Estimation of monthly average daily solar radiation from measured meteorological data in Yangtze River Basin in China

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. (2012)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/joc.3442

Estimation of monthly average daily solar radiation frommeasured meteorological data in Yangtze River

Basin in China

Ji-Long Chena,b and Guo-Sheng Lia*a Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China

b Graduate University of Chinese Academy of Sciences, Beijing 100039, China

ABSTRACT: Solar radiation is the principal and fundamental energy for many physical, chemical and biological processes.However, it is measured at a very limited number of meteorological stations in the world. Estimation of solar radiationfrom measured meteorological variables offers an important alternative in absence of measured solar radiation. In thiswork, 20 developed models using measured meteorological variables are explored to estimate monthly average dailysolar radiation at 13 stations in Yangtze River Basin in China. Two scenarios are considered. When sunshine duration isavailable, monthly average daily atmospheric water vapor pressure, relative humidity and precipitation do not contributeto the improvement in estimation accuracy of the sunshine-based models. It is therefore unnecessary to take them intoaccount, and the newly developed model 6 is proposed and can provide a good method for the estimation of monthlyaverage daily solar radiation in the study area. If sunshine duration is not available, inclusion of monthly average dailyatmospheric water vapor pressure, relative humidity and multiplication maximum by minimum ambient temperatures cansignificantly improve the estimation accuracy of the temperature-based models. While monthly average daily precipitationdoes not contribute to the improvement in estimation accuracy. And model 20 is proposed and it is more applicable inarea with larger ambient temperature range. Copyright 2012 Royal Meteorological Society

KEY WORDS solar radiation; meteorological variables; models; Yangtze River Basin

Received 31 July 2011; Revised 11 January 2012; Accepted 21 January 2012

1. Introduction

Solar radiation at the earth’s surface is the principaland fundamental energy for many physical, chemical andbiological processes; it is also an important variable tomany models. Despite its significance, it is not widelyavailable because of the cost of measuring equipmentand its difficult maintenance and calibration (Hunt et al.,1998). Only a few meteorological stations measure solarradiation. For example, in America, the ratio of meteoro-logical stations measuring solar radiation relative to thosemeasuring ambient temperature is approximately 1 : 100(NCDC, 1995; Thorton and Running, 1999). In China,more than 2000 stations have records of meteorologicaldata, only 122 stations measure solar radiation. There-fore, developing methods to estimate solar radiation forthe station where no solar radiation is readily availablehas been the focus of many studies.

Major methods including satellite-derived (Pinkeret al., 1995; Olseth and Skartveit, 2001; Senkal, 2010),stochastic algorithm (Richardson, 1981; Hansen, 1999;Wilks and Wilby, 1999), empirical relationship(Angstrom, 1924; Prescott, 1940; Hargreaves et al.,

∗ Correspondence to: G.-S. Li, Institute of Geographic Sciences andNatural Resources Research, Chinese Academy of Sciences, Beijing100101, China. E-mail: [email protected]

1985), interpolation (Hay and Suckling, 1979;D’Agostino and Zelenka, 1992; Rivington et al., 2006)and learning machine method (Tymvios et al., 2005;Lam et al., 2008; Chen et al., 2011) have been devel-oped for the purpose. Among these methods, the empir-ical relationship method using measured meteorologi-cal data is attractive because of the good data avail-ability and simplicity. The well-known sunshine-basedAngstrom–Prescott (A–P) (Angstrom, 1924; Prescott,1940) and ambient temperature-based Hargreaves andSamani (H–S) models (Hargreaves et al., 1985) arewidely used in the word.

A–P model was proposed by Angstrom (1924) and fur-ther modified by Prescott (1940). Since its establishment,several modifications centered on improvement in esti-mation accuracy have been made by adding more addi-tional meteorological variables such as ambient temper-ature range (the difference between maximum and min-imum ambient temperature) (Chen et al., 2004), relativehumidity (Ojosu and Komolafe, 1987; Gopinathan, 1988;Ododo et al., 1995), atmospheric water vapor pressure(Garg and Garg, 1982; Abdalla, 1994;) and precipitation(Ertekin and Yaldiz, 1999; Trabea and Shaltout, 2000).Although some authors claimed that these modified mod-els outperformed the original A–P model, this may notalways be the case in many comparative studies (Kuye

Copyright 2012 Royal Meteorological Society

J.-L. CHEN AND G.-S. LI

and Jagtap, 1994; Ertekin and Yaldiz, 2000; Iziomon andMayer, 2002; Mossad, 2005; Wu et al., 2007). Guey-mard et al. (1995) posed some fundamental questions thatamong these available climatological variables, whichone can significantly influence the relationship betweensolar radiation and sunshine duration. How can the orig-inal A–P model be improved by the climatological vari-ables, and hence be used in lieu of the A–P model, whichseems to have far overreached its predictive limits, andbelieved these research questions remain unanswered.Therefore, more investigation is clearly needed to assessimprovement of such modifications in estimation accu-racy of the original A–P model.

Although it is generally recognized that the sunshine-based models are more accurate than other meteorologicalvariable-based models (Podesta et al., 2004; Trnka et al.,2005), it is often limited since sunshine duration isnot commonly measured as ambient temperature. Inthis context, solar radiation estimation models basedon ambient temperature range are attractive and viableoptions. Hargreaves and Samani (1985) proposed a modelto estimate solar radiation using ambient temperaturerange. Then many other modified formulations weredeveloped and validated in distinct places around theworld. However, the improvement of these modificationslargely depends on the regions. For example, Hunt et al.(1998) introduced precipitation in an additive form thatsignificantly outperformed H–S model, with the averageRMSE decreased from 4.6 to 3.6 MJ m−2 at 8 stationsin Canada. De and Stewart (1993) reported that therevised model by introducing precipitation performedbetter with the correlation coefficient increased from 0.44to 0.57 in western Canada. However, these two modifiedformulations performed worse than the model which usedambient temperature only at 39 stations across Australia(Liu and Scott, 2001). While Manual et al. (2003)reported that models using both ambient temperatureand precipitation, and only temperature gave similarperformances at Hyderabad region of India. Thornton andRunning (1999) presented a formulation using ambienttemperature, relative humidity and atmospheric watervapor pressure, and the new model produced betterresults than the model using ambient temperature onlyat 40 stations over a wide range of climates in America,while this new model returned similar fits and errorswith H–S model in north America (Ball et al., 2004).However, there has been hardly any assessment on suchmodifications to the ambient temperature-based models.Therefore, more investigation, as well as the work forassessing improvement in estimation accuracy of theA–P model, should be carried out in other regions.

