# Improvement in Solar-Radiation Forecasting Based on Evolutionary KNEA Method and Numerical Weather Prediction

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}= 0.782–0.829, RMSE = 3.240–3.685 MJ m

^{−2}d

^{−1}, MAE = 2.465–2.799 MJ m

^{−2}d

^{−1}, and NRMSE = 0.152–0.173.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Region

^{−2}y

^{−1}. The annual average air temperature is 9 °C and annual precipitation is less than 200 mm y

^{−1}. These stations are affiliated with the Meteorological Data Center of the China Meteorological Administration, and the data include the total daily surface radiation from 2006 to 2015. The data was divided into two parts, the first part (2005–2010) was used for training the model and the other was used to test the model. When the Rs of a day was higher than the extraterrestrial radiation, the data of that day were deleted [31]. The global solar radiation for different months at each station is outlined in Table 1.

_{f}), maximum temperature (Tmax

_{f}), minimum temperature (Tmin

_{f}), relative humidity (RH

_{f}) at 2 m height and wind speed (U

_{f}) at 10 m height every 3 h for the next 72 h, and converted the 3 h time-resolution data into daily data. That means that, for 3 h to 24 h (27 h to 48 h and 51 to 72 h), the eight data points were converted to daily scale. Tmax

_{f}and Tmin

_{f}are the highest and lowest temperature of the eight time scale in one day. RH

_{f}and U

_{f}are the mean of the eight-point time scale in one day. Rs

_{f}is the sum of the eight-point time scale in a day. The output of the models is the measured Rs corresponding to the GEFS data on the same day.

#### 2.2. Quantile Mapping (QM)

#### 2.3. Equiratio Cumulative Distribution Function Matching (EDCDFm)

#### 2.4. Machine-Learning Algorithms

#### 2.4.1. Long-Short Term Memory (LSTM)

_{f}, Tmax

_{f}, Tmin

_{f}, RH

_{f}and U

_{f}for the forecast target day and observed Rs values during the previous 3–6 days. To achieve this model, Python 3.7 (https://www.python.org/downloads/release/python-370/ (accessed on 25 April 2022)) was used to develop the model.

#### 2.4.2. Support Vector Machine (SVM)

^{*}), Equation (5) can be rewritten as:

#### 2.4.3. Extreme Gradient Boosting (XGBoost)

#### 2.4.4. Kernel-Based Nonliear Extension of Arps Decline (KNEA)

_{0}prediction and groundwater-level prediction [42,43]. The KNEA synthesizes nonlinear models of past state and present effects. The main function of KNEA algorithm can be expressed as:

#### 2.4.5. Bat Algorithm

#### 2.4.6. Particle Swarm Optimization Algorithm (PSO)

#### 2.5. Statistical Indicators

^{2}):

## 3. Results

#### 3.1. Empirical Statistics Methods

_{f}forecasting data and the results from QM and EDCDFm methods. In general, with the extension of the forecast period, the errors of NWP raw Rs

_{f}data and the Rs

_{f}correct by QM and EDCDFm methods gradually increase. In Altay, the performance of the QM and EDCDFm methods were very similar, and both o

_{f}them were slightly better than that of the NWP raw Rs

_{f}data. In Kashgar, the error of the raw Rs

_{f}data was relatively large. However, the QM and EDCDFm methods were superior to the raw Rs

_{f}, with RMSE decreased by 28.2–31% and 28.6–31.5%, and MAE decreased by 27.9–31.1% and 27.7–31.1%, respectively, during 1–3 d ahead. In Ruoqiang, the error of the raw Rs

_{f}was large, and its RMSE was more than 5 MJ m

^{−2}d

^{−1}. After correcting by QM and EDCDFm method correction, RMSE decreased by 17.4–18.5% and 19.7–20.1% for 1–3 d ahead, and MAE decreased by 16–17.7% and 17.7–19.4%, respectively. However, the R

^{2}of the raw Rs

_{f}was slightly higher than that of the two statistical methods. This indicates that the statistical method improved the overestimation (or underestimation) problem. The performance for Khotan station was similar to that of Ruoqiang station. Compared with the raw Rs

_{f}over the four stations, the RMSE and MAE of QM and EDCDFm models decreased by 20% and 15%, respectively. It can be seen from the above results that empirical statistical methods can improve forecasting accuracy.

