Simulation of Diffuse Solar Radiation with Tree-Based Evolutionary Hybrid Models and Satellite Data

Abstract

Diffuse solar radiation (R_d) provides basic data for designing and optimizing solar energy systems. Owing to the notable unavailability in many regions of the world, R_d is traditionally estimated by models through other easily available meteorological factors. However, in the absence of ground weather station data, such models often need to be supplemented according to satellite remote sensing data. The performance of Himawari-7 satellite inversion of R_d was evaluated in the study, and hybrid models were established (XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO), so as to improve the satellite data and achieve a better utilization effect. The meteorological data of 14 R_d stations in mainland China from 2011 to 2015 were used. Four input combinations (L1–L4) and eight input combinations (S1–S8) of meteorological factors corresponding to satellite remote sensing data were used for model simulation, while two optimal combinations (S7 and S8) were selected for cross-station application. The results revealed that the accuracy of Himawari-7 satellite R_d data was low, with RMSE, R², MAE, and MBE values of 2.498 MJ·m⁻²·d⁻¹, 0.617, 1.799 MJ·m⁻²·d⁻¹, and 0.323 MJ·m⁻²·d⁻¹, respectively. The performance of these coupled models based on satellite data was significantly improved. The RMSE and MAE values increased by 15.5% and 9.4%, respectively, while the R² value decreased by 10.9 %. Compared with others based on satellite data, the XGBoost_GOA model exhibited optimal performance. The mean values of RMSE, R², and MAE were 1.63 MJ·m⁻²·d⁻¹, 0.76 and 1.21 MJ·m⁻²·d⁻¹, respectively. The XGBoost_GWO model exhibited optimal performance in the cross-station application, and the average RMSE value was reduced by 2.3–10.5% compared with the other models. The meteorological factors input by the models exhibited different levels of significance in different scenarios. R_d_s was the main meteorological parameter that affected the model based on satellite data, while RH exhibited a significant improvement in the XGBoost_FPA and XGBoost_GWO models based on ground weather stations data. Accordingly, the present authors believe that the XGBoost_GOA model has excellent ability for simulating R_d, while the XGBoost_GWO model allows for cross-station simulation of R_d from satellite data.

1. Introduction

Amongst the background of the continuous consumption of non-renewable high-carbon energy, there has been a significant increase in the demand for renewable pollution-free energy. As a kind of pollution-free energy source, solar energy is highly preferred due to the abundant reserves, wide geographical distribution, long-term stability, and low maintenance costs thereof [1]. In the evaluation of the solar energy resources of any type of solar-concentrating thermal or photovoltaic technology, R_d is indispensable. However, the measurement of R_d requires solar trackers and other additional equipment. The difficulty and cost of measurement are considerably higher than the measurement of other meteorological data, which has resulted in a scarcity of R_d data [2,3]. As such, the separation model was commonly adopted for the prediction of R_d data. In China, most solar radiation stations only record the global solar horizontal radiation, and the number of stations is as many as 700, of which only 17 stations measure R_d. The significance of measuring R_d lies in that after acquisition, the performance of some solar equipment on various inclined surfaces can be evaluated [4].

Numerous researchers have developed different models for the prediction of R_d. Among such developments, the empirical model has emerged as the most commonly used prediction method because of the easy input and low computational cost thereof [5]. Clearness index is a meteorological factor highly correlated with R_d [3]; Liu and Jordan [6] proposed the first empirical model in which the clearness index was linked with the R_d, so as to enhance the effect of the model in different functional forms. Such research became a foundation for new empirical models proposed by subsequent researchers. Notably, many developing countries cannot afford the cost of measuring R_d. To establish an empirical model based on sunshine duration, Ali [7] used the R_d data and mathematical formulas of two cities in Iraq, Baghdad, and Mosul. Sabzpooshani et al. [8] established 16 new empirical models based on clearness index to simulate the average R_d in Isfahan, central Iran. For simulation of the daily R_d in northern Sudan, Mohammed et al. [9] used the sunshine hours and solar radiation values recorded by two observation stations to establish seven new empirical models. Despite such efforts, a large number of research results have shown that empirical models have various limitations in respect to the prediction of R_d. Thus, several researchers used machine learning models to overcome the aforementioned issues. Jiang [10] input solar radiation data from nine observatories with different climatic conditions in China into an ANN model and compared the results with other empirical regression models. The results showed that the prediction results of ANN were close to the measured values and the model was superior to other models. Based on the meteorological data of Lhasa, Urumqi, Beijing, and Wuhan from 1981 to 2010, Liu et al. [11] established three models: SVM-FFA, CNQR, and an empirical model. During the validation period, the performance of the three models was as follows: SVM-FFA > CNQR > empirical model. Therefore, owing to the high accuracy, a machine learning model is generally used to predict R_d instead of an empirical model.

Commonly used machine learning models include SVM, RF, and others, which traditionally use a combination of ground weather station data for prediction. Based on the observation database of one-minute irradiance and auxiliary data from 54 sites around the world, Aler [5] used gradient lifting machine learning algorithms to improve the separation of solar radiation components. Husain [12] input the clearness index as the only meteorological factor into 12 machine learning models, and the results revealed that the KNN model had the optimal effect in the training period and test period. At present, direct measurement at ground weather stations and measurement by satellites are the two commonly used methods for obtaining the predicted solar radiation information. There are still many remote areas in the world with sufficient solar energy but a lack of ground weather stations which are significantly needed for the development of solar energy resources. Therefore, satellite remote sensing data need to be used to supplement the lack of ground weather station data. As a rapidly developed method in recent years, measurement by geosynchronous meteorological satellites has advantages in scanning large areas with high spatial and temporal resolution [13]. Based on satellite remote sensing data, Rusen et al. [14] compared and evaluated the effectiveness of solar radiation and scattered solar radiation prediction methods at nine sites in Turkey. Ground measurement data was applied to examine the method, and the results revealed that the HELIOSAT method was the most reliable alternative to ground measurement data. Several researchers chose to use an optimization algorithm and a machine learning model for coupling prediction, so as to further improve the model prediction ability. For simulation of the R_d in air-polluted areas, Fan et al. [15] proposed three optimization algorithms (PSO, BAT, and WOA) combined with the SVM. The results showed that compared with SVM, SVM-BAT promoted the convergence speed of the R_d model, which indicated that the coupled model could significantly improve the prediction performance of a single model.