Yangtze River Basin is characterized by abundantwater resources, and thus plays significant role in watersupply for agriculture industry, because economy ofmuch of the Yangtze River Basin is focused largely onagricultural production. It is one of the major grain pro-duction areas of China and hence the eco-environmentalmodels and crop growth simulation are widely studied.However, only a few meteorological stations provide

solar radiation recorders, while about 170 stations haverecords of sunshine duration, more than 480 stationsfor ambient temperature, relative humidity, precipitationand atmospheric water vapor pressure. Therefore, solarradiation estimation using these measured meteorologicalvariables is of vital importance and significance. Someworks have reported the validation of the existing sun-shine duration (Lin and Lu, 1999; Chen et al., 2004; Liuet al., 2009) and ambient temperature (Chen et al., 2004,2011; Wu et al., 2007) based models for solar radiationestimation in China. A few revised models were subse-quently developed. Chen et al. (2004) introduced ambienttemperature range to A–P model and claimed a betterresult at 32 stations (10 located in Yangtze River Basin)all over China. While the new model was reported togive similar fit with A–P model at Nanchang station(Wu et al., 2007). In another work, Chen et al. (2006)introduced precipitation in an additive form that had lit-tle higher accuracy than A–P model at 51 (10 located inYangtze River Basin) stations all over China. It is ques-tionable whether it is worthwhile to revise A–P modelby adding more meteorological variables to gain proba-bly negligible accuracy. Moreover, many of the stationsdo not have records of sunshine duration, in this con-text; the ambient temperature-based models are of vitalimportance. However, models using ambient temperatureonly sometimes cannot produce ideal results (Chen et al.,2004). Therefore, how can the ambient temperature-basedmodels be improved by the other available meteorolog-ical variables? The main objectives of this study are(1) to estimate monthly average daily solar radiationusing measured meteorological variables data, includ-ing monthly average daily sunshine duration, maximumand minimum ambient temperatures, relative humidity,atmospheric water vapor pressure and precipitation; (2) toassess the improvement of additional meteorological vari-ables in estimation accuracy of the sunshine duration andambient temperature-based models; and (3) to proposea model selection strategy for solar radiation estimationunder different situations of available meteorological datain Yangtze River Basin. Two scenarios are considered:(1) all of those meteorological data are available and(2) sunshine duration is not available.

2. Materials and methods

2.1. Study area and stations

The current study focuses on the Yangtze River Basin(Figure 1). The Yangtze River, over 6300 km long witha basin area of 180 × 104 km2, is the largest andlongest river in China, and the third longest in the world.The source of the Yangtze River lies to the west ofGeladandong Mountain. The river flows from west toeast, finally emptying into the East China Sea. A largepart of the Yangtze River Basin is subtropical monsoonclimate, with plenty of rainfall all year round. A totalof 13 stations with long-term available records of solarradiation are used in this study. The mapping of stations

Copyright 2012 Royal Meteorological Society Int. J. Climatol. (2012)

SOLAR RADIATION ESTIMATION FROM METEOROLOGICAL VARIABLES

Figure 1. Location of the study meteorological stations in Yangtze River Basin (stations are numbered in compliance with Table I).

Table I. Detail information of the study stations in Yangtze River Basin.

Station ID Station name Latitude (N) Longitude (E) Altitude (m) Calibration period Validation period

1 Chengdu 30.67 104.02 506 1973–1992 1993–20002 Chongqing 29.58 106.47 259 1973–1992 1993–20003 Changsha 28.22 112.92 68 1987–1996 1997–20004 Hefei 31.87 117.23 28 1978–1992 1993–20005 Hangzhou 30.23 120.17 42 1973–1992 1993–20006 Nanchong 30.78 106.10 309 1974–1985 1986–19907 Nanchang 28.60 115.92 47 1973–1991 1993–20008 Nanjing 32.00 118.80 9 1973–1992 1993–20009 Shanghai 31.17 121.43 3 1961–1983 1983–1990

10 Wuhan 30.62 114.13 23 1973–1983 1993–20001985–1992

11 Yichang 30.70 111.30 133 1973–1992 1993–200012 Zunyi 27.7 106.88 844 1973–1984 1985–199013 Guiyang 26.58 106.72 1074 1973–1992 1993–2000

roughly range from 26° to 34° latitude North, from 100° to121° longitude East. Table I shows the temporal periodand the geographical information of the meteorologicalstations.

2.2. Data collection

The monthly average daily solar radiation (MJ m−2), sun-shine duration (h), ambient temperatures (°C) includingmaximum and minimum temperatures, relative humid-ity(%), atmospheric water vapour pressure (kPa) and pre-cipitation (mm) are used in this study. The data wereobtained from the National Meteorological InformationCenter (NMIC), China Meteorological Administration(CMA). The period of records ranges from 6 to 30 yearscovering the period between 1961 and 2000. Quality con-trol tests were conducted by the suppliers. A year withmore than 5 d of missing or faulty data in the same

month was discarded (e.g. the year of 1992 for Nan-chang and the year of 1984 for Wuhan). Two data setswere created for each station. About 70% of the totalrecords were used to calibrate the parameters of mod-els in Table II, and the remainder for evaluation. Thecalibration is achieved by least square regression of thedependent (Rs/Ra) on independent variables to determinethe parameters of the model that best describes the rela-tionship between expected and measured data sets byminimizing the sum of the squared residuals.

2.3. Data description

Figures 2–5 show the distributions of the monthly aver-age daily solar radiation, sunshine duration, maximumand minimum ambient temperature of the study stations,respectively. Generally, monthly average daily solar radi-ation of each station shows the similar change trend with



Table II. General formulas of monthly average daily solar radiation estimation using measured meteorological variables.

Model no. Equationa Parameter

1b Rs = Ra(a1S/So +b) a1, b

2 Rs = Ra(a1S/So +a2(Tmax − Tmin)0.5 + b) a1, a2, b

3 Rs = Ra(a1S/So +a3AP +b) a1, a3, b

4 Rs = Ra(a1S/So +a4RH +b) a1, a4, b

5 Rs = Ra(a1S/So +a5P + b) a1, a5, b

6 Rs = Ra(a1S/So +a6Tmax + a7Tmin + b) a1, a6, a7, b

7 Rs = Ra(a1S/So +a6Tmax + a7Tmin + a3AP +b) a1, a3, a6, a7, b

8 Rs = Ra(a1S/So +a6Tmax + a7Tmin + a4RH +b) a1, a4, a6, a7, b

9 Rs = Ra(a1S/So +a6Tmax + a7Tmin + a5P + b) a1, a5, a6, a7, b

10c Rs = Ra(a2(Tmax − Tmin)0.5 + b) a2, b

11d Rs = Ra(a2ln(Tmax − Tmin) + b) a2, b

12 Rs = Ra(a2(Tmax − Tmin) + b) a2, b

13 Rs = Ra(a2(Tmax − Tmin)0.5 + a3AP +b) a2, a3, b

14 Rs = Ra(a2(Tmax − Tmin)0.5 + a4RH +b) a2, a4, b

15 Rs = Ra(a2(Tmax − Tmin)0.5 + a5P + b) a2, a5, b

16 Rs = Ra(a2(Tmax − Tmin)0.5 + a3AP +a4RH +b) a2, a3, a4, b

17 Rs = Ra(a6Tmax + a7Tmin + b) a6, a7, b

18 Rs = Ra(a6Tmax + a7Tmin + a3AP +a4RH +b) a3, a4, a6, a7, b

19 Rs = Ra(a6Tmax + a7Tmin + a8Tmin × Tmax + b) a6, a7, a8, b

20 Rs = Ra(a6Tmax + a7Tmin + a8Tmin × Tmax + a3AP +a4RH +b) a3, a4, a6, a7, a8, b

a Rs, Ra, S, So, Tmax, Tmin, AP, RH and P are monthly average daily global radiation, extraterrestrial solar radiation, sunshine duration, potentialsunshine duration, maximum ambient temperature, minimum ambient temperature, atmospheric water vapour pressure, relative humidity andprecipitation, respectively.b Angstrom (1924) and Prescott (1940).c Hargreaves et al. (1985).d Chen et al. (2004).

