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

Authors

  • Ji-Long Chen,

    1. Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
    2. Graduate University of Chinese Academy of Sciences, Beijing 100039, China
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  • Guo-Sheng Li

    Corresponding author
    1. Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
    • Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China.
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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 radiation from measured meteorological variables offers an important alternative in absence of measured solar radiation. In this work, 20 developed models using measured meteorological variables are explored to estimate monthly average daily solar radiation at 13 stations in Yangtze River Basin in China. Two scenarios are considered. When sunshine duration is available, monthly average daily atmospheric water vapor pressure, relative humidity and precipitation do not contribute to the improvement in estimation accuracy of the sunshine-based models. It is therefore unnecessary to take them into account, and the newly developed model 6 is proposed and can provide a good method for the estimation of monthly average daily solar radiation in the study area. If sunshine duration is not available, inclusion of monthly average daily atmospheric water vapor pressure, relative humidity and multiplication maximum by minimum ambient temperatures can significantly improve the estimation accuracy of the temperature-based models. While monthly average daily precipitation does not contribute to the improvement in estimation accuracy. And model 20 is proposed and it is more applicable in area with larger ambient temperature range. Copyright © 2012 Royal Meteorological Society

1. Introduction

Solar radiation at the earth's surface is the principal and fundamental energy for many physical, chemical and biological processes; it is also an important variable to many models. Despite its significance, it is not widely available because of the cost of measuring equipment and its difficult maintenance and calibration (Hunt et al., 1998). Only a few meteorological stations measure solar radiation. For example, in America, the ratio of meteorological stations measuring solar radiation relative to those measuring ambient temperature is approximately 1:100 (NCDC, 1995; Thorton and Running, 1999). In China, more than 2000 stations have records of meteorological data, only 122 stations measure solar radiation. Therefore, developing methods to estimate solar radiation for the station where no solar radiation is readily available has been the focus of many studies.

Major methods including satellite-derived (Pinker et al., 1995; Olseth and Skartveit, 2001; Şenkal, 2010), stochastic algorithm (Richardson, 1981; Hansen, 1999; Wilks and Wilby, 1999), empirical relationship (Ångström, 1924; Prescott, 1940; Hargreaves et al., 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 developed for the purpose. Among these methods, the empirical relationship method using measured meteorological data is attractive because of the good data availability and simplicity. The well-known sunshine-based Ångström–Prescott (A–P) (Ångström, 1924; Prescott, 1940) and ambient temperature-based Hargreaves and Samani (H–S) models (Hargreaves et al., 1985) are widely used in the word.

A–P model was proposed by Ångström (1924) and further modified by Prescott (1940). Since its establishment, several modifications centered on improvement in estimation accuracy have been made by adding more additional meteorological variables such as ambient temperature range (the difference between maximum and minimum ambient temperature) (Chen et al., 2004), relative humidity (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 models outperformed the original A–P model, this may not always be the case in many comparative studies (Kuye and Jagtap, 1994; Ertekin and Yaldiz, 2000; Iziomon and Mayer, 2002; Mossad, 2005; Wu et al., 2007). Gueymard et al. (1995) posed some fundamental questions that among these available climatological variables, which one can significantly influence the relationship between solar radiation and sunshine duration. How can the original A–P model be improved by the climatological variables, and hence be used in lieu of the A–P model, which seems to have far overreached its predictive limits, and believed these research questions remain unanswered. Therefore, more investigation is clearly needed to assess improvement of such modifications in estimation accuracy of the original A–P model.

Although it is generally recognized that the sunshine-based models are more accurate than other meteorological variable-based models (Podestá et al., 2004; Trnka et al., 2005), it is often limited since sunshine duration is not commonly measured as ambient temperature. In this context, solar radiation estimation models based on ambient temperature range are attractive and viable options. Hargreaves and Samani (1985) proposed a model to estimate solar radiation using ambient temperature range. Then many other modified formulations were developed and validated in distinct places around the world. However, the improvement of these modifications largely depends on the regions. For example, Hunt et al. (1998) introduced precipitation in an additive form that significantly outperformed H–S model, with the average RMSE decreased from 4.6 to 3.6 MJ m−2 at 8 stations in Canada. De and Stewart (1993) reported that the revised model by introducing precipitation performed better with the correlation coefficient increased from 0.44 to 0.57 in western Canada. However, these two modified formulations performed worse than the model which used ambient temperature only at 39 stations across Australia (Liu and Scott, 2001). While Manual et al. (2003) reported that models using both ambient temperature and precipitation, and only temperature gave similar performances at Hyderabad region of India. Thornton and Running (1999) presented a formulation using ambient temperature, relative humidity and atmospheric water vapor pressure, and the new model produced better results than the model using ambient temperature only at 40 stations over a wide range of climates in America, while this new model returned similar fits and errors with H–S model in north America (Ball et al., 2004). However, there has been hardly any assessment on such modifications to the ambient temperature-based models. Therefore, more investigation, as well as the work for assessing improvement in estimation accuracy of the A–P model, should be carried out in other regions.

