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

1State Key Laboratory of Hydraulics and Mountain River Engineering and College of Water Resource and Hydropower, Sichuan University, Chengdu, China 2Key Laboratory of Water Saving Agriculture in Hill Areas in Southern China of Sichuan Province, Chengdu, China 3State Engineering Laboratory of Efficient Water Use of Crops and Disaster Loss Mitigation/Key Laboratory for Dryland Agriculture, Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing, China 4Hebei University of Water Resources and Electric Engineering, Cangzhou, China


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][9][10].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 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   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.

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 ( max ) and minimum ( min ) 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.

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 sunshine-based models, cloud-based models, temperaturebased 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   , including 9 sunshine-based models and 3 temperaturebased models.

Sunshine-Based Models
Model 1 ( Ångström-Prescott model (AP)).Ångström [14] derived a simple linear relationship between the ratio of Advances in Meteorology 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 second-order 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 Ångström-Prescott model through the use of the ratio of (/ ℎ ) instead of (/); the equation is presented as follows: where  and  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  as an additional input and was valid for  < 60 ∘ : where  and  are the empirical coefficients.
where  is the latitude of the location (rad); , , , and  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   : where , , , and  are the empirical coefficients.

Temperature-Based Models
Model 1 (Hargreaves-Samani 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  max and  min 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 Hargreaves-Samani 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 (Bristow-Campbell 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.

Statistical Evaluation.
The performance of the studied models to estimate   was evaluated in terms of the following statistical error tests: coefficient of determination ( 2 ), 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).

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 −1 for the indicator  2 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.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].

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 ( < 0.01).The statistical results showed that the sunshine-based models were more accurate for daily   estimation at the 7 subzones of China compared with the temperature-based models.
In Central China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and LO models, with average  2 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  2 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 average  2 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  2 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 average        Comparison between estimated and measured monthly average daily   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   had good agreements.In addition to Wuhan, Nanchang, Shanghai, Chengdu, and Kunming stations, the estimated and measured   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   compared with the temperaturebased 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   .Overall, there were large differences for models in under/overestimating   at different climatic zones.

Discussion
Results indicated that the prediction accuracy of each model for estimating   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 temperaturebased models.Trnka et al. [41] analyzed 7 methods for estimating daily   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   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   than temperaturebased 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 of   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   models with measured daily data in China; the results showed that the estimated daily   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   between the temperature-based models.Quej et al. [17] evaluated the prediction accuracy and applicability of 13 empirical   models for warm subhumid regions (Yucatán Peninsula, Mexico), and results showed that the BC model was the best temperature-based model for estimating   .Chen et al. [43] also found that the BC model was more accurate for   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.

Conclusion
In this study, 12 solar radiation models were evaluated using daily meteorological data for estimating   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 daily   had statistically significant correlations ( < 0.01) for all models at 21 meteorological stations.The sunshine-based models were more accurate for   estimation than the temperature-based models.For the 7 subzones, the BA model had the best estimation precision for daily   estimation among the 12 models.In China, the BA model also showed the best daily   estimation compared with other sunshine-based models, followed by OG and DL models, with average         (2) At monthly scale, the sunshine-based models also had a better performance compared with the temperature-based models for monthly average daily   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 daily   and the OG model is recommended to estimate monthly average daily   in China when the sunshine hours are available, and the BC model is recommended to estimate both daily   and monthly average daily   when only temperature data are available.
Complete and accurate   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.

Figure 1 :
Figure 1: Geographical positions of the meteorological stations.

Figure 2 :
Figure 2: Comparison between monthly average daily global solar radiation and relative error of each model in China.

Table 1 :
The geographical locations of each radiation station and its annual mean meteorological parameters.

Table 2 :
Calibration empirical coefficients for the studied models in different subzones of China.

Table 3 :
Statistics performances of the 12 models in estimating global solar radiation in North China.

Table 4 :
Statistics performances of the 12 models in estimating global solar radiation in Central China.

Table 5 :
Statistics performances of the 12 models in estimating global solar radiation in Eastern China.

Table 6 :
Statistics performances of the 12 models in estimating global solar radiation in South China.

Table 7 :
Statistics performances of the 12 models in estimating global solar radiation in Northeast China.

Table 8 :
Statistics performances of the 12 models in estimating global solar radiation in Northwest China.

Table 9 :
Statistics performances of the 12 models in estimating global solar radiation in Southwest China.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  2 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.