0

1

2

3

4

5

6

7

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Sola

r ra

diat

ion

(kW

m-2

)

changsha

chengdu

chongqing

guiyang

hangzhou

hefei

zunyi

nanchang

nanchong

nanjing

shanghai

wuhan

yichang

Figure 2. Distribution of the monthly average daily solar radiation of the study stations in Yangtze River Basin.

maximum in summer (June, July and August, average16.24 MJ m−2 in July) and minimum in Winter (Decem-ber, January and February, average 5.61 MJ m−2 in Jan-uary). Monthly average daily sunshine duration variesbetween 0.5 and 9 h. Monthly average daily maximumand minimum ambient temperatures have a similar ten-dency with July or August as the warmest month and Jan-uary as the coldest month. Figures 6–8 show the distribu-tions of monthly average daily atmospheric water vapourpressure, relative humidity and precipitation, respec-tively. Monthly average daily atmospheric water vapourpressure, which varies between 85 and 105 kPa, shows

a very similar change trend with maximum in Decemberand minimum in July. The rain mainly occurs in Sum-mer which could account for 36–61% (average 44%)of the annual precipitation. The relative humidity rangesbetween 68 and 90% (averaged 78%). It is obvious thatthe solar radiation and the other measured meteorologicalvariables show a monthly behaviour.

2.4. Method

A total of 20 models using measured meteorological vari-ables are developed and compared in this work (Table II).Model 1 (A–P) was proposed by Angstrom (1924) and



0

2

4

6

8

10


Suns

hine

dur

atio

n (h

)

changsha

chengdu

chongqing

guiyang

hangzhou

hefei

zunyi

nanchang

nanchong

nanjing

shanghai

wuhan

yichang

Figure 3. Distribution of the monthly average daily sunshine duration of the study stations in Yangtze River Basin.

0

8

16

24

32

40


Max

imum

am

bien

t te

mpe

ratu

re(˚

C)

changsha

chengdu

chongqing

guiyang

hangzhou

hefei

zunyi

nanchang

nanchong

nanjing

shanghai

wuhan

yichang

Figure 4. Distribution of the monthly average daily maximum ambient temperature of the study stations in Yangtze River Basin.

-7

0

7

14

21

28

35


Min

imum

am

bien

t te

mpe

ratu

re(˚

C)

changsha

chengdu

chongqingguiyang

hangzhou

hefeizunyi

nanchang

nanchong

nanjingshanghai

wuhan

yichang

Figure 5. Distribution of the monthly average daily minimum ambient temperature of the study stations in Yangtze River Basin.

further modified by Prescott (1940). Models 2–9 aremodifications to model 1 by introducing other meteoro-logical variables. Among the ambient temperature-basemodels (models 10–20), model 10 was developed byHargreaves et al. (1985), and model 11 by Chen et al.(2004). Models 10–16 use ambient temperature range,while models 17–20 maximum and minimum ambienttemperatures. A common feature of these models is that

they account for latitude, solar declination, day lengthand atmospheric transmissivity by including the extrater-restrial radiation (Ra) term in the model, it is calculatedusing the equations detailed by Allen et al. (1998).

Ra = 37.6d(ω sin ϕ sin δ + cos ϕ cos δ sin ω) (1)

d = 1 + 0.033 cos(

2π

365n

)(2)



80

85

90

95

100

105

110


Atm

osph

eric

wat

er v

apor

pre

ssur

e (k

Pa )

changsha

chengdu

chongqing

guiyang

hangzhou

hefei

zunyi

nanchang

nanchong

nanjing

shanghai

wuhan

yichang

Figure 6. Distribution of the monthly average daily atmospheric pressure of the study stations in Yangtze River Basin.

60

68

76

84

92

100


changshachengduchongqingguiyanghangzhouhefeizunyinanchangnanchongnanjingshanghaiwuhanyichang

Rel

ativ

e h

umid

ity (%

)

Figure 7. Distribution of the monthly average daily relative humidity of the study stations in Yangtze River Basin.

0

3

6

9

12


Prec

ipita

tion

(mm

)

changsha

chengdu

chongqing

guiyang

hangzhou

hefei

zunyi

nanchang

nanchong

nanjing

shanghai

wuhan

yichang

Figure 8. Distribution of the monthly average daily precipitation of the study stations in Yangtze River Basin.

δ = 0.4093 sin(

2π

365n − 1.39

)(3)

ω = arccos(− tan ϕ tan δ) (4)

where d is the relative distance between the sun and theearth, ω is sunset hour angle (rad), ϕ is latitude (rad), δ

is solar declination angle (rad), n is the number of theday of year starting from the first of January.

2.5. Performance criteria

To assess the performances of the models, root meansquare error (RMSE), relative root mean square error



(RRMSE) (%) and coefficient of determination (R2) aredetermined. The metric R2 varying between 0 and 1 isadopted to measure the fit of model. RMSE providesinformation on the short-term performance of the correla-tions by allowing a term by term comparison of the actualdeviation between the estimated and measured values.RRMSE is a dimensionless index allowing comparisonsamong a range of different model responses regardless ofunits. RMSE and RRMSE are calculated by the followingequations.

RMSE =

√√√√√√n∑

i=1

(yi − yi )2

n(5)

RRMSE = 100

y

√√√√√√n∑

i=1

(yi − yi )2

n(6)

where n, y, y and y represent the number of testing data,the observed value, the estimated value and the averagevalue of the observation, respectively.

3. Results and discussion

3.1. Performances of models

3.1.1. Sunshine-based models

The parameters and performances of the models arepresented in Tables III and IV, respectively. All thesunshine-based models give good estimation perfor-mances with RMSE < 2.1 MJ m−2 (average 1.157 MJm−2) and RRMSE < 20% (average 10.73%). Models2–5 return similar R2, RMSE and RRMSE with model1. Models 6–9 which include maximum and minimumambient temperatures significantly outperform model 1,while models 7–9 have similar RMSE and RRMSE withmodel 6.

Generally, for empirical modes such as those presentedhere, the more variables a model has, the higher chancethe model gives a better performance. However, in thepresent work, models 2–5 give similar performances withthe simple A–P model. This suggests that monthly aver-age daily ambient temperature range, atmospheric watervapour pressure, relative humidity and precipitation, asintroduced in an additive form, do not adequately accountfor the improvement in estimation accuracy of the A–Pmodel. Our results are different from those reported byChen et al. (2004) who introduced ambient temperaturerange to A–P model and claimed a better performance at48 meteorological stations (10 located in Yangtze RiverBasin) in China, but are consistent with Wu et al. (2007)who compared the revised A–P model by Chen et al.(2004) with the original A–P model at Nanchang stationand reported the similar performances, and also agreewith Chen et al. (2006) who introduced precipitation inan additive form that had little higher accuracy than A–Pmodel at 51 stations (10 located in Yangtze River Basin)all over China.

Models 6–9 show a 1–40% (average 13%) lowerRMSE than model 1, this suggests that inclusion ofmaximum and minimum ambient temperatures can sig-nificantly improve the estimation accuracy of the A–Pmodel. Models 7–9, which are modifications to model6, return similar performances with model 6, furtherconfirming that atmospheric water vapour pressure, rela-tive humidity and precipitation do not contribute to theimprovement in estimation accuracy of the sunshine-based models. Therefore, if all of these meteorologi-cal variables are available, it is unnecessary to takeinto account atmospheric water vapour pressure, rela-tive humidity and precipitation because of the little orno improvement in estimation accuracy of the sunshine-based models, and model 6 is proposed and can providea good method for estimation of monthly average dailysolar radiation with greater accuracy in Yangtze RiverBasin in China.

Table III. Calibrated parameters of the study models.