Yangtze River Basin is characterized by abundant water resources, and thus plays significant role in water supply for agriculture industry, because economy of much of the Yangtze River Basin is focused largely on agricultural production. It is one of the major grain production areas of China and hence the eco-environmental models and crop growth simulation are widely studied. However, only a few meteorological stations provide solar radiation recorders, while about 170 stations have records of sunshine duration, more than 480 stations for ambient temperature, relative humidity, precipitation and atmospheric water vapor pressure. Therefore, solar radiation estimation using these measured meteorological variables is of vital importance and significance. Some works have reported the validation of the existing sunshine duration (Lin and Lu, 1999; Chen et al., 2004; Liu et al., 2009) and ambient temperature (Chen et al., 2004, 2011; Wu et al., 2007) based models for solar radiation estimation in China. A few revised models were subsequently developed. Chen et al. (2004) introduced ambient temperature range to A–P model and claimed a better result at 32 stations (10 located in Yangtze River Basin) all over China. While the new model was reported to give 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 little higher accuracy than A–P model at 51 (10 located in Yangtze River Basin) stations all over China. It is questionable whether it is worthwhile to revise A–P model by adding more meteorological variables to gain probably negligible accuracy. Moreover, many of the stations do not have records of sunshine duration, in this context; the ambient temperature-based models are of vital importance. However, models using ambient temperature only sometimes cannot produce ideal results (Chen et al., 2004). Therefore, how can the ambient temperature-based models be improved by the other available meteorological variables? The main objectives of this study are (1) to estimate monthly average daily solar radiation using measured meteorological variables data, including monthly average daily sunshine duration, maximum and minimum ambient temperatures, relative humidity, atmospheric water vapor pressure and precipitation; (2) to assess the improvement of additional meteorological variables in estimation accuracy of the sunshine duration and ambient temperature-based models; and (3) to propose a model selection strategy for solar radiation estimation under different situations of available meteorological data in 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 with a basin area of 180 × 104 km2, is the largest and longest river in China, and the third longest in the world. The source of the Yangtze River lies to the west of Geladandong Mountain. The river flows from west to east, finally emptying into the East China Sea. A large part of the Yangtze River Basin is subtropical monsoon climate, with plenty of rainfall all year round. A total of 13 stations with long-term available records of solar radiation are used in this study. The mapping of stations roughly range from 26° to 34° latitude North, from 100° to 121° longitude East. Table I shows the temporal period and the geographical information of the meteorological stations.

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 IDStation nameLatitude (N)Longitude (E)Altitude (m)Calibration periodValidation period
1Chengdu30.67104.025061973–19921993–2000
2Chongqing29.58106.472591973–19921993–2000
3Changsha28.22112.92681987–19961997–2000
4Hefei31.87117.23281978–19921993–2000
5Hangzhou30.23120.17421973–19921993–2000
6Nanchong30.78106.103091974–19851986–1990
7Nanchang28.60115.92471973–19911993–2000
8Nanjing32.00118.8091973–19921993–2000
9Shanghai31.17121.4331961–19831983–1990
10Wuhan30.62114.13231973–19831993–2000
     1985–1992 
11Yichang30.70111.301331973–19921993–2000
12Zunyi27.7106.888441973–19841985–1990
13Guiyang26.58106.7210741973–19921993–2000

2.2. Data collection

The monthly average daily solar radiation (MJ m−2), sunshine duration (h), ambient temperatures ( °C) including maximum and minimum temperatures, relative humidity(%), atmospheric water vapour pressure (kPa) and precipitation (mm) are used in this study. The data were obtained from the National Meteorological Information Center (NMIC), China Meteorological Administration (CMA). The period of records ranges from 6 to 30 years covering the period between 1961 and 2000. Quality control tests were conducted by the suppliers. A year with more than 5 d of missing or faulty data in the same month was discarded (e.g. the year of 1992 for Nanchang and the year of 1984 for Wuhan). Two data sets were created for each station. About 70% of the total records were used to calibrate the parameters of models in Table II, and the remainder for evaluation. The calibration is achieved by least square regression of the dependent (Rs/Ra) on independent variables to determine the parameters of the model that best describes the relationship between expected and measured data sets by minimizing the sum of the squared residuals.

Table II. General formulas of monthly average daily solar radiation estimation using measured meteorological variables
Model no.EquationaParameter
  • a

    Rs, Ra, S, So, Tmax, Tmin, AP, RH and P are monthly average daily global radiation, extraterrestrial solar radiation, sunshine duration, potential sunshine duration, maximum ambient temperature, minimum ambient temperature, atmospheric water vapour pressure, relative humidity and precipitation, respectively.

  • b

    Ångström (1924) and Prescott (1940).

  • c

    Hargreaves et al. (1985).

  • d

    Chen et al. (2004).