Himawari-7 was a satellite developed by Japan for meteorological and environmental observation missions on the geostationary orbit and was used to collect and distribute second-generation multi-purpose transport satellites in the Asia-Pacific region. The payload of Himawari-7 was used for meteorological observation and aviation control. As an orbiting spare satellite, Himawari-7 replaced Himawari-6 in 2010. As a three-axis stabilized aircraft, Himawari-7 was equipped with a solar panel that could rotate to track the sun, so that the north-facing passive radiation cooler of the imager was facing towards space. The satellite’s visual camera had a resolution of 1 km, while its infrared camera had a resolution of 4 km. The R_d is provided with a spatial resolution of 5 km. R_d has been investigated using meteorological data measured by the Himawari series of satellites. For prediction of solar diffuse radiation based on Himawari-8 satellite data, Ma et al. [16] developed a hybrid method combined with deep neural network (DNN), and the results showed that the hybrid method performed well.

In the present study, meteorological data were obtained from 14 solar diffuse radiation measurement stations in China, as well as Himawari-7 data. They were established into 12 combinations and input into the model coupled with the XGBoost model by four heuristic algorithms. Additionally, four relatively close groups of stations were selected for cross-station application. Notably, there is a scarcity of research in which the ability of coupling models is evaluated based on different databases for the simulation of R_d. There is also a limited number of studies on the comprehensive comparison of models based on cross-station application using various coupling models, especially in solar diffuse radiation, for which no researchers have applied such method. Therefore, for the development of solar energy resources in remote areas where solar energy is urgently needed, selection of the appropriate model and parameter combination to estimate the R_d and cross-station application at the appropriate station is of considerable significance.

2. Materials and Methods

2.1. Study Area and Meteorological Data

2.1.1. Himawari-7 Data

The data of Himawari-7 from 2011 to 2015 at 14 stations with R_d measurement capabilities in mainland China were downloaded from the NSRDB (Figure 1) [17,18]. The meteorological data obtained included maximum/minimum temperature (Tmax_s/Tmin_s), relative humidity (RH_s), precipitation (P_s), solar horizontal total radiation (Rs_s), and solar diffuse radiation (R_d_s). The detailed geographic locations and satellite weather information for the 14 stations are shown in

Table 1. Summary of geographical location and meteorological data for 14 stations in China during 2011–2015.

Station	Latitude (°N)	Longitude (°E)	Elevation (m)	Tmax_s	Tmin_s	RH_s	Rs_s	P_s	Rd_s	Tmax	Tmin	RH	Rs	P	Ra	Rd
Mohe	52.58	122.31	297.30	−3.09	−12.48	82.18	9.87	19.81	5.00	1.37	−14.43	68.83	9.45	14.91	19.65	5.17
Harbin	45.51	126.39	143.00	5.69	−4.82	73.11	12.00	29.11	5.67	6.69	−3.27	68.00	10.45	17.49	23.08	5.61
Urumqi	43.47	87.39	918.70	5.41	−5.14	58.63	13.29	17.43	5.91	7.21	−1.16	64.16	9.90	10.80	22.19	4.66
Ejinaqi	41.57	101.04	941.30	9.00	−2.86	36.73	12.81	18.08	5.95	9.95	−2.82	34.32	12.65	1.28	21.49	5.53
Golmud	36.25	94.55	2809.20	−1.23	−13.36	45.25	13.21	7.80	5.58	8.44	−4.15	33.66	13.29	1.47	24.12	5.83
Shengyang	41.44	123.31	45.20	10.05	−0.53	68.41	12.39	33.21	6.09	10.28	−0.86	66.84	10.81	17.61	24.15	5.75
Beijing	39.48	116.28	54.70	15.73	4.42	58.37	12.86	39.56	6.82	15.35	6.18	54.73	10.69	17.77	25.45	6.07
Lhasa	29.4	91.08	3650.10	5.27	−7.86	45.09	18.27	9.73	6.02	13.39	−0.50	32.01	16.00	9.02	27.09	5.74
Kunming	25	102.39	1896.80	21.85	10.25	73.90	14.19	53.27	8.01	21.05	11.10	72.95	13.52	29.70	31.66	6.96
Zhengzhou	34.43	113.39	111.30	18.79	7.98	63.07	12.67	51.63	7.80	18.35	9.47	58.61	10.42	18.81	27.98	7.43
Wuhan	30.36	114.03	27.00	19.90	11.42	76.76	11.77	70.39	7.68	19.58	10.96	80.72	9.45	40.78	29.68	6.74
Baoshan	31.24	121.27	8.20	18.53	12.45	80.79	11.97	67.98	7.23	19.07	12.81	72.85	10.09	41.65	29.42	6.80
Guangzhou	23.13	113.29	4.20	26.66	17.96	80.57	14.63	103.59	8.61	25.51	17.89	79.48	11.29	63.80	32.53	7.80
Sanya	18.13	109.35	7.00	26.89	24.46	83.97	14.60	111.86	9.05	24.88	20.27	89.97	13.78	54.25	32.99	8.94

.

2.1.2. Ground Weather Stations Data

Some meteorological factors from 14 ground weather stations in mainland China were collected, including maximum/minimum temperature (Tmax/Tmin), relative humidity (RH), solar radiation (R_s), precipitation (P), and diffuse solar radiation (R_d). Daily extraterrestrial radiation (Ra) was calculated at latitude and each day of the year [19]. Table 1 showed the detailed geographical location and data of the selected stations, including the average values of meteorological factors obtained from 14 ground weather stations in 2011–2015. Each station has an average of more than 400 rows of data missing. Incomplete meteorological data were deleted during data processing.