Station Model 1 Model 2 Model 3 Model 4

a1 b R2 a1 a2 b R2 a1 a3 b R2 a1 a4 b R2

Chengdu 0.550 0.164 0.747 0.414 0.068 0.015 0.775 0.475 −0.020 2.078 0.773 0.520 −0.236 0.366 0.764Chongqing 0.585 0.118 0.867 0.387 0.089 −0.057 0.895 0.499 −0.023 2.363 0.881 0.508 −0.306 0.380 0.878Changsha 0.621 0.125 0.867 0.602 0.015 0.092 0.868 0.576 −0.018 1.907 0.883 0.617 −0.015 0.139 0.867Hefei 0.590 0.103 0.773 0.481 0.065 −0.033 0.788 0.589 −0.001 0.197 0.773 0.541 −0.158 0.244 0.782Hangzhou 0.586 0.117 0.786 0.567 0.013 0.089 0.787 0.574 −0.010 1.113 0.795 0.602 0.059 0.065 0.787Nanchong 0.565 0.157 0.877 0.408 0.077 0.003 0.894 0.497 −0.019 2.006 0.889 0.531 −0.119 0.260 0.880Nanchang 0.579 0.120 0.915 0.559 0.017 0.083 0.915 0.581 0.001 0.043 0.915 0.566 −0.057 0.170 0.916Nanjing 0.536 0.147 0.785 0.518 0.011 0.122 0.786 0.537 0.001 0.017 0.786 0.515 −0.101 0.233 0.790Shanghai 0.565 0.158 0.867 0.512 0.054 0.034 0.882 0.576 0.010 −0.818 0.876 0.535 −0.207 0.335 0.881Wuhan 0.564 0.110 0.771 0.540 0.021 0.060 0.773 0.564 0.000 0.087 0.771 0.555 −0.048 0.151 0.772Yichang 0.594 0.120 0.810 0.603 −0.006 0.133 0.811 0.591 −0.001 0.196 0.811 0.592 −0.014 0.131 0.811Zunyi 0.580 0.131 0.895 0.404 0.086 −0.059 0.923 0.555 −0.011 1.181 0.898 0.549 −0.201 0.298 0.899Guiyang 0.582 0.133 0.870 0.476 0.071 −0.032 0.891 0.586 0.003 −0.099 0.870 0.517 −0.303 0.382 0.887



Table III. (Continued ).

Station Model 5 Model 6 Model 7

a1 a5 b R2 a1 a6 a7 b R2 a1 a6 a7 a3 b R2

Chengdu 0.531 1.46E-03 0.165 0.750 0.293 0.017 −0.014 0.076 0.818 0.293 0.017 −0.014 0.003 −0.241 0.818Chongqing 0.579 8.25E-04 0.117 0.868 0.348 0.018 −0.017 0.044 0.897 0.350 0.017 −0.016 −0.002 0.216 0.897Changsha 0.634 3.30E-03 0.108 0.874 0.475 0.009 −0.006 0.074 0.891 0.459 0.009 −0.005 0.015 −1.497 0.892Hefei 0.578 −1.71E-03 0.112 0.775 0.466 0.012 −0.012 0.053 0.789 0.464 0.012 −0.011 0.006 −0.575 0.789Hangzhou 0.602 1.85E-03 0.104 0.789 0.548 0.003 −0.002 0.100 0.795 0.554 0.002 −0.002 −0.005 0.576 0.795Nanchong 0.553 2.05E-03 0.155 0.880 0.359 0.017 −0.016 0.089 0.897 0.401 0.011 −0.013 −0.027 2.792 0.903Nanchang 0.578 −1.25E-04 0.121 0.915 0.552 0.003 −0.003 0.105 0.915 0.524 0.004 −0.001 0.027 −2.639 0.919Nanjing 0.528 −1.24E-03 0.154 0.788 0.528 0.001 −0.001 0.144 0.787 0.539 0.000 −0.002 −0.011 1.277 0.788Shanghai 0.543 −3.88E-03 0.179 0.878 0.530 0.008 −0.008 0.120 0.883 0.525 0.008 −0.008 0.007 −0.628 0.884Wuhan 0.553 −2.19E-03 0.123 0.777 0.516 0.005 −0.005 0.082 0.774 0.516 0.005 −0.005 0.001 0.006 0.774Yichang 0.596 −7.32E-04 0.121 0.811 0.602 −0.001 0.001 0.126 0.811 0.603 −0.001 0.001 −0.001 0.190 0.811Zunyi 0.574 1.07E-03 0.129 0.896 0.342 0.017 −0.016 0.041 0.929 0.322 0.019 −0.016 0.023 −2.107 0.933Guiyang 0.589 −1.33E-03 0.135 0.872 0.471 0.013 −0.013 0.061 0.891 0.462 0.014 −0.014 0.007 −0.580 0.892



a1 a6 a7 a4 b R2 a1 a6 a7 a5 b R2 a2 b R2

Chengdu 0.313 0.011 −0.008 −0.238 0.305 0.828 0.300 0.016 −0.014 −8.88E-04 0.076 0.818 0.196 −0.227 0.614Chongqing 0.320 0.012 −0.010 −0.244 0.267 0.901 0.325 0.019 −0.016 −3.34E-03 0.037 0.901 0.225 −0.305 0.813Changsha 0.397 0.005 −0.001 −0.353 0.406 0.899 0.467 0.009 −0.006 −5.49E-04 0.076 0.891 0.298 −0.466 0.55Hefei 0.453 0.008 −0.007 −0.166 0.216 0.794 0.461 0.011 −0.010 −1.95E-03 0.067 0.791 0.247 −0.337 0.6Hangzhou 0.502 −0.001 0.002 −0.196 0.283 0.798 0.543 0.003 −0.002 −4.08E-04 0.103 0.795 0.249 −0.33 0.483Nanchong 0.358 0.017 −0.016 −0.013 0.102 0.897 0.374 0.017 −0.016 1.60E-03 0.091 0.897 0.248 −0.312 0.768Nanchang 0.502 0.001 0.001 −0.176 0.268 0.919 0.538 0.004 −0.003 −7.51E-04 0.109 0.916 0.331 −0.507 0.622Nanjing 0.519 −0.001 0.001 −0.128 0.261 0.790 0.520 0.001 −0.001 −1.17E-03 0.150 0.788 0.161 −0.086 0.403Shanghai 0.503 0.007 −0.006 −0.160 0.260 0.886 0.513 0.008 −0.008 −2.35E-03 0.133 0.886 0.229 −0.21 0.405Wuhan 0.512 0.005 −0.004 −0.029 0.109 0.774 0.463 0.006 −0.004 −4.02E-03 0.103 0.784 0.209 −0.238 0.34Yichang 0.596 −0.003 0.004 −0.078 0.198 0.812 0.594 −0.002 0.003 −2.13E-03 0.134 0.813 0.243 −0.344 0.515Zunyi 0.320 0.016 −0.014 −0.178 0.196 0.932 0.321 0.018 −0.015 −3.47E-03 0.039 0.932 0.233 −0.36 0.814Guiyang 0.438 0.010 −0.010 −0.206 0.245 0.897 0.459 0.014 −0.013 −1.36E-03 0.060 0.893 0.253 −0.405 0.643


