Complete and accurate global solar radiation (
Solar energy is the most fundamental renewable energy source on the earth’s surface, and global solar radiation (
Thus, different
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
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
Geographical positions of the meteorological stations.
Daily measurements of global solar radiation (
The geographical locations of each radiation station and its annual mean meteorological parameters.
Subzones | WMO number | Station | Latitude | Longitude | Altitude | | | | RH | |
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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 | |
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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 | |
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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 | |
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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 | |
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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 | |
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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 | |
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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 |
A number of empirical correlations which determine the relation between
Ångström [
Ögelman et al. [
Through the use of
Bahel et al. [
Louche et al. [
Glover and McCulloch [
Through the use of sunshine duration and geographical parameters, Elagib and Mansell [
Almorox and Hontoria [
Through taking into account the effect of latitude of the site as an additional input, Dogniaux and Lemoine [
Hargreaves and Samani [
Annandale et al. [
Bristow and Campbell [
The performance of the studied models to estimate
In order to overcome the discrepancy and to further improve the outcomes of statistical analysis, a new factor was proposed by Despotovic et al. [
The empirical coefficients of the 12 models were calibrated based on the least squares method for
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 |
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Ångström-Prescott (AP) | | | | | | | | |
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Ögelman (OG) | | | | | | | | |
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Jin | | | | | | | | |
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Bahel (BA) | | | | | | | | |
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Louche (LO) | | | | | | | | |
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Glover-McCulloch (GM) | | | | | | | | |
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Elagib-Mansell (EM) | | | | | | | | |
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Almorox-Hontoria (AH) | | | | | | | | |
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Dogniaux-Lemoine (DL) | | | | | | | | |
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Hargreaves-Samani (HS) | | | | | | | | |
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Annandale (AN) | | | | | | | | |
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Bristow-Campbell (BC) | | | | | | | | |
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The statistic performances of the analyzed models in estimating daily
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 |
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Beijing | | | | | | | | | | | | | |
RMSE | | | | | | | | | | | | | |
RRMSE | | | | | | | | | | | | | |
NS | | | | | | | | | | | | | |
MAE | | | | | | | | | | | | 2.986 | |
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Laoting | | | | | | | | | | | | | |
RMSE | | | | | | | | | | | | | |
RRMSE | | | | | | | | | | | | | |
NS | | | | | | | | | | | | | |
MAE | | | | | | | | | | | | 2.665 | |
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Taiyuan | | | | | | | | | | | | | |
RMSE | | | | | | | | | | | | | |
RRMSE | | | | | | | | | | | | | |
NS | | | | | | | | | | | | | |
MAE | | | | | | | | | | | | 3.370 | |
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Average | | | | | | | | | | | | | |
RMSE | | | | | | | | | | | | | |
RRMSE | | | | | | | | | | | | | |
NS | | | | | | | | | | | | | |
MAE | | | | | | | | | | | | | |
GPI | | | | | | | | | | | | | |
Rank | | | | | | | | | | | | 10 |
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 |
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Wuhan | | | | | | | | | | | | | |
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 | |
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Changsha | | | | | | | | | | | | | |
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 | |
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Zhengzhou | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
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 |
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Jinan | | | | | | | | | | | | | |
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 | |
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Nanchang | | | | | | | | | | | | | |
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 | |
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Shanghai | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
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 |
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Guangzhou | | | | | | | | | | | | | |
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 | |
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Haikou | | | | | | | | | | | | | |
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 | |
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Nanning | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
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 |
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Harbin | | | | | | | | | | | | | |
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 | |
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Shenyang | | | | | | | | | | | | | |
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 | |
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Changchun | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
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 |
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Urumqi | | | | | | | | | | | | | |
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 | |
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Xian | | | | | | | | | | | | | |
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 | |
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Xining | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
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 | | | | | | | | | | | | | |
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 | |
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Kunming | | | | | | | | | | | | | |
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 | |
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Lasa | | | | | | | | | | | | | |
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 | |
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Average | | | | | | | | | | | | | |
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 | 10 |
In North China, the BA model had the best estimation precision among the sunshine-based models, followed by Jin and DL models, with average
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
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
In South China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and LO models, with average
In Northeast China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with average
In Northwest China, the BA model showed the highest prediction accuracy among the sunshine-based models, followed by OG and EM models, with average
In Southwest China, the BA model had the best estimation precision compared with other sunshine-based models, followed by OG and AP models, with average
Comparison between estimated and measured monthly average daily
Comparison between monthly average daily global solar radiation and relative error of each model in China.
North China
Central China
East China
South China
Northeast China
Northwest China
Southwest China
Results indicated that the prediction accuracy of each model for estimating
In addition, the present study found that Bahel model showed the best estimation precision of
In this study, 12 solar radiation models were evaluated using daily meteorological data for estimating
(1) The estimated and measured daily
(2) At monthly scale, the sunshine-based models also had a better performance compared with the temperature-based models for monthly average daily
(3) Overall, the BA model is recommended to estimate daily
Complete and accurate
The authors declare that they have no conflicts of interest.
The authors would like to thank the National Climatic Centre of the China Meteorological Administration for providing the climate database used in this study. This work was also supported by the National Key Research and Development Program of China (no. 2016YFC0400206), National Natural Science Foundation of China (51779161), and National Key Technologies R&D Program of China (no. 2015BAD24B01).