2.2. Extreme Gradient Boosting

XGBoost was proposed by Chen et al. [20]. Through additional training to avoid overfitting, XGBoost integrates many weak learners and develops a strong learner, which is essentially a kind of boosting algorithm for ensemble learning in supervised learning. The objective function of XGBoost is expressed as the sum of the loss function and the regularization term. A smaller loss function indicates better model fitting effect, while a smaller regularization term indicates a lower model complexity. Similar to the traditional model, XGBoost uses residuals. Its algorithm utilizes split data in the data set to model separately [21], and unlike traditional, this is also a parameter-based algorithm. When the model is dealing with classification or regression problems, the model does not need to change the determined parameters. XGBoost has higher accuracy and greater flexibility. It adds regular terms to the objective function to prevent overfitting, which is one of the characteristics of XGBoost that is superior to traditional GBDT. However, it needs to traverse the data set in the process of node splitting. The pre-sorting process has high space complexity and consumes a lot of memory. The expressions are as follows:

$$f_i^{(t)}={\displaystyle \sum _{k=1}^t{f}_k(x_i)}=f_i^{(t-1)}+f_t(x_i)$$

(1)

where f_i^(t) is the simulation result of sample i after the t-th iteration, and f_i^(t−1) is the simulation result of step t − 1.

The accuracy of the model depends on the variance and deviation of the model, where the deviation is related to the loss function. In order to reduce the variance of the model and prevent overfitting, the regularization term needs to be added to the objective function. Therefore, the objective function consists of a loss function and a regularization term, which is defined as follows:

$$L={\displaystyle \sum _{i=1}^{n}l(y_i,\overline{y_i})}$$

(2)

$$Obj={\displaystyle \sum _{i=1}^{n}l(y_i,\overline{y_i})}+{\displaystyle \sum _{i=1}^t\mathsf{\Omega }(f_i)}$$

(3)

where L is the loss function, n is the number of samples, Obj is the objective function, and Ω is the sum of the complexity of all trees. Further computational programs and more information about XGBoost can be found in Chen’s research [22].

2.3. Heuristic Algorithms

2.3.1. Differential Evolution (DE) Algorithm

First proposed by Storn and Price [23], the DE algorithm is a kind of evolutionary algorithm that is extensively used in data mining, pattern recognition, electromagnetics, and other fields, owing to the simple structure and strong robustness thereof [24]. The optimization of DE algorithm firstly is to use floating point vector encoding to generate individuals, and select two individuals to generate a difference vector. Secondly, sum the difference vector generated in the previous step with another individual to generate an experimental individual; then, operate the individual generated by the previous generation and the experimental individual to generate a new generation of individuals; finally, choose the most suitable individual between the two generations to enter the next generation. The core idea of the DE algorithm is to use mutation and crossover operation to generate a test population and evaluate the fitness, and then compare the original population and test population one by one through the selection mechanism of greedy thought, and select the next generation. The DE algorithm has the advantages of simple operation, less controllable parameters, fast convergence speed, and strong global search ability, but it inevitably has the problem of stagnation when optimizing complex problems such as high dimension, multi-peak and multi-objective problems. The specific steps and expressions are as follows:

(1)

Initialization population

$$x_{i,j}(0)=x_{i,j}^L+rand(0,1)(x_{i,j}^U-x_{i,j}^L)$$

(4)

where x_i,j^L and x_i,j^U denote the upper and lower bounds of dimension j, respectively, and rand(0,1) denotes the random number on the interval [0, 1].

(2)

Variation

The DE algorithm realizes individual mutation through differentiation strategy. The common differential strategy is to randomly select two different individuals in the population, and synthesize the vector with the individual to be mutated after the vector difference is scaled.

$$V_i(g+1)=X_{r1}(g)+F(X_{r2}(g)-X_{r3}(g))$$

(5)

where r₁, r₂ and r₃ are three random numbers in the interval [1, NP], F is the scaling factor, and g is the g-th generation.

(3)

Crossover

The purpose of crossover operation is to randomly select individuals.

$$U_{i,j}(g+1)=\left\{\begin{array}{c}{V}_{i,j}(g+1)\hspace{1em}if\hspace{1em}rand(0,1)\le CR\\ x_{i,j}(g)\hspace{1em}otherwise\end{array}\right.$$

(6)

where CR is the crossover probability, which generates new individuals according to different probabilities.

(4)

Selection

DE algorithm selects the better individual as the new individual.

$$X_i(g+1)=\left\{\begin{array}{c}{U}_i(g+1)\hspace{1em}if\hspace{1em}f(U_i(g+1))\le f(X_i(g))\\ X_i(g)\end{array}\right.$$

(7)

Further details about the differential evolution algorithm can be found in Storn and Price’s research [23].

2.3.2. Flower Pollination Algorithm (FPA)

The flower pollination algorithm (FPA) is a new meta-heuristic swarm intelligence optimization algorithm proposed by Yang [25]. The basic concept of the FPA was derived from the simulation of self-pollination and cross-pollination of flowers in nature. The algorithm is more effective than the genetic algorithm, and the convergence speed of the FPA is almost exponential. The algorithm follows the following four standardization principles: (1) during cross-pollination, the pollinator performs Lévy flight (long-distance movement), which is mapped to a global search process; (2) self-pollination is considered to be a local search process; (3) the stability of flowers can be regarded as the ratio of reproduction probability and similarity of two flowers during pollination; (4) the change of pollination method is controlled by switching probability p(p ∈ [0, 1]), that is, when random number “rand” < p, self-pollination is executed; otherwise, cross-pollination is executed. The algorithm imitates two mechanisms of natural flower pollination. Owing to the reliance on pollinators to spread pollen remotely, cross-pollination corresponds to a global search process, while self-pollination corresponds to the local search process due to the close distance in the physical position of pollination. A switching probability p(p ∈ [0, 1]) is introduced to weigh the ratio between the two search processes. The FPA is simple in theory and easy to implement, but there are still problems such as low convergence accuracy and sensitivity to dimensions. The expressions are as follows:

(1)

Cross-pollination formula:

$$X_i^{t+1}=X_i^t+L(X_i^t-g_{\ast }^t)$$

(8)

where X_i^t denotes the i-th solution of the t-th generation respectively; g_∗^t is the t-th generation optimal solution; L is the step length.

(2)

Self-pollination formula:

The design idea of self-pollination algorithm is to simulate the close pollination between flowers of the same species in nature. The mathematical description is as follows:

$$X_i^{t+1}=X_i^t+\epsilon (X_j^t-X_k^t)$$

(9)

where ε ∈ [0, 1] denotes the random number, X_j^t and X_k^t denote the j-th and k-th solutions in the t-th population, respectively. Further details about the flower pollination algorithm can be found in Yang’s research [25].