_{f}in the future 1–3 d was not higher than 30 MJ m

^{−2}d

^{−1}, which was slightly lower than the extreme value of Rs. The main problem of the GEFS data set lay in the existence of many overestimated discrete points when the observed value was lower than 25 MJ m

^{−2}d

^{−1}. However, the QM and EDCDFm methods can alleviate this problem, and the R

^{2}of the two methods was slightly higher than the corresponding value of raw Rs

_{f}data.

#### 3.2. Machine-Learning Methods

^{2}average increased by 0.046, and the average RMSE and MAE increased by 13.4% and 13.1%, compared with the first day. Among the seven machine-learning models, the BA-KNEA model was superior to other machine−learning models each day, and the RMSE, MAE and NRMSE of the BA-KNEA model decreased by 2.1–10.3%, 2.5–12.0% and 2.8–12.4% than other machine-learning models for 1 d ahead, decreased by 1.8–8.8%, 1.7% to 10.1% and 1.6–9.9% for 2 d ahead, and decreased by 2.2–8.2%, 2.2–9.6% and 2.0–9.5% for 3 d ahead. The performance of the BA-SVM model was ranked second, followed by BA-XGBoost, PSO-KNEA, PSO-SVM, LSTM and PSO-XGBoost models.

_{f}by seven machine-learning models are shown in Figure 5. Among all the machine-learning models, it can be seen that the BA-KENA model performed slightly better than other models, followed by the BA-SVM model. The slope of all the regression equations in the Figure was less than 1, and the intercept was greater than 0, which means that all the models exhibit the problem that when Rs is very large, the model will underestimate the result, and when Rs is very small, the model will underestimate the result.

^{−2}d

^{−1}for the six models was around 60%; the proportion of PSO-KNEA and BA-KNEA was slightly higher than in other models; and had a AE > 6 MJ m

^{−2}d

^{−1}days ratio, the BA-KNEA had a slight advantage over the other models. The performance on 2 d ahead was slightly worse than that on 1 d ahead: the proportion of days with AE < 2 MJ m

^{−2}d

^{−1}for all six models was below 60%, while the number of days with AE > 6 MJ m

^{−2}d

^{−1}showed little change compared with 1 d ahead, with the BA-KNEA model having a slight advantage over the other models in the number of days with AE > 6 MJ m

^{−2}d

^{−1}. In the 3 d ahead, the accuracy of the six models continued to decline compared with the previous 2 d, and the BA-KNEA model had a slightly lower proportion of days with AE > 6 MJ m

^{−2}d

^{−1}than the other models.

#### 3.3. Comparison of Statistical Models and Machine-learning Models

^{2}or the lowest RMSE, MAE or NRMSE would rank first, and so on. When the ranking of different statistical indicators is different, the model with more indicators at the top ranks first. It can be seen that the rank of different models in 1–3 d ahead were the same. The BA-KNEA model was the best, followed by the BA-SVM, BA-XGBoost, PSO-KNEA, PSO-SVM, LSTM, PSO-XGBoost, EDCDFm and QM models. The above results prove that the machine−learning model is superior to the empirical-statistical model, and the new BA-KNEA model has the best performance in accuracy. In addition, the Taylor plots of different stations on the first day of the forecast period are shown in Figure 6. It can also be seen that the results of the BA-KNEA model were the closest to the observations, while the GEFS raw data had the largest error.