Station Model 11 Model 12 Model 13 Model 14

a2 b R2 a2 b R2 a2 a3 b R2 a2 a4 b R2

Chengdu 0.036 0.036 0.605 0.261 −0.213 0.617 0.156 −0.037 3.373 0.725 0.213 0.183 −0.422 0.621Chongqing 0.046 −0.037 0.829 0.267 −0.225 0.787 0.197 −0.017 1.483 0.819 0.194 −0.293 0.005 0.821Changsha 0.055 −0.068 0.534 0.392 −0.437 0.559 0.262 −0.051 4.814 0.712 0.221 −0.542 0.18 0.578Hefei 0.043 0.019 0.591 0.353 −0.369 0.605 0.251 −0.015 1.205 0.628 0.237 −0.055 −0.266 0.601Hangzhou 0.046 0.005 0.48 0.332 −0.314 0.482 0.241 −0.013 1.008 0.497 0.218 −0.207 −0.084 0.495Nanchong 0.051 −0.01 0.781 0.301 −0.238 0.747 0.196 −0.028 2.519 0.828 0.241 0.005 −0.301 0.802Nanchang 0.064 −0.082 0.618 0.419 −0.443 0.619 0.312 −0.027 2.32 0.666 0.291 −0.225 −0.226 0.634Nanjing 0.027 0.152 0.399 0.236 −0.121 0.404 0.174 −0.019 1.795 0.454 0.156 −0.036 −0.044 0.403Shanghai 0.042 0.104 0.401 0.312 −0.209 0.407 0.251 −0.024 2.174 0.462 0.207 −0.155 −0.028 0.411Wuhan 0.035 0.071 0.328 0.306 −0.279 0.349 0.244 −0.049 4.621 0.544 0.197 −0.082 −0.138 0.341Yichang 0.044 −0.011 0.511 0.328 −0.337 0.511 0.222 −0.016 1.315 0.536 0.261 0.141 −0.495 0.522Zunyi 0.045 −0.065 0.831 0.292 −0.304 0.786 0.215 −0.02 1.492 0.822 0.215 −0.286 −0.082 0.823Guiyang 0.047 −0.065 0.64 0.336 −0.386 0.64 0.233 −0.03 2.308 0.669 0.203 −0.404 0.041 0.666





a2 a5 b R2 a2 a3 a4 b R2 a6 a7 b R2

Chengdu 0.182 6.56E-03 −0.204 0.702 0.152 −0.037 −0.043 3.486 0.725 0.032 −0.028 0.019 0.757Chongqing 0.229 −1.27E-03 −0.312 0.813 0.146 −0.024 −0.378 2.562 0.832 0.039 −0.036 −0.032 0.844Changsha 0.304 2.11E-03 −0.491 0.553 0.141 −0.058 −0.832 6.474 0.776 0.044 −0.038 −0.075 0.773Hefei 0.255 1.65E-03 −0.364 0.602 0.212 −0.019 −0.212 1.871 0.638 0.043 −0.041 −0.007 0.633Hangzhou 0.237 −3.34E-03 −0.283 0.493 0.105 −0.043 −0.749 5.041 0.576 0.043 −0.041 −0.002 0.525Nanchong 0.231 3.41E-03 −0.284 0.811 0.169 −0.031 −0.152 3.051 0.831 0.041 −0.038 −0.002 0.816Nanchang 0.314 −3.12E-03 −0.448 0.633 0.133 −0.062 −0.856 6.947 0.767 0.056 −0.052 −0.085 0.714Nanjing 0.159 −2.06E-04 −0.082 0.403 0.149 −0.022 −0.203 2.316 0.463 0.031 −0.028 0.098 0.478Shanghai 0.211 −3.86E-03 −0.144 0.415 0.151 −0.054 −0.884 6.138 0.565 0.048 −0.045 0.019 0.506Wuhan 0.211 2.64E-04 −0.244 0.34 0.189 −0.052 −0.377 5.425 0.565 0.041 −0.036 −0.044 0.586Yichang 0.243 2.64E-03 −0.352 0.523 0.211 −0.019 −0.071 1.748 0.536 0.038 −0.035 0.001 0.571Zunyi 0.228 2.12E-03 −0.352 0.817 0.191 −0.023 −0.329 2.099 0.833 0.037 −0.034 −0.049 0.872Guiyang 0.251 3.26E-03 −0.406 0.657 0.151 −0.043 −0.593 4.147 0.714 0.041 −0.036 −0.065 0.748



a3 a4 a6 a7 b R2 a6 a7 a8 b R2 a3 a4 a6 a7 a8 b R2

Chengdu 0.003 −0.138 0.031 −0.025 −0.131 0.761 0.031 −0.032 1.77E-04 0.051 0.768 0.026 −0.287 0.026 −0.031 3.28E-04 −2.209 0.786Chongqing 0.021 −0.472 0.027 −0.021 −1.617 0.863 0.032 −0.042 3.51E-04 0.071 0.871 0.034 −0.314 0.027 −0.033 3.54E-04 −3.062 0.887Changsha 0.063 −0.876 0.016 −0.002 −5.624 0.861 0.044 −0.057 5.37E-04 −0.003 0.843 0.082 −0.474 0.026 −0.027 4.59E-04 −7.841 0.897Hefei 0.031 −0.345 0.031 −0.026 −2.745 0.661 0.045 −0.058 4.52E-04 0.001 0.738 0.051 −0.247 0.037 −0.045 4.78E-04 −4.938 0.771Hangzhou 0.044 −0.905 0.013 −0.003 −3.578 0.674 0.042 −0.053 3.79E-04 0.041 0.588 0.062 −0.678 0.021 −0.021 3.12E-04 −5.694 0.708Nanchong −0.002 −0.128 0.036 −0.033 0.376 0.849 0.036 −0.043 3.02E-04 0.075 0.838 0.013 −0.161 0.031 −0.037 2.83E-04 −1.048 0.869Nanchang 0.035 −0.682 0.025 −0.015 −2.992 0.816 0.052 −0.062 3.76E-04 −0.011 0.759 0.08 −0.432 0.029 −0.031 4.07E-04 −7.731 0.856Nanjing 0.038 −0.391 0.023 −0.017 −3.411 0.521 0.032 −0.041 3.70E-04 0.093 0.569 0.053 −0.331 0.026 −0.031 3.96E-04 −4.999 0.621Shanghai 0.015 −0.925 0.031 −0.023 −0.715 0.639 0.049 −0.065 6.02E-04 0.058 0.706 0.053 −0.418 0.041 −0.051 5.81E-04 −5.028 0.785Wuhan 0.029 −0.425 0.029 −0.021 −2.616 0.616 0.041 −0.053 5.31E-04 −0.005 0.692 0.058 −0.013 0.039 −0.048 5.84E-04 −5.912 0.717Yichang 0.048 −0.148 0.034 −0.025 −4.783 0.609 0.037 −0.045 3.10E-04 0.044 0.605 0.083 0.005 0.037 −0.043 4.83E-04 −8.402 0.678Zunyi 0.041 −0.396 0.032 −0.026 −3.512 0.901 0.035 −0.038 2.11E-04 −0.015 0.882 0.058 −0.282 0.032 −0.033 2.93E-04 −5.176 0.916Guiyang 0.022 −0.471 0.03 −0.024 −1.653 0.793 0.039 −0.046 3.41E-04 −0.025 0.773 0.057 −0.322 0.033 −0.041 4.99E-04 −4.816 0.834

3.1.2. Temperature-based models

Overall, all the ambient temperature-based models pro-duce acceptable results with RMSE < 2.5 MJ m−2

(average 1.658 MJ m−2) and RRMSE < 25% (average15.63%). This result is different with Chen et al. (2004)who reported that models using ambient temperature onlyare not suitable for solar radiation estimation in China.Among the temperature-based models, model 20 usingmonthly average daily maximum and minimum ambienttemperature, relative humidity, atmospheric water vapourpressure and the multiplication maximum by minimumtemperatures gives best performance, with lowest RMSE(average 1.216 MJ m−2) and RRMSE (average 11.6%).