2.3.3. Grasshopper Optimization Algorithm (GOA)

The grasshopper optimization algorithm (GOA) is a swarm intelligence optimization algorithm proposed by Saremi et al. [26]. Similar to most other intelligence optimization algorithms, the GOA ensures that the algorithm can effectively search globally and avoid stopping at local optimum in both exploration and development. The life cycle of grasshoppers is primarily divided into two stages: larvae and adults. The main feature of the larvae stage is that grasshoppers move slowly in a small range, while in the adult stage, grasshoppers have strong hind legs and are good at jumping, being able to move long distances quickly. The exploration process of the GOA is equivalent to the adult stage, and the development process is equivalent to the larval stage. Looking for food sources is another main feature of the grasshopper population, with a food source being equivalent to the optimal solution, and the search for food being the process of finding the optimal solution. The GOA is stable and has good local search ability. However, its convergence speed is not fast. Since each individual accumulates other individuals except itself, the new position difference between individuals is small, and the locusts are easy to fall into local optimum in group aggregation. The expressions are as follows:

$$X_i^d=c\left({\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne i\end{array}}^{N}c\frac{u{b}_d-l{b}_d}{2}s\left(\left|x_j^d-\left.x_i^d\right|\right.\right)\frac{x_j-x_i}{d_{ij}}}\right)+\overline{T_d}$$

(10)

where X_i^d is the position of the i-th locust in the d-th dimension; ub_d and lb_d are the upper and lower bounds of the variable of the i-th locust in the d-th dimension; t is the target position of locust swarm.

$$c=c_{\max }-t\frac{c_{\max }-c_{\min }}{T_{\max }}$$

(11)

where t represents the current number of iterations, T_max is the maximum number of iterations, c_max and c_min are the maximum and minimum values of parameter c, respectively. Further details about the GOA can be found in Saremi’s research [26].

2.3.4. Gray Wolf Optimizer (GWO) Algorithm

Inspired by the predation activities of gray wolves, the gray wolf optimization (GWO) algorithm is a swarm intelligence optimization algorithm proposed by Mirjalili et al. [27]. The algorithm has the characteristics of strong convergence performance and easy implementation. Gray wolves strictly abide by a social dominance hierarchy. When designing a GWO algorithm, the gray wolf social hierarchy model needs to be firstly constructed, the fitness of each individual needs to be calculated, and the three gray wolves with the best fitness need to be placed on the higher level in turn. Gray wolves approach prey when searching, but gray wolves cannot determine the exact location of prey. The higher-level gray wolves are assumed to have stronger ability to obtain location information about their prey than lower-level ones for simulating the hunting behavior of gray wolves. Therefore, in each iteration process, several optimal gray wolves are kept, and the locations of other gray wolves are updated according to their location information. Compared with other algorithms, the optimization process of the GWO algorithm is faster. However, the GWO algorithm is a heuristic optimization algorithm, and the optimal solution is only close to the original optimal solution, not the real optimal solution of the problem. The expressions are as follows:

$$D=\left|C\cdot X_p\left(t\right)-\right.\left.X\left(t\right)\right|$$

(12)

$$X\left(t+1\right)=X_p\left(t\right)-A\cdot D$$

(13)

Equation (11) represents the distance between the individual and the prey, and Equation (12) is the position update formula of the gray wolf. Where t is the current number of iterations, X_p and X are the position vectors of prey and gray wolf, respectively, and A and C are the coefficient vectors. The calculation formulas are as follows:

$$A=2a\cdot r_1-a$$

(14)

$$C=2\cdot r_2$$

(15)

where a is the convergence factor. As the number of iterations decreases linearly from 2 to 0, r₁ and r₂ are random numbers in the interval [0, 1].

After the gray wolf recognizes the location of the prey, β and δ, led by α, guide the wolves to surround the prey. The expression is as follows:

$$\left\{\begin{array}{c}{D}_{\alpha }=\left|C_1\cdot X_{\alpha }-\left.X\right|\right.\\ D_{\beta }=\left|C_2\cdot X_{\beta }-\left.X\right|\right.\\ D_{\delta }=\left|C_3\cdot X_{\delta }-\left.X\right|\right.\end{array}\right.$$

(16)

where D_α, D_β and D_δ represent the distance between α, β and δ and other individuals, respectively; X_α, X_β and X_δ denote the current positions α, β and δ, respectively. C₁, C₂ and C₃ are random vectors, and X is the current position of the gray wolf.

$$\left\{\begin{array}{c}{X}_1=X_{\alpha }-A_1\cdot \left(D_{\alpha }\right)\\ X_2=X_{\beta }-A_2\cdot \left(D_{\beta }\right)\\ X_3=X_{\delta }-A_3\cdot \left(D_{\delta }\right)\end{array}\right.$$

(17)

$$X\left(t+1\right)=\frac{X_1+X_2+X_3}{3}$$

(18)

Equation (15) defines the step length and direction of ω individuals in the wolf pack towards α, β and δ, respectively. Equation (16) defines the final position ω. More details about the GWO algorithm can be found in Mirjalili’s research [27].

2.4. Input Combinations Based on Satellite and Ground Weather Station Data

Twelve meteorological environment variable input combinations of four coupling models were used to evaluate the effects of various input factors on R_d prediction: (1) eight combinations of input parameters were set based on satellite data (see

Table 2. The input combinations based on satellite data for four coupling models.

