Research Article  Open Access
Qingwen Zhang, Ningbo Cui, Yu Feng, Yue Jia, Zhuo Li, Daozhi Gong, "Comparative Analysis of Global Solar Radiation Models in Different Regions of China", Advances in Meteorology, vol. 2018, Article ID 3894831, 21 pages, 2018. https://doi.org/10.1155/2018/3894831
Comparative Analysis of Global Solar Radiation Models in Different Regions of China
Abstract
Complete and accurate global solar radiation () 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 had statistically significant correlations () for all the 12 models in 7 subzones of China. The Bahel model showed the best performance for daily estimation among the sunshinebased models, with average 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 BristowCampbell (BC) model showed the best performance among the temperaturebased models, with average 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 sunshinebased models, with average RE of 5.66%. The BC model showed the best performance among the temperaturebased models, with average RE of 8.26%. Generally, the sunshinebased models were more accurate than the temperaturebased models. Overall, the Bahel model is recommended to estimate daily , Ögelman model is recommended to estimate monthly average daily in China when the sunshine duration is available, and the BC model is recommended to estimate both daily and monthly average daily when only temperature data are available.
1. Introduction
Solar energy is the most fundamental renewable energy source on the earth’s surface, and global solar radiation () plays an important role in a wide range of applications in areas such as meteorology and hydrology [1]. Changes in the amount of greatly influence the hydrological cycle, terrestrial ecological systems, and the climate [2]. Complete and accurate 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 information for clean energy technology development [3, 4]. The best method to determine the amount of 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 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 observing instruments [7]. Furthermore, even for those stations where is observed, there are many data which are missing or lie outside the expected range due to equipment failure and other difficulties [8–10].
Thus, different models have been proposed for estimating daily or monthly 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 databased 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 sunshinebased and temperaturebased models [6, 11]. The primary sunshinebased model can be traced back to Ångström model, using sunshine duration and clear sky radiation data to estimate [11, 13, 14]. Prescott [15] suggested using the extraterrestrial radiation to replace clear sky radiation and presented the ÅngströmPrescott (AP) model. Several Ångströmtype regression models, namely, the linear, quadratic, cubic, logarithmic, and exponential models, were compared to estimate on horizontal surfaces at 4 meteorological stations in Tunisia, and the statistical results indicated that the models were considered suited to accurately estimate , and the cubic model showed the best regression fit and performed slightly better than the others [16]. Although the sunshinebased models are generally more accurate for estimating , their application is often limited by the lack of sunshine records [1, 9, 17]. In this context, 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 temperaturebased models were only based on air temperature data which can be measured easily [18]. HargreavesSamani (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 . Annandale et al. [20] modified the HS model by accounting for the effects of reduced altitude and atmosphere thickness on . In order to calculate the average monthly , Allen [21, 22] also proposed a selfcalibrated model based on HS model. Bristow and Campbell [23] presented a simple model for estimating daily , in which was an exponential function in terms of temperature. Goodin et al. [24] modified BristowCampbell (BC) model by adding the extraterrestrial term meant to act as a scaling factor. Liu et al. [10] evaluated the accuracy and applicability of 16 temperaturebased 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 temperaturebased models and compared these models with Annandale, Allen, and Goodin models to estimate monthly average daily 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 sunshinebased models are more accurate than temperaturebased 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 of is very important for the operation of solarpowered 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 sunshinebased models and 3 temperaturebased models to estimate daily 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 (Figure 1), and each subzone contains 3 meteorological stations.
Daily measurements of global solar radiation () and meteorological variables, including maximum () and minimum () 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 qualitycontrolled 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.

2.2. Models for Estimation of Solar Radiation
A number of empirical correlations which determine the relation between and various meteorological parameters have been developed to estimate daily or monthly in the literature, such as sunshinebased models, cloudbased models, temperaturebased models, and other meteorological parameterbased models [6, 26]. The sunshinebased and temperaturebased models are the most commonly used around the world [6, 9]. In this paper, 12 representative models were chosen to predict , including 9 sunshinebased models and 3 temperaturebased models.