Among the models using ambient temperature rangeonly (models 10–12), model 10 (H–S) was developedby Hargreaves et al. (1985), and model 11 by Chen et al.(2004) who revised H–S model and claimed a betterperformance. However, in the present work, models10–12 have similar R2, RMSE and RRMSE. This resultagrees with Wu et al. (2007) who presented that model10 returned same R2 and RMSE with those of model11 at Nanchang station. These results suggest that thevariations of the ambient temperature range are generallynot very effective and give little or no improvement.

Models 13–15 are modifications to model 10 by addingone meteorological variable only. Model 13 includingmonthly average daily atmospheric water vapour pressureis superior to models 14 and 15 with 1–22% (average8%) lower RMSE than model 10, while model 15including monthly average daily precipitation returnshigher RMSE and RRMSE at 7 stations. Model 16 whichincludes both monthly average daily atmospheric watervapor pressure and relative humidity is superior to model13 with 1–32% (average 14%) higher accuracy thanmodel 10. These results suggest that additional inclusionof monthly average daily atmospheric water vapourpressure and relative humidity can significantly improvethe estimation accuracy of the temperature-based models.However, precipitation does not adequately account forthe improvement in estimation accuracy, and thereforeadditional inclusion of precipitation is unnecessary.

Overall, model 17 significantly outperforms model 10with an average 15% higher accuracy, and at somestations (Changsha, Nanchang, Guiyang and Wuhan), theRMSE could be 22–31% lower, indicating that modelusing maximum and minimum ambient temperaturesis superior to model using ambient temperature range.This is also indicated by the lower RMSE (average13%) of the model 18 than model 16. Model 19 was



Table IV. Estimation accuracy of the study models.

Station Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7

RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RRMSE RRMSE

Chengdu 0.879 10.21% 0.865 10.05% 0.867 10.07% 0.871 10.11% 0.843 9.79% 0.823 9.55% 0.825 9.58%Chongqing 1.169 13.43% 1.170 13.44% 1.169 13.43% 1.182 13.58% 1.139 13.08% 0.712 8.18% 0.711 8.16%Changsha 1.048 9.79% 1.046 9.76% 1.020 9.52% 1.053 9.83% 1.060 9.90% 0.839 7.83% 0.817 7.63%Hefei 1.857 15.24% 1.878 15.41% 1.841 15.10% 1.799 14.76% 1.869 15.33% 1.442 11.83% 1.446 11.87%Hangzhou 1.419 12.15% 1.400 11.98% 1.396 11.95% 1.430 12.25% 1.397 11.96% 1.278 10.94% 1.284 10.99%Nanchong 0.964 10.41% 1.012 10.93% 0.943 10.18% 0.977 10.55% 0.950 10.26% 0.929 10.03% 0.989 10.68%Nanchang 1.173 9.88% 1.166 9.82% 1.183 9.96% 1.202 10.12% 1.178 9.92% 0.774 6.52% 0.745 6.27%Nanjing 0.674 5.66% 0.673 5.64% 0.681 5.71% 0.675 5.66% 0.672 5.64% 0.644 5.40% 0.652 5.47%Shanghai 1.097 9.16% 1.064 8.88% 1.133 9.46% 1.095 9.14% 1.138 9.50% 1.018 8.50% 1.003 8.37%Wuhan 1.348 11.82% 1.371 12.02% 1.350 11.84% 1.334 11.69% 1.386 12.15% 1.321 11.59% 1.321 11.58%Yichang 1.685 15.66% 1.695 15.76% 1.674 15.56% 1.691 15.72% 1.703 15.83% 1.396 12.98% 1.396 12.98%Zunyi 0.965 11.40% 0.968 11.44% 1.004 11.86% 0.985 11.64% 0.960 11.35% 0.927 10.95% 0.929 10.97%Guiyang 2.013 19.89% 1.983 19.59% 1.999 19.75% 2.009 19.84% 2.021 19.97% 1.661 16.41% 1.680 16.59%

Table IV. (Continued ).

Station Model 8 Model 9 Model 10 Model 11 Model 12 Model 13 Model 14

RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RRMSE RRMSE

Chengdu 0.850 9.87% 0.827 9.61% 1.612 9.59% 1.683 10.01% 1.564 9.30% 1.607 9.56% 1.591 9.46%Chongqing 0.717 8.23% 0.749 8.60% 1.322 15.36% 1.321 15.34% 1.336 15.51% 1.266 14.70% 1.267 14.71%Changsha 0.904 8.44% 0.834 7.79% 1.238 14.22% 1.363 15.66% 1.257 13.29% 1.197 13.75% 1.224 14.06%Hefei 1.400 11.49% 1.399 11.48% 2.250 21.01% 2.252 21.03% 2.266 21.16% 1.868 17.44% 2.178 20.33%Hangzhou 1.223 10.47% 1.276 10.92% 2.202 18.07% 2.195 18.01% 2.206 18.10% 1.941 15.92% 2.186 17.93%Nanchong 0.924 9.97% 0.949 10.24% 1.698 18.33% 1.681 18.14% 1.730 18.68% 1.611 17.39% 1.575 17.00%Nanchang 0.744 6.27% 0.766 6.45% 2.017 16.98% 1.997 16.81% 2.048 17.25% 1.794 15.10% 2.006 16.89%Nanjing 0.633 5.31% 0.629 5.28% 1.629 13.67% 1.629 13.67% 1.629 13.67% 1.474 12.36% 1.624 13.62%Shanghai 1.069 8.92% 0.997 8.32% 2.047 17.08% 2.052 17.13% 2.043 17.05% 2.026 16.91% 2.041 17.03%Wuhan 1.304 11.43% 1.329 11.66% 2.479 21.73% 2.495 21.88% 2.459 21.56% 1.921 16.84% 2.411 21.14%Yichang 1.399 13.00% 1.409 13.10% 1.962 18.24% 1.957 18.20% 1.972 18.33% 1.815 16.88% 1.901 17.67%Zunyi 0.963 11.38% 0.960 11.34% 1.176 14.09% 1.239 14.85% 1.142 13.68% 1.166 13.78% 1.193 14.09%Guiyang 1.629 16.09% 1.665 16.45% 2.314 22.86% 2.294 22.66% 2.336 23.08% 2.126 21.00% 2.255 22.27%

Table IV. (Continued ).

