# Comparative Analysis of Global Solar Radiation Models in Different Regions of China

Authors: Qingwen Zhang; Ningbo Cui; Yu Feng; Yue Jia; Zhuo Li; Daozhi Gong
Journal: Advances in Meteorology
 (2018)

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## Abstract

Complete and accurate global solar radiation (Rs) data at a specific region are crucial for regional climate assessment and crop growth modeling. The objective of this paper was to evaluate the capability of 12 solar radiation models based on meteorological data obtained from 21 meteorological stations in China. The results showed that the estimated and measured daily Rs had statistically significant correlations (P<0.01) for all the 12 models in 7 subzones of China. The Bahel model showed the best performance for daily Rs estimation among the sunshine-based models, with average R2 of 0.910, average RMSE of 2.306 MJ m−2 d−1, average RRMSE of 17.3%, average MAE of 1.724 MJ m−2 d−1, and average NS of 0.895, respectively. The Bristow-Campbell (BC) model showed the best performance among the temperature-based models, with average R2 of 0.710, average RMSE of 3.952 MJ m−2 d−1, average RRMSE of 29.5%, average MAE of 2.958 MJ m−2 d−1, and average NS of 0.696, respectively. On monthly scale, Ögelman model showed the best performance among the sunshine-based models, with average RE of 5.66%. The BC model showed the best performance among the temperature-based models, with average RE of 8.26%. Generally, the sunshine-based models were more accurate than the temperature-based models. Overall, the Bahel model is recommended to estimate daily Rs, Ögelman model is recommended to estimate monthly average daily Rs in China when the sunshine duration is available, and the BC model is recommended to estimate both daily Rs and monthly average daily Rs when only temperature data are available.


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## Body

## 1. Introduction

Solar energy is the most fundamental renewable energy source on the earth’s surface, and global solar radiation (Rs) plays an important role in a wide range of applications in areas such as meteorology and hydrology [1]. Changes in the amount of Rs greatly influence the hydrological cycle, terrestrial ecological systems, and the climate [2]. Complete and accurate Rs data at a specific region are highly crucial to regional crop growth modeling, evapotranspiration estimation, irrigation system development, and utilization of solar energy resources. Meanwhile, due to the fast growth in the global energy demand and destructive effects of fossil fuels on the environment, there is a growing demand for reliable Rs information for clean energy technology development [3, 4]. The best method to determine the amount of Rs at any site is to install measuring instruments such as pyranometers or pyrheliometers at every specific location. Monitoring their daily recording and maintenance, however, is a very troublesome business and costly exercise [5, 6]. In fact, the reliable measurement of Rs data is relatively scarce in many developing countries due to the expensive instruments, technical equipment, and maintenance requirements [6]. Currently, only 122 out of 752 national meteorological stations in China have Rs observing instruments [7]. Furthermore, even for those stations where Rs is observed, there are many Rs data which are missing or lie outside the expected range due to equipment failure and other difficulties [8–10].Thus, differentRs models have been proposed for estimating daily or monthly Rs using different techniques, such as geostationary satellite images, neural networks, time series methods, physically radiative transfer models, and stochastic weather methods, which were generally based on different types of data including meteorological and geographical data [11, 12]. Among them, meteorological data-based models using empirical correlations depend on the most common meteorological elements including cloud cover, sunshine duration, temperature, and relative humidity, making them the most commonly examined and widely used models around the world, especially the sunshine-based and temperature-based models [6, 11]. The primary sunshine-based model can be traced back to Ångström model, using sunshine duration and clear sky radiation data to estimate Rs [11, 13, 14]. Prescott [15] suggested using the extraterrestrial radiation to replace clear sky radiation and presented the Ångström-Prescott (AP) model. Several Ångström-type regression models, namely, the linear, quadratic, cubic, logarithmic, and exponential models, were compared to estimate Rs on horizontal surfaces at 4 meteorological stations in Tunisia, and the statistical results indicated that the models were considered suited to accurately estimate Rs, and the cubic model showed the best regression fit and performed slightly better than the others [16]. Although the sunshine-based models are generally more accurate for estimating Rs, their application is often limited by the lack of sunshine records [1, 9, 17]. In this context, Rs forecast models based on geographical location, air temperature, and/or precipitation, recorded at the great majority of the meteorological stations, are attractive and viable options [1, 8]. The temperature-based models were only based on air temperature data which can be measured easily [18]. Hargreaves-Samani (HS) model [19] was proposed as a more convenient, effective, and strong applicability model with fewer input parameters, based on the daily maximum and minimum temperature to estimate Rs. Annandale et al. [20] modified the HS model by accounting for the effects of reduced altitude and atmosphere thickness on Rs. In order to calculate the average monthly Rs, Allen [21, 22] also proposed a self-calibrated model based on HS model. Bristow and Campbell [23] presented a simple model for estimating daily Rs, in which Rs was an exponential function in terms of temperature. Goodin et al. [24] modified Bristow-Campbell (BC) model by adding the extraterrestrial Rs term meant to act as a scaling factor. Liu et al. [10] evaluated the accuracy and applicability of 16 temperature-based models, including modified versions of the BC and HS models in 15 meteorological stations of Northeast China, North China Plain, and Northwest China, and the results showed that the original BC model performed similarly to the best performing modified HS model but significantly outperformed the original HS model with a 4~7% higher accuracy. Hassan et al. [11] established 17 new temperature-based models and compared these models with Annandale, Allen, and Goodin models to estimate monthly average daily Rs in Egypt and found that the local formula for the most accurate new model provided good predictions at different locations, especially at coastal sites. In general, the sunshine-based models are more accurate than temperature-based models [11, 25]. However, sunshine data are not widely available compared with ambient temperature data at standard meteorological stations [11].China is an agricultural country, and agricultural application of solar energy has an important guiding significance to the agricultural clean production, energy conservation, and emissions reduction. Therefore, reliable estimation ofRs is very important for the operation of solar-powered pump station systems and solar irrigation systems, lift irrigated projects, and potential yield of crops in China [17]. In particular, it is of great significance for developing and utilizing solar energy resources in nonradiation observation areas due to the lack of observation stations and meteorological stations. In this paper, we analyzed the accuracy and applicability of 9 sunshine-based models and 3 temperature-based models to estimate daily Rs using the widely measured meteorological variable obtained from 21 meteorological stations in China, and the empirical coefficients of each model were calibrated based on the least squares method.


## 2. Materials and Methods

### 2.1. Study Area and Experimental Data

According to the natural geographical features, China is divided into 7 subzones: North China, Central China, East China, South China, Northeast, Northwest, and Southwest China. In the current study, 21 meteorological stations located in different climatic zones of China were selected (Figure1), and each subzone contains 3 meteorological stations.Figure 1
Geographical positions of the meteorological stations.Daily measurements of global solar radiation (Rs) and meteorological variables, including maximum (Tmax) and minimum (Tmin) air temperature at 2 m height, relative humidity (RH), and sunshine duration (n) were obtained from 21 national meteorological stations during 1995~2014. The data of 1995~2010 were used to calibrate the empirical coefficients of the 12 models and the data of 2011~2014 were used to evaluate the performance of the models. The data sets were provided and rigorously quality-controlled by the National Meteorological Information Center of China Meteorological Administration (http://data.cma.cn/). Missing data were reconstructed based on linear interpolation. The geographical locations of each station and annual mean meteorological variables are presented in Table 1.Table 1
The geographical locations of each radiation station and its annual mean meteorological parameters.
Subzones WMO number Station Latitude(°N) Longitude(°E) Altitude(m) T m a x  (°C) T m i n (°C) n (h) RH(%) R s (MJ m−2 d−1) North China 54511 Beijing 39.8 116.5 31.3 18.5 8.4 6.7 53.4 13.5 54539 Laoting 39.4 118.9 10.5 17.0 7.4 6.6 64.1 13.9 53772 Taiyuan 37.8 112.6 778.3 17.8 5.3 6.7 55.8 13.6  Central China 57494 Wuhan 30.6 114.1 23.1 22.0 14.2 5.0 74.2 11.7 57687 Changsha 28.2 112.9 68.0 22.2 15.0 4.3 76.0 10.8 57083 Zhengzhou 34.7 113.7 110.4 21.2 10.8 5.1 61.2 12.8  East China 54823 Jinan 36.6 117.1 170.3 19.8 10.8 6.0 56.7 13.2 58606 Nanchang 28.6 115.9 46.9 22.4 15.5 5.0 74.0 12.1 58362 Shanghai 31.4 121.5 5.5 20.8 14.3 4.8 72.6 12.5  South China 59287 Guangzhou 23.2 113.3 41.0 26.9 19.3 4.3 74.8 11.7 59758 Haikou 20.0 110.3 63.5 28.4 22.1 5.0 81.5 14.1 59431 Nanning 22.6 108.2 121.6 26.5 18.5 4.1 78.8 12.4  Northeast China 50953 Harbin 45.8 126.8 142.3 10.7 0.2 6.3 63.6 12.9 54342 Shenyang 41.7 123.5 49.0 14.4 3.2 6.5 63.9 13.4 54161 Changchun 43.9 125.2 236.8 11.7 1.7 7.0 60.8 13.4  Northwest China 51463 Urumqi 43.8 87.7 935.0 13.2 3.7 7.3 56.2 14.1 57036 Hsian 34.3 108.9 397.5 20.1 10.6 4.7 64.0 12.0 52866 Xining 36.7 101.8 2295.2 14.5 −0.4 6.9 58.2 15.6  Southwest China 56294 Chengdu 30.7 104.0 506.1 20.9 13.6 2.6 77.7 9.3 56778 Kunming 25.0 102.7 1886.5 21.8 11.8 6.0 68.3 15.4 55591 Lasa 29.7 91.1 3648.9 16.8 3.1 8.2 40.3 20.4


### 2.2. Models for Estimation of Solar Radiation

A number of empirical correlations which determine the relation betweenRs and various meteorological parameters have been developed to estimate daily or monthly Rs in the literature, such as sunshine-based models, cloud-based models, temperature-based models, and other meteorological parameter-based models [6, 26]. The sunshine-based and temperature-based models are the most commonly used around the world [6, 9]. In this paper, 12 representative models were chosen to predict Rs, including 9 sunshine-based models and 3 temperature-based models.


#### 2.2.1. Sunshine-Based Models

Model 1 (Ångström-Prescott model (AP)).
Ångström [14] derived a simple linear relationship between the ratio of average daily Rs and the corresponding value on a completely clear day at a given location and the ratio of average daily sunshine duration to the maximum possible sunshine duration, which is the most widely used correlation for estimating daily Rs [27]. Prescott [15] modified the method and proposed the following equation:(1)Rs=a+bnN×Ra,where Rs is the global solar radiation (MJ m−2 d−1), Ra is the extraterrestrial radiation (MJ m−2 d−1), n is sunshine duration (h), N is maximum possible sunshine duration (h), and a and b are the empirical coefficients.Model 2 (Ögelman model (OG)).
Ögelman et al. [28] suggested a second-order polynomial equation for estimating Rs as follows:(2)Rs=a+bnN+cnN2×Ra,where a, b, and c are the empirical coefficients.Model 3 (Jin model (Jin)).
Through the use ofRs data and some geographical parameters like altitude and latitude, Jin et al. [29] derived the following model:(3)Rs=a+bcos⁡φ+cZ+dnN×Ra,where φ is the latitude of the location (°) and Z is the altitude of the location (km); a, b, c, and d are the empirical coefficients.Model 4 (Bahel model (BA)).
Bahel et al. [30] suggested a famous correlation with varied meteorological conditions and a wide distribution of geographic location; the equation is as follows:(4)Rs=a+bnN+cnN2+dnN3×Ra,where a, b, c, and d are the empirical coefficients.Model 5 (Louche model (LO)).
Louche et al. [31] have modified the Ångström-Prescott model through the use of the ratio of (n/Nnh) instead of (n/N); the equation is presented as follows:(5)Rs=a+bnNnh×Ra,1Nnh=0.8706N+0.0003,where a and b are the empirical coefficients.Model 6 (Glover-McCulloch model (GM)).
Glover and McCulloch [32] suggested the following model, which took into account the effect of latitude of the site φ as an additional input and was valid for φ<60°:(6)Rs=acos⁡φ+bnN×Ra,where a and b are the empirical coefficients.Model 7 (Elagib-Mansell model (EM)).
Through the use of sunshine duration and geographical parameters, Elagib and Mansell [33] derived a new equation for estimating Rs as(7)Rs=a+bL+cZ+dnN×Ra,where L is the latitude of the location (rad); a, b, c, and d are the empirical coefficients.Model 8 (Almorox-Hontoria model (AH)).
Almorox and Hontoria [34] derived an exponential type equation as follows:(8)Rs=a+bexp⁡nN×Ra,where a and b are the empirical coefficients.Model 9 (Dogniaux-Lemoine model (DL)).
Through taking into account the effect of latitude of the site as an additional input, Dogniaux and Lemoine [35] derived the following equation for estimating Rs:(9)Rs=a+bnN+cL+dnN×Ra,where a, b, c, and d are the empirical coefficients.


#### 2.2.2. Temperature-Based Models

Model 10 (Hargreaves-Samani model (HS)).
Hargreaves and Samani [19, 36] recommended a simple equation to estimate Rs which required only maximum and minimum temperature data; the equation is presented as follows:(10)Rs=aTmax-Tmin0.5×Ra,where Tmax and Tmin are the maximum daily temperature and minimum daily temperature (°), respectively; a is the empirical coefficient.Model 11 (Annandale model (AN)).
Annandale et al. [20] derived a model based on Hargreaves-Samani model by accounting for the effects of reduced altitude and atmospheric thickness on Rs; the equation is presented as follows:(11)Rs=a1+2.7×10-5ZTmax-Tmin0.5×Ra,where a is the empirical coefficient.Model 12 (Bristow-Campbell model (BC)).
Bristow and Campbell [23] proposed a method for daily Rs based on the difference of maximum and minimum temperatures; the equation is presented as follows:(12)Rs=a1-exp⁡-bTmax-Tminc×Ra,where a, b, and c are the empirical coefficients.