#### 3.4. BA-KNEA with Different Input Combinations

_{f}, the accuracy of the BA-KNEA model was better than that of the QM and EDCDFm methods with the same input at four stations (Table 3), and the RMSE and MAE of the BA-KNEA model was 1.7–7.9% and was 1.6–7.6% lower in the forecast period of 1–3 days, relative to the EDCDFm method. This model was also better than the model established with temperature and extraterrestrial radiation as inputs (Combination 5), which shows that the solar radiation accuracy of the GEFSv12 dataset is better than that of the traditional temperature-based machine-learning model method. In Altay, when only the maximum and minimum air temperature was used as input, the error was larger than the model with Rs input: R

^{2}was between 0.712–0.723, RMSE was between 4.705–4.812 MJ m

^{−2}d

^{−1}, and MAE was between 3.766–3.799 MJ m

^{−2}d

^{−1}, and NRMSE was between 0.241–0.243. Adding RH

_{f}, U

_{f}, Tmax

_{f}and Tmin

_{f}based on the Rs

_{f}can improve the prediction accuracy of Rs, among which the increase in wind speed was the largest, followed by air temperature, and, finally, relative humidity. Compared with Combination 2, 3, and 4, the accuracy of combination 6 was higher, and it can be seen that the accuracy of the multi-factor was higher than that of the two-factor combination. This shows that the multi-factor combination contains more nonlinear information related to Rs than the two-factor combination, which helps improve the model accuracy further. At Kashgar station, adding relative humidity based on Rs did not improve the accuracy significantly, and when the forecast period was 2 and 3 days, adding wind speed based on Rs slightly improved the accuracy. Adding the temperature model based on Rs improves the model’s accuracy to a certain extent, but it is not much different from the accuracy of the complete combination (Combination 6). This is mainly due to the limited contribution of RH and U to improving the accuracy of the model. The performance of the BA-KNEA model on the first two days of Ruoqiang Station was similar to that on Altay, but on the third day, Combination 3 outperformed the complete input combination. Due to poor forecast accuracy of wind speed and relative humidity, adding these factors will increase the noise in the model. At Khotan station, on the first day, the complete combination was close to the Combination 2, 3, and 4 but superior to those during the other two days. The complete combination is slightly better than the other combinations. As seen from the above, the complete combination was slightly better than the other combinations over the four stations.

## 4. Discussion

## 5. Conclusions

^{2}= 0.782–0.829, RMSE= 3.240–3.685 MJ m

^{−2}d

^{−1}, MAE = 2.465–2.799 MJ m

^{−2}d

^{−1}, NRMSE = 0.152–0.173.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Scatter plots of measured Rs vs. forecasting Rs at Kashgar station during the testing period, GEFSv12 raw Rs forecasting data on (

**a**) 1 d ahead, (

**b**) 2 d ahead, (

**c**) 3 d ahead; QM method forecasting Rs on (

**d**) 1 d ahead, (

**e**) 2 d ahead, (

**f**) 3 d ahead; EDCDFm method forecasting Rs on (

**g**) 1 d ahead, (

**h**) 2 d ahead, (

**i**) 3 d ahead.

**Figure 5.**Scatter plots of measured Rs vs. forecasting Rs at Kashgar station during the testing period, LSTM method forecasting data on (

**a**) 1 d ahead, (

**b**) 2 d ahead, (

**c**) 3 d ahead; PSO-SVM method forecasting Rs on (

**d**) 1 d ahead, (

**e**) 2 d ahead, (

**f**) 3 d ahead; BA-SVM method forecasting Rs on (

**g**) 1 d ahead, (

**h**) 2 d ahead, (

**i**) 3 d ahead; PSO-XGBoost method forecasting Rs on (

**j**) 1 d ahead, (

**k**) 2 d ahead, (

**l**) 3 d ahead; BA-XGBoost method forecasting Rs on (

**m**) 1 d ahead, (

**n**) 2 d ahead, (

**o**) 3 d ahead; PSO-KNEA method forecasting Rs on (

**p**) 1 d ahead, (

**q**) 2 d ahead, (

**r**) 3 d ahead; BA-KNEA method forecasting Rs on (

**s**) 1 d ahead, (

**t**) 2 d ahead, (

**u**) 3 d ahead.

Station | Period | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Altay | Train | 7 ± 2.7 | 11.1 ± 3.5 | 15.7 ± 4.8 | 20.3 ± 5.9 | 23.8 ± 7.5 | 25.3 ± 7.1 | 24.2 ± 7 | 21.3 ± 6.3 | 17 ± 5.7 | 10.2 ± 4.6 | 6.1 ± 3.1 | 5.3 ± 2.4 |

