10-4 xLg- 2.5318 x 10-3 xLa - 4.6482 x 10-6 xAL + 0.2242b = -3.7143 x 10-4 xLg- 8.4269 x 10-4 x La + 6.5681 x 10-7 x AL - 1.5521 x 10-2m = -8.5609 x 10-3 x Lg+ 0.3568 x La - 1.2468 x 10-4 x AL - 7.1950


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M.-F. Li et al. / Energy Conversion and Management 70 (2013) 139148 147

Table 6General model and its coefficients based on sunshine hours for each Rs zone.

Zone Best model Coefficient

1 5 a = 3.3411 x 10-3 xLg- 2.5937 x 10-3 xLa + 4.0251 x 10-5 xAL + 0.2394m = -4.0154 x 10-3 xLg- 1.437 x 10-4 xLa + 4.7267 x 10-6 xAL + 0.5809

2 5 a = 5.1597 x 10-3 xLg- 9.0242 x 10-3 xLa + 4.1183 x 10-5 xAL + 0.2754m = -1.6791 x 10-3 x Lg- 2.8984 x 10-3 xLa - 3.1107 x 10-5 xAL + 0.5764

3 5 a = 1.9863 x 10-3 xLg- 4.0733 x 10-3 xLa + 3.7908 x 10-6 xAL + 0.4855

m = -4.0766 x 10-3

xLg+ 7.2451 x 10-3

xLa + 2.2822 x 10-5

x AL + 0.35254 5 a = 3.8595 x 10-3 xLg+ 8.1466 x 10-4 xLa + 1.455 x 10-4 xAL + 0.0953

m = -1.4409 x 10-3 x Lg- 4.8707 x 10-4 xLa - 1.9018 x 10-5 xAL + 0.3285 5 a = 8.7085 x 10-4 xLg+ 1.1277 x 10-3 xLa + 3.4923 x 10-6 xAL + 0.4038

m = -9.9688 x 10-4 xLg+ 2.4799 x 10-3 xLa + 8.3594 x 10-6 x AL + 0.1827

Lg: longitude (E); La: latitude (N); AL: altitude (m).

3; Changsha, Gushi, Nanjing, Shanghai, Hangzhou, Cixi, Lushan,Nanchang, Fuzhou, Shaoguan in zone 4 and Heihe, Hailaer, Harbin,Altai, Qitai, Yining, Turpan, Datong, Taiyuan, Xilinhot, Changchun,Chaoyang, Shenyang, Beijing, Tianjin, Leting, Dalian, Yantai, Jinanin zone 5.

General model based on sunshine hours performed better than thatbased on temperatures. And accordin g to %RMSE, general modelsof zones 2 and 5 were good (%RMSE < 20%) while general modelsof zones 1, 3 and 4 were fair (20% < %RMSE < 30%). For sta-tions,there were 51 stations had good validation results (%RMSE < 20%)based on sunshine general models. Since there was little workfocused on daily Rs estimation for Rs zone in China, the currentresult was compared with Lam et al. [28]. They applied ANN toestimate daily Rs for nine climatic zones [28]. RMSE value yieldedby the current study based on sunshine data was 2.3252.916 MJ m-2d-1 whereas RMSE of ANN model [28] for climatic zones was 1.423.98 MJ m-2 d-1. This indicated that the current general models hadacceptable accuracy in daily Rs estimation for Rs zones in China. Thecomparison between the observed daily Rs and best modeled andgeneral modeled Rs were shown in Fig. 2. The closeness of measuredRs and estimated Rs confirmed the abil-ity of the general model to

estimate daily Rs in mainland China.

4. Conclusions

The long term measured daily global solar radiation, relativehumidity, maximum and minimum temperature s, and sunshinehours from 83 stations in mainland China were collected and ana-lyzed. Five solar radiation zones were identified by k-means clus-tering based on the measured daily mean Rs. Models based ontemperature s and sunshine hours were developed and validated,respectively . According to RMSE, MBE, MPE, %RMSE andCRM, the best model (temperature- and sunshine-ba sed,respectively) for estimating daily Rs was determined . Linearregression between the coefficients of the best site-depend entmodel and the geo-graphical parameters (latitude, longitude andelevation) of the cor-responding station were carried out to developthe general model (temperature- and sunshine -based, respectivel y)for each solar radiation zone. The results showed that the proposedgeneral mod-els for each solar radiation zone should be appreciated.The devel-oped models are useful to estimate solar radiation wheneither temperature and humidity data or sunshine hour data areavailable for the locations in mainland China.

Acknowled gements

The work described in this paper was supported by Chongqin gKey Laborato ry of Digital Agriculture, Southwest University Sci-ence and Technology Innovation Fund for graduate student (No.2010014), the Fundamental Research Funds for the Central Univer-

sities (XDJK2011D001) and Science, and Technolo gy Projects ofChina National Tobacco Corporation (CNTC) Chongqing companies(NY20110601070002).

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