### 2.3. Statistical Evaluation

The performance of the studied models to estimateRs was evaluated in terms of the following statistical error tests: coefficient of determination (R2), root mean square error (RMSE), relative root mean square error (RRMSE), Nash–Sutcliffe coefficient (NS), and mean absolute error (MAE), which are defined in the following equations [37, 38]: (13)R2=∑i=1nXi-X-Yi-Y¯2∑i=1nXi-X-2∑i=1nYi-Y¯2,RMSE=1n∑i=1nYi-Xi2,RRMSE=1/n∑i=1nYi-Xi2X¯,NS=1-∑i=1nYi-Xi2∑i=1nXi-X-2,MAE=1n∑i=1nYi-Xi,where Xi and Yi denote the measured and estimated values, Xi¯ and Yi¯ represent the corresponding mean Rs values, respectively, the subscript i refers to the ith value of the solar irradiation, and n is the number of data. RMSE and MAE are both in MJ m−2 d−1; RRMSE is dimensionless, taking on a value from 0 (perfect fit) to ∞ (the worst fit); NS is dimensionless, taking on a value from 1 (perfect fit) to −∞ (the worst fit).


### 2.4. Global Performance Indicator

In order to overcome the discrepancy and to further improve the outcomes of statistical analysis, a new factor was proposed by Despotovic et al. [39] known as the Global Performance Indicator (GPI), which was a worthy tool to combine the effects of individual statistical indicators. The equation is presented as follows:(14)GPIi=∑j=15αjyj-yij,where αj is equal to -1 for the indicator R2 and NS, while for other indicators it is equal to +1. yj is the median of scaled values of indicator j, and yij is the scaled value of indicator j for model i. A higher value of GPI results in a higher accuracy of the model.


## 2.1. Study Area and Experimental Data

According to the natural geographical features, China is divided into 7 subzones: North China, Central China, East China, South China, Northeast, Northwest, and Southwest China. In the current study, 21 meteorological stations located in different climatic zones of China were selected (Figure1), and each subzone contains 3 meteorological stations.Figure 1
Geographical positions of the meteorological stations.Daily measurements of global solar radiation (Rs) and meteorological variables, including maximum (Tmax) and minimum (Tmin) air temperature at 2 m height, relative humidity (RH), and sunshine duration (n) were obtained from 21 national meteorological stations during 1995~2014. The data of 1995~2010 were used to calibrate the empirical coefficients of the 12 models and the data of 2011~2014 were used to evaluate the performance of the models. The data sets were provided and rigorously quality-controlled by the National Meteorological Information Center of China Meteorological Administration (http://data.cma.cn/). Missing data were reconstructed based on linear interpolation. The geographical locations of each station and annual mean meteorological variables are presented in Table 1.Table 1
The geographical locations of each radiation station and its annual mean meteorological parameters.
Subzones WMO number Station Latitude(°N) Longitude(°E) Altitude(m) T m a x  (°C) T m i n (°C) n (h) RH(%) R s (MJ m−2 d−1) North China 54511 Beijing 39.8 116.5 31.3 18.5 8.4 6.7 53.4 13.5 54539 Laoting 39.4 118.9 10.5 17.0 7.4 6.6 64.1 13.9 53772 Taiyuan 37.8 112.6 778.3 17.8 5.3 6.7 55.8 13.6  Central China 57494 Wuhan 30.6 114.1 23.1 22.0 14.2 5.0 74.2 11.7 57687 Changsha 28.2 112.9 68.0 22.2 15.0 4.3 76.0 10.8 57083 Zhengzhou 34.7 113.7 110.4 21.2 10.8 5.1 61.2 12.8  East China 54823 Jinan 36.6 117.1 170.3 19.8 10.8 6.0 56.7 13.2 58606 Nanchang 28.6 115.9 46.9 22.4 15.5 5.0 74.0 12.1 58362 Shanghai 31.4 121.5 5.5 20.8 14.3 4.8 72.6 12.5  South China 59287 Guangzhou 23.2 113.3 41.0 26.9 19.3 4.3 74.8 11.7 59758 Haikou 20.0 110.3 63.5 28.4 22.1 5.0 81.5 14.1 59431 Nanning 22.6 108.2 121.6 26.5 18.5 4.1 78.8 12.4  Northeast China 50953 Harbin 45.8 126.8 142.3 10.7 0.2 6.3 63.6 12.9 54342 Shenyang 41.7 123.5 49.0 14.4 3.2 6.5 63.9 13.4 54161 Changchun 43.9 125.2 236.8 11.7 1.7 7.0 60.8 13.4  Northwest China 51463 Urumqi 43.8 87.7 935.0 13.2 3.7 7.3 56.2 14.1 57036 Hsian 34.3 108.9 397.5 20.1 10.6 4.7 64.0 12.0 52866 Xining 36.7 101.8 2295.2 14.5 −0.4 6.9 58.2 15.6  Southwest China 56294 Chengdu 30.7 104.0 506.1 20.9 13.6 2.6 77.7 9.3 56778 Kunming 25.0 102.7 1886.5 21.8 11.8 6.0 68.3 15.4 55591 Lasa 29.7 91.1 3648.9 16.8 3.1 8.2 40.3 20.4


## 2.2. Models for Estimation of Solar Radiation

A number of empirical correlations which determine the relation betweenRs and various meteorological parameters have been developed to estimate daily or monthly Rs in the literature, such as sunshine-based models, cloud-based models, temperature-based models, and other meteorological parameter-based models [6, 26]. The sunshine-based and temperature-based models are the most commonly used around the world [6, 9]. In this paper, 12 representative models were chosen to predict Rs, including 9 sunshine-based models and 3 temperature-based models.


### 2.2.1. Sunshine-Based Models

Model 1 (Ångström-Prescott model (AP)).
Ångström [14] derived a simple linear relationship between the ratio of average daily Rs and the corresponding value on a completely clear day at a given location and the ratio of average daily sunshine duration to the maximum possible sunshine duration, which is the most widely used correlation for estimating daily Rs [27]. Prescott [15] modified the method and proposed the following equation:(1)Rs=a+bnN×Ra,where Rs is the global solar radiation (MJ m−2 d−1), Ra is the extraterrestrial radiation (MJ m−2 d−1), n is sunshine duration (h), N is maximum possible sunshine duration (h), and a and b are the empirical coefficients.Model 2 (Ögelman model (OG)).
Ögelman et al. [28] suggested a second-order polynomial equation for estimating Rs as follows:(2)Rs=a+bnN+cnN2×Ra,where a, b, and c are the empirical coefficients.Model 3 (Jin model (Jin)).
Through the use ofRs data and some geographical parameters like altitude and latitude, Jin et al. [29] derived the following model:(3)Rs=a+bcos⁡φ+cZ+dnN×Ra,where φ is the latitude of the location (°) and Z is the altitude of the location (km); a, b, c, and d are the empirical coefficients.Model 4 (Bahel model (BA)).
Bahel et al. [30] suggested a famous correlation with varied meteorological conditions and a wide distribution of geographic location; the equation is as follows:(4)Rs=a+bnN+cnN2+dnN3×Ra,where a, b, c, and d are the empirical coefficients.Model 5 (Louche model (LO)).
Louche et al. [31] have modified the Ångström-Prescott model through the use of the ratio of (n/Nnh) instead of (n/N); the equation is presented as follows:(5)Rs=a+bnNnh×Ra,1Nnh=0.8706N+0.0003,where a and b are the empirical coefficients.Model 6 (Glover-McCulloch model (GM)).
Glover and McCulloch [32] suggested the following model, which took into account the effect of latitude of the site φ as an additional input and was valid for φ<60°:(6)Rs=acos⁡φ+bnN×Ra,where a and b are the empirical coefficients.Model 7 (Elagib-Mansell model (EM)).
Through the use of sunshine duration and geographical parameters, Elagib and Mansell [33] derived a new equation for estimating Rs as(7)Rs=a+bL+cZ+dnN×Ra,where L is the latitude of the location (rad); a, b, c, and d are the empirical coefficients.Model 8 (Almorox-Hontoria model (AH)).
Almorox and Hontoria [34] derived an exponential type equation as follows:(8)Rs=a+bexp⁡nN×Ra,where a and b are the empirical coefficients.Model 9 (Dogniaux-Lemoine model (DL)).
Through taking into account the effect of latitude of the site as an additional input, Dogniaux and Lemoine [35] derived the following equation for estimating Rs:(9)Rs=a+bnN+cL+dnN×Ra,where a, b, c, and d are the empirical coefficients.


### 2.2.2. Temperature-Based Models

Model 10 (Hargreaves-Samani model (HS)).
Hargreaves and Samani [19, 36] recommended a simple equation to estimate Rs which required only maximum and minimum temperature data; the equation is presented as follows:(10)Rs=aTmax-Tmin0.5×Ra,where Tmax and Tmin are the maximum daily temperature and minimum daily temperature (°), respectively; a is the empirical coefficient.Model 11 (Annandale model (AN)).
Annandale et al. [20] derived a model based on Hargreaves-Samani model by accounting for the effects of reduced altitude and atmospheric thickness on Rs; the equation is presented as follows:(11)Rs=a1+2.7×10-5ZTmax-Tmin0.5×Ra,where a is the empirical coefficient.Model 12 (Bristow-Campbell model (BC)).
Bristow and Campbell [23] proposed a method for daily Rs based on the difference of maximum and minimum temperatures; the equation is presented as follows:(12)Rs=a1-exp⁡-bTmax-Tminc×Ra,where a, b, and c are the empirical coefficients.


## 2.2.1. Sunshine-Based Models

Model 1 (Ångström-Prescott model (AP)).
Ångström [14] derived a simple linear relationship between the ratio of average daily Rs and the corresponding value on a completely clear day at a given location and the ratio of average daily sunshine duration to the maximum possible sunshine duration, which is the most widely used correlation for estimating daily Rs [27]. Prescott [15] modified the method and proposed the following equation:(1)Rs=a+bnN×Ra,where Rs is the global solar radiation (MJ m−2 d−1), Ra is the extraterrestrial radiation (MJ m−2 d−1), n is sunshine duration (h), N is maximum possible sunshine duration (h), and a and b are the empirical coefficients.Model 2 (Ögelman model (OG)).
Ögelman et al. [28] suggested a second-order polynomial equation for estimating Rs as follows:(2)Rs=a+bnN+cnN2×Ra,where a, b, and c are the empirical coefficients.Model 3 (Jin model (Jin)).
Through the use ofRs data and some geographical parameters like altitude and latitude, Jin et al. [29] derived the following model:(3)Rs=a+bcos⁡φ+cZ+dnN×Ra,where φ is the latitude of the location (°) and Z is the altitude of the location (km); a, b, c, and d are the empirical coefficients.Model 4 (Bahel model (BA)).
Bahel et al. [30] suggested a famous correlation with varied meteorological conditions and a wide distribution of geographic location; the equation is as follows:(4)Rs=a+bnN+cnN2+dnN3×Ra,where a, b, c, and d are the empirical coefficients.Model 5 (Louche model (LO)).
Louche et al. [31] have modified the Ångström-Prescott model through the use of the ratio of (n/Nnh) instead of (n/N); the equation is presented as follows:(5)Rs=a+bnNnh×Ra,1Nnh=0.8706N+0.0003,where a and b are the empirical coefficients.Model 6 (Glover-McCulloch model (GM)).
Glover and McCulloch [32] suggested the following model, which took into account the effect of latitude of the site φ as an additional input and was valid for φ<60°:(6)Rs=acos⁡φ+bnN×Ra,where a and b are the empirical coefficients.Model 7 (Elagib-Mansell model (EM)).
Through the use of sunshine duration and geographical parameters, Elagib and Mansell [33] derived a new equation for estimating Rs as(7)Rs=a+bL+cZ+dnN×Ra,where L is the latitude of the location (rad); a, b, c, and d are the empirical coefficients.Model 8 (Almorox-Hontoria model (AH)).
Almorox and Hontoria [34] derived an exponential type equation as follows:(8)Rs=a+bexp⁡nN×Ra,where a and b are the empirical coefficients.Model 9 (Dogniaux-Lemoine model (DL)).
Through taking into account the effect of latitude of the site as an additional input, Dogniaux and Lemoine [35] derived the following equation for estimating Rs:(9)Rs=a+bnN+cL+dnN×Ra,where a, b, c, and d are the empirical coefficients.


## 2.2.2. Temperature-Based Models

Model 10 (Hargreaves-Samani model (HS)).
Hargreaves and Samani [19, 36] recommended a simple equation to estimate Rs which required only maximum and minimum temperature data; the equation is presented as follows:(10)Rs=aTmax-Tmin0.5×Ra,where Tmax and Tmin are the maximum daily temperature and minimum daily temperature (°), respectively; a is the empirical coefficient.Model 11 (Annandale model (AN)).
Annandale et al. [20] derived a model based on Hargreaves-Samani model by accounting for the effects of reduced altitude and atmospheric thickness on Rs; the equation is presented as follows:(11)Rs=a1+2.7×10-5ZTmax-Tmin0.5×Ra,where a is the empirical coefficient.Model 12 (Bristow-Campbell model (BC)).
Bristow and Campbell [23] proposed a method for daily Rs based on the difference of maximum and minimum temperatures; the equation is presented as follows:(12)Rs=a1-exp⁡-bTmax-Tminc×Ra,where a, b, and c are the empirical coefficients.