Test | 6 ± 2.7 | 9.6 ± 3.6 | 15 ± 4.4 | 18.7 ± 5.9 | 22.5 ± 6.7 | 24.6 ± 5.6 | 23.7 ± 5.5 | 20.4 ± 5.1 | 15.9 ± 4.4 | 10 ± 4 | 6.1 ± 2.7 | 4.9 ± 2.3 | |

Kashgar | Train | 8.3 ± 2.5 | 9.6 ± 3.8 | 13.8 ± 4.6 | 19 ± 5.8 | 22.3 ± 6.2 | 26.4 ± 5 | 25.2 ± 4.6 | 21.3 ± 5 | 17.3 ± 4.4 | 13.1 ± 3.2 | 8.3 ± 2.4 | 6.2 ± 1.9 |

Test | 6.8 ± 2.4 | 9.1 ± 3.5 | 13 ± 4.7 | 17.2 ± 5.6 | 20.7 ± 6.1 | 24.7 ± 5 | 22.9 ± 5.6 | 19.7 ± 4.5 | 16.1 ± 4.1 | 12.3 ± 3.3 | 8.5 ± 2.5 | 6.4 ± 2 | |

Ruoqiang | Train | 9.3 ± 2.5 | 10.9 ± 2.7 | 16 ± 4.3 | 20.1 ± 4.7 | 22.1 ± 5.9 | 22.9 ± 6.6 | 24.1 ± 6.7 | 21.9 ± 6.1 | 19 ± 3.5 | 14.8 ± 3.1 | 9.5 ± 2.7 | 8 ± 1.8 |

Test | 8.6 ± 2.6 | 11.2 ± 2.8 | 15.4 ± 3.8 | 18.8 ± 5.2 | 21.8 ± 6 | 23 ± 5 | 21.5 ± 5.9 | 20.3 ± 5.5 | 17.9 ± 4 | 14.2 ± 2.8 | 10.6 ± 2.2 | 7.8 ± 1.9 | |

Khotan | Train | 10.1 ± 2.5 | 11.6 ± 3.3 | 15.5 ± 4 | 19.8 ± 5.4 | 23.4 ± 5.8 | 23.9 ± 6 | 22.3 ± 6.3 | 20.1 ± 5.4 | 18.6 ± 4.8 | 16.3 ± 2.8 | 11.1 ± 2.3 | 8.8 ± 2.6 |

Test | 9.1 ± 3 | 11.2 ± 3.8 | 15.2 ± 4.6 | 18.9 ± 5.2 | 21.5 ± 5.1 | 22.1 ± 5.4 | 21.3 ± 5.9 | 19.2 ± 4.6 | 16.2 ± 4.9 | 14.9 ± 2.8 | 10.8 ± 2.2 | 8.7 ± 1.7 |

^{−2}d

^{−1}.

Model | Parameter Names | Range |
---|---|---|

SVM | Regularization coefficient | [0.01, 10,000] |

Kernel parameter | [0.01, 10,000] | |

XGBoost | Number of trees | [50, 1000] |

Maximum tree depth | [2, 50] | |

Learning rate | [0.01, 0.3] | |

KNEA | Regularization coefficient | [0.1, 10,000] |

Kernel parameter | [0.1, 10,000] |

**Table 3.**Statistical indicators of solar-radiation forecast by GEFS NWP raw data and two empirical-statistics methods.

