Acta Optica Sinica, Volume. 40, Issue 19, 1901001(2020)
Modeling and Validation Analysis of Sigmoid Function for Solar Radiation Diffuse Fraction
Figures & Tables(5)
Fig. 1. Fitting curves and surfaces of diffuse fraction Sigmoid model. (a) S0 model fitting curve based on 1 h training data; (b) S0 model fitting curve based on 10 min training data; (c) S0 model fitting curve based on 1 min training data; (d) S1 model fitting surface based on 1 h training data; (e) S1 model fitting surface based on 10 min training data; (f) S1 model fitting surface based on 1 min training data
Fig. 2. Validation comparison diagrams for S0 models with different parameters. (a) Validation comparison diagram for S0 model using 1 h radiation data collected in May, 2012 at Lijiang station; (b) validation comparison diagram for S0 model using 10-min radiation data collected in May, 2012 at Lijiang station; (c) validation comparison diagram for S0 model using 1 h radiation data collected in July, 2012 at Kazuo station; (d) validation comparison diagram for S0 model using 10-min radiation data collec
Fig. 3. Validation comparison diagrams for S1 models with different parameters. (a)--(c) Validation comparison diagrams for S1 model using 1-h data collected in May, 2012 at Lijiang station; (d)--(f) validation comparison diagrams for S1 model using 10-min data collected in May, 2012 at Lijiang station; (g)--(i) validation comparison diagrams for S1 model using 1-h data collected in July, 2012 at Kazuo station; (j)--(l) validation comparison diagrams for S1 model using 10-min data collected in December,
Table 1. Parameters of diffuse fraction sigmoid models S0 and S1
View tableTable 1. Parameters of diffuse fraction sigmoid models S0 and S1
Model Training data a1 a2 a3 a4 a5 S0 1-h data 0.2258 (0.2057, 0.2458) (with 95% confidence bounds) -0.7401 (-0.7886, -0.6916) (with 95% confidence bounds) -5.141 (-5.955, -4.327) (with 95% confidence bounds) 8.406 (7.116, 9.696) (with 95% confidence bounds) 10-min data 0.1949 (0.1698, 0.2201) (with 95% confidence bounds) -0.8155 (-0.8903, -0.7407) (with 95% confidence bounds) -3.121 (-3.639, -2.604) (with 95% confidence bounds) 5.446 (4.609, 6.283) (with 95% confidence bounds) 1-min data 0.2146 (0.2089, 0.2203) (with 95% confidence bounds) -0.7548 (-0.7749, -0.7346) (with 95% confidence bounds) -3.604 (-3.803, -3.405) (with 95% confidence bounds) 6.202 (5.889, 6.515) (with 95% confidence bounds) S1 1-h data 0.2338 -0.7386 -5.5787 8.6573 0.2926 10-min data 0.2074 -0.8187 -3.2986 5.5718 0.1356 1-min data 0.2251 -0.7648 -3.9509 6.4351 0.2379
Table 2. Statistical results of diffuse fraction calculated by S0 and S1 models
View tableTable 2. Statistical results of diffuse fraction calculated by S0 and S1 models
Model Training data Validating data r EMBD ERMSD t Skewness Kurtosis S0 1-h data 1-h data collected in May, 2012 from Lijiang station 0.9298 0.0406 0.1279 5.8873 0.9493 3.7014 10-min data 0.9396 0.0059 0.1147 0.9097 0.4265 2.9275 1-min data 0.9386 0.0930 0.1168 1.4137 0.4543 2.8173 S1 1-h data 0.9325 0.0417 0.1261 6.1695 0.7483 3.6499 10-min data 0.9426 0.0105 0.1120 1.6507 0.2871 2.9649 1-min data 0.9426 0.0141 0.1128 2.2154 0.3039 3.0297 S0 1-h data 10-min data collected in May, 2012 from Lijiang station 0.9347 0.0299 0.1221 10.9822 0.8327 3.7552 10-min data 0.9441 -0.0045 0.1124 1.7282 0.2793 2.8329 1-min data 0.9434 -7.9555×10-4 0.1141 0.3028 0.3438 2.7508 S1 1-h data 0.9364 0.0310 0.1209 11.5256 0.5323 3.6769 10-min data 0.9450 2.3221×10-4 0.1108 0.0910 0.0815 2.9916 1-min data 0.9447 0.0043 0.1115 1.6576 0.0801 3.1446 Model Training data Validating data r EMBD ERMSD t Skewness