## 2.3. Statistical Evaluation

The performance of the studied models to estimateRs was evaluated in terms of the following statistical error tests: coefficient of determination (R2), root mean square error (RMSE), relative root mean square error (RRMSE), Nash–Sutcliffe coefficient (NS), and mean absolute error (MAE), which are defined in the following equations [37, 38]: (13)R2=∑i=1nXi-X-Yi-Y¯2∑i=1nXi-X-2∑i=1nYi-Y¯2,RMSE=1n∑i=1nYi-Xi2,RRMSE=1/n∑i=1nYi-Xi2X¯,NS=1-∑i=1nYi-Xi2∑i=1nXi-X-2,MAE=1n∑i=1nYi-Xi,where Xi and Yi denote the measured and estimated values, Xi¯ and Yi¯ represent the corresponding mean Rs values, respectively, the subscript i refers to the ith value of the solar irradiation, and n is the number of data. RMSE and MAE are both in MJ m−2 d−1; RRMSE is dimensionless, taking on a value from 0 (perfect fit) to ∞ (the worst fit); NS is dimensionless, taking on a value from 1 (perfect fit) to −∞ (the worst fit).


## 2.4. Global Performance Indicator

In order to overcome the discrepancy and to further improve the outcomes of statistical analysis, a new factor was proposed by Despotovic et al. [39] known as the Global Performance Indicator (GPI), which was a worthy tool to combine the effects of individual statistical indicators. The equation is presented as follows:(14)GPIi=∑j=15αjyj-yij,where αj is equal to -1 for the indicator R2 and NS, while for other indicators it is equal to +1. yj is the median of scaled values of indicator j, and yij is the scaled value of indicator j for model i. A higher value of GPI results in a higher accuracy of the model.


## 3. Results

### 3.1. Calibration of Empirical Coefficients

The empirical coefficients of the 12 models were calibrated based on the least squares method forRs estimation using the meteorological variables obtained from 21 meteorological stations during 1995~2010, and the adjusted coefficients of each subzone are shown in Table 2. As shown in Table 2, the calibrated a and b of the AP model ranged between 0.161~0.214 and 0.532~0.555, respectively. The calibrated a, b, and c of the OG model ranged between 0.144~0.202, 0.605~0.798, and −0.313~−0.082, respectively. The calibrated a, b, c, and d of Jin model ranged between 1.805~2.068, −2.227~−2.048, −0.101~0.027, and 0.532~0.555, respectively. The calibrated a, b, c, and d of the BA model ranged between 0.134~0.190, 0.867~1.261, −1.799~−0.739, and 0.443~1.158, respectively. The calibrated a and b of the LO model ranged between 0.161~0.214 and 0.608~0.635, respectively. The calibrated a and b of the GM model ranged between 0.185~0.269 and 0.532~0.555, respectively. The calibrated a, b, c, and d of the EM model ranged between 0.130~0.163, 0.005~0.034, 0.029~0.037, and 0.532~0.555, respectively. The calibrated a and b of the AH model ranged between −0.165~−0.085 and 0.325~0.358, respectively. The calibrated a, b, c, and d of the DL model ranged between 0.198~0.260, 0.082~0.109, −0.090~−0.065, and 0.456~0.524, respectively. The calibrated a of HS and AN models were both in the range 0.139~0.155. The calibrated a, b, and c of the BC model ranged between 0.552~0.695, 0.018~0.030, and 1.740~2.269, respectively. The regression coefficients were different in different climate zones. This can be explained as a consequence of local and seasonal changes in the type and thickness of cloud cover, the effects of snow covered surfaces, the concentrations of pollutants, and latitude [6, 34, 40].Table 2
Calibration empirical coefficients for the studied models in different subzones of China.
Model Coefficient North China Central China East China South China Northeast Northwest Southwest Ångström-Prescott (AP) a 0.182 0.161 0.167 0.171 0.193 0.193 0.214 b 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Ögelman (OG) a 0.174 0.144 0.149 0.154 0.180 0.180 0.202 b 0.605 0.798 0.785 0.793 0.655 0.685 0.685 c - 0.082 - 0.313 - 0.283 - 0.307 - 0.126 - 0.163 - 0.167  Jin a 1.896 1.975 1.965 2.068 1.805 1.977 2.061 b - 2.174 - 2.124 - 2.130 - 2.048 - 2.227 - 2.110 - 2.052 c - 0.018 0.021 0.016 0.027 - 0.015 - 0.101 - 0.027 d 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Bahel (BA) a 0.160 0.134 0.138 0.142 0.171 0.174 0.190 b 1.011 1.261 1.209 1.224 0.867 0.912 0.992 c - 1.265 - 1.799 - 1.610 - 1.745 - 0.739 - 0.860 - 1.148 d 0.856 1.147 1.006 1.158 0.443 0.524 0.776  Louche (LO) a 0.182 0.161 0.167 0.171 0.193 0.193 0.214 b 0.608 0.621 0.630 0.635 0.617 0.623 0.631  Glover-McCulloch (GM) a 0.234 0.189 0.198 0.185 0.269 0.246 0.244 b 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Elagib-Mansell (EM) a 0.154 0.149 0.154 0.163 0.163 0.142 0.130 b 0.024 0.017 0.016 0.018 0.034 0.013 0.005 c 0.032 0.030 0.030 0.029 0.030 0.037 0.037 d 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Almorox-Hontoria (AH) a - 0.114 - 0.165 - 0.156 - 0.165 - 0.099 - 0.107 - 0.085 b 0.325 0.344 0.345 0.358 0.325 0.331 0.336  Dogniaux-Lemoine (DL) a 0.243 0.209 0.216 0.198 0.260 0.252 0.246 b 0.102 0.097 0.101 0.082 0.109 0.108 0.095 c - 0.090 - 0.089 - 0.088 - 0.069 - 0.087 - 0.088 - 0.065 d 0.462 0.490 0.494 0.524 0.456 0.471 0.504  Hargreaves-Samani (HS) a 0.148 0.139 0.155 0.148 0.153 0.148 0.149  Annandale (AN) a 0.148 0.139 0.155 0.148 0.153 0.148 0.149  Bristow-Campbell (BC) a 0.602 0.552 0.552 0.561 0.619 0.647 0.695 b 0.023 0.018 0.025 0.028 0.030 0.027 0.019 c 1.872 2.194 2.269 2.051 1.801 1.740 1.848