ID | 1 d | 2 d | 3 d | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE |

51076 Altay | ||||||||||||

NWP | 0.816 | 3.939 | 3.120 | 0.250 | 0.766 | 4.313 | 3.417 | 0.274 | 0.745 | 4.582 | 3.482 | 0.292 |

QM | 0.821 | 3.843 | 3.077 | 0.246 | 0.787 | 4.194 | 3.304 | 0.269 | 0.768 | 4.387 | 3.442 | 0.281 |

EDCDFm | 0.820 | 3.838 | 3.071 | 0.246 | 0.788 | 4.189 | 3.301 | 0.268 | 0.768 | 4.384 | 3.437 | 0.281 |

51709 Kashgar | ||||||||||||

NWP | 0.795 | 5.016 | 3.822 | 0.327 | 0.772 | 5.214 | 3.955 | 0.340 | 0.757 | 5.378 | 4.080 | 0.351 |

QM | 0.816 | 3.460 | 2.633 | 0.217 | 0.792 | 3.707 | 2.798 | 0.233 | 0.776 | 3.862 | 2.943 | 0.243 |

EDCDFm | 0.820 | 3.437 | 2.633 | 0.216 | 0.795 | 3.699 | 2.815 | 0.232 | 0.780 | 3.841 | 2.950 | 0.241 |

51777 Ruoqiang | ||||||||||||

NWP | 0.753 | 4.547 | 3.102 | 0.280 | 0.726 | 4.859 | 3.312 | 0.299 | 0.697 | 5.156 | 3.478 | 0.317 |

QM | 0.754 | 3.708 | 2.553 | 0.224 | 0.713 | 4.002 | 2.762 | 0.241 | 0.681 | 4.257 | 2.920 | 0.257 |

EDCDFm | 0.758 | 3.632 | 2.499 | 0.219 | 0.719 | 3.912 | 2.709 | 0.236 | 0.688 | 4.138 | 2.864 | 0.250 |

51828 Khotan | ||||||||||||

NWP | 0.701 | 4.822 | 3.398 | 0.296 | 0.668 | 5.127 | 3.628 | 0.315 | 0.650 | 5.354 | 3.788 | 0.329 |

QM | 0.720 | 3.674 | 2.750 | 0.219 | 0.665 | 4.057 | 3.048 | 0.241 | 0.649 | 4.178 | 3.143 | 0.249 |

EDCDFm | 0.721 | 3.637 | 2.733 | 0.216 | 0.669 | 4.012 | 3.044 | 0.239 | 0.652 | 4.145 | 3.151 | 0.247 |

ID | 1 d | 2 d | 3 d | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE |

51076 Altay | ||||||||||||

LSTM | 0.813 | 3.889 | 3.086 | 0.202 | 0.798 | 4.178 | 3.314 | 0.216 | 0.787 | 4.258 | 3.168 | 0.207 |

PSO-SVM | 0.817 | 3.875 | 2.988 | 0.191 | 0.792 | 4.116 | 3.181 | 0.204 | 0.773 | 4.292 | 3.319 | 0.213 |

BA-SVM | 0.837 | 3.627 | 2.854 | 0.183 | 0.811 | 3.91 | 3.032 | 0.194 | 0.793 | 4.091 | 3.174 | 0.203 |

PSO-XGBoost | 0.816 | 3.917 | 3.118 | 0.2 | 0.79 | 4.178 | 3.28 | 0.21 | 0.773 | 4.33 | 3.403 | 0.218 |

BA-XGBoost | 0.833 | 3.685 | 2.893 | 0.185 | 0.803 | 4.005 | 3.114 | 0.199 | 0.786 | 4.171 | 3.243 | 0.208 |