No.	Models				Input Combinations
	XGBoost_DE	XGBoost_FPA	XGBoost_GOA	XGBoost_GWO
S1	XGBoost_DE1	XGBoost_FPA1	XGBoost_GOA1	XGBoost_GWO1	Tmax_s, Tmin_s, Rs_s, Ra
S2	XGBoost_DE2	XGBoost_FPA2	XGBoost_GOA2	XGBoost_GWO2	Tmax_s, Tmin_s, Rs_s, Ra, RH_s
S3	XGBoost_DE3	XGBoost_FPA3	XGBoost_GOA3	XGBoost_GWO3	Tmax_s, Tmin_s, Rs_s, Ra, P_s
S4	XGBoost_DE4	XGBoost_FPA4	XGBoost_GOA4	XGBoost_GWO4	Tmax_s, Tmin_s, Rs_s, Ra, RH_s, P_s
S5	XGBoost_DE5	XGBoost_FPA5	XGBoost_GOA5	XGBoost_GWO5	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra
S6	XGBoost_DE6	XGBoost_FPA6	XGBoost_GOA6	XGBoost_GWO6	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra, RH_s
S7	XGBoost_DE7	XGBoost_FPA7	XGBoost_GOA7	XGBoost_GWO7	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra, P_s
S8	XGBoost_DE8	XGBoost_FPA8	XGBoost_GOA8	XGBoost_GWO8	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra, RH_s, P_s

); and (2) four combinations of input parameters were set based on ground weather station data (see

Table 3. The input combinations based on ground weather station for four coupling models.

No.	Models				Input Combinations
	XGBoost_DE	XGBoost_FPA	XGBoost_GOA	XGBoost_GWO
L1	XGBoost_DE9	XGBoost_FPA9	XGBoost_GOA9	XGBoost_GWO9	Tmax, Tmin, Rs, Ra
L2	XGBoost_DE10	XGBoost_FPA10	XGBoost_GOA10	XGBoost_GWO10	Tmax, Tmin, Rs, Ra, RH
L3	XGBoost_DE11	XGBoost_FPA11	XGBoost_GOA11	XGBoost_GWO11	Tmax, Tmin, Rs, Ra, P
L4	XGBoost_DE12	XGBoost_FPA12	XGBoost_GOA12	XGBoost_GWO12	Tmax, Tmin, Rs, Ra, RH, P

). The K-fold cross-validation method was used for all the data obtained in the modeling process. The first three fifths (2011–2013) of these data were used to train these models, and the last two fifths (2014 and 2015) were used to test and verify these models.

XGBoost_DE1-8 represents the coupling model with combined S1-S8 inputs based on satellite data (see Table 2). XGBoost_DE9-12 represents the coupling model with combined L1-L4 input based on ground weather station data (see Table 3), and the symbolic meaning of others are the same as above.

2.5. Input Combinations Based on Cross-Station Application

According to the location of 14 stations, the relatively close stations were divided into pairs to test and verify the model of the adjacent stations based on satellite data of the target station. On the basis of satellite data, two sets of optimal-simulated combinations (see

Table 4. The input combination of Himawari-7 satellite data based on four target stations and four neighboring stations in different periods.

No.	Models				Train	Test	Pred	Input Combinations
1	XGBoost_ DE	XGBoost_ FPA	XGBoost_ GOA	XGBoost_ GWO	Mohe	Harbin	Harbin	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra, P_s	Rd_s, Tmax_s, Tmin_s, Rs_s, Ra, RH_s, P_s
2	XGBoost_ DE	XGBoost_ FPA	XGBoost_ GOA	XGBoost_ GWO	Urumqi	Ejinaqi	Ejinaqi
3	XGBoost_ DE	XGBoost_ FPA	XGBoost_ GOA	XGBoost_ GWO	Shengyang	Beijing	Beijing
4	XGBoost_ DE	XGBoost_ FPA	XGBoost_ GOA	XGBoost_ GWO	Zhengzhou	Wuhan	Wuhan

) were selected for cross-station application and four sets of stations with the highest data accuracy and optimal model performance were presented.

2.6. Statistical Indicators

The performance evaluation of four coupled models for simulation of the level of daily R_d was based on four widely adopted statistical indicators, including MAE, MBE, RMSE, and R². RMSE reflects the overall estimation accuracy of the model, and R² represents the percentage of data that the model can describe. MAE is used to describe the average deviation degree of each point, and MBE reflects the positive and negative deviation of the model. The formula of the statistical indicators could be denoted below:

$$\mathrm{MAE}=\frac{1}{\mathrm{t}}{\displaystyle \sum _{i=1}^{\mathrm{t}}\left|X_{i,m}-X_{i,e}\right|}$$

(19)

$$\mathrm{MBE}=\frac{1}{\mathrm{t}}{\displaystyle \sum _{i=1}^{\mathrm{t}}(X_{i,m}-X_{i,e})}$$

(20)

$$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{t}}{\displaystyle \sum _{i=1}^{\mathrm{t}}{(X_{i,m}-X_{i,e})}^2}}$$

(21)

$${\mathrm{R}}^2=\frac{{[{\displaystyle {\sum }_{i=1}^{\mathrm{t}}(X_{i,e}-\overline{X_{i,e}})(X_{i,m}-\overline{X_{i,m}})}]}^2}{{\displaystyle {\sum }_{i=1}^{\mathrm{t}}{(X_{i,e}-\overline{X_{i,e}})}^2{\displaystyle {\sum }_{i=1}^{\mathrm{t}}{(X_{i,m}-\overline{X_{i,m}})}^2}}}$$

(22)

where X_i,m, X_i,e, X_i,m, X_i,e and t are the measured value of R_d, the simulated value of R_d, the average measured value of R_d, the average simulated value of R_d, and the data sample size, respectively. Higher R² (close to 1) and lower MAE, MBE, and RMSE (close to 0) indicate better model fit and higher model performance.

3. Results

3.1. Accuracy Assessment of Diffuse Solar Radiation Data from Satellites

The R_d_s values of 14 stations in mainland China were obtained from Himawari-7 data, and the satellite measurements were statistically analyzed with the ground weather station measurements of the corresponding stations (see

Table 5. Statistical results of R_d_s obtained by Himawari-7 satellite and R_d obtained by ground weather stations.