### 3.2. Performances of the Models

The statistic performances of the analyzed models in estimating dailyRs for each zone of China are shown in Tables 3–9. As shown in Tables 3–9, there were good agreements between the estimations and the measurements. The estimated and measured daily Rs had statistically significant correlations for all the 12 models at the 21 meteorological stations (P<0.01). The statistical results showed that the sunshine-based models were more accurate for daily Rs estimation at the 7 subzones of China compared with the temperature-based models.Table 3
Statistics performances of the 12 models in estimating global solar radiation in North China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Beijing R 2 0.928 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.930 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.921 ∗ ∗ 0.928 ∗ ∗ 0.659 ∗ ∗ 0.659 ∗ ∗ 0.710 ∗ ∗ RMSE 2.030 2.037 2.028 2.007 2.027 2.029 2.035 2.103 2.027 4.273 4.273 3.965 RRMSE 14.7 14.7 14.7 14.5 14.7 14.7 14.7 15.2 14.7 30.9 30.9 28.7 NS 0.921 0.921 0.921 0.923 0.921 0.921 0.921 0.915 0.921 0.651 0.651 0.699 MAE 1.463 1.471 1.461 1.404 1.459 1.462 1.467 1.505 1.459 3.314 3.314 2.986   Laoting R 2 0.929 ∗ ∗ 0.928 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.920 ∗ ∗ 0.929 ∗ ∗ 0.690 ∗ ∗ 0.690 ∗ ∗ 0.747 ∗ ∗ RMSE 1.866 1.878 1.863 1.855 1.866 1.867 1.868 1.971 1.863 3.866 3.866 3.493 RRMSE 13.5 13.6 13.5 13.5 13.5 13.6 13.6 14.3 13.5 28.1 28.1 25.4 NS 0.927 0.927 0.928 0.928 0.927 0.927 0.927 0.919 0.928 0.689 0.689 0.746 MAE 1.350 1.374 1.348 1.335 1.349 1.351 1.351 1.401 1.348 2.991 2.991 2.665   Taiyuan R 2 0.906 ∗ ∗ 0.905 ∗ ∗ 0.906 ∗ ∗ 0.909 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.901 ∗ ∗ 0.906 ∗ ∗ 0.709 ∗ ∗ 0.709 ∗ ∗ 0.747 ∗ ∗ RMSE 2.809 2.814 2.802 2.765 2.802 2.806 2.814 2.828 2.804 4.592 4.592 4.400 RRMSE 18.7 18.7 18.7 18.4 18.7 18.7 18.7 18.8 18.7 30.6 30.6 29.3 NS 0.864 0.863 0.864 0.868 0.864 0.864 0.863 0.862 0.864 0.635 0.635 0.665 MAE 2.115 2.121 2.109 2.070 2.110 2.113 2.119 2.118 2.111 3.579 3.579 3.370   Average R 2 0.921 ∗ ∗ 0.920 ∗ ∗ 0.921 ∗ ∗ 0.923 ∗ ∗ 0.921 ∗ ∗ 0.921 ∗ ∗ 0.921 ∗ ∗ 0.914 ∗ ∗ 0.921 ∗ ∗ 0.686 ∗ ∗ 0.686 ∗ ∗ 0.735 ∗ ∗ RMSE 2.235 2.243 2.231 2.209 2.232 2.234 2.239 2.301 2.231 4.244 4.244 3.953 RRMSE 15.6 15.7 15.6 15.5 15.6 15.6 15.7 16.1 15.6 29.9 29.9 27.8 NS 0.904 0.903 0.904 0.906 0.904 0.904 0.904 0.899 0.904 0.658 0.658 0.703 MAE 1.643 1.655 1.639 1.603 1.640 1.642 1.646 1.675 1.639 3.295 3.295 3.007 GPI 0.003 - 0.017 0.011 0.069 0.010 0.006 - 0.003 - 0.130 0.011 - 4.931 - 4.931 - 4.084 Rank 6 8 2 1 4 5 7 9 3 12 11 10 Note. R2, NS, and GPI are dimensionless; RRMSE is a percentage (%); RMSE and MAE are both in MJ m−1 d−1; ∗∗ means a statistically significant correlation (P<0.01) (the same as shown in Tables 4–9).Table 4
Statistics performances of the 12 models in estimating global solar radiation in Central China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Wuhan R 2 0.850 ∗ ∗ 0.857 ∗ ∗ 0.850 ∗ ∗ 0.863 ∗ ∗ 0.850 ∗ ∗ 0.850 ∗ ∗ 0.850 ∗ ∗ 0.830 ∗ ∗ 0.850 ∗ ∗ 0.644 ∗ ∗ 0.644 ∗ ∗ 0.647 ∗ ∗ RMSE 3.141 3.067 3.147 3.016 3.142 3.147 3.142 3.340 3.142 5.141 5.141 4.709 RRMSE 26.1 25.4 26.1 25.0 26.1 26.1 26.1 27.7 26.1 42.6 42.6 39.1 NS 0.839 0.846 0.838 0.851 0.839 0.838 0.838 0.818 0.838 0.568 0.568 0.637 MAE 2.326 2.219 2.333 2.166 2.329 2.333 2.328 2.544 2.329 3.998 3.998 3.380   Changsha R 2 0.935 ∗ ∗ 0.931 ∗ ∗ 0.935 ∗ ∗ 0.937 ∗ ∗ 0.935 ∗ ∗ 0.935 ∗ ∗ 0.935 ∗ ∗ 0.921 ∗ ∗ 0.935 ∗ ∗ 0.675 ∗ ∗ 0.675 ∗ ∗ 0.731 ∗ ∗ RMSE 2.062 2.085 2.066 2.018 2.060 2.061 2.062 2.292 2.063 4.874 4.874 4.047 RRMSE 18.9 19.1 19.0 18.5 18.9 18.9 18.9 21.0 18.9 44.7 44.7 37.1 NS 0.927 0.926 0.927 0.930 0.928 0.927 0.927 0.910 0.927 0.594 0.594 0.720 MAE 1.648 1.676 1.651 1.602 1.646 1.648 1.648 1.846 1.649 3.984 3.984 2.903   Zhengzhou R 2 0.902 ∗ ∗ 0.908 ∗ ∗ 0.902 ∗ ∗ 0.917 ∗ ∗ 0.902 ∗ ∗ 0.902 ∗ ∗ 0.902 ∗ ∗ 0.883 ∗ ∗ 0.902 ∗ ∗ 0.688 ∗ ∗ 0.688 ∗ ∗ 0.727 ∗ ∗ RMSE 2.246 2.182 2.244 2.069 2.246 2.244 2.245 2.436 2.243 4.180 4.180 3.753 RRMSE 17.3 16.8 17.3 15.9 17.3 17.3 17.3 18.8 17.3 32.2 32.2 28.9 NS 0.900 0.906 0.900 0.915 0.900 0.900 0.900 0.882 0.900 0.653 0.653 0.721 MAE 1.646 1.606 1.644 1.484 1.645 1.644 1.645 1.818 1.643 3.269 3.269 2.780   Average R 2 0.896 ∗ ∗ 0.898 ∗ ∗ 0.896 ∗ ∗ 0.906 ∗ ∗ 0.896 ∗ ∗ 0.896 ∗ ∗ 0.896 ∗ ∗ 0.878 ∗ ∗ 0.896 ∗ ∗ 0.669 ∗ ∗ 0.669 ∗ ∗ 0.701 ∗ ∗ RMSE 2.483 2.445 2.486 2.368 2.482 2.484 2.483 2.689 2.483 4.732 4.732 4.170 RRMSE 20.8 20.5 20.8 19.8 20.8 20.8 20.8 22.5 20.8 39.9 39.9 35.0 NS 0.889 0.892 0.888 0.899 0.889 0.889 0.889 0.870 0.889 0.605 0.605 0.693 MAE 1.873 1.833 1.876 1.751 1.873 1.875 1.874 2.069 1.874 3.751 3.751 3.021 GPI 0.001 0.078 −0.003 0.236 0.002 −0.001 0.001 −0.407 0.002 −4.764 −4.764 −3.485 Rank 5 2 8 1 3 7 6 9 4 12 11 10Table 5
Statistics performances of the 12 models in estimating global solar radiation in Eastern China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Jinan R 2 0.906 ∗ ∗ 0.908 ∗ ∗ 0.906 ∗ ∗ 0.912 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.891 ∗ ∗ 0.907 ∗ ∗ 0.610 ∗ ∗ 0.610 ∗ ∗ 0.665 ∗ ∗ RMSE 2.565 2.565 2.558 2.491 2.570 2.523 2.569 2.679 2.456 4.828 4.828 4.592 RRMSE 18.0 18.0 18.0 17.5 18.0 17.7 18.0 18.8 17.2 33.9 33.9 32.2 NS 0.876 0.876 0.877 0.883 0.875 0.880 0.876 0.865 0.886 0.561 0.561 0.603 MAE 1.971 1.978 1.965 1.894 1.977 1.931 1.975 2.049 1.867 3.904 3.904 3.578   Nanchang R 2 0.898 ∗ ∗ 0.903 ∗ ∗ 0.898 ∗ ∗ 0.908 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.879 ∗ ∗ 0.898 ∗ ∗ 0.619 ∗ ∗ 0.619 ∗ ∗ 0.682 ∗ ∗ RMSE 2.507 2.449 2.507 2.384 2.506 2.504 2.508 2.725 2.506 5.190 5.190 4.438 RRMSE 20.2 19.8 20.2 19.2 20.2 20.2 20.3 22.0 20.2 41.9 41.9 35.8 NS 0.896 0.901 0.896 0.906 0.897 0.897 0.896 0.878 0.897 0.556 0.556 0.675 MAE 1.825 1.800 1.825 1.702 1.824 1.823 1.825 2.039 1.824 4.152 4.152 3.238   Shanghai R 2 0.895 ∗ ∗ 0.916 ∗ ∗ 0.895 ∗ ∗ 0.923 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.861 ∗ ∗ 0.895 ∗ ∗ 0.536 ∗ ∗ 0.536 ∗ ∗ 0.573 ∗ ∗ RMSE 2.410 2.177 2.417 2.100 2.455 2.413 2.413 2.754 2.414 4.929 4.928 4.715 RRMSE 18.8 17.0 18.8 16.4 19.1 18.8 18.8 21.5 18.8 38.4 38.4 36.8 NS 0.888 0.908 0.887 0.915 0.884 0.888 0.888 0.854 0.888 0.531 0.531 0.571 MAE 1.859 1.658 1.864 1.594 1.894 1.861 1.861 2.171 1.862 3.973 3.970 3.680   Average R 2 0.900 ∗ ∗ 0.909 ∗ ∗ 0.900 ∗ ∗ 0.914 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.877 ∗ ∗ 0.900 ∗ ∗ 0.588 ∗ ∗ 0.588 ∗ ∗ 0.640 ∗ ∗ RMSE 2.494 2.397 2.494 2.325 2.510 2.480 2.497 2.720 2.458 4.982 4.982 4.582 RRMSE 19.0 18.3 19.0 17.7 19.1 18.9 19.0 20.8 18.8 38.1 38.1 34.9 NS 0.887 0.895 0.887 0.901 0.885 0.888 0.887 0.865 0.890 0.549 0.549 0.616 MAE 1.885 1.812 1.885 1.730 1.898 1.872 1.887 2.086 1.851 4.010 4.009 3.499 GPI 0.002 0.160 0.002 0.284 −0.021 0.022 −0.002 −0.388 0.053 −4.716 −4.715 −3.838 Rank 5 2 6 1 8 4 7 9 3 12 11 10Table 6
Statistics performances of the 12 models in estimating global solar radiation in South China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Guangzhou R 2 0.897 ∗ ∗ 0.902 ∗ ∗ 0.897 ∗ ∗ 0.911 ∗ ∗ 0.896 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.871 ∗ ∗ 0.897 ∗ ∗ 0.613 ∗ ∗ 0.613 ∗ ∗ 0.705 ∗ ∗ RMSE 2.302 2.266 2.298 2.222 2.235 2.292 2.300 2.498 2.299 4.426 4.426 3.546 RRMSE 17.8 17.6 17.8 17.2 17.3 17.8 17.8 19.4 17.8 34.3 34.3 27.5 NS 0.868 0.872 0.868 0.877 0.875 0.869 0.868 0.844 0.868 0.510 0.510 0.686 MAE 1.926 1.904 1.922 1.870 1.857 1.916 1.924 2.055 1.923 3.759 3.759 2.775   Haikou R 2 0.882 ∗ ∗ 0.889 ∗ ∗ 0.882 ∗ ∗ 0.896 ∗ ∗ 0.882 ∗ ∗ 0.882 ∗ ∗ 0.882 ∗ ∗ 0.860 ∗ ∗ 0.882 ∗ ∗ 0.612 ∗ ∗ 0.612 ∗ ∗ 0.635 ∗ ∗ RMSE 2.725 2.669 2.729 2.554 2.727 2.727 2.721 2.951 2.724 5.190 5.190 4.753 RRMSE 19.0 18.6 19.0 17.8 19.0 19.0 18.9 20.5 19.0 36.1 36.1 33.1 NS 0.877 0.882 0.877 0.892 0.877 0.877 0.877 0.856 0.877 0.554 0.554 0.626 MAE 2.173 2.105 2.175 2.007 2.175 2.174 2.170 2.399 2.172 4.249 4.249 3.764   Nanning R 2 0.912 ∗ ∗ 0.921 ∗ ∗ 0.912 ∗ ∗ 0.927 ∗ ∗ 0.912 ∗ ∗ 0.912 ∗ ∗ 0.912 ∗ ∗ 0.886 ∗ ∗ 0.912 ∗ ∗ 0.732 ∗ ∗ 0.732 ∗ ∗ 0.748 ∗ ∗ RMSE 2.068 1.963 2.068 1.888 2.068 2.069 2.069 2.355 2.067 4.157 4.157 3.513 RRMSE 16.7 15.8 16.7 15.2 16.7 16.7 16.7 19.0 16.7 33.5 33.5 28.3 NS 0.911 0.920 0.911 0.926 0.911 0.911 0.911 0.885 0.911 0.642 0.642 0.744 MAE 1.624 1.540 1.623 1.451 1.624 1.625 1.625 1.905 1.623 3.466 3.466 2.654   Average R 2 0.897 ∗ ∗ 0.904 ∗ ∗ 0.897 ∗ ∗ 0.911 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.872 ∗ ∗ 0.897 ∗ ∗ 0.652 ∗ ∗ 0.652 ∗ ∗ 0.696 ∗ ∗ RMSE 2.365 2.299 2.365 2.222 2.343 2.363 2.363 2.601 2.363 4.591 4.591 3.937 RRMSE 17.8 17.3 17.8 16.7 17.7 17.8 17.8 19.6 17.8 34.6 34.6 29.6 NS 0.885 0.891 0.885 0.898 0.888 0.886 0.885 0.862 0.885 0.569 0.569 0.685 MAE 1.908 1.850 1.907 1.776 1.885 1.905 1.906 2.119 1.906 3.825 3.825 3.064 GPI −0.001 0.127 −0.001 0.278 0.035 0.003 0.001 −0.473 0.001 −4.722 −4.722 −3.273 Rank 8 2 7 1 3 4 6 9 5 12 11 10Table 7
Statistics performances of the 12 models in estimating global solar radiation in Northeast China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Harbin R 2 0.900 ∗ ∗ 0.903 ∗ ∗ 0.900 ∗ ∗ 0.904 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.886 ∗ ∗ 0.900 ∗ ∗ 0.711 ∗ ∗ 0.711 ∗ ∗ 0.732 ∗ ∗ RMSE 2.816 2.770 2.826 2.789 2.818 2.819 2.822 3.006 2.835 4.061 4.061 3.941 RRMSE 21.1 20.7 21.1 20.9 21.1 21.1 21.1 22.5 21.2 30.4 30.4 29.5 NS 0.855 0.860 0.854 0.858 0.855 0.855 0.855 0.835 0.853 0.699 0.699 0.717 MAE 2.132 2.089 2.141 2.106 2.134 2.134 2.137 2.298 2.149 3.062 3.062 2.939   Shenyang R 2 0.909 ∗ ∗ 0.911 ∗ ∗ 0.909 ∗ ∗ 0.913 ∗ ∗ 0.909 ∗ ∗ 0.909 ∗ ∗ 0.909 ∗ ∗ 0.895 ∗ ∗ 0.909 ∗ ∗ 0.656 ∗ ∗ 0.656 ∗ ∗ 0.692 ∗ ∗ RMSE 2.226 2.209 2.223 2.181 2.225 2.223 2.222 2.360 2.228 4.310 4.310 4.096 RRMSE 15.7 15.5 15.6 15.3 15.7 15.6 15.6 16.6 15.7 30.3 30.3 28.8 NS 0.906 0.908 0.906 0.910 0.906 0.906 0.906 0.894 0.906 0.648 0.648 0.682 MAE 1.628 1.629 1.626 1.595 1.628 1.626 1.624 1.712 1.630 3.357 3.357 3.140   Changchun R 2 0.945 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.946 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.934 ∗ ∗ 0.945 ∗ ∗ 0.680 ∗ ∗ 0.680 ∗ ∗ 0.731 ∗ ∗ RMSE 1.715 1.710 1.713 1.701 1.715 1.714 1.714 1.859 1.714 4.096 4.096 3.795 RRMSE 12.7 12.7 12.7 12.6 12.7 12.7 12.7 13.8 12.7 30.4 30.4 28.2 NS 0.944 0.944 0.944 0.945 0.944 0.944 0.944 0.934 0.944 0.679 0.679 0.724 MAE 1.296 1.290 1.294 1.281 1.296 1.295 1.295 1.403 1.295 3.098 3.098 2.786   Average R 2 0.918 ∗ ∗ 0.920 ∗ ∗ 0.918 ∗ ∗ 0.921 ∗ ∗ 0.918 ∗ ∗ 0.918 ∗ ∗ 0.918 ∗ ∗ 0.905 ∗ ∗ 0.918 ∗ ∗ 0.682 ∗ ∗ 0.682 ∗ ∗ 0.718 ∗ ∗ RMSE 2.252 2.230 2.254 2.224 2.253 2.252 2.253 2.408 2.259 4.156 4.156 3.944 RRMSE 16.5 16.3 16.5 16.3 16.5 16.5 16.5 17.6 16.5 30.4 30.4 28.8 NS 0.902 0.904 0.901 0.904 0.902 0.902 0.902 0.888 0.901 0.675 0.675 0.708 MAE 1.685 1.669 1.687 1.661 1.686 1.685 1.686 1.805 1.691 3.172 3.172 2.955 GPI 0.003 0.055 −0.001 0.072 0.002 0.003 0.002 −0.350 −0.011 −4.928 −4.928 −4.275 Rank 3 2 7 1 5 4 6 9 8 12 11 10Table 8
Statistics performances of the 12 models in estimating global solar radiation in Northwest China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Urumqi R 2 0.859 ∗ ∗ 0.857 ∗ ∗ 0.859 ∗ ∗ 0.858 ∗ ∗ 0.859 ∗ ∗ 0.859 ∗ ∗ 0.859 ∗ ∗ 0.858 ∗ ∗ 0.859 ∗ ∗ 0.660 ∗ ∗ 0.660 ∗ ∗ 0.675 ∗ ∗ RMSE 3.319 3.332 3.317 3.327 3.321 3.321 3.318 3.349 3.318 4.999 4.999 4.887 RRMSE 23.1 23.2 23.1 23.2 23.1 23.2 23.1 23.3 23.1 34.8 34.8 34.1 NS 0.849 0.848 0.849 0.848 0.849 0.849 0.849 0.846 0.849 0.657 0.657 0.672 MAE 2.344 2.356 2.342 2.350 2.344 2.346 2.343 2.384 2.343 3.668 3.668 3.619   Xian R 2 0.872 ∗ ∗ 0.874 ∗ ∗ 0.872 ∗ ∗ 0.877 ∗ ∗ 0.872 ∗ ∗ 0.872 ∗ ∗ 0.872 ∗ ∗ 0.857 ∗ ∗ 0.872 ∗ ∗ 0.659 ∗ ∗ 0.659 ∗ ∗ 0.726 ∗ ∗ RMSE 2.955 2.915 2.966 2.897 2.973 2.961 2.953 3.106 2.955 4.721 4.721 4.104 RRMSE 24.2 23.9 24.3 23.7 24.3 24.2 24.2 25.4 24.2 38.6 38.6 33.6 NS 0.853 0.857 0.852 0.859 0.852 0.853 0.854 0.838 0.853 0.626 0.626 0.717 MAE 2.172 2.193 2.180 2.155 2.184 2.176 2.171 2.273 2.172 3.681 3.681 2.957   Xining R 2 0.934 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.936 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.922 ∗ ∗ 0.934 ∗ ∗ 0.734 ∗ ∗ 0.734 ∗ ∗ 0.785 ∗ ∗ RMSE 1.808 1.806 1.807 1.771 1.807 1.809 1.807 1.969 1.807 3.594 3.594 3.233 RRMSE 11.6 11.5 11.6 11.3 11.6 11.6 11.6 12.6 11.6 23.0 23.0 20.7 NS 0.932 0.932 0.932 0.935 0.932 0.932 0.932 0.920 0.932 0.732 0.732 0.783 MAE 1.309 1.320 1.309 1.291 1.309 1.310 1.309 1.414 1.309 2.533 2.533 2.244   Average R 2 0.888 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.890 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.879 ∗ ∗ 0.888 ∗ ∗ 0.685 ∗ ∗ 0.685 ∗ ∗ 0.729 ∗ ∗ RMSE 2.694 2.684 2.697 2.665 2.700 2.697 2.693 2.808 2.693 4.438 4.438 4.075 RRMSE 19.6 19.5 19.7 19.4 19.7 19.7 19.6 20.4 19.6 32.2 32.2 29.4 NS 0.878 0.879 0.878 0.881 0.878 0.878 0.878 0.868 0.878 0.672 0.672 0.724 MAE 1.942 1.956 1.944 1.932 1.946 1.944 1.941 2.024 1.941 3.294 3.294 2.940 GPI 0.008 0.013 0.001 0.071 −0.006 0.001 0.010 −0.275 0.009 −4.929 −4.929 −3.787 Rank 5 2 6 1 8 7 3 9 4 12 11 10Table 9
Statistics performances of the 12 models in estimating global solar radiation in Southwest China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Chengdu R 2 0.875 ∗ ∗ 0.891 ∗ ∗ 0.875 ∗ ∗ 0.901 ∗ ∗ 0.875 ∗ ∗ 0.875 ∗ ∗ 0.875 ∗ ∗ 0.844 ∗ ∗ 0.875 ∗ ∗ 0.760 ∗ ∗ 0.760 ∗ ∗ 0.820 ∗ ∗ RMSE 2.771 2.600 2.794 2.550 2.774 2.779 2.772 3.039 2.786 3.697 3.697 2.830 RRMSE 27.7 26.0 28.0 25.5 27.8 27.8 27.8 30.4 27.9 37.0 37.0 28.3 NS 0.818 0.840 0.815 0.846 0.818 0.817 0.818 0.782 0.816 0.677 0.677 0.811 MAE 2.249 2.089 2.269 2.049 2.252 2.256 2.249 2.481 2.262 2.913 2.913 2.152   Kunming R 2 0.898 ∗ ∗ 0.893 ∗ ∗ 0.898 ∗ ∗ 0.901 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.881 ∗ ∗ 0.898 ∗ ∗ 0.648 ∗ ∗ 0.648 ∗ ∗ 0.735 ∗ ∗ RMSE 2.087 2.120 2.090 2.074 2.085 2.088 2.084 2.260 2.083 4.015 4.015 3.312 RRMSE 12.8 13.0 12.9 12.8 12.8 12.8 12.8 13.9 12.8 24.7 24.7 20.4 NS 0.894 0.890 0.893 0.895 0.894 0.894 0.894 0.875 0.894 0.606 0.606 0.732 MAE 1.555 1.598 1.558 1.535 1.553 1.556 1.552 1.757 1.551 3.264 3.264 2.432   Lasa R 2 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.907 ∗ ∗ 0.911 ∗ ∗ 0.670 ∗ ∗ 0.670 ∗ ∗ 0.702 ∗ ∗ RMSE 1.759 1.769 1.773 1.772 1.761 1.771 1.764 1.785 1.767 2.972 2.972 2.863 RRMSE 8.7 8.8 8.8 8.8 8.7 8.8 8.8 8.9 8.8 14.8 14.8 14.2 NS 0.882 0.880 0.880 0.880 0.881 0.880 0.881 0.878 0.881 0.662 0.662 0.687 MAE 1.247 1.251 1.258 1.259 1.248 1.256 1.250 1.311 1.253 2.235 2.235 2.072   Average R 2 0.895 ∗ ∗ 0.898 ∗ ∗ 0.895 ∗ ∗ 0.904 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.878 ∗ ∗ 0.895 ∗ ∗ 0.693 ∗ ∗ 0.693 ∗ ∗ 0.753 ∗ ∗ RMSE 2.206 2.163 2.219 2.132 2.207 2.212 2.206 2.361 2.212 3.561 3.561 3.002 RRMSE 16.4 16.0 16.5 15.7 16.4 16.5 16.4 17.7 16.5 25.5 25.5 21.0 NS 0.865 0.870 0.863 0.874 0.864 0.864 0.864 0.845 0.864 0.648 0.648 0.743 MAE 1.684 1.646 1.695 1.614 1.684 1.689 1.684 1.850 1.689 2.804 2.804 2.218 GPI 0.019 0.172 −0.019 0.290 0.016 0.000 0.017 −0.529 0.000 −4.710 −4.710 −2.662 Rank 3 2 8 1 5 6 4 9 7 11 12 10In North China, the BA model had the best estimation precision among the sunshine-based models, followed by Jin and DL models, with averageR2 of 0.923, 0.921, and 0.921, average RMSE of 2.209, 2.231, and 2.231 MJ m−2 d−1, average RRMSE of 15.5%, 15.6%, and 15.6%, average MAE of 1.603, 1.639, and 1.639 MJ m−2 d−1, average NS of 0.906, 0.904, and 0.904, and GPI of 0.069, 0.011, and 0.011, respectively. The BC model showed the highest estimation precision among the temperature-based models, with average R2 of 0.735, average RMSE of 3.953 MJ m−2 d−1, average RRMSE of 27.8%, average MAE of 3.007 MJ m−2 d−1, average NS of 0.703, and GPI of −4.084.In Central China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and LO models, with averageR2 of 0.906, 0.898, and 0.896, average RMSE of 2.368, 2.445, and 2.482 MJ m−2 d−1, average RRMSE of 19.8%, 20.5%, and 20.8%, average MAE of 1.751, 1.833, and 1.873 MJ m−2 d−1, average NS of 0.899, 0.892, and 0.889, and GPI of 0.236, 0.078, and 0.002, respectively. The BC model showed the best estimation precision among the temperature-based models, with average R2 of 0.701, average RMSE of 4.170 MJ m−2 d−1, average RRMSE of 35.0%, average MAE of 3.021 MJ m−2 d−1, average NS of 0.693, and GPI of −3.485.In Eastern China, the BA model showed the best estimation precision compared with other sunshine-based models, followed by OG and DL models, with averageR2 of 0.914, 0.909, and 0.900, average RMSE of 2.325, 2.397, and 2.458 MJ m−2 d−1, average RRMSE of 17.7%, 18.3%, and 18.8%, average MAE of 1.730, 1.812, and 1.851 MJ m−2 d−1, average NS of 0.901, 0.895, and 0.890, and GPI of 0.284, 0.160, and 0.035, respectively. The BC model showed the best performance among the temperature-based models, with average R2 of 0.640, average RMSE of 4.582 MJ m−2 d−1, average RRMSE of 34.9%, average MAE of 3.449 MJ m−2 d−1, average NS of 0.616, and GPI of −3.838.In South China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and LO models, with averageR2 of 0.911, 0.904, and 0.897, average RMSE of 2.222, 2.299, and 2.343 MJ m−2 d−1, average RRMSE of 16.7%, 17.3%, and 17.7%, average MAE of 1.776, 1.850, and 1.885 MJ m−2 d−1, average NS of 0.898, 0.891, and 0.888, and GPI of 0.278, 0.127, and 0.035, respectively. The BC model had the best estimation precision compared with the other temperature-based models, with average R2 of 0.696, average RMSE of 3.937 MJ m−2 d−1, average RRMSE of 29.6%, average MAE of 3.064 MJ m−2 d−1, average NS of 0.685, and GPI of −3.273.In Northeast China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with averageR2 of 0.921, 0.920, and 0.918, average RMSE of 2.224, 2.230, and 2.252 MJ m−2 d−1, average RRMSE of 16.3%, 16.3%, and 16.5%, average MAE of 1.661, 1.669, and 1.685 MJ m−2 d−1, average NS of 0.904, 0.904, and 0.902, and GPI of 0.072, 0.055, and 0.003, respectively. The BC model had the highest estimation precision among the temperature-based models, with average R2 of 0.718, average RMSE of 3.944 MJ m−2 d−1, average RRMSE of 28.8%, average MAE of 2.955 MJ m−2 d−1, average NS of 0.708, and GPI of −4.275.In Northwest China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and EM models, with averageR2 of 0.890, 0.888, and 0.888, average RMSE of 2.665, 2.684, and 2.693 MJ m−2 d−1, average RRMSE of 19.4%, 19.5%, and 19.6%, average MAE of 1.932, 1.956, and 1.941 MJ m−2 d−1, average NS of 0.881, 0.879, and 0.878, and GPI of 0.071, 0.013, and 0.010, respectively. The BC model had the best estimation precision compared with the temperature-based models, with average R2 of 0.729, average RMSE of 4.075 MJ m−2 d−1, average RRMSE of 29.4%, average MAE of 2.940 MJ m−2 d−1, average NS of 0.724, and GPI of −3.787.In Southwest China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with averageR2 of 0.904, 0.898, and 0.895, average RMSE of 2.132, 2.163, and 2.206 MJ m−2 d−1, average RRMSE of 15.7%, 16.0%, and 16.4%, average MAE of 1.614, 1.646, and 1.684 MJ m−2 d−1, average NS of 0.874, 0.870, and 0.865, and GPI of 0.290, 0.172, and 0.019, respectively. The BC model showed the best performance among the temperature-based models, with average R2 of 0.753, average RMSE of 3.002 MJ m−2 d−1, average RRMSE of 21.0%, average MAE of 2.218 MJ m−2 d−1, average NS of 0.743, and GPI of −2.662.Comparison between estimated and measured monthly average dailyRs and relative error (RE) of different models for each subzone are presented in Figure 2. As shown in Figure 2, the estimated and measured monthly average daily Rs had good agreements. In addition to Wuhan, Nanchang, Shanghai, Chengdu, and Kunming stations, the estimated and measured Rs all presented parabolic variation. For the 9 sunshine-based models (AP, OG, Jin, BA, LO, GM, EM, AH, and DL), the average RE was in the range 1.71%~12.94%, 1.59%~12.72%, 1.71%~13.38%, 1.61%~13.17%, 1.67%~12.98%, 1.74%~13.09%, 1.70%~12.95%, 1.93%~13.19%, and 1.68%~13.20%, respectively. For the 3 temperature-based models (HS, AN, and BC), the average RE was in the range 3.33%~21.96%, 3.33%~21.96%, and 3.18%~15.16%, respectively. This means the sunshine-based models had a better performance for monthly average daily Rs compared with the temperature-based models, and the OG model had the lowest RE value between the sunshine-based models, followed by DL and GM models, with average RE of 5.66%, 5.73%, and 5.80%. In the temperature-based models, BC model had the lowest RE value, with average RE of 8.26%, and the RE of HS and AN models RE had a large variation in a year. For the 7 subzones (North China, Central China, East China, South China, Northeast China, Northwest China, and Southwest China), the models with the lowest RE were Jin, OG, DL, LO, AP, OG, and HS models, respectively, with average RE of 4.87%, 6.77%, 4.79%, 4.81%, 5.71%, 5.09%, and 5.08%. In Taiyuan, Jinan, Harbin, and Chengdu stations, all the models trended to underestimate the monthly average daily Rs. Overall, there were large differences for models in under/overestimating Rs at different climatic zones.Figure 2
Comparison between monthly average daily global solar radiation and relative error of each model in China.
(a)
North China (b)
Central China  (c)
East China (d)
South China  (e)
Northeast China (f)
Northwest China  (g)
Southwest China