1bRs = Ra(a1S/So + b)a1, b
2Rs = Ra(a1S/So + a2(TmaxTmin)0.5 + b)a1, a2, b
3Rs = Ra(a1S/So + a3AP + b)a1, a3, b
4Rs = Ra(a1S/So + a4RH + b)a1, a4, b
5Rs = Ra(a1S/So + a5P + b)a1, a5, b
6Rs = Ra(a1S/So + a6Tmax + a7Tmin + b)a1, a6, a7, b
7Rs = Ra(a1S/So + a6Tmax + a7Tmin + a3AP + b)a1, a3, a6, a7, b
8Rs = Ra(a1S/So + a6Tmax + a7Tmin + a4RH + b)a1, a4, a6, a7, b
9Rs = Ra(a1S/So + a6Tmax + a7Tmin + a5P + b)a1, a5, a6, a7, b
10cRs = Ra(a2(TmaxTmin)0.5 + b)a2, b
11dRs = Ra(a2ln(TmaxTmin) + b)a2, b
12Rs = Ra(a2(TmaxTmin) + b)a2, b
13Rs = Ra(a2(TmaxTmin)0.5 + a3AP + b)a2, a3, b
14Rs = Ra(a2(TmaxTmin)0.5 + a4RH + b)a2, a4, b
15Rs = Ra(a2(TmaxTmin)0.5 + a5P + b)a2, a5, b
16Rs = Ra(a2(TmaxTmin)0.5 + a3AP + a4RH + b)a2, a3, a4, b
17Rs = Ra(a6Tmax + a7Tmin + b)a6, a7, b
18Rs = Ra(a6Tmax + a7Tmin + a3AP + a4RH + b)a3, a4, a6, a7, b
19Rs = Ra(a6Tmax + a7Tmin + a8Tmin × Tmax + b)a6, a7, a8, b
20Rs = Ra(a6Tmax + a7Tmin + a8Tmin × Tmax + a3AP + a4RH + b)a3, a4, a6, a7, a8, b

2.3. Data description

Figures 2–5 show the distributions of the monthly average daily solar radiation, sunshine duration, maximum and minimum ambient temperature of the study stations, respectively. Generally, monthly average daily solar radiation of each station shows the similar change trend with maximum in summer (June, July and August, average 16.24 MJ m−2 in July) and minimum in Winter (December, January and February, average 5.61 MJ m−2 in January). Monthly average daily sunshine duration varies between 0.5 and 9 h. Monthly average daily maximum and minimum ambient temperatures have a similar tendency with July or August as the warmest month and January as the coldest month. Figures 6–8 show the distributions of monthly average daily atmospheric water vapour pressure, relative humidity and precipitation, respectively. Monthly average daily atmospheric water vapour pressure, which varies between 85 and 105 kPa, shows a very similar change trend with maximum in December and minimum in July. The rain mainly occurs in Summer which could account for 36–61% (average 44%) of the annual precipitation. The relative humidity ranges between 68 and 90% (averaged 78%). It is obvious that the solar radiation and the other measured meteorological variables show a monthly behaviour.

Figure 2.

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

Figure 3.

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

Figure 4.

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

Figure 5.

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

Figure 6.

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

Figure 7.

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

Figure 8.

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

2.4. Method

A total of 20 models using measured meteorological variables are developed and compared in this work (Table II). Model 1 (A–P) was proposed by Ångström (1924) and further modified by Prescott (1940). Models 2–9 are modifications to model 1 by introducing other meteorological variables. Among the ambient temperature-base models (models 10–20), model 10 was developed by Hargreaves 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 ambient temperatures. A common feature of these models is that they account for latitude, solar declination, day length and atmospheric transmissivity by including the extraterrestrial radiation (Ra) term in the model, it is calculated using the equations detailed by Allen et al. (1998).

equation image(1)
equation image(2)
equation image(3)
equation image(4)

where d is the relative distance between the sun and the earth, ω is sunset hour angle (rad), φ is latitude (rad), δ is solar declination angle (rad), n is the number of the day of year starting from the first of January.

2.5. Performance criteria

To assess the performances of the models, root mean square error (RMSE), relative root mean square error (RRMSE) (%) and coefficient of determination (R2) are determined. The metric R2 varying between 0 and 1 is adopted to measure the fit of model. RMSE provides information on the short-term performance of the correlations by allowing a term by term comparison of the actual deviation between the estimated and measured values. RRMSE is a dimensionless index allowing comparisons among a range of different model responses regardless of units. RMSE and RRMSE are calculated by the following equations.

equation image(5)
equation image(6)

where n, y, ŷ and ȳ represent the number of testing data, the observed value, the estimated value and the average value 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 are presented in Tables III and IV, respectively. All the sunshine-based models give good estimation performances with RMSE < 2.1 MJ m−2 (average 1.157 MJ m−2) and RRMSE < 20% (average 10.73%). Models 2–5 return similar R2, RMSE and RRMSE with model 1. Models 6–9 which include maximum and minimum ambient temperatures significantly outperform model 1, while models 7–9 have similar RMSE and RRMSE with model 6.