2.2.1. SunshineBased Models
Model 1 (ÅngströmPrescott model (AP)). Ångström [14] derived a simple linear relationship between the ratio of average daily 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 [27]. Prescott [15] modified the method and proposed the following equation:where is the global solar radiation (MJ m^{−2} d^{−1}), is the extraterrestrial radiation (MJ m^{−2} d^{−1}), is sunshine duration (h), is maximum possible sunshine duration (h), and and are the empirical coefficients.
Model 2 (Ögelman model (OG)). Ögelman et al. [28] suggested a secondorder polynomial equation for estimating as follows:where , , and are the empirical coefficients.
Model 3 (Jin model (Jin)). Through the use of data and some geographical parameters like altitude and latitude, Jin et al. [29] derived the following model:where is the latitude of the location (°) and is the altitude of the location (km); , , , and 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:where , , , and are the empirical coefficients.
Model 5 (Louche model (LO)). Louche et al. [31] have modified the ÅngströmPrescott model through the use of the ratio of () instead of (); the equation is presented as follows:where and are the empirical coefficients.
Model 6 (GloverMcCulloch model (GM)). Glover and McCulloch [32] suggested the following model, which took into account the effect of latitude of the site as an additional input and was valid for :where and are the empirical coefficients.
Model 7 (ElagibMansell model (EM)). Through the use of sunshine duration and geographical parameters, Elagib and Mansell [33] derived a new equation for estimating aswhere is the latitude of the location (rad); , , , and are the empirical coefficients.
Model 8 (AlmoroxHontoria model (AH)). Almorox and Hontoria [34] derived an exponential type equation as follows:where and are the empirical coefficients.
Model 9 (DogniauxLemoine 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 :where , , , and are the empirical coefficients.
2.2.2. TemperatureBased Models
Model 10 (HargreavesSamani model (HS)). Hargreaves and Samani [19, 36] recommended a simple equation to estimate which required only maximum and minimum temperature data; the equation is presented as follows:where and are the maximum daily temperature and minimum daily temperature (°), respectively; is the empirical coefficient.
Model 11 (Annandale model (AN)). Annandale et al. [20] derived a model based on HargreavesSamani model by accounting for the effects of reduced altitude and atmospheric thickness on ; the equation is presented as follows:where is the empirical coefficient.
Model 12 (BristowCampbell model (BC)). Bristow and Campbell [23] proposed a method for daily based on the difference of maximum and minimum temperatures; the equation is presented as follows:where , , and are the empirical coefficients.
2.3. Statistical Evaluation
The performance of the studied models to estimate was evaluated in terms of the following statistical error tests: coefficient of determination (), 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]: where and denote the measured and estimated values, and represent the corresponding mean values, respectively, the subscript refers to the th value of the solar irradiation, and 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:where is equal to for the indicator and NS, while for other indicators it is equal to +1. is the median of scaled values of indicator , and is the scaled value of indicator for model . 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 for 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 and of the AP model ranged between 0.161~0.214 and 0.532~0.555, respectively. The calibrated , , and of the OG model ranged between 0.144~0.202, 0.605~0.798, and −0.313~−0.082, respectively. The calibrated , , , and 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 , , , and 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 and of the LO model ranged between 0.161~0.214 and 0.608~0.635, respectively. The calibrated and of the GM model ranged between 0.185~0.269 and 0.532~0.555, respectively. The calibrated , , , and 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 and of the AH model ranged between −0.165~−0.085 and 0.325~0.358, respectively. The calibrated , , , and 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 of HS and AN models were both in the range 0.139~0.155. The calibrated , , and 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].

3.2. Performances of the Models
The statistic performances of the analyzed models in estimating daily 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 had statistically significant correlations for all the 12 models at the 21 meteorological stations (). The statistical results showed that the sunshinebased models were more accurate for daily estimation at the 7 subzones of China compared with the temperaturebased models.