## 3.1. Calibration of Empirical Coefficients

The empirical coefficients of the 12 models were calibrated based on the least squares method forRs estimation using the meteorological variables obtained from 21 meteorological stations during 1995~2010, and the adjusted coefficients of each subzone are shown in Table 2. As shown in Table 2, the calibrated a and b of the AP model ranged between 0.161~0.214 and 0.532~0.555, respectively. The calibrated a, b, and c of the OG model ranged between 0.144~0.202, 0.605~0.798, and −0.313~−0.082, respectively. The calibrated a, b, c, and d of Jin model ranged between 1.805~2.068, −2.227~−2.048, −0.101~0.027, and 0.532~0.555, respectively. The calibrated a, b, c, and d of the BA model ranged between 0.134~0.190, 0.867~1.261, −1.799~−0.739, and 0.443~1.158, respectively. The calibrated a and b of the LO model ranged between 0.161~0.214 and 0.608~0.635, respectively. The calibrated a and b of the GM model ranged between 0.185~0.269 and 0.532~0.555, respectively. The calibrated a, b, c, and d of the EM model ranged between 0.130~0.163, 0.005~0.034, 0.029~0.037, and 0.532~0.555, respectively. The calibrated a and b of the AH model ranged between −0.165~−0.085 and 0.325~0.358, respectively. The calibrated a, b, c, and d of the DL model ranged between 0.198~0.260, 0.082~0.109, −0.090~−0.065, and 0.456~0.524, respectively. The calibrated a of HS and AN models were both in the range 0.139~0.155. The calibrated a, b, and c of the BC model ranged between 0.552~0.695, 0.018~0.030, and 1.740~2.269, respectively. The regression coefficients were different in different climate zones. This can be explained as a consequence of local and seasonal changes in the type and thickness of cloud cover, the effects of snow covered surfaces, the concentrations of pollutants, and latitude [6, 34, 40].Table 2
Calibration empirical coefficients for the studied models in different subzones of China.
Model Coefficient North China Central China East China South China Northeast Northwest Southwest Ångström-Prescott (AP) a 0.182 0.161 0.167 0.171 0.193 0.193 0.214 b 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Ögelman (OG) a 0.174 0.144 0.149 0.154 0.180 0.180 0.202 b 0.605 0.798 0.785 0.793 0.655 0.685 0.685 c - 0.082 - 0.313 - 0.283 - 0.307 - 0.126 - 0.163 - 0.167  Jin a 1.896 1.975 1.965 2.068 1.805 1.977 2.061 b - 2.174 - 2.124 - 2.130 - 2.048 - 2.227 - 2.110 - 2.052 c - 0.018 0.021 0.016 0.027 - 0.015 - 0.101 - 0.027 d 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Bahel (BA) a 0.160 0.134 0.138 0.142 0.171 0.174 0.190 b 1.011 1.261 1.209 1.224 0.867 0.912 0.992 c - 1.265 - 1.799 - 1.610 - 1.745 - 0.739 - 0.860 - 1.148 d 0.856 1.147 1.006 1.158 0.443 0.524 0.776  Louche (LO) a 0.182 0.161 0.167 0.171 0.193 0.193 0.214 b 0.608 0.621 0.630 0.635 0.617 0.623 0.631  Glover-McCulloch (GM) a 0.234 0.189 0.198 0.185 0.269 0.246 0.244 b 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Elagib-Mansell (EM) a 0.154 0.149 0.154 0.163 0.163 0.142 0.130 b 0.024 0.017 0.016 0.018 0.034 0.013 0.005 c 0.032 0.030 0.030 0.029 0.030 0.037 0.037 d 0.532 0.543 0.551 0.555 0.540 0.545 0.552  Almorox-Hontoria (AH) a - 0.114 - 0.165 - 0.156 - 0.165 - 0.099 - 0.107 - 0.085 b 0.325 0.344 0.345 0.358 0.325 0.331 0.336  Dogniaux-Lemoine (DL) a 0.243 0.209 0.216 0.198 0.260 0.252 0.246 b 0.102 0.097 0.101 0.082 0.109 0.108 0.095 c - 0.090 - 0.089 - 0.088 - 0.069 - 0.087 - 0.088 - 0.065 d 0.462 0.490 0.494 0.524 0.456 0.471 0.504  Hargreaves-Samani (HS) a 0.148 0.139 0.155 0.148 0.153 0.148 0.149  Annandale (AN) a 0.148 0.139 0.155 0.148 0.153 0.148 0.149  Bristow-Campbell (BC) a 0.602 0.552 0.552 0.561 0.619 0.647 0.695 b 0.023 0.018 0.025 0.028 0.030 0.027 0.019 c 1.872 2.194 2.269 2.051 1.801 1.740 1.848