Station Model 15 Model 16 Model 17 Model 18 Model 19 Model 20

RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE RMSE RRMSE

Chengdu 1.624 9.66% 1.555 9.25% 1.407 8.37% 1.402 8.34% 1.407 8.37% 1.392 8.28%Chongqing 1.250 14.51% 1.213 14.08% 1.404 16.30% 1.349 15.66% 1.402 16.27% 1.332 15.47%Changsha 1.260 14.47% 1.124 12.91% 1.041 11.95% 0.942 10.82% 0.788 9.05% 0.710 8.15%Hefei 2.261 21.11% 1.680 15.68% 1.664 15.54% 1.321 12.34% 1.164 10.87% 0.955 8.92%Hangzhou 2.208 18.12% 1.830 15.02% 1.871 15.35% 1.664 13.65% 1.594 13.08% 1.452 11.92%Nanchong 1.606 17.33% 1.515 16.35% 1.614 17.42% 1.401 15.12% 1.495 16.13% 1.197 12.92%Nanchang 2.027 17.07% 1.499 12.62% 1.565 13.17% 1.105 9.30% 1.357 11.43% 0.780 6.57%Nanjing 1.628 13.66% 1.445 12.12% 1.376 11.54% 1.241 10.42% 1.090 9.14% 0.911 7.65%Shanghai 2.018 16.84% 1.946 16.24% 2.001 16.02% 2.001 16.70% 1.649 13.76% 1.594 13.31%Wuhan 2.478 21.72% 1.685 14.77% 1.693 14.84% 1.469 12.88% 1.498 13.13% 1.377 12.07%Yichang 1.872 17.40% 1.813 16.86% 1.688 15.69% 1.651 15.35% 1.515 14.09% 1.399 13.00%Zunyi 1.190 14.06% 1.160 13.70% 1.167 13.98% 1.136 13.42% 1.127 13.50% 1.110 13.11%Guiyang 2.151 21.25% 2.006 19.81% 1.781 17.59% 1.736 17.15% 1.674 16.53% 1.672 16.52%

more accurate than model 17 with an average 12%higher accuracy, and at some stations (Nanjing, Nanchangand Changsha), the accuracy could be 20–30% higher,indicating that inclusion of multiplication maximumby minimum temperatures significantly improves theestimation accuracy of the temperature-based models.Model 20 performs best with lowest RMSE (average

1.216 MJ m−2) and RMSE (average 11.6%). It performsmuch better than model 17 with an average 22% higheraccuracy, further confirming that additional inclusionof monthly average daily atmospheric water vapourpressure, relative humidity and multiplication maximumby minimum temperatures can significantly improve theestimation accuracy of the temperature-based models.



3.2. Analyses of influencing factors of model accuracy

The values of RMSE and RRMSE of the proposed mod-els vary considerably from station to station. Conse-quently, the correlation analysis between RMSE, RRMSEand other factors including longitude, latitude, alti-tude, average daily sunshine duration, sunshine ratio,maximum and minimum ambient temperature, temper-ature range, atmospheric water vapour pressure, relativehumidity and precipitation is investigated, and the sum-mary is presented in Table V.

The correlation coefficients show that there is nocorrelation between RMSE of model 6 with these factors.While RRMSE correlates significantly with monthlyaverage daily sunshine duration (r = −0.458, p < 0.05),and sunshine ratio (r = −0.454, p < 0.05), generallyindicating that model 6 is more applicable in area withlonger sunshine duration, and higher sunshine ratio.Also, RMSE of model 20 correlates with none ofthese factors. While RRMSE correlates significantlywith ambient temperature range (r = −0.529, p < 0.05),generally indicating that model 20 is more applicablein areas with larger temperature range. Based on thesecorrelations, climate change may affect the accuracy ofmodel 6 and model 20. For most of our study stations (11stations), sunshine duration and sunshine ratio showeddecreasing trend. Although maximum and minimumambient temperatures showed increasing trend, but thetemperature range showed decreasing trend because theincrease of minimum is larger than that of maximum.This trend is also widely reported globally (Easterlinget al., 1997) and regionally (Liu et al., 2004).

It is noted that RMSE and RRMSE not alwaysshow the same correlation trend with the same factor.RMSE is an absolute measure of fit and site-specific,for example, model 19 gives higher RMSE in Shanghai(1.649 MJ m−2) than that in Nanchong (1.495 MJ m−2),

Table V. Correlation coefficients for model 6 and model 20.

Indicatora Model6 Model20

RMSE RRMSE RMSE RRMSE

Latitude −0.054 −0.080 0.093 −0.126Longitude 0.093 −0.083 0.089 −0.404Altitude 0.006 −0.077 0.253 0.320Tmax −0.147 −0.081 0.044 −0.417Tmin −0.063 0.182 −0.342 −0.391Tmax − Tmin −0.009 −0.328 −0.276 −0.538∗AP −0.015 0.049 −0.242 −0.013RH −0.170 0.190 −0.398 −0.068P −0.051 −0.160 −0.337 −0.343S −0.029 −0.458∗ – –S/So −0.023 −0.454∗ – –

∗ Significant at 0.05 significance level.a Tmax, Tmin, Tmax − Tmin, AP, RH, P, S, So are monthly average dailymaximum temperature, minimum ambient temperature, the differencebetween maximum and minimum temperature, atmospheric watervapour pressure, relative humidity, precipitation, sunshine duration,potential sunshine duration, respectively.

but model 19 actually performs slightly better in Nan-chong than in Shanghai because solar radiation in Shang-hai (average 12.655 MJ m−2) is much higher than that inNanchong (average 9.944 MJ m−2). So, it is suggestedto use RRMSE to measure the model performance whenmake comparisons among different stations.

4. Conclusions

Estimation of solar radiation from measured meteorologi-cal variables offers an important alternative in absence ofmeasured solar radiation. 20 developed models are com-paratively studied and evaluated using monthly averagedaily solar radiation and other measured meteorologicaldata, including monthly average daily sunshine duration,maximum and minimum ambient temperatures, relativehumidity, atmospheric pressure and precipitation at 13stations in Yangtze River Basin in China. The preferredmodels are proposed under two different scenarios. Inthe first scenario, sunshine duration is available. Monthlyaverage daily atmospheric water vapour pressure, rela-tive humidity and precipitation do not contribute to theimprovement in estimation accuracy of A–P model. It istherefore unnecessary to take them into account, and thenewly developed model 6 is proposed and can provide agood method for the estimation of monthly average dailysolar radiation in Yangtze River Basin in China. And itis more applicable in area with longer sunshine duration,and higher sunshine ratio. In the second case, sunshineduration is not available. Inclusion of monthly averagedaily atmospheric water vapour pressure, relative humid-ity and multiplication maximum by minimum temper-atures can significantly improve the estimation accuracyof the temperature-based models. While monthly averagedaily precipitation does not contribute to the improve-ment in estimation accuracy. And model 20 is proposedand it is more applicable in areas with larger temperaturerange. We believe that these models allow widespreadapplication due to the good data availability and accuracyin Yangtze River Basin in China. The principal limita-tion is that they require calibration using measured solarradiation data and it is therefore open to question howtransferable these calibration values are to other locations.Therefore, our future study shall explore solar radiationestimation at the station where no solar radiation is avail-able for calibration the empirical models.

Acknowledgements

The work was supported by the Geological Surveyprogram of China Geological Survey (1212010611402)and Special Fund for Land and Resources Research inthe Public Interest (201111023). We thank the NationalMeteorological Information Center, China Meteorolog-ical Administration for providing the long-term datarecords. Many thanks go to the anonymous reviewers forthe comments on the manuscript.



References

Abdalla YAG. 1994. New correlation of global solar radiation withmeteorological parameters for Bahrain. International Journal ofSolar Energy 16: 111–120.

Allen RG, Pereira LS, Raes D, Smith M. 1998. Crop evapotranspiration-guidelines for computing crop water requirements. FAO Irrigationand Drainage Paper 56. Food and Agriculture Organization of theUnited Nations: Rome.

Angstrom A. 1924. Solar and terrestrial radiation. Quarterly Journal ofthe Royal Meteorological Society 50: 121–126.

Ball RA, Purcell LC, Carey SK. 2004. Evaluation of Solar radiationprediction models in North America. Agronomy Journal 96:391–397.

Chen RS, Ersi K, Yang JP, Lu SH, Zhao WZ. 2004. Validation of fiveglobal radiation models with measured daily data in China. EnergyConversion and Management 45: 1759–1769.