Kurtosis S0 1-h data 1-h data collected in July, 2012 from Kazuo station 0.9088 -0.0128 0.1260 1.7631 0.2680 3.0993 10-min data 0.9045 -0.0690 0.1492 8.9895 0.2047 2.4575 1-min data 0.9065 -0.0630 0.1549 8.2535 0.2440 2.4820 S1 1-h data 0.9255 -0.0389 0.1210 5.8554 -0.0042 3.0082 10-min data 0.9115 -0.0833 0.1533 11.1526 0.1538 2.4256 1-min data 0.9136 -0.0864 0.1537 11.7033 0.1515 2.4872 S0 1-h data 10-min data collected in December, 2012 from Kazuo station 0.9624 0.0128 0.0838 5.6638 -0.3398 3.4018 10-min data 0.9599 -0.0397 0.1054 14.8894 -06306 2.4770 1-min data 0.9623 -0.0333 0.1013 12.7599 -0.5861 2.4319 S1 1-h data 0.9560 -0.0680 0.1113 28.2822 -1.1048 4.6325 10-1-min data 0.9555 -0.0929 0.1379 33.3518 -0.6255 2.6717 1-min data 0.9424 -0.0989 0.1421 35.5077 -0.7060 3.0019 S0 1-h data 1-h data collected in July, 2012 from Guangzhou station 0.8768 -0.0290 0.1263 4.3277 -0.2584 4.2410 10-min data 0.8326 -0.0785 0.1624 10.1203 -0.1641 3.1330 1-min data 0.8446 -0.0785 0.1565 10.6224 -0.1482 3.3136 S1 1-h data 0.8795 -0.0240 0.1240 3.6184 -0.2628 4.0508 10-min data 0.8326 -0.0698 0.1590 8.9599 -0.1949 3.1146 1-min data 0.8455 -0.0662 0.1514 8.9060 -0.2141 3.2803 S0 1-h data 10-min data collected in December, 2012 from Guangzhou station 0.9419 0.0141 0.0999 5.3019 -0.2218 3.2726 10-min data 0.9391 -0.0407 0.1177 13.6514 -0.4412 2.3907 1-min data 0.9420 -0.0342 0.1138 11.6802 -0.3992 2.4080 S1 1-h data 0.9448 -0.0737 0.1209 28.4774 -1.0439 4.4547 10-1-min data 0.9400 -0.0964 0.1470 32.2035 -0.5575 2.6305 1-min data 0.9283 -0.1167 0.1658 36.7535 -0.6546 2.9579 S0 1-h data 1-h data collected in July, 2012 from Wuhan station 0.9302 -0.0480 0.1203 7.3646 -0.2067 4.6677 10-min data 0.9111 -0.0972 0.1569 13.3550 -0.1598 3.2799 1-min data 0.9166 -0.0943 0.1517 13.4203 -0.0818 3.5798 S1 1-h data 0.9304 -0.0455 0.1194 6.9757 -0.4988 4.7733 10-min data 0.9097 -0.0898 0.1534 12.1976 -0.3180 3.3477 1-min data 0.9146 -0.0848 0.1475 11.8862 -0.3789 3.7344 S0 1-h data 10-min data collected in December, 2012 from Wuhan station 0.9296 0.0335 0.1196 10.7714 1.6448 8.0956 10-min data 0.9165 -5.8784×10-5 0.1257 0.0172 1.1780 7.8858 1-min data 0.9217 0.0029 0.1230 0.8583 1.0676 7.1379 S1 1-h data 0.9177 -0.0203 0.1255 6.0476 1.4370 9.5559 10-min data 0.9029 -0.0354 0.1387 9.7338 1.1877 8.2914 1-min data 0.8941 -0.0473 0.1475 12.4817 0.8640 7.1872 S0 1-h data 1-h data collected in July, 2012 from Urumqi station 0.9483 0.0091 0.0999 3.1903 -0.5119 2.9069 10-min data 0.9438 -0.0452 0.1280 13.1603 -0.6870 2.2919 1-min data 0.9467 -0.0382 0.1230 11.3951 -0.6702 2.2984 S1 1-h data 0.9479 -0.0823 0.1294 28.8043 -1.0369 4.0392 10-min data 0.9453 -0.1022 0.1583 29.5406 -0.6745 2.4640 1-min data 0.9316 -0.1218 0.1761 33.4283 -0.6958 2.7061 S0 1-h data 10-1-min data collected in December, 2012 from Urumqi station 0.8482 -0.0832 0.1834 5.6485 -0.0880 2.4156 10-min data 0.8258 -0.1376 0.2230 8.6948 -0.0104 2.0106 1-min data 0.8318 -0.1292 0.2160 8.2784 -0.0151 2.0626 S1 1-h data 0.8569 -0.0784 0.1773 5.4667 -0.1258 2.2557 10-min data 0.8312 -0.1315 0.2174 8.4246 -0.0445 1.9770 1-min data 0.8394 -0.1216 0.2084 7.9730 -0.0731 2.0014
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Wei Chong, Wenhua Lü, Jian Zhang, Jing Liang, Xiaotong Yang, Guoyu Zhang. Modeling and Validation Analysis of Sigmoid Function for Solar Radiation Diffuse Fraction[J]. Acta Optica Sinica, 2020, 40(19): 1901001
Paper Information
Category: Atmospheric Optics and Oceanic Optics
Received: Apr. 2, 2020
Accepted: Jun. 23, 2020
Published Online: Oct. 12, 2020
The Author Email: Chong Wei (chongwei@cma.cn)
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