PSO-KNEA | 0.826 | 3.723 | 2.903 | 0.186 | 0.794 | 4.053 | 3.088 | 0.198 | 0.77 | 4.281 | 3.268 | 0.209 |

BA-KNEA | 0.844 | 3.552 | 2.785 | 0.178 | 0.819 | 3.839 | 2.98 | 0.191 | 0.803 | 4.002 | 3.105 | 0.199 |

51709 Kashgar | ||||||||||||

LSTM | 0.834 | 3.485 | 2.81 | 0.177 | 0.808 | 3.735 | 2.75 | 0.173 | 0.799 | 3.908 | 3.033 | 0.191 |

PSO-SVM | 0.838 | 3.436 | 2.641 | 0.166 | 0.809 | 3.735 | 2.863 | 0.18 | 0.789 | 3.824 | 2.886 | 0.181 |

BA-SVM | 0.861 | 3.38 | 2.707 | 0.17 | 0.838 | 3.596 | 2.854 | 0.179 | 0.799 | 3.923 | 3.136 | 0.197 |

PSO-XGBoost | 0.84 | 3.445 | 2.7 | 0.17 | 0.811 | 3.754 | 2.933 | 0.184 | 0.8 | 3.808 | 2.982 | 0.187 |

BA-XGBoost | 0.845 | 3.345 | 2.55 | 0.16 | 0.819 | 3.661 | 2.775 | 0.174 | 0.808 | 3.677 | 2.796 | 0.176 |

PSO-KNEA | 0.841 | 3.231 | 2.438 | 0.153 | 0.824 | 3.45 | 2.629 | 0.165 | 0.801 | 3.618 | 2.748 | 0.173 |

BA-KNEA | 0.869 | 3.056 | 2.37 | 0.149 | 0.837 | 3.434 | 2.654 | 0.167 | 0.834 | 3.487 | 2.733 | 0.172 |

51777 Ruoqiang | ||||||||||||

LSTM | 0.784 | 3.401 | 2.431 | 0.147 | 0.74 | 3.821 | 2.547 | 0.159 | 0.719 | 3.852 | 2.749 | 0.168 |

PSO-SVM | 0.796 | 3.313 | 2.331 | 0.141 | 0.76 | 3.603 | 2.528 | 0.153 | 0.732 | 3.796 | 2.711 | 0.164 |

BA-SVM | 0.803 | 3.266 | 2.296 | 0.139 | 0.764 | 3.592 | 2.542 | 0.153 | 0.733 | 3.811 | 2.693 | 0.163 |

PSO-XGBoost | 0.787 | 3.423 | 2.429 | 0.147 | 0.75 | 3.688 | 2.614 | 0.158 | 0.731 | 3.822 | 2.746 | 0.166 |

BA-XGBoost | 0.796 | 3.319 | 2.304 | 0.139 | 0.753 | 3.639 | 2.542 | 0.153 | 0.721 | 3.853 | 2.728 | 0.165 |

PSO-KNEA | 0.785 | 3.552 | 2.41 | 0.145 | 0.739 | 3.86 | 2.6 | 0.157 | 0.717 | 4.069 | 2.736 | 0.165 |

BA-KNEA | 0.819 | 3.123 | 2.196 | 0.133 | 0.791 | 3.354 | 2.387 | 0.144 | 0.752 | 3.674 | 2.624 | 0.158 |

51828 Khotan | ||||||||||||

LSTM | 0.762 | 3.331 | 2.619 | 0.155 | 0.717 | 3.739 | 2.74 | 0.161 | 0.696 | 3.873 | 2.822 | 0.166 |

PSO-SVM | 0.752 | 3.459 | 2.665 | 0.159 | 0.71 | 3.731 | 2.815 | 0.167 | 0.697 | 3.81 | 2.883 | 0.172 |

BA-SVM | 0.771 | 3.384 | 2.664 | 0.159 | 0.737 | 3.755 | 2.968 | 0.177 | 0.704 | 3.969 | 3.116 | 0.185 |

PSO-XGBoost | 0.755 | 3.32 | 2.621 | 0.151 | 0.723 | 3.885 | 3.003 | 0.179 | 0.703 | 3.991 | 3.197 | 0.189 |