Chen RS, Ersi K, Ji XB, Yang JP, Zhao WZ. 2006. Trends of the globalradiation and sunshine hours in 1961–1998 and their relationshipsin China. Energy Conversion and Management 47: 2859–2866.

Chen JL, Liu HB, Wu W, Xie DT. 2011. Estimation of monthlysolar radiation from measured temperatures using support vectormachines – a case study. Renewable Energy 36(1): 413–420.

De JR, Stewart DW. 1993. Estimating global solar radiation fromcommon meteorological observations in western Canada. CanadianJournal of Plant Science 73: 509–518.

D’Agostino V, Zelenka A. 1992. Supplementing solar radiationnetwork data by co-Kriging with satellite images. InternationalJournal of Climatology 12: 749–761.

Easterling DR, Horton B, Jones PD, Peterson TC, Karl TR, ParkerDE, Salinger MJ, Razuvayev V, Plummer N, Jamason P, FollandCK. 1997. Maximum and minimum temperature trends for the globe.Science 277: 364–367.

Ertekin C, Yaldiz O. 2000. Comparison of some existing modelsfor estimating global solar radiation for Antalya (Turkey). EnergyConversion and Management 41: 311–320.

Ertekin C, Yaldiz O. 1999. Estimation of monthly average daily globalradiation on horizontal surface for Antalya, Turkey. RenewableEnergy 17: 95–102.

Garg HP, Garg ST. 1982. Prediction of global solar radiation frombright sunshine hours and other meteorological parameters. In Solar-India, Proceedings of the National Solar Energy Convention. AlliedPublishers: New Delhi, 1004–1007.

Gopinathan KK. 1988. A general formula for computing the coefficientsof the correlations connecting global solar radiation to sunshineduration. Solar Energy 41: 499–502.

Gueymard C, Jidra P, Eatrada CV. 1995. A critical look at recentinterpretations of the Angstrom approach and its future in globalsolar irradiation prediction. Solar Energy 54: 357–363.

Hansen JW. 1999. Stochastic daily solar irradiance for biologicalmodeling applications. Agricultural and Forest Meteorology 94:53–63.

Hargreaves GL, Hargreaves GH, Riley JP. 1985. Irrigation waterrequirement for Senegal River Basin. Journal of Irrigation andDrainage Engineering: ASCE 111(3): 265–275.

Hargreaves GH, Samani ZA. 1985. Estimating potential evapotranspi-ration. J. Irrig. Drain. Eng: ASCE 108(3): 225–230.

Hay JE, Suckling PW. 1979. An assessment of the net-worksfor measuring and modelling solar radiation in British Columbiaand adjacent areas of western Canada. Canadian Geography 23:222–238.

Hunt LA, Kuchar L, Swanton CJ. 1998. Estimation of solar radiationfor use in crop modeling. Agricultural and Forest Meteorology 91:293–300.

Iziomon MG, Mayer H, 2002. Assessment of some global solarradiation parameterizations. Journal of Atmospheric and TerrestrialPhysics 64: 1631–1643.

Kuye A, Jagtap SS. 1994. Correlation of solar radiation withclimatological data for Port Harcourt, Nigeria. International Journalof Climatology 14: 815–825.

Lam JC, Wan KKW, Yang L. 2008. Solar radiation modeling usingANNs for different climates in China. Energy Conversion andManagement 49(5): 1080–1090.

Lin WX, Lu ER. 1999. Validation of eight sunshine-based globalradiation models with measured data at seven places in YunnanProvince, China. Energy Conversion and Management 40: 519–525.

Liu DL, Scott BJ. 2001. Estimation of solar radiation in Australiafrom rainfall and temperature observations. Agricultural and ForestMeteorology 106: 41–59.

Liu BH, Xu M, Henderson M, Qi Y, Li YQ. 2004. Taking China’stemperature: daily range, warming trends, and regional variations,1955–2000. Journal of Climate 17: 4453–4462.

Liu XY, Mei XR, Li YZ, Zhang YQ, Wang QS, 2009. Calibration ofthe Angstrom–Prescott coefficients (a, b) under different time scalesand their impacts in estimating global solar radiation in the YellowRiver basin. Agricultural and Forest Meteorology 149: 697–710.

Manual UK, Victor US, Rao KV, Srivastava NN, Vittal KPR.2003. Estimation of solar radiation from temperature and rainfallobservations. Journal of Agromeleorology 5(2): 15–26.

Mossad EM. 2005. Sunshine and global solar radiation estimation atdifferent sites in Egypt. Journal of Atmospheric and Solar-TerrestrialPhysics 67: 1331–1342.

NCDC (National Climatic Data Center). 1995. Cooperative summary ofthe day, dataset TD 3200. U.S. Department of Commerce, NationalOceanographic and Atmospheric Administration, National ClimaticData Center, Asheville, NC.

Ododo JC, Sulaiman AT, Aidan J, Yguda MM, Ogbu FA. 1995. Theimportance of maximum air temperature in the parameterization ofsolar radiation in Nigeria. Renewable Energy 6: 751–763.

Ojosu JO, Komolafe LK. 1987. Models for estimating solar radiationavailability in South Western Nigeria. Nigerian Journal of SolarEnergy 6: 69–77.

Olseth A, Skartveit A. 2001. Solar irradiance, sunshine durationand daylight illuminance derived from METEOSAT data forsome European sites. Theoretical and Applied Climatology 69:239–252.

Pinker RT, Frouin R, Li Z. 1995. A review of satellite methods toderive shortwave irradiance. Remote Sensing of Environment 51:108–124.

Podesta GP, Nunez L, Villanueva CA, Skansi MA. 2004. Estimatingdaily solar radiation in the Argentine Pampas. Agricultural andForest Meteorology 123: 41–53.

Prescott JA. 1940. Evaporation from a water surface in relation to solarradiation. Transactions of The Royal Society of South Australia 64:114–118.

Richardson CW. 1981. Stochastic simulation of daily precipitation,temperature, and solar radiation. Water Resources Research 17:182–190.

Rivington M, Matthews KB, Bellocchi G, Buchan K. 2006. Evaluatinguncertainty introduced to process-based simulation model estimatesby alternative sources of meteorological data. Agricultural Systems88: 451–471.

Senkal O. 2010. Modeling of solar radiation using remote sensing andartificial neural network in Turkey. Energy 35(12): 4795–4801.

Thornton PE, Running SW. 1999. An improved algorithm forestimating incident daily solar radiation from measurements oftemperature, humidity, and precipitation. Agricultural and ForestMeteorology 93: 211–228.

Trabea AA, Shaltout MAM. 2000. Correlation of global solar radiationwith meteorological parameters over Egypt. Renewable Energy 21:297–308.

Trnka M, Zalud Z, Eitzinger J, Dubrovsky M. 2005. Global solarradiation in Central European lowlands estimated by variousempirical formulae. Agricultural and Forest Meteorology 131:54–76.

Tymvios FS, Jacovides CP, Michaelides SC, Scouteli C. 2005.Comparative study of Angstrom’s and artificial neural network’smethodologies in estimating global solar radiation. Solar Energy 78:752–762.

Wilks DS, Wilby RL. 1999. The weather generation game: a reviewof stochastic weather models. Progress in Physical Geography 23:329–357.

Wu GF, Liu YL, Wang TJ. 2007. Methods and strategy for modelingdaily global solar radiation with measured meteorological data – acase study in Nanchang station, China. Energy Conversion andManagement 48: 2447–2452.


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Estimation of monthly average daily solar radiation from measured meteorological data in Yangtze River Basin in China