## 3.2. Performances of the Models

The statistic performances of the analyzed models in estimating dailyRs for each zone of China are shown in Tables 3–9. As shown in Tables 3–9, there were good agreements between the estimations and the measurements. The estimated and measured daily Rs had statistically significant correlations for all the 12 models at the 21 meteorological stations (P<0.01). The statistical results showed that the sunshine-based models were more accurate for daily Rs estimation at the 7 subzones of China compared with the temperature-based models.Table 3
Statistics performances of the 12 models in estimating global solar radiation in North China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Beijing R 2 0.928 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.930 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.928 ∗ ∗ 0.921 ∗ ∗ 0.928 ∗ ∗ 0.659 ∗ ∗ 0.659 ∗ ∗ 0.710 ∗ ∗ RMSE 2.030 2.037 2.028 2.007 2.027 2.029 2.035 2.103 2.027 4.273 4.273 3.965 RRMSE 14.7 14.7 14.7 14.5 14.7 14.7 14.7 15.2 14.7 30.9 30.9 28.7 NS 0.921 0.921 0.921 0.923 0.921 0.921 0.921 0.915 0.921 0.651 0.651 0.699 MAE 1.463 1.471 1.461 1.404 1.459 1.462 1.467 1.505 1.459 3.314 3.314 2.986   Laoting R 2 0.929 ∗ ∗ 0.928 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.929 ∗ ∗ 0.920 ∗ ∗ 0.929 ∗ ∗ 0.690 ∗ ∗ 0.690 ∗ ∗ 0.747 ∗ ∗ RMSE 1.866 1.878 1.863 1.855 1.866 1.867 1.868 1.971 1.863 3.866 3.866 3.493 RRMSE 13.5 13.6 13.5 13.5 13.5 13.6 13.6 14.3 13.5 28.1 28.1 25.4 NS 0.927 0.927 0.928 0.928 0.927 0.927 0.927 0.919 0.928 0.689 0.689 0.746 MAE 1.350 1.374 1.348 1.335 1.349 1.351 1.351 1.401 1.348 2.991 2.991 2.665   Taiyuan R 2 0.906 ∗ ∗ 0.905 ∗ ∗ 0.906 ∗ ∗ 0.909 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.901 ∗ ∗ 0.906 ∗ ∗ 0.709 ∗ ∗ 0.709 ∗ ∗ 0.747 ∗ ∗ RMSE 2.809 2.814 2.802 2.765 2.802 2.806 2.814 2.828 2.804 4.592 4.592 4.400 RRMSE 18.7 18.7 18.7 18.4 18.7 18.7 18.7 18.8 18.7 30.6 30.6 29.3 NS 0.864 0.863 0.864 0.868 0.864 0.864 0.863 0.862 0.864 0.635 0.635 0.665 MAE 2.115 2.121 2.109 2.070 2.110 2.113 2.119 2.118 2.111 3.579 3.579 3.370   Average R 2 0.921 ∗ ∗ 0.920 ∗ ∗ 0.921 ∗ ∗ 0.923 ∗ ∗ 0.921 ∗ ∗ 0.921 ∗ ∗ 0.921 ∗ ∗ 0.914 ∗ ∗ 0.921 ∗ ∗ 0.686 ∗ ∗ 0.686 ∗ ∗ 0.735 ∗ ∗ RMSE 2.235 2.243 2.231 2.209 2.232 2.234 2.239 2.301 2.231 4.244 4.244 3.953 RRMSE 15.6 15.7 15.6 15.5 15.6 15.6 15.7 16.1 15.6 29.9 29.9 27.8 NS 0.904 0.903 0.904 0.906 0.904 0.904 0.904 0.899 0.904 0.658 0.658 0.703 MAE 1.643 1.655 1.639 1.603 1.640 1.642 1.646 1.675 1.639 3.295 3.295 3.007 GPI 0.003 - 0.017 0.011 0.069 0.010 0.006 - 0.003 - 0.130 0.011 - 4.931 - 4.931 - 4.084 Rank 6 8 2 1 4 5 7 9 3 12 11 10 Note. R2, NS, and GPI are dimensionless; RRMSE is a percentage (%); RMSE and MAE are both in MJ m−1 d−1; ∗∗ means a statistically significant correlation (P<0.01) (the same as shown in Tables 4–9).Table 4
Statistics performances of the 12 models in estimating global solar radiation in Central China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Wuhan R 2 0.850 ∗ ∗ 0.857 ∗ ∗ 0.850 ∗ ∗ 0.863 ∗ ∗ 0.850 ∗ ∗ 0.850 ∗ ∗ 0.850 ∗ ∗ 0.830 ∗ ∗ 0.850 ∗ ∗ 0.644 ∗ ∗ 0.644 ∗ ∗ 0.647 ∗ ∗ RMSE 3.141 3.067 3.147 3.016 3.142 3.147 3.142 3.340 3.142 5.141 5.141 4.709 RRMSE 26.1 25.4 26.1 25.0 26.1 26.1 26.1 27.7 26.1 42.6 42.6 39.1 NS 0.839 0.846 0.838 0.851 0.839 0.838 0.838 0.818 0.838 0.568 0.568 0.637 MAE 2.326 2.219 2.333 2.166 2.329 2.333 2.328 2.544 2.329 3.998 3.998 3.380   Changsha R 2 0.935 ∗ ∗ 0.931 ∗ ∗ 0.935 ∗ ∗ 0.937 ∗ ∗ 0.935 ∗ ∗ 0.935 ∗ ∗ 0.935 ∗ ∗ 0.921 ∗ ∗ 0.935 ∗ ∗ 0.675 ∗ ∗ 0.675 ∗ ∗ 0.731 ∗ ∗ RMSE 2.062 2.085 2.066 2.018 2.060 2.061 2.062 2.292 2.063 4.874 4.874 4.047 RRMSE 18.9 19.1 19.0 18.5 18.9 18.9 18.9 21.0 18.9 44.7 44.7 37.1 NS 0.927 0.926 0.927 0.930 0.928 0.927 0.927 0.910 0.927 0.594 0.594 0.720 MAE 1.648 1.676 1.651 1.602 1.646 1.648 1.648 1.846 1.649 3.984 3.984 2.903   Zhengzhou R 2 0.902 ∗ ∗ 0.908 ∗ ∗ 0.902 ∗ ∗ 0.917 ∗ ∗ 0.902 ∗ ∗ 0.902 ∗ ∗ 0.902 ∗ ∗ 0.883 ∗ ∗ 0.902 ∗ ∗ 0.688 ∗ ∗ 0.688 ∗ ∗ 0.727 ∗ ∗ RMSE 2.246 2.182 2.244 2.069 2.246 2.244 2.245 2.436 2.243 4.180 4.180 3.753 RRMSE 17.3 16.8 17.3 15.9 17.3 17.3 17.3 18.8 17.3 32.2 32.2 28.9 NS 0.900 0.906 0.900 0.915 0.900 0.900 0.900 0.882 0.900 0.653 0.653 0.721 MAE 1.646 1.606 1.644 1.484 1.645 1.644 1.645 1.818 1.643 3.269 3.269 2.780   Average R 2 0.896 ∗ ∗ 0.898 ∗ ∗ 0.896 ∗ ∗ 0.906 ∗ ∗ 0.896 ∗ ∗ 0.896 ∗ ∗ 0.896 ∗ ∗ 0.878 ∗ ∗ 0.896 ∗ ∗ 0.669 ∗ ∗ 0.669 ∗ ∗ 0.701 ∗ ∗ RMSE 2.483 2.445 2.486 2.368 2.482 2.484 2.483 2.689 2.483 4.732 4.732 4.170 RRMSE 20.8 20.5 20.8 19.8 20.8 20.8 20.8 22.5 20.8 39.9 39.9 35.0 NS 0.889 0.892 0.888 0.899 0.889 0.889 0.889 0.870 0.889 0.605 0.605 0.693 MAE 1.873 1.833 1.876 1.751 1.873 1.875 1.874 2.069 1.874 3.751 3.751 3.021 GPI 0.001 0.078 −0.003 0.236 0.002 −0.001 0.001 −0.407 0.002 −4.764 −4.764 −3.485 Rank 5 2 8 1 3 7 6 9 4 12 11 10Table 5
Statistics performances of the 12 models in estimating global solar radiation in Eastern China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Jinan R 2 0.906 ∗ ∗ 0.908 ∗ ∗ 0.906 ∗ ∗ 0.912 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.906 ∗ ∗ 0.891 ∗ ∗ 0.907 ∗ ∗ 0.610 ∗ ∗ 0.610 ∗ ∗ 0.665 ∗ ∗ RMSE 2.565 2.565 2.558 2.491 2.570 2.523 2.569 2.679 2.456 4.828 4.828 4.592 RRMSE 18.0 18.0 18.0 17.5 18.0 17.7 18.0 18.8 17.2 33.9 33.9 32.2 NS 0.876 0.876 0.877 0.883 0.875 0.880 0.876 0.865 0.886 0.561 0.561 0.603 MAE 1.971 1.978 1.965 1.894 1.977 1.931 1.975 2.049 1.867 3.904 3.904 3.578   Nanchang R 2 0.898 ∗ ∗ 0.903 ∗ ∗ 0.898 ∗ ∗ 0.908 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.879 ∗ ∗ 0.898 ∗ ∗ 0.619 ∗ ∗ 0.619 ∗ ∗ 0.682 ∗ ∗ RMSE 2.507 2.449 2.507 2.384 2.506 2.504 2.508 2.725 2.506 5.190 5.190 4.438 RRMSE 20.2 19.8 20.2 19.2 20.2 20.2 20.3 22.0 20.2 41.9 41.9 35.8 NS 0.896 0.901 0.896 0.906 0.897 0.897 0.896 0.878 0.897 0.556 0.556 0.675 MAE 1.825 1.800 1.825 1.702 1.824 1.823 1.825 2.039 1.824 4.152 4.152 3.238   Shanghai R 2 0.895 ∗ ∗ 0.916 ∗ ∗ 0.895 ∗ ∗ 0.923 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.861 ∗ ∗ 0.895 ∗ ∗ 0.536 ∗ ∗ 0.536 ∗ ∗ 0.573 ∗ ∗ RMSE 2.410 2.177 2.417 2.100 2.455 2.413 2.413 2.754 2.414 4.929 4.928 4.715 RRMSE 18.8 17.0 18.8 16.4 19.1 18.8 18.8 21.5 18.8 38.4 38.4 36.8 NS 0.888 0.908 0.887 0.915 0.884 0.888 0.888 0.854 0.888 0.531 0.531 0.571 MAE 1.859 1.658 1.864 1.594 1.894 1.861 1.861 2.171 1.862 3.973 3.970 3.680   Average R 2 0.900 ∗ ∗ 0.909 ∗ ∗ 0.900 ∗ ∗ 0.914 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.877 ∗ ∗ 0.900 ∗ ∗ 0.588 ∗ ∗ 0.588 ∗ ∗ 0.640 ∗ ∗ RMSE 2.494 2.397 2.494 2.325 2.510 2.480 2.497 2.720 2.458 4.982 4.982 4.582 RRMSE 19.0 18.3 19.0 17.7 19.1 18.9 19.0 20.8 18.8 38.1 38.1 34.9 NS 0.887 0.895 0.887 0.901 0.885 0.888 0.887 0.865 0.890 0.549 0.549 0.616 MAE 1.885 1.812 1.885 1.730 1.898 1.872 1.887 2.086 1.851 4.010 4.009 3.499 GPI 0.002 0.160 0.002 0.284 −0.021 0.022 −0.002 −0.388 0.053 −4.716 −4.715 −3.838 Rank 5 2 6 1 8 4 7 9 3 12 11 10Table 6
Statistics performances of the 12 models in estimating global solar radiation in South China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Guangzhou R 2 0.897 ∗ ∗ 0.902 ∗ ∗ 0.897 ∗ ∗ 0.911 ∗ ∗ 0.896 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.871 ∗ ∗ 0.897 ∗ ∗ 0.613 ∗ ∗ 0.613 ∗ ∗ 0.705 ∗ ∗ RMSE 2.302 2.266 2.298 2.222 2.235 2.292 2.300 2.498 2.299 4.426 4.426 3.546 RRMSE 17.8 17.6 17.8 17.2 17.3 17.8 17.8 19.4 17.8 34.3 34.3 27.5 NS 0.868 0.872 0.868 0.877 0.875 0.869 0.868 0.844 0.868 0.510 0.510 0.686 MAE 1.926 1.904 1.922 1.870 1.857 1.916 1.924 2.055 1.923 3.759 3.759 2.775   Haikou R 2 0.882 ∗ ∗ 0.889 ∗ ∗ 0.882 ∗ ∗ 0.896 ∗ ∗ 0.882 ∗ ∗ 0.882 ∗ ∗ 0.882 ∗ ∗ 0.860 ∗ ∗ 0.882 ∗ ∗ 0.612 ∗ ∗ 0.612 ∗ ∗ 0.635 ∗ ∗ RMSE 2.725 2.669 2.729 2.554 2.727 2.727 2.721 2.951 2.724 5.190 5.190 4.753 RRMSE 19.0 18.6 19.0 17.8 19.0 19.0 18.9 20.5 19.0 36.1 36.1 33.1 NS 0.877 0.882 0.877 0.892 0.877 0.877 0.877 0.856 0.877 0.554 0.554 0.626 MAE 2.173 2.105 2.175 2.007 2.175 2.174 2.170 2.399 2.172 4.249 4.249 3.764   Nanning R 2 0.912 ∗ ∗ 0.921 ∗ ∗ 0.912 ∗ ∗ 0.927 ∗ ∗ 0.912 ∗ ∗ 0.912 ∗ ∗ 0.912 ∗ ∗ 0.886 ∗ ∗ 0.912 ∗ ∗ 0.732 ∗ ∗ 0.732 ∗ ∗ 0.748 ∗ ∗ RMSE 2.068 1.963 2.068 1.888 2.068 2.069 2.069 2.355 2.067 4.157 4.157 3.513 RRMSE 16.7 15.8 16.7 15.2 16.7 16.7 16.7 19.0 16.7 33.5 33.5 28.3 NS 0.911 0.920 0.911 0.926 0.911 0.911 0.911 0.885 0.911 0.642 0.642 0.744 MAE 1.624 1.540 1.623 1.451 1.624 1.625 1.625 1.905 1.623 3.466 3.466 2.654   Average R 2 0.897 ∗ ∗ 0.904 ∗ ∗ 0.897 ∗ ∗ 0.911 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.897 ∗ ∗ 0.872 ∗ ∗ 0.897 ∗ ∗ 0.652 ∗ ∗ 0.652 ∗ ∗ 0.696 ∗ ∗ RMSE 2.365 2.299 2.365 2.222 2.343 2.363 2.363 2.601 2.363 4.591 4.591 3.937 RRMSE 17.8 17.3 17.8 16.7 17.7 17.8 17.8 19.6 17.8 34.6 34.6 29.6 NS 0.885 0.891 0.885 0.898 0.888 0.886 0.885 0.862 0.885 0.569 0.569 0.685 MAE 1.908 1.850 1.907 1.776 1.885 1.905 1.906 2.119 1.906 3.825 3.825 3.064 GPI −0.001 0.127 −0.001 0.278 0.035 0.003 0.001 −0.473 0.001 −4.722 −4.722 −3.273 Rank 8 2 7 1 3 4 6 9 5 12 11 10Table 7
Statistics performances of the 12 models in estimating global solar radiation in Northeast China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Harbin R 2 0.900 ∗ ∗ 0.903 ∗ ∗ 0.900 ∗ ∗ 0.904 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.900 ∗ ∗ 0.886 ∗ ∗ 0.900 ∗ ∗ 0.711 ∗ ∗ 0.711 ∗ ∗ 0.732 ∗ ∗ RMSE 2.816 2.770 2.826 2.789 2.818 2.819 2.822 3.006 2.835 4.061 4.061 3.941 RRMSE 21.1 20.7 21.1 20.9 21.1 21.1 21.1 22.5 21.2 30.4 30.4 29.5 NS 0.855 0.860 0.854 0.858 0.855 0.855 0.855 0.835 0.853 0.699 0.699 0.717 MAE 2.132 2.089 2.141 2.106 2.134 2.134 2.137 2.298 2.149 3.062 3.062 2.939   Shenyang R 2 0.909 ∗ ∗ 0.911 ∗ ∗ 0.909 ∗ ∗ 0.913 ∗ ∗ 0.909 ∗ ∗ 0.909 ∗ ∗ 0.909 ∗ ∗ 0.895 ∗ ∗ 0.909 ∗ ∗ 0.656 ∗ ∗ 0.656 ∗ ∗ 0.692 ∗ ∗ RMSE 2.226 2.209 2.223 2.181 2.225 2.223 2.222 2.360 2.228 4.310 4.310 4.096 RRMSE 15.7 15.5 15.6 15.3 15.7 15.6 15.6 16.6 15.7 30.3 30.3 28.8 NS 0.906 0.908 0.906 0.910 0.906 0.906 0.906 0.894 0.906 0.648 0.648 0.682 MAE 1.628 1.629 1.626 1.595 1.628 1.626 1.624 1.712 1.630 3.357 3.357 3.140   Changchun R 2 0.945 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.946 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.945 ∗ ∗ 0.934 ∗ ∗ 0.945 ∗ ∗ 0.680 ∗ ∗ 0.680 ∗ ∗ 0.731 ∗ ∗ RMSE 1.715 1.710 1.713 1.701 1.715 1.714 1.714 1.859 1.714 4.096 4.096 3.795 RRMSE 12.7 12.7 12.7 12.6 12.7 12.7 12.7 13.8 12.7 30.4 30.4 28.2 NS 0.944 0.944 0.944 0.945 0.944 0.944 0.944 0.934 0.944 0.679 0.679 0.724 MAE 1.296 1.290 1.294 1.281 1.296 1.295 1.295 1.403 1.295 3.098 3.098 2.786   Average R 2 0.918 ∗ ∗ 0.920 ∗ ∗ 0.918 ∗ ∗ 0.921 ∗ ∗ 0.918 ∗ ∗ 0.918 ∗ ∗ 0.918 ∗ ∗ 0.905 ∗ ∗ 0.918 ∗ ∗ 0.682 ∗ ∗ 0.682 ∗ ∗ 0.718 ∗ ∗ RMSE 2.252 2.230 2.254 2.224 2.253 2.252 2.253 2.408 2.259 4.156 4.156 3.944 RRMSE 16.5 16.3 16.5 16.3 16.5 16.5 16.5 17.6 16.5 30.4 30.4 28.8 NS 0.902 0.904 0.901 0.904 0.902 0.902 0.902 0.888 0.901 0.675 0.675 0.708 MAE 1.685 1.669 1.687 1.661 1.686 1.685 1.686 1.805 1.691 3.172 3.172 2.955 GPI 0.003 0.055 −0.001 0.072 0.002 0.003 0.002 −0.350 −0.011 −4.928 −4.928 −4.275 Rank 3 2 7 1 5 4 6 9 8 12 11 10Table 8