BA-XGBoost | 0.754 | 3.37 | 2.678 | 0.157 | 0.734 | 3.689 | 2.847 | 0.167 | 0.722 | 3.788 | 2.895 | 0.175 |

PSO-KNEA | 0.743 | 3.506 | 2.587 | 0.154 | 0.689 | 3.834 | 2.8 | 0.167 | 0.671 | 3.929 | 2.899 | 0.172 |

BA-KNEA | 0.783 | 3.227 | 2.509 | 0.149 | 0.754 | 3.483 | 2.676 | 0.159 | 0.737 | 3.576 | 2.732 | 0.163 |

Model | 1 d | 2 d | 3 d |
---|---|---|---|

GEFS raw | 10 | 10 | 10 |

QM | 9 | 9 | 9 |

EDCDFm | 8 | 8 | 8 |

LSTM | 6 | 6 | 6 |

PSO-SVM | 5 | 5 | 5 |

BA-SVM | 2 | 2 | 3 |

PSO-XGBoost | 7 | 7 | 7 |

BA-XGBoost | 3 | 3 | 2 |

PSO-KNEA | 4 | 4 | 4 |

BA-KNEA | 1 | 1 | 1 |

ID | Input | 1 d | 2 d | 3 d | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE | R^{2} | RMSE | MAE | NRMSE | ||

51076 Altay | |||||||||||||

1 | Rs_{f} | 0.824 | 3.778 | 3.019 | 0.193 | 0.789 | 4.139 | 3.23 | 0.207 | 0.771 | 4.312 | 3.382 | 0.217 |

2 | Rs_{f}, RH_{f} | 0.828 | 3.741 | 2.978 | 0.191 | 0.799 | 4.051 | 3.164 | 0.203 | 0.781 | 4.226 | 3.305 | 0.212 |

3 | Rs_{f}, Tmax_{f}, Tmin_{f} | 0.832 | 3.687 | 2.913 | 0.187 | 0.805 | 3.983 | 3.079 | 0.197 | 0.787 | 4.178 | 3.269 | 0.209 |

4 | Rs_{f}, U_{f} | 0.835 | 3.651 | 2.862 | 0.183 | 0.808 | 3.943 | 3.057 | 0.196 | 0.792 | 4.097 | 3.169 | 0.203 |

5 | Tmax_{f}, Tmin_{f}, Ra | 0.723 | 4.705 | 3.766 | 0.241 | 0.721 | 4.757 | 3.737 | 0.239 | 0.712 | 4.812 | 3.799 | 0.243 |

6 | All | 0.844 | 3.552 | 2.785 | 0.178 | 0.819 | 3.839 | 2.98 | 0.191 | 0.803 | 4.002 | 3.105 | 0.199 |

51709 Kashgar | |||||||||||||

1 | Rs_{f} | 0.852 | 3.21 | 2.499 | 0.157 | 0.829 | 3.494 | 2.711 | 0.17 | 0.814 | 3.663 | 2.87 | 0.18 |

2 | Rs_{f}, RH_{f} | 0.859 | 3.23 | 2.551 | 0.16 | 0.84 | 3.456 | 2.705 | 0.17 | 0.823 | 3.632 | 2.869 | 0.18 |

3 | Rs_{f}, Tmax_{f}, Tmin_{f} | 0.867 | 3.185 | 2.535 | 0.159 | 0.846 | 3.388 | 2.634 | 0.165 | 0.832 | 3.488 | 2.741 | 0.172 |

4 | Rs_{f}, U_{f} | 0.87 | 3.223 | 2.55 | 0.16 | 0.841 | 3.464 | 2.701 | 0.17 | 0.826 | 3.502 | 2.705 | 0.17 |

5 | Tmax_{f}, Tmin_{f}, Ra | 0.796 | 3.958 | 3.09 | 0.194 | 0.785 | 3.809 | 2.93 | 0.184 | 0.776 | 3.838 | 2.954 | 0.186 |