Table III. Calibrated parameters of the study models
StationModel 1Model 2Model 3Model 4
 a1bR2a1a2bR2a1a3bR2a1a4bR2
Chengdu0.5500.1640.7470.4140.0680.0150.7750.475− 0.0202.0780.7730.520− 0.2360.3660.764
Chongqing0.5850.1180.8670.3870.089− 0.0570.8950.499− 0.0232.3630.8810.508− 0.3060.3800.878
Changsha0.6210.1250.8670.6020.0150.0920.8680.576− 0.0181.9070.8830.617− 0.0150.1390.867
Hefei0.5900.1030.7730.4810.065− 0.0330.7880.589− 0.0010.1970.7730.541− 0.1580.2440.782
Hangzhou0.5860.1170.7860.5670.0130.0890.7870.574− 0.0101.1130.7950.6020.0590.0650.787
Nanchong0.5650.1570.8770.4080.0770.0030.8940.497− 0.0192.0060.8890.531− 0.1190.2600.880
Nanchang0.5790.1200.9150.5590.0170.0830.9150.5810.0010.0430.9150.566− 0.0570.1700.916
Nanjing0.5360.1470.7850.5180.0110.1220.7860.5370.0010.0170.7860.515− 0.1010.2330.790
Shanghai0.5650.1580.8670.5120.0540.0340.8820.5760.010− 0.8180.8760.535− 0.2070.3350.881
Wuhan0.5640.1100.7710.5400.0210.0600.7730.5640.0000.0870.7710.555− 0.0480.1510.772
Yichang0.5940.1200.8100.603− 0.0060.1330.8110.591− 0.0010.1960.8110.592− 0.0140.1310.811
Zunyi0.5800.1310.8950.4040.086− 0.0590.9230.555− 0.0111.1810.8980.549− 0.2010.2980.899
Guiyang0.5820.1330.8700.4760.071− 0.0320.8910.5860.003− 0.0990.8700.517− 0.3030.3820.887
StationModel 5Model 6Model 7
 a1a5bR2a1a6a7bR2a1a6a7a3bR2
Chengdu0.531− 1.46E-030.1650.7500.2930.017− 0.0140.0760.8180.2930.017− 0.0140.003− 0.2410.818
Chongqing0.579− 8.25E-040.1170.8680.3480.018− 0.0170.0440.8970.3500.017− 0.016− 0.0020.2160.897
Changsha0.634− 3.30E-030.1080.8740.4750.009− 0.0060.0740.8910.4590.009− 0.0050.015− 1.4970.892
Hefei0.578− 1.71E-030.1120.7750.4660.012− 0.0120.0530.7890.4640.012− 0.0110.006− 0.5750.789
Hangzhou0.602− 1.85E-030.1040.7890.5480.003− 0.0020.1000.7950.5540.002− 0.002− 0.0050.5760.795
Nanchong0.553− 2.05E-030.1550.8800.3590.017− 0.0160.0890.8970.4010.011− 0.013− 0.0272.7920.903
Nanchang0.578− 1.25E-040.1210.9150.5520.003− 0.0030.1050.9150.5240.004− 0.0010.027− 2.6390.919
Nanjing0.528− 1.24E-030.1540.7880.5280.001− 0.0010.1440.7870.5390.000− 0.002− 0.0111.2770.788
Shanghai0.543− 3.88E-030.1790.8780.5300.008− 0.0080.1200.8830.5250.008− 0.0080.007− 0.6280.884
Wuhan0.553− 2.19E-030.1230.7770.5160.005− 0.0050.0820.7740.5160.005− 0.0050.0010.0060.774
Yichang0.596− 7.32E-040.1210.8110.602− 0.0010.0010.1260.8110.603− 0.0010.001− 0.0010.1900.811
Zunyi0.574− 1.07E-030.1290.8960.3420.017− 0.0160.0410.9290.3220.019− 0.0160.023− 2.1070.933
Guiyang0.589− 1.33E-030.1350.8720.4710.013− 0.0130.0610.8910.4620.014− 0.0140.007− 0.5800.892
StationModel 8Model 9Model 10
 a1a6a7a4bR2a1a6a7a5bR2a2bR2
Chengdu0.3130.011− 0.008− 0.2380.3050.8280.3000.016− 0.014− 8.88E-040.0760.8180.196− 0.2270.614
Chongqing0.3200.012− 0.010− 0.2440.2670.9010.3250.019− 0.016− 3.34E-030.0370.9010.225− 0.3050.813
Changsha0.3970.005− 0.001− 0.3530.4060.8990.4670.009− 0.006− 5.49E-040.0760.8910.298− 0.4660.55
Hefei0.4530.008− 0.007− 0.1660.2160.7940.4610.011− 0.010− 1.95E-030.0670.7910.247− 0.3370.6
Hangzhou0.502− 0.0010.002− 0.1960.2830.7980.5430.003− 0.002− 4.08E-040.1030.7950.249− 0.330.483
Nanchong0.3580.017− 0.016− 0.0130.1020.8970.3740.017− 0.016− 1.60E-030.0910.8970.248− 0.3120.768
Nanchang0.5020.0010.001− 0.1760.2680.9190.5380.004− 0.003− 7.51E-040.1090.9160.331− 0.5070.622
Nanjing0.519− 0.0010.001− 0.1280.2610.7900.5200.001− 0.001− 1.17E-030.1500.7880.161− 0.0860.403
Shanghai0.5030.007− 0.006− 0.1600.2600.8860.5130.008− 0.008− 2.35E-030.1330.8860.229− 0.210.405
Wuhan0.5120.005− 0.004− 0.0290.1090.7740.4630.006− 0.004− 4.02E-030.1030.7840.209− 0.2380.34
Yichang0.596− 0.0030.004− 0.0780.1980.8120.594− 0.0020.003− 2.13E-030.1340.8130.243− 0.3440.515
Zunyi0.3200.016− 0.014− 0.1780.1960.9320.3210.018− 0.015− 3.47E-030.0390.9320.233− 0.360.814
Guiyang0.4380.010− 0.010− 0.2060.2450.8970.4590.014− 0.013− 1.36E-030.0600.8930.253− 0.4050.643
StationModel 11Model 12Model 13Model 14
 a2bR2a2bR2a2a3bR2a2a4bR2
Chengdu0.0360.0360.6050.261− 0.2130.6170.156− 0.0373.3730.7250.2130.183− 0.4220.621
Chongqing0.046− 0.0370.8290.267− 0.2250.7870.197− 0.0171.4830.8190.194− 0.2930.0050.821
Changsha0.055− 0.0680.5340.392− 0.4370.5590.262− 0.0514.8140.7120.221− 0.5420.180.578
Hefei0.0430.0190.5910.353− 0.3690.6050.251− 0.0151.2050.6280.237− 0.055− 0.2660.601
Hangzhou0.0460.0050.480.332− 0.3140.4820.241− 0.0131.0080.4970.218− 0.207− 0.0840.495
Nanchong0.051− 0.010.7810.301− 0.2380.7470.196− 0.0282.5190.8280.2410.005− 0.3010.802
Nanchang0.064− 0.0820.6180.419− 0.4430.6190.312− 0.0272.320.6660.291− 0.225− 0.2260.634
Nanjing0.0270.1520.3990.236− 0.1210.4040.174− 0.0191.7950.4540.156− 0.036− 0.0440.403
Shanghai0.0420.1040.4010.312− 0.2090.4070.251− 0.0242.1740.4620.207− 0.155− 0.0280.411
Wuhan0.0350.0710.3280.306− 0.2790.3490.244− 0.0494.6210.5440.197− 0.082− 0.1380.341
Yichang0.044− 0.0110.5110.328− 0.3370.5110.222− 0.0161.3150.5360.2610.141− 0.4950.522
Zunyi0.045− 0.0650.8310.292− 0.3040.7860.215− 0.021.4920.8220.215− 0.286− 0.0820.823
Guiyang0.047− 0.0650.640.336− 0.3860.640.233− 0.032.3080.6690.203− 0.4040.0410.666
StationModel 15Model 16Model 17
 a2a5bR2a2a3a4bR2a6a7bR2
Chengdu0.182− 6.56E-03− 0.2040.7020.152− 0.037− 0.0433.4860.7250.032− 0.0280.0190.757
Chongqing0.229− 1.27E-03− 0.3120.8130.146− 0.024− 0.3782.5620.8320.039− 0.036− 0.0320.844
Changsha0.304− 2.11E-03− 0.4910.5530.141− 0.058− 0.8326.4740.7760.044− 0.038− 0.0750.773
Hefei0.255− 1.65E-03− 0.3640.6020.212− 0.019− 0.2121.8710.6380.043− 0.041− 0.0070.633
Hangzhou0.237− 3.34E-03− 0.2830.4930.105− 0.043− 0.7495.0410.5760.043− 0.041− 0.0020.525
Nanchong0.231− 3.41E-03− 0.2840.8110.169− 0.031− 0.1523.0510.8310.041− 0.038− 0.0020.816
Nanchang0.314− 3.12E-03− 0.4480.6330.133− 0.062− 0.8566.9470.7670.056− 0.052− 0.0850.714