Stations/Statistical Indicators	RMSE	R2	MAE	MBE
Mohe	2.151	0.678	1.424	0.377
Harbin	1.741	0.765	1.196	0.230
Urumqi	3.671	0.328	2.466	0.414
Ejinaqi	2.379	0.596	1.750	0.348
Golmud	2.068	0.687	1.503	0.317
Shengyang	2.135	0.677	1.479	0.284
Beijing	1.953	0.796	1.317	0.201
Lhasa	2.171	0.810	1.491	0.331
Kunming	3.462	0.510	2.539	0.408
Zhengzhou	2.158	0.725	1.549	0.239
Wuhan	2.582	0.656	1.927	0.300
Baoshan	2.029	0.691	1.506	0.248
Guangzhou	2.907	0.387	2.196	0.307
Sanya	3.561	0.327	2.850	0.509

). During the validation period, an observation can be made from Table 5 that the RMSE and MAE of Harbin station were the lowest, being 1.741 MJ·m⁻²·d⁻¹ and 1.196 MJ·m⁻²·d⁻¹, respectively. The R² of Lhasa station was the highest, being 0.81, and the MBE of Beijing station was the lowest, being 0.201 MJ·m⁻²·d⁻¹. Compared with the other 12 stations, the satellite R_d data of Harbin and Beijing stations were more accurate. The average RMSE, MAE, and MBE values were 41.1%, 50.4%, and 57.8% lower, respectively, than the other stations, and the average R² was 32.4% higher. In general, only a small number of stations could obtain a higher data accuracy by using R_d_s obtained by Himawari-7 data. The accuracy of Himawari-7 data at most stations was low and the error was large. Among them, the accuracy of satellite measurements of R_d_s in Urumqi, Guangzhou, and Sanya stations is significantly different from that of other stations. This may be due to the thickness of clouds at these stations and the changes of aerosols and water vapor on sunny days. There are difficulties in obtaining the ideal effect in practical application, and improvements are needed. This section analyzed and evaluated the accuracy of the R_d and measured values of 14 stations measured by Himawari-7, and these data were used for comparison with the simulation results of the tree-based coupling model in the following sections.

3.2. Model Performance Based on Himawari-7 Data

Four optimization algorithms (DE, FPA, GOA, and GWO) were used for coupling with the XGBoost model, so as to make better use of satellite data and improve the accuracy. Seven different parameters were selected: Tmax_s, Tmin_s, R_s_s, R_d_s, P_s, RH_s, and Ra. The parameters were divided into eight different input combinations to drive the four aforementioned coupling models (see Table 2). Based on satellite data of 14 stations, the R_d was predicted. The statistical summary of the verification period is shown in Table 6.

An observation can be made from the table that the four coupling models exhibited different accuracies under the input of different parameter combinations. Most models had MBE values less than 0 at most stations, so the simulation of R_d was generally underestimated. The RMSE, R², and MAE values of the XGBoost_DE model were 1.948–2.11 MJ·m⁻²·d⁻¹, 0.652–0.692, and 1.484–1.618 MJ·m⁻²·d⁻¹, respectively. The RMSE, R², and MAE values of the XGBoost_FPA model were 1.97–2.112 MJ·m⁻²·d⁻¹, 0.642–0.682, and 1.493–1.607 MJ·m⁻²·d⁻¹, respectively. The accuracy fluctuation of the XGBoost_DE model was the largest, followed by XGBoost_FPA model, while the accuracy fluctuations of the XGBoost_GOA and XGBoost_GWO model were small and considerably close.

The XGBoost_GOA model performed most optimally in simulating R_d based on satellite data, with RMSE and MAE values of 1.874 MJ·m⁻²·d⁻¹ and 1.422 MJ·m⁻²·d⁻¹, respectively. The XGBoost_DE model exhibited worse performance than the other three models, with RMSE and MAE values of 2.039 MJ·m⁻²·d⁻¹ and 1.556 MJ·m⁻²·d⁻¹, respectively. The analytical results reveal that the XGBoost_GOA model exhibited better performance. Scatter plots were used to present the simulated and measured values of the models for the Beijing station (Figure 2), so as to better compare the simulation performance of the XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO coupling models for R_d. As Figure 2 illustrates, the four coupling models showed high accuracy in simulating R_d. Among the four, the XGBoost_GOA model showed the most reliable estimation trend, and the dispersion level of the scatter was markedly lower than that of the XGBoost_DE and XGBoost_FPA model, and slightly lower than XGBoost_GWO model.

In order to explore whether relative humidity, precipitation, and satellite-measured R_d were dominant factors in simulating R_d, eight combinations were set up to respectively drive the model. Table 6 shows that the addition of P_s and RH_s could improve the simulation accuracy of R_d. Taking XGBoost_GOA model as an example, MBE, S1, S3, and S4 were used as input to obtain a smaller positive value, while the four groups of S5–S8 were significantly underestimated, and MBE was less than −0.15 MJ·m⁻²·d⁻¹. In terms of RMSE and MAE, the model performed best when S8 was used as input, and the values were 1.856 MJ·m⁻²·d⁻¹ and 1.409 MJ·m⁻²·d⁻¹, respectively. When S1 was used as input, the model performed worst, with RMSE and MAE values of 1.905 MJ·m⁻²·d⁻¹ and 1.451 MJ·m⁻²·d⁻¹, respectively. As such, based on temperature, solar radiation, R_d, relative humidity, and precipitation, the XGBoost_GOA model was more accurate than the XGBoost_GOA model in terms of temperature and solar radiation. For the XGBoost_FPA model, when S7 was used as input, the RMSE, MAE, and MBE values of the model were better than those of the model when S8 was input, with differences of 0.27%, 0.35%, and 14.2%, respectively. For the XGBoost_DE model, in terms of R², when S6 was used as input, R² was the highest, being 0.692, but performed poorly in terms of MBE, being −0.198 MJ·m⁻²·d⁻¹, second only to S7, which showed a serious underestimation of the model. With S2 as the input, the MBE was optimal at 0.011 MJ·m⁻²·d⁻¹. For the XGBoost_GWO model, when S2 was used as input, the model performed optimally in terms of RMSE and MBE, which were 1.848 MJ·m⁻²·d⁻¹ and 0.015 MJ·m⁻²·d⁻¹, respectively, and there was no obvious overestimation. In terms of R², the model performance was second only to S6 and S8, thereby demonstrating that the accuracy of the XGBoost_GWO model simulation and the R_d value measured by the satellite were less significant than the other three models under the input of the model. The aforementioned analysis results show that precipitation was more significant than relative humidity in simulating R_d using the XGBoost_FPA model. For the XGBoost_FPA and XGBoost_GOA models, the R_d values measured by satellites were more significant than those of the other two models. Figure 2 clearly illustrates the different effects of different factors’ inputs on the accuracy of these four models for simulating R_d. For XGBoost_DE and XGBoost_GOA model, the first seven combinations had higher errors, and the model input S8 (R_d_s, Tmax_s, Tmin_s, R_s_s, Ra, and RH_s, P_s) could produce higher simulation accuracy.