6 | All | 0.869 | 3.056 | 2.37 | 0.149 | 0.837 | 3.434 | 2.654 | 0.167 | 0.834 | 3.487 | 2.733 | 0.172 |

51777 Ruoqiang | |||||||||||||

1 | Rs_{f} | 0.789 | 3.403 | 2.352 | 0.142 | 0.755 | 3.64 | 2.504 | 0.151 | 0.73 | 3.818 | 2.663 | 0.161 |

2 | Rs_{f}, RH_{f} | 0.798 | 3.302 | 2.286 | 0.138 | 0.767 | 3.527 | 2.479 | 0.15 | 0.741 | 3.732 | 2.639 | 0.159 |

3 | Rs_{f}, Tmax_{f}, Tmin_{f} | 0.811 | 3.199 | 2.296 | 0.139 | 0.782 | 3.467 | 2.467 | 0.149 | 0.756 | 3.649 | 2.616 | 0.158 |

4 | Rs_{f}, U_{f} | 0.814 | 3.222 | 2.245 | 0.135 | 0.774 | 3.511 | 2.445 | 0.148 | 0.74 | 3.746 | 2.649 | 0.16 |

5 | Tmax_{f}, Tmin_{f}, Ra | 0.745 | 3.764 | 2.792 | 0.168 | 0.724 | 3.875 | 2.871 | 0.173 | 0.702 | 4.035 | 2.96 | 0.179 |

6 | All | 0.819 | 3.123 | 2.196 | 0.133 | 0.791 | 3.354 | 2.387 | 0.144 | 0.752 | 3.674 | 2.624 | 0.158 |

51828 Khotan | |||||||||||||

1 | Rs_{f} | 0.747 | 3.44 | 2.607 | 0.155 | 0.694 | 3.787 | 2.827 | 0.168 | 0.671 | 3.948 | 2.998 | 0.178 |

2 | Rs_{f}, RH_{f} | 0.769 | 3.293 | 2.523 | 0.15 | 0.719 | 3.645 | 2.767 | 0.165 | 0.705 | 3.729 | 2.818 | 0.168 |

3 | Rs_{f}, Tmax_{f}, Tmin_{f} | 0.782 | 3.236 | 2.5 | 0.149 | 0.751 | 3.564 | 2.771 | 0.165 | 0.731 | 3.678 | 2.833 | 0.169 |

4 | Rs_{f}, U_{f} | 0.763 | 3.337 | 2.504 | 0.149 | 0.725 | 3.643 | 2.786 | 0.166 | 0.708 | 3.765 | 2.867 | 0.171 |

5 | Tmax_{f}, Tmin_{f}, Ra | 0.73 | 3.602 | 2.775 | 0.165 | 0.716 | 3.718 | 2.857 | 0.17 | 0.697 | 3.823 | 2.919 | 0.174 |

6 | All | 0.783 | 3.227 | 2.509 | 0.149 | 0.754 | 3.483 | 2.676 | 0.159 | 0.737 | 3.576 | 2.732 | 0.163 |

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## Share and Cite

**MDPI and ACS Style**

Duan, G.; Wu, L.; Liu, F.; Wang, Y.; Wu, S.
Improvement in Solar-Radiation Forecasting Based on Evolutionary KNEA Method and Numerical Weather Prediction. *Sustainability* **2022**, *14*, 6824.
https://doi.org/10.3390/su14116824

**AMA Style**

Duan G, Wu L, Liu F, Wang Y, Wu S.
Improvement in Solar-Radiation Forecasting Based on Evolutionary KNEA Method and Numerical Weather Prediction. *Sustainability*. 2022; 14(11):6824.
https://doi.org/10.3390/su14116824

**Chicago/Turabian Style**

Duan, Guosheng, Lifeng Wu, Fa Liu, Yicheng Wang, and Shaofei Wu.
2022. "Improvement in Solar-Radiation Forecasting Based on Evolutionary KNEA Method and Numerical Weather Prediction" *Sustainability* 14, no. 11: 6824.
https://doi.org/10.3390/su14116824