Nanjing0.159− 2.06E-04− 0.0820.4030.149− 0.022− 0.2032.3160.4630.031− 0.0280.0980.478
Shanghai0.211− 3.86E-03− 0.1440.4150.151− 0.054− 0.8846.1380.5650.048− 0.0450.0190.506
Wuhan0.211− 2.64E-04− 0.2440.340.189− 0.052− 0.3775.4250.5650.041− 0.036− 0.0440.586
Yichang0.243− 2.64E-03− 0.3520.5230.211− 0.019− 0.0711.7480.5360.038− 0.0350.0010.571
Zunyi0.228− 2.12E-03− 0.3520.8170.191− 0.023− 0.3292.0990.8330.037− 0.034− 0.0490.872
Guiyang0.251− 3.26E-03− 0.4060.6570.151− 0.043− 0.5934.1470.7140.041− 0.036− 0.0650.748
StationModel 18Model 19Model 20
 a3a4a6a7bR2a6a7a8bR2a3a4a6a7a8bR2
Chengdu− 0.003− 0.1380.031− 0.025− 0.1310.7610.031− 0.0321.77E-04− 0.0510.7680.026− 0.2870.026− 0.0313.28E-04− 2.2090.786
Chongqing− 0.021− 0.4720.027− 0.021− 1.6170.8630.032− 0.0423.51E-04− 0.0710.8710.034− 0.3140.027− 0.0333.54E-04− 3.0620.887
Changsha− 0.063− 0.8760.016− 0.002− 5.6240.8610.044− 0.0575.37E-04− 0.0030.8430.082− 0.4740.026− 0.0274.59E-04− 7.8410.897
Hefei− 0.031− 0.3450.031− 0.026− 2.7450.6610.045− 0.0584.52E-04− 0.0010.7380.051− 0.2470.037− 0.0454.78E-04− 4.9380.771
Hangzhou− 0.044− 0.9050.013− 0.003− 3.5780.6740.042− 0.0533.79E-04− 0.0410.5880.062− 0.6780.021− 0.0213.12E-04− 5.6940.708
Nanchong− 0.002− 0.1280.036− 0.033− 0.3760.8490.036− 0.0433.02E-04− 0.0750.8380.013− 0.1610.031− 0.0372.83E-04− 1.0480.869
Nanchang− 0.035− 0.6820.025− 0.015− 2.9920.8160.052− 0.0623.76E-04− 0.0110.7590.08− 0.4320.029− 0.0314.07E-04− 7.7310.856
Nanjing− 0.038− 0.3910.023− 0.017− 3.4110.5210.032− 0.0413.70E-04− 0.0930.5690.053− 0.3310.026− 0.0313.96E-04− 4.9990.621
Shanghai− 0.015− 0.9250.031− 0.023− 0.7150.6390.049− 0.0656.02E-04− 0.0580.7060.053− 0.4180.041− 0.0515.81E-04− 5.0280.785
Wuhan− 0.029− 0.4250.029− 0.021− 2.6160.6160.041− 0.0535.31E-04− 0.0050.6920.058− 0.0130.039− 0.0485.84E-04− 5.9120.717
Yichang− 0.048− 0.1480.034− 0.025− 4.7830.6090.037− 0.0453.10E-04− 0.0440.6050.083− 0.0050.037− 0.0434.83E-04− 8.4020.678
Zunyi− 0.041− 0.3960.032− 0.026− 3.5120.9010.035− 0.0382.11E-04− 0.0150.8820.058− 0.2820.032− 0.0332.93E-04− 5.1760.916
Guiyang− 0.022− 0.4710.03−− 0.024− 1.6530.7930.039− 0.0463.41E-04− 0.0250.7730.057− 0.3220.033− 0.0414.99E-04− 4.8160.834
Table IV. Estimation accuracy of the study models
StationModel 1Model 2Model 3Model 4Model 5Model 6Model 7
 RMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSERRMSERRMSE
Chengdu0.87910.21%0.86510.05%0.86710.07%0.87110.11%0.8439.79%0.8239.55%0.8259.58%
Chongqing1.16913.43%1.17013.44%1.16913.43%1.18213.58%1.13913.08%0.7128.18%0.7118.16%
Changsha1.0489.79%1.0469.76%1.0209.52%1.0539.83%1.0609.90%0.8397.83%0.8177.63%
Hefei1.85715.24%1.87815.41%1.84115.10%1.79914.76%1.86915.33%1.44211.83%1.44611.87%
Hangzhou1.41912.15%1.40011.98%1.39611.95%1.43012.25%1.39711.96%1.27810.94%1.28410.99%
Nanchong0.96410.41%1.01210.93%0.94310.18%0.97710.55%0.95010.26%0.92910.03%0.98910.68%
Nanchang1.1739.88%1.1669.82%1.1839.96%1.20210.12%1.1789.92%0.7746.52%0.7456.27%
Nanjing0.6745.66%0.6735.64%0.6815.71%0.6755.66%0.6725.64%0.6445.40%0.6525.47%
Shanghai1.0979.16%1.0648.88%1.1339.46%1.0959.14%1.1389.50%1.0188.50%1.0038.37%
Wuhan1.34811.82%1.37112.02%1.35011.84%1.33411.69%1.38612.15%1.32111.59%1.32111.58%
Yichang1.68515.66%1.69515.76%1.67415.56%1.69115.72%1.70315.83%1.39612.98%1.39612.98%
Zunyi0.96511.40%0.96811.44%1.00411.86%0.98511.64%0.96011.35%0.92710.95%0.92910.97%
Guiyang2.01319.89%1.98319.59%1.99919.75%2.00919.84%2.02119.97%1.66116.41%1.68016.59%
StationModel 8Model 9Model 10Model 11Model 12Model 13Model 14
 RMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSERRMSERRMSE
Chengdu0.8509.87%0.8279.61%1.6129.59%1.68310.01%1.5649.30%1.6079.56%1.5919.46%
Chongqing0.7178.23%0.7498.60%1.32215.36%1.32115.34%1.33615.51%1.26614.70%1.26714.71%
Changsha0.9048.44%0.8347.79%1.23814.22%1.36315.66%1.25713.29%1.19713.75%1.22414.06%
Hefei1.40011.49%1.39911.48%2.25021.01%2.25221.03%2.26621.16%1.86817.44%2.17820.33%
Hangzhou1.22310.47%1.27610.92%2.20218.07%2.19518.01%2.20618.10%1.94115.92%2.18617.93%
Nanchong0.9249.97%0.94910.24%1.69818.33%1.68118.14%1.73018.68%1.61117.39%1.57517.00%
Nanchang0.7446.27%0.7666.45%2.01716.98%1.99716.81%2.04817.25%1.79415.10%2.00616.89%
Nanjing0.6335.31%0.6295.28%1.62913.67%1.62913.67%1.62913.67%1.47412.36%1.62413.62%
Shanghai1.0698.92%0.9978.32%2.04717.08%2.05217.13%2.04317.05%2.02616.91%2.04117.03%
Wuhan1.30411.43%1.32911.66%2.47921.73%2.49521.88%2.45921.56%1.92116.84%2.41121.14%
Yichang1.39913.00%1.40913.10%1.96218.24%1.95718.20%1.97218.33%1.81516.88%1.90117.67%
Zunyi0.96311.38%0.96011.34%1.17614.09%1.23914.85%1.14213.68%1.16613.78%1.19314.09%
Guiyang1.62916.09%1.66516.45%2.31422.86%2.29422.66%2.33623.08%2.12621.00%2.25522.27%
StationModel 15Model 16Model 17Model 18Model 19Model 20
 RMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSERMSERRMSE
Chengdu1.6249.66%1.5559.25%1.4078.37%1.4028.34%1.4078.37%1.3928.28%
Chongqing1.25014.51%1.21314.08%1.40416.30%1.34915.66%1.40216.27%1.33215.47%
Changsha1.26014.47%1.12412.91%1.04111.95%0.94210.82%0.7889.05%0.7108.15%
Hefei2.26121.11%1.68015.68%1.66415.54%1.32112.34%1.16410.87%0.9558.92%
Hangzhou2.20818.12%1.83015.02%1.87115.35%1.66413.65%1.59413.08%1.45211.92%
Nanchong1.60617.33%1.51516.35%1.61417.42%1.40115.12%1.49516.13%1.19712.92%
Nanchang2.02717.07%1.49912.62%1.56513.17%1.1059.30%1.35711.43%0.7806.57%
Nanjing1.62813.66%1.44512.12%1.37611.54%1.24110.42%1.0909.14%0.9117.65%
Shanghai2.01816.84%1.94616.24%2.00116.02%2.00116.70%1.64913.76%1.59413.31%
Wuhan2.47821.72%1.68514.77%1.69314.84%1.46912.88%1.49813.13%1.37712.07%
Yichang1.87217.40%1.81316.86%1.68815.69%1.65115.35%1.51514.09%1.39913.00%
Zunyi1.19014.06%1.16013.70%1.16713.98%1.13613.42%1.12713.50%1.11013.11%
Guiyang2.15121.25%2.00619.81%1.78117.59%1.73617.15%1.67416.53%1.67216.52%

Generally, for empirical modes such as those presented here, the more variables a model has, the higher chance the model gives a better performance. However, in the present work, models 2–5 give similar performances with the simple A–P model. This suggests that monthly average daily ambient temperature range, atmospheric water vapour pressure, relative humidity and precipitation, as introduced in an additive form, do not adequately account for the improvement in estimation accuracy of the A–P model. Our results are different from those reported by Chen et al. (2004) who introduced ambient temperature range to A–P model and claimed a better performance at 48 meteorological stations (10 located in Yangtze River Basin) 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 station and reported the similar performances, and also agree with Chen et al. (2006) who introduced precipitation in an additive form that had little higher accuracy than A–P model at 51 stations (10 located in Yangtze River Basin) all over China.

Models 6–9 show a 1–40% (average 13%) lower RMSE than model 1, this suggests that inclusion of maximum and minimum ambient temperatures can significantly improve the estimation accuracy of the A–P model. Models 7–9, which are modifications to model 6, return similar performances with model 6, further confirming that atmospheric water vapour pressure, relative humidity and precipitation do not contribute to the improvement in estimation accuracy of the sunshine-based models. Therefore, if all of these meteorological variables are available, it is unnecessary to take into account atmospheric water vapour pressure, relative humidity and precipitation because of the little or no improvement in estimation accuracy of the sunshine-based models, and model 6 is proposed and can provide a good method for estimation of monthly average daily solar radiation with greater accuracy in Yangtze River Basin in China.

3.1.2. Temperature-based models

Overall, all the ambient temperature-based models produce acceptable results with RMSE < 2.5 MJ m−2 (average 1.658 MJ m−2) and RRMSE < 25% (average 15.63%). This result is different with Chen et al. (2004) who reported that models using ambient temperature only are not suitable for solar radiation estimation in China. Among the temperature-based models, model 20 using monthly average daily maximum and minimum ambient temperature, relative humidity, atmospheric water vapour pressure and the multiplication maximum by minimum temperatures gives best performance, with lowest RMSE (average 1.216 MJ m−2) and RRMSE (average 11.6%).

Among the models using ambient temperature range only (models 10–12), model 10 (H–S) was developed by Hargreaves et al. (1985), and model 11 by Chen et al. (2004) who revised H–S model and claimed a better performance. However, in the present work, models 10–12 have similar R2, RMSE and RRMSE. This result agrees with Wu et al. (2007) who presented that model 10 returned same R2 and RMSE with those of model 11 at Nanchang station. These results suggest that the variations of the ambient temperature range are generally not very effective and give little or no improvement.

Models 13–15 are modifications to model 10 by adding one meteorological variable only. Model 13 including monthly average daily atmospheric water vapour pressure is superior to models 14 and 15 with 1–22% (average 8%) lower RMSE than model 10, while model 15 including monthly average daily precipitation returns higher RMSE and RRMSE at 7 stations. Model 16 which includes both monthly average daily atmospheric water vapor pressure and relative humidity is superior to model 13 with 1–32% (average 14%) higher accuracy than model 10. These results suggest that additional inclusion of monthly average daily atmospheric water vapour pressure and relative humidity can significantly improve the estimation accuracy of the temperature-based models. However, precipitation does not adequately account for the improvement in estimation accuracy, and therefore additional inclusion of precipitation is unnecessary.