Boxplots were used to demonstrate the differences between the four coupled models for simulating R_d based on the Himawari-7 data at 14 stations in mainland China (Figure 3). Figure 3 shows that the abnormal values detected by the four combinations of S5–S8 were less than those of S1–S4. In terms of RMSE, the levels of the XGBoost_GOA and XGBoost_GWO model outperformed others. In terms of R², the XGBoost_GOA model had better effect than the XGBoost_GWO model. In the case of input S1–S4, the dispersion degrees of the XGBoost_DE and XGBoost_FPA model simulation values were higher, while the dispersion degree of the XGBoost_GOA model simulation value was the lowest. As Figure 3 clearly shows, the simulation values of the XGBoost_GOA model were concentrated and showed high simulation levels in S3–S8. Although XGBoost_DE performed well in terms of the MBE values in S7–S8, the average simulation level was markedly lower than others.

In general, the XGBoost_GOA model performed optimally in the verification period, and R_d_s had the most remarkable effect on the performance of these models. Due to the limited number of research stations and the large span of the climate zone, the accuracy of the model based on satellite data to simulate the level of R_d was not high. Thus, attempts were made to investigate the performance of four coupling models to simulate R_d based on ground weather station data of the same 14 stations, and to compare the accuracy differences with the satellite data model.

Table 6. Statistical results of the XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for R_d prediction with eight combinations based on satellite data.

Models	Combinations/Statistical Indicators	RMSE	R2	MAE	MBE
XGBoost_DE1-8	S1	2.084	0.652	1.577	0.164
	S2	2.094	0.688	1.600	0.011
	S3	2.019	0.652	1.553	0.215
	S4	2.110	0.673	1.618	−0.033
	S5	2.058	0.654	1.563	−0.383
	S6	1.970	0.692	1.499	−0.198
	S7	2.033	0.670	1.554	−0.186
	S8	1.948	0.686	1.484	−0.120
XGBoost_FPA1-8	S1	2.112	0.642	1.607	0.205
	S2	2.032	0.673	1.548	0.195
	S3	2.040	0.660	1.560	0.182
	S4	1.970	0.673	1.493	0.047
	S5	2.081	0.669	1.586	−0.261
	S6	2.078	0.682	1.564	−0.271
	S7	2.016	0.678	1.531	−0.142
	S8	2.022	0.680	1.536	−0.166
XGBoost_GOA1-8	S1	1.905	0.678	1.451	0.038
	S2	1.858	0.699	1.416	−0.042
	S3	1.878	0.686	1.433	0.025
	S4	1.863	0.696	1.418	0.022
	S5	1.889	0.695	1.425	−0.263
	S6	1.872	0.706	1.41	−0.236
	S7	1.871	0.703	1.413	−0.193
	S8	1.856	0.709	1.409	−0.24
XGBoost_GWO1-8	S1	1.905	0.68	1.457	0.035
	S2	1.848	0.701	1.416	0.015
	S3	1.889	0.685	1.447	0.069
	S4	1.853	0.696	1.421	0.029
	S5	1.902	0.696	1.434	−0.225
	S6	1.858	0.713	1.409	−0.239
	S7	1.888	0.701	1.426	−0.193
	S8	1.851	0.713	1.402	−0.237

Table 6. Statistical results of the XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for R_d prediction with eight combinations based on satellite data.

Models	Combinations/Statistical Indicators	RMSE	R2	MAE	MBE
XGBoost_DE1-8	S1	2.084	0.652	1.577	0.164
	S2	2.094	0.688	1.600	0.011
	S3	2.019	0.652	1.553	0.215
	S4	2.110	0.673	1.618	−0.033
	S5	2.058	0.654	1.563	−0.383
	S6	1.970	0.692	1.499	−0.198
	S7	2.033	0.670	1.554	−0.186
	S8	1.948	0.686	1.484	−0.120
XGBoost_FPA1-8	S1	2.112	0.642	1.607	0.205
	S2	2.032	0.673	1.548	0.195
	S3	2.040	0.660	1.560	0.182
	S4	1.970	0.673	1.493	0.047
	S5	2.081	0.669	1.586	−0.261
	S6	2.078	0.682	1.564	−0.271
	S7	2.016	0.678	1.531	−0.142
	S8	2.022	0.680	1.536	−0.166
XGBoost_GOA1-8	S1	1.905	0.678	1.451	0.038
	S2	1.858	0.699	1.416	−0.042
	S3	1.878	0.686	1.433	0.025
	S4	1.863	0.696	1.418	0.022
	S5	1.889	0.695	1.425	−0.263
	S6	1.872	0.706	1.41	−0.236
	S7	1.871	0.703	1.413	−0.193
	S8	1.856	0.709	1.409	−0.24
XGBoost_GWO1-8	S1	1.905	0.68	1.457	0.035
	S2	1.848	0.701	1.416	0.015
	S3	1.889	0.685	1.447	0.069
	S4	1.853	0.696	1.421	0.029
	S5	1.902	0.696	1.434	−0.225
	S6	1.858	0.713	1.409	−0.239
	S7	1.888	0.701	1.426	−0.193
	S8	1.851	0.713	1.402	−0.237

Figure 2. Scatter plots of R_d predicted by the coupling models based on Himawari-7 data in Beijing.

Figure 2. Scatter plots of R_d predicted by the coupling models based on Himawari-7 data in Beijing.

Figure 3. Boxplot of statistical indicators for the prediction of R_d by the coupling model based on Himawari-7 data.

Figure 3. Boxplot of statistical indicators for the prediction of R_d by the coupling model based on Himawari-7 data.