Statistics performances of the 12 models in estimating global solar radiation in Northwest China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Urumqi R 2 0.859 ∗ ∗ 0.857 ∗ ∗ 0.859 ∗ ∗ 0.858 ∗ ∗ 0.859 ∗ ∗ 0.859 ∗ ∗ 0.859 ∗ ∗ 0.858 ∗ ∗ 0.859 ∗ ∗ 0.660 ∗ ∗ 0.660 ∗ ∗ 0.675 ∗ ∗ RMSE 3.319 3.332 3.317 3.327 3.321 3.321 3.318 3.349 3.318 4.999 4.999 4.887 RRMSE 23.1 23.2 23.1 23.2 23.1 23.2 23.1 23.3 23.1 34.8 34.8 34.1 NS 0.849 0.848 0.849 0.848 0.849 0.849 0.849 0.846 0.849 0.657 0.657 0.672 MAE 2.344 2.356 2.342 2.350 2.344 2.346 2.343 2.384 2.343 3.668 3.668 3.619   Xian R 2 0.872 ∗ ∗ 0.874 ∗ ∗ 0.872 ∗ ∗ 0.877 ∗ ∗ 0.872 ∗ ∗ 0.872 ∗ ∗ 0.872 ∗ ∗ 0.857 ∗ ∗ 0.872 ∗ ∗ 0.659 ∗ ∗ 0.659 ∗ ∗ 0.726 ∗ ∗ RMSE 2.955 2.915 2.966 2.897 2.973 2.961 2.953 3.106 2.955 4.721 4.721 4.104 RRMSE 24.2 23.9 24.3 23.7 24.3 24.2 24.2 25.4 24.2 38.6 38.6 33.6 NS 0.853 0.857 0.852 0.859 0.852 0.853 0.854 0.838 0.853 0.626 0.626 0.717 MAE 2.172 2.193 2.180 2.155 2.184 2.176 2.171 2.273 2.172 3.681 3.681 2.957   Xining R 2 0.934 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.936 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.934 ∗ ∗ 0.922 ∗ ∗ 0.934 ∗ ∗ 0.734 ∗ ∗ 0.734 ∗ ∗ 0.785 ∗ ∗ RMSE 1.808 1.806 1.807 1.771 1.807 1.809 1.807 1.969 1.807 3.594 3.594 3.233 RRMSE 11.6 11.5 11.6 11.3 11.6 11.6 11.6 12.6 11.6 23.0 23.0 20.7 NS 0.932 0.932 0.932 0.935 0.932 0.932 0.932 0.920 0.932 0.732 0.732 0.783 MAE 1.309 1.320 1.309 1.291 1.309 1.310 1.309 1.414 1.309 2.533 2.533 2.244   Average R 2 0.888 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.890 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.888 ∗ ∗ 0.879 ∗ ∗ 0.888 ∗ ∗ 0.685 ∗ ∗ 0.685 ∗ ∗ 0.729 ∗ ∗ RMSE 2.694 2.684 2.697 2.665 2.700 2.697 2.693 2.808 2.693 4.438 4.438 4.075 RRMSE 19.6 19.5 19.7 19.4 19.7 19.7 19.6 20.4 19.6 32.2 32.2 29.4 NS 0.878 0.879 0.878 0.881 0.878 0.878 0.878 0.868 0.878 0.672 0.672 0.724 MAE 1.942 1.956 1.944 1.932 1.946 1.944 1.941 2.024 1.941 3.294 3.294 2.940 GPI 0.008 0.013 0.001 0.071 −0.006 0.001 0.010 −0.275 0.009 −4.929 −4.929 −3.787 Rank 5 2 6 1 8 7 3 9 4 12 11 10Table 9
Statistics performances of the 12 models in estimating global solar radiation in Southwest China.
Stations Evaluation index AP OG Jin BA LO GM EM AH DL HS AN BC Chengdu R 2 0.875 ∗ ∗ 0.891 ∗ ∗ 0.875 ∗ ∗ 0.901 ∗ ∗ 0.875 ∗ ∗ 0.875 ∗ ∗ 0.875 ∗ ∗ 0.844 ∗ ∗ 0.875 ∗ ∗ 0.760 ∗ ∗ 0.760 ∗ ∗ 0.820 ∗ ∗ RMSE 2.771 2.600 2.794 2.550 2.774 2.779 2.772 3.039 2.786 3.697 3.697 2.830 RRMSE 27.7 26.0 28.0 25.5 27.8 27.8 27.8 30.4 27.9 37.0 37.0 28.3 NS 0.818 0.840 0.815 0.846 0.818 0.817 0.818 0.782 0.816 0.677 0.677 0.811 MAE 2.249 2.089 2.269 2.049 2.252 2.256 2.249 2.481 2.262 2.913 2.913 2.152   Kunming R 2 0.898 ∗ ∗ 0.893 ∗ ∗ 0.898 ∗ ∗ 0.901 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.898 ∗ ∗ 0.881 ∗ ∗ 0.898 ∗ ∗ 0.648 ∗ ∗ 0.648 ∗ ∗ 0.735 ∗ ∗ RMSE 2.087 2.120 2.090 2.074 2.085 2.088 2.084 2.260 2.083 4.015 4.015 3.312 RRMSE 12.8 13.0 12.9 12.8 12.8 12.8 12.8 13.9 12.8 24.7 24.7 20.4 NS 0.894 0.890 0.893 0.895 0.894 0.894 0.894 0.875 0.894 0.606 0.606 0.732 MAE 1.555 1.598 1.558 1.535 1.553 1.556 1.552 1.757 1.551 3.264 3.264 2.432   Lasa R 2 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.911 ∗ ∗ 0.907 ∗ ∗ 0.911 ∗ ∗ 0.670 ∗ ∗ 0.670 ∗ ∗ 0.702 ∗ ∗ RMSE 1.759 1.769 1.773 1.772 1.761 1.771 1.764 1.785 1.767 2.972 2.972 2.863 RRMSE 8.7 8.8 8.8 8.8 8.7 8.8 8.8 8.9 8.8 14.8 14.8 14.2 NS 0.882 0.880 0.880 0.880 0.881 0.880 0.881 0.878 0.881 0.662 0.662 0.687 MAE 1.247 1.251 1.258 1.259 1.248 1.256 1.250 1.311 1.253 2.235 2.235 2.072   Average R 2 0.895 ∗ ∗ 0.898 ∗ ∗ 0.895 ∗ ∗ 0.904 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.895 ∗ ∗ 0.878 ∗ ∗ 0.895 ∗ ∗ 0.693 ∗ ∗ 0.693 ∗ ∗ 0.753 ∗ ∗ RMSE 2.206 2.163 2.219 2.132 2.207 2.212 2.206 2.361 2.212 3.561 3.561 3.002 RRMSE 16.4 16.0 16.5 15.7 16.4 16.5 16.4 17.7 16.5 25.5 25.5 21.0 NS 0.865 0.870 0.863 0.874 0.864 0.864 0.864 0.845 0.864 0.648 0.648 0.743 MAE 1.684 1.646 1.695 1.614 1.684 1.689 1.684 1.850 1.689 2.804 2.804 2.218 GPI 0.019 0.172 −0.019 0.290 0.016 0.000 0.017 −0.529 0.000 −4.710 −4.710 −2.662 Rank 3 2 8 1 5 6 4 9 7 11 12 10In North China, the BA model had the best estimation precision among the sunshine-based models, followed by Jin and DL models, with averageR2 of 0.923, 0.921, and 0.921, average RMSE of 2.209, 2.231, and 2.231 MJ m−2 d−1, average RRMSE of 15.5%, 15.6%, and 15.6%, average MAE of 1.603, 1.639, and 1.639 MJ m−2 d−1, average NS of 0.906, 0.904, and 0.904, and GPI of 0.069, 0.011, and 0.011, respectively. The BC model showed the highest estimation precision among the temperature-based models, with average R2 of 0.735, average RMSE of 3.953 MJ m−2 d−1, average RRMSE of 27.8%, average MAE of 3.007 MJ m−2 d−1, average NS of 0.703, and GPI of −4.084.In Central China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and LO models, with averageR2 of 0.906, 0.898, and 0.896, average RMSE of 2.368, 2.445, and 2.482 MJ m−2 d−1, average RRMSE of 19.8%, 20.5%, and 20.8%, average MAE of 1.751, 1.833, and 1.873 MJ m−2 d−1, average NS of 0.899, 0.892, and 0.889, and GPI of 0.236, 0.078, and 0.002, respectively. The BC model showed the best estimation precision among the temperature-based models, with average R2 of 0.701, average RMSE of 4.170 MJ m−2 d−1, average RRMSE of 35.0%, average MAE of 3.021 MJ m−2 d−1, average NS of 0.693, and GPI of −3.485.In Eastern China, the BA model showed the best estimation precision compared with other sunshine-based models, followed by OG and DL models, with averageR2 of 0.914, 0.909, and 0.900, average RMSE of 2.325, 2.397, and 2.458 MJ m−2 d−1, average RRMSE of 17.7%, 18.3%, and 18.8%, average MAE of 1.730, 1.812, and 1.851 MJ m−2 d−1, average NS of 0.901, 0.895, and 0.890, and GPI of 0.284, 0.160, and 0.035, respectively. The BC model showed the best performance among the temperature-based models, with average R2 of 0.640, average RMSE of 4.582 MJ m−2 d−1, average RRMSE of 34.9%, average MAE of 3.449 MJ m−2 d−1, average NS of 0.616, and GPI of −3.838.In South China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and LO models, with averageR2 of 0.911, 0.904, and 0.897, average RMSE of 2.222, 2.299, and 2.343 MJ m−2 d−1, average RRMSE of 16.7%, 17.3%, and 17.7%, average MAE of 1.776, 1.850, and 1.885 MJ m−2 d−1, average NS of 0.898, 0.891, and 0.888, and GPI of 0.278, 0.127, and 0.035, respectively. The BC model had the best estimation precision compared with the other temperature-based models, with average R2 of 0.696, average RMSE of 3.937 MJ m−2 d−1, average RRMSE of 29.6%, average MAE of 3.064 MJ m−2 d−1, average NS of 0.685, and GPI of −3.273.In Northeast China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with averageR2 of 0.921, 0.920, and 0.918, average RMSE of 2.224, 2.230, and 2.252 MJ m−2 d−1, average RRMSE of 16.3%, 16.3%, and 16.5%, average MAE of 1.661, 1.669, and 1.685 MJ m−2 d−1, average NS of 0.904, 0.904, and 0.902, and GPI of 0.072, 0.055, and 0.003, respectively. The BC model had the highest estimation precision among the temperature-based models, with average R2 of 0.718, average RMSE of 3.944 MJ m−2 d−1, average RRMSE of 28.8%, average MAE of 2.955 MJ m−2 d−1, average NS of 0.708, and GPI of −4.275.In Northwest China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and EM models, with averageR2 of 0.890, 0.888, and 0.888, average RMSE of 2.665, 2.684, and 2.693 MJ m−2 d−1, average RRMSE of 19.4%, 19.5%, and 19.6%, average MAE of 1.932, 1.956, and 1.941 MJ m−2 d−1, average NS of 0.881, 0.879, and 0.878, and GPI of 0.071, 0.013, and 0.010, respectively. The BC model had the best estimation precision compared with the temperature-based models, with average R2 of 0.729, average RMSE of 4.075 MJ m−2 d−1, average RRMSE of 29.4%, average MAE of 2.940 MJ m−2 d−1, average NS of 0.724, and GPI of −3.787.In Southwest China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with averageR2 of 0.904, 0.898, and 0.895, average RMSE of 2.132, 2.163, and 2.206 MJ m−2 d−1, average RRMSE of 15.7%, 16.0%, and 16.4%, average MAE of 1.614, 1.646, and 1.684 MJ m−2 d−1, average NS of 0.874, 0.870, and 0.865, and GPI of 0.290, 0.172, and 0.019, respectively. The BC model showed the best performance among the temperature-based models, with average R2 of 0.753, average RMSE of 3.002 MJ m−2 d−1, average RRMSE of 21.0%, average MAE of 2.218 MJ m−2 d−1, average NS of 0.743, and GPI of −2.662.Comparison between estimated and measured monthly average dailyRs and relative error (RE) of different models for each subzone are presented in Figure 2. As shown in Figure 2, the estimated and measured monthly average daily Rs had good agreements. In addition to Wuhan, Nanchang, Shanghai, Chengdu, and Kunming stations, the estimated and measured Rs all presented parabolic variation. For the 9 sunshine-based models (AP, OG, Jin, BA, LO, GM, EM, AH, and DL), the average RE was in the range 1.71%~12.94%, 1.59%~12.72%, 1.71%~13.38%, 1.61%~13.17%, 1.67%~12.98%, 1.74%~13.09%, 1.70%~12.95%, 1.93%~13.19%, and 1.68%~13.20%, respectively. For the 3 temperature-based models (HS, AN, and BC), the average RE was in the range 3.33%~21.96%, 3.33%~21.96%, and 3.18%~15.16%, respectively. This means the sunshine-based models had a better performance for monthly average daily Rs compared with the temperature-based models, and the OG model had the lowest RE value between the sunshine-based models, followed by DL and GM models, with average RE of 5.66%, 5.73%, and 5.80%. In the temperature-based models, BC model had the lowest RE value, with average RE of 8.26%, and the RE of HS and AN models RE had a large variation in a year. For the 7 subzones (North China, Central China, East China, South China, Northeast China, Northwest China, and Southwest China), the models with the lowest RE were Jin, OG, DL, LO, AP, OG, and HS models, respectively, with average RE of 4.87%, 6.77%, 4.79%, 4.81%, 5.71%, 5.09%, and 5.08%. In Taiyuan, Jinan, Harbin, and Chengdu stations, all the models trended to underestimate the monthly average daily Rs. Overall, there were large differences for models in under/overestimating Rs at different climatic zones.Figure 2
Comparison between monthly average daily global solar radiation and relative error of each model in China.
(a)
North China (b)
Central China  (c)
East China (d)
South China  (e)
Northeast China (f)
Northwest China  (g)
Southwest China


## 4. Discussion

Results indicated that the prediction accuracy of each model for estimatingRs was different in each subzone of China. This may be due to the vast territory of China, which leads to a wide difference of topography and climate in different areas. Generally, the sunshine-based models had a better performance for the 7 subzones compared with the temperature-based models. Trnka et al. [41] analyzed 7 methods for estimating daily Rs in the Central Europe case study area (lowlands of Austria and the Czech Republic), where the sunshine-based models were found to be the best of all tested models, followed by cloud-based models, precipitation-based models, and temperature-based models. Mecibah et al. [42] introduced the best model for predicting the monthly mean daily Rs on a horizontal surface for 6 Algerian cities, and the results obtained in this study confirmed the previous studies, which indicated that the sunshine-based models were generally more accurate to estimate Rs than temperature-based models. The amount of solar radiation reaching the earth’s surface is closely related to sunshine duration. At the same time, clouds and their accompanying weather patterns are also one of the most important atmospheric phenomena that restrict the solar radiation on the earth’s surface, and this is the main reason for the higher accuracy of the sunshine-based models and cloud-based models. Solar radiation reaching the earth’s surface is absorbed by the atmosphere or emitted into the air in the form of long wave radiation, and the portion absorbed by the atmosphere causes an increase in atmospheric temperature. Therefore, the effect of temperature on solar radiation is less than sunshine duration, which led to the lower calculation accuracy of the temperature-based models compared with sunshine-based models.In addition, the present study found that Bahel model showed the best estimation precision ofRs in the 7 subzones. Chelbi et al. [16] compared several Ångström-type regression models, namely, the linear, quadratic, cubic, logarithmic, and exponential models, in Tunisia, and the results showed that the cubic model (Bahel model) showed the best regression fit and performed slightly better. Chen et al. [43] compared 5 Rs models with measured daily data in China; the results showed that the estimated daily Rs was relatively accurate using sunshine-based models, and the Bahel model was slightly better than the Ångström model with average NS of 0.84 and 0.83, respectively. This research found that the BC model had the best estimation precision for Rs between the temperature-based models. Quej et al. [17] evaluated the prediction accuracy and applicability of 13 empirical Rs models for warm subhumid regions (Yucatán Peninsula, Mexico), and results showed that the BC model was the best temperature-based model for estimating Rs. Chen et al. [43] also found that the BC model was more accurate for Rs than HS model, with average NS of 0.47 and 0.44, respectively. This is consistent with the results in the present study. In addition, we should analyze the influence of different geographical and meteorological factors on the accuracy of different models.


## 5. Conclusion

In this study, 12 solar radiation models were evaluated using daily meteorological data for estimatingRs at 21 meteorological stations across China. The performance of each model has been evaluated and compared using the RMSE, RRMSE, NS, MAE, RE, and GPI. The main conclusions of this study are shown as follows.(1) The estimated and measured dailyRs had statistically significant correlations (P<0.01) for all models at 21 meteorological stations. The sunshine-based models were more accurate for Rs estimation than the temperature-based models. For the 7 subzones, the BA model had the best estimation precision for daily Rs estimation among the 12 models. In China, the BA model also showed the best daily Rs estimation compared with other sunshine-based models, followed by OG and DL models, with average R2 of 0.910, 0.905, and 0.902, average RMSE of 2.306, 2.352, and 2.386 MJ m−2 d−1, average RRMSE of 17.3%, 17.7%, and 17.9%, average MAE of 1.724, 1.775, and 1.799 MJ m−2 d−1, average NS of 0.895, 0.891, and 0.887, and GPI of 0.191, 0.084, and 0.008, respectively. The BC model had the best estimation accuracy among the temperature-based models, with average R2 of 0.710, average RMSE of 3.952 MJ m−2 d−1, average RRMSE of 29.5%, average MAE of 2.958 MJ m−2 d−1, average NS of 0.696, and GPI of −3.650, respectively.(2) At monthly scale, the sunshine-based models also had a better performance compared with the temperature-based models for monthly average dailyRs estimation, and the OG model had the lowest RE value between the sunshine-based models, followed by DL and GM models, with average RE of 5.66%, 5.73%, and 5.80%. In the temperature-based models, the BC model had the lowest RE value, with average RE of 8.26%. For the 7 subzones (North China, Central China, East China, South China, Northeast China, Northwest China, and Southwest China), the models with the lowest RE are Jin, OG, DL, LO, AP, OG, and HS models, respectively, with average RE of 4.87%, 6.77%, 4.79%, 4.81%, 5.71%, 5.09%, and 5.08%.(3) Overall, the BA model is recommended to estimate dailyRs and the OG model is recommended to estimate monthly average daily Rs in China when the sunshine hours are available, and the BC model is recommended to estimate both daily Rs and monthly average daily Rs when only temperature data are available.Complete and accurateRs data at a specific region are highly crucial to regional crop growth modeling, irrigation system development and utilization of solar energy resources. The main objective of this study is to evaluate the applicability of different radiation models in 7 subzones of China. When sunlight passes through the atmosphere, a portion of sunlight is scattered, reflected, or absorbed by gases, clouds, and dust in the atmosphere, which varies with time in temperature and composition. Unfortunately, our work ignored the question and did not take into account the effects of climate change and human activities on solar radiation. We mainly consider the application of clean energy in agricultural production, and we will take into account this question in the future research.



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*Source: 3894831-2018-04-30.xml*