Overall, model 17 significantly outperforms model 10 with an average 15% higher accuracy, and at some stations (Changsha, Nanchang, Guiyang and Wuhan), the RMSE could be 22–31% lower, indicating that model using maximum and minimum ambient temperatures is superior to model using ambient temperature range. This is also indicated by the lower RMSE (average 13%) of the model 18 than model 16. Model 19 was more accurate than model 17 with an average 12% higher accuracy, and at some stations (Nanjing, Nanchang and Changsha), the accuracy could be 20–30% higher, indicating that inclusion of multiplication maximum by minimum temperatures significantly improves the estimation 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 performs much better than model 17 with an average 22% higher accuracy, further confirming that additional inclusion of monthly average daily atmospheric water vapour pressure, relative humidity and multiplication maximum by minimum temperatures can significantly improve the estimation accuracy of the temperature-based models.

3.2. Analyses of influencing factors of model accuracy

The values of RMSE and RRMSE of the proposed models vary considerably from station to station. Consequently, the correlation analysis between RMSE, RRMSE and other factors including longitude, latitude, altitude, average daily sunshine duration, sunshine ratio, maximum and minimum ambient temperature, temperature range, atmospheric water vapour pressure, relative humidity and precipitation is investigated, and the summary is presented in Table V.

Table V. Correlation coefficients for model 6 and model 20
IndicatoraModel6Model20
 RMSERRMSERMSERRMSE
  • *

    Significant at 0.05 significance level.

  • a

    Tmax, Tmin, TmaxTmin, AP, RH, P, S, So are monthly average daily maximum temperature, minimum ambient temperature, the difference between maximum and minimum temperature, atmospheric water vapour pressure, relative humidity, precipitation, sunshine duration, potential sunshine duration, respectively.

Latitude− 0.054− 0.0800.093− 0.126
Longitude0.093− 0.0830.089− 0.404
Altitude0.006− 0.0770.2530.320
Tmax− 0.147− 0.0810.044− 0.417
Tmin− 0.0630.182− 0.342− 0.391
TmaxTmin− 0.009− 0.328− 0.276− 0.538*
AP− 0.0150.049− 0.242− 0.013
RH− 0.1700.190− 0.398− 0.068
P− 0.051− 0.160− 0.337− 0.343
S− 0.029− 0.458*
S/So− 0.023− 0.454*

The correlation coefficients show that there is no correlation between RMSE of model 6 with these factors. While RRMSE correlates significantly with monthly average daily sunshine duration (r = − 0.458, p < 0.05), and sunshine ratio (r = − 0.454, p < 0.05), generally indicating that model 6 is more applicable in area with longer sunshine duration, and higher sunshine ratio. Also, RMSE of model 20 correlates with none of these factors. While RRMSE correlates significantly with ambient temperature range (r = − 0.529, p < 0.05), generally indicating that model 20 is more applicable in areas with larger temperature range. Based on these correlations, climate change may affect the accuracy of model 6 and model 20. For most of our study stations (11 stations), sunshine duration and sunshine ratio showed decreasing trend. Although maximum and minimum ambient temperatures showed increasing trend, but the temperature range showed decreasing trend because the increase of minimum is larger than that of maximum. This trend is also widely reported globally (Easterling et al., 1997) and regionally (Liu et al., 2004).

It is noted that RMSE and RRMSE not always show 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), but model 19 actually performs slightly better in Nanchong than in Shanghai because solar radiation in Shanghai (average 12.655 MJ m−2) is much higher than that in Nanchong (average 9.944 MJ m−2). So, it is suggested to use RRMSE to measure the model performance when make comparisons among different stations.

4. Conclusions

Estimation of solar radiation from measured meteorological variables offers an important alternative in absence of measured solar radiation. 20 developed models are comparatively studied and evaluated using monthly average daily solar radiation and other measured meteorological data, including monthly average daily sunshine duration, maximum and minimum ambient temperatures, relative humidity, atmospheric pressure and precipitation at 13 stations in Yangtze River Basin in China. The preferred models are proposed under two different scenarios. In the first scenario, sunshine duration is available. Monthly average daily atmospheric water vapour pressure, relative humidity and precipitation do not contribute to the improvement in estimation accuracy of A–P model. It is therefore unnecessary to take them into account, and the newly developed model 6 is proposed and can provide a good method for the estimation of monthly average daily solar radiation in Yangtze River Basin in China. And it is more applicable in area with longer sunshine duration, and higher sunshine ratio. In the second case, sunshine duration is not available. Inclusion of monthly average daily atmospheric water vapour pressure, relative humidity and multiplication maximum by minimum temperatures can significantly improve the estimation accuracy of the temperature-based models. While monthly average daily precipitation does not contribute to the improvement in estimation accuracy. And model 20 is proposed and it is more applicable in areas with larger temperature range. We believe that these models allow widespread application due to the good data availability and accuracy in Yangtze River Basin in China. The principal limitation is that they require calibration using measured solar radiation data and it is therefore open to question how transferable these calibration values are to other locations. Therefore, our future study shall explore solar radiation estimation at the station where no solar radiation is available for calibration the empirical models.

Acknowledgements

The work was supported by the Geological Survey program of China Geological Survey (1212010611402) and Special Fund for Land and Resources Research in the Public Interest (201111023). We thank the National Meteorological Information Center, China Meteorological Administration for providing the long-term data records. Many thanks go to the anonymous reviewers for the comments on the manuscript.

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