3.3. Model Performance Based on Ground Weather Station Data

The factors obtained from the ground weather station, namely Tmax, Tmin, R_s, RH, and P, were applied to simulate the R_d. The five parameters were divided into four groups (see Table 3) and input into four coupling models. The statistical indicators of the simulated R_d were contrasted with the statistical indicators based on Himawari-7 data simulation. Based on the observation stations and satellite data, the significance of parameters from observation station to the performance of these models’ simulation and the differences in the performance of the simulated R_d were evaluated (see Table 7). An observation can be made from the table that in the case of inputting the same meteorological factors, the XGBoost_GOA model (mean RMSE = 1.381 MJ·m⁻²·d⁻¹, R² = 0.832, MAE = 0.993 MJ·m⁻²·d⁻¹, MBE = 0.162 MJ·m⁻²·d⁻¹) was significantly better than others (mean RMSE = 1.387–1.589 MJ·m⁻²·d⁻¹, R² = 0.799–0.831, MAE = 0.996–1.167 MJ·m⁻²·d⁻¹, MBE = 0.1–0.235 MJ·m⁻²·d⁻¹). Scatter plots of the four coupling models were drawn based on the data observed in Beijing station (Figure 4). Figure 4 showed that the capability of the XGBoost_GOA model and the XGBoost_GWO model exhibited a similar simulation trend, being closer to the fitting line and more evenly distributed than the other two models. The dispersion degree of each model in the case of inputting the L4 combination was lower than the dispersion degrees of the other three combinations.

Table 7 shows that the accuracy of each model was different when different parameter combinations were input. For the XGBoost_DE model, the model showed the optimal simulation level in the case of inputting the L1 combination. Compared with the L2-L4 combinations, the RMSE and MAE values were reduced by 0.2–11.1%, 1–13.4%, and R² increased by 0.8–1.6%. For the XGBoost_FPA model, when the L2 combination was input, the RMSE and MAE values of the model were the lowest, being 1.495 MJ·m⁻²·d⁻¹ and 1.097 MJ·m⁻²·d⁻¹, respectively. For the XGBoost_GOA model, the four input effects of the model were significantly better than the XGBoost_DE and XGBoost_FPA models. The accuracy performance was as follows: L3 > L4 > L1 > L2. The L3 input combination performed most optimally among all models and combinations, with RMSE, R², MAE, and MBE values of 1.362 MJ·m⁻²·d⁻¹, 0.834, 0.979 MJ·m⁻²·d⁻¹, and 0.129 MJ·m⁻²·d⁻¹, respectively. For the XGBoost_GWO model, the relatively complex parameter combination of L4 had the optimal model simulation effect (RMSE = 1.374 MJ·m⁻²·d⁻¹, MAE = 0.988 MJ·m⁻²·d⁻¹), which was slightly better than the L3 combination (RMSE = 1.375 MJ·m⁻²·d⁻¹, MAE = 0.99 MJ·m⁻²·d⁻¹). From the aforementioned analysis, an observation can be made that relative humidity and precipitation had an adverse effect on the XGBoost_DE model. Relative humidity can refine the ability of the XGBoost_FPA model. Precipitation has a positive effect on the XGBoost_GOA model, and the co-input of such meteorological factors significantly refined the performance of the XGBoost_GWO model.

The statistical indicators of the model simulation values based on ground weather station data are shown in Figure 5. An observation can be made from the boxplots that the data of the XGBoost_DE model fluctuated greatly with the input combinations of L2 and L4, and the data of the XGBoost_FPA model fluctuated greatly with the input combinations of L1 and L3. Overall, the RMSE values of the XGBoost_GOA and XGBoost_GWO model were markedly lower than those of others. As the complexity of the input meteorological factors increased, the data for the XGBoost_GWO model became more concentrated. As such, the XGBoost_GOA model and the XGBoost_GWO model were superior to others in simulating R_d, thereby revealing the significance of the input of two meteorological factors, relative humidity and precipitation, to the XGBoost_GWO model simulation.

Table 7. Statistical results of the XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for R_d prediction with four combinations based on ground weather stations data.

Models	Combination/Statistical Indicators	RMSE	R2	MAE	MBE
XGBoost_DE9-12	L1	1.478	0.821	1.070	0.057
	L2	1.605	0.819	1.167	0.056
	L3	1.480	0.814	1.082	0.148
	L4	1.662	0.808	1.235	0.140
XGBoost_FPA9-12	L1	1.643	0.777	1.215	0.321
	L2	1.495	0.800	1.097	0.224
	L3	1.695	0.812	1.251	0.086
	L4	1.523	0.808	1.104	0.310
XGBoost_GOA9-12	L1	1.390	0.832	1.005	0.186
	L2	1.392	0.831	1.000	0.162
	L3	1.362	0.834	0.979	0.129
	L4	1.378	0.831	0.989	0.170
XGBoost_GWO9-12	L1	1.408	0.828	1.010	0.178
	L2	1.393	0.830	0.997	0.173
	L3	1.375	0.834	0.990	0.158
	L4	1.374	0.833	0.988	0.159

Table 7. Statistical results of the XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for R_d prediction with four combinations based on ground weather stations data.

Models	Combination/Statistical Indicators	RMSE	R2	MAE	MBE
XGBoost_DE9-12	L1	1.478	0.821	1.070	0.057
	L2	1.605	0.819	1.167	0.056
	L3	1.480	0.814	1.082	0.148
	L4	1.662	0.808	1.235	0.140
XGBoost_FPA9-12	L1	1.643	0.777	1.215	0.321
	L2	1.495	0.800	1.097	0.224
	L3	1.695	0.812	1.251	0.086
	L4	1.523	0.808	1.104	0.310
XGBoost_GOA9-12	L1	1.390	0.832	1.005	0.186
	L2	1.392	0.831	1.000	0.162
	L3	1.362	0.834	0.979	0.129
	L4	1.378	0.831	0.989	0.170
XGBoost_GWO9-12	L1	1.408	0.828	1.010	0.178
	L2	1.393	0.830	0.997	0.173
	L3	1.375	0.834	0.990	0.158
	L4	1.374	0.833	0.988	0.159

Figure 4. Scatter plots of R_d predicted by the coupling models based on ground weather station data in Beijing.

Figure 4. Scatter plots of R_d predicted by the coupling models based on ground weather station data in Beijing.

Figure 5. Boxplot of statistical indicators for the prediction of R_d by the coupling model based on ground weather station data.

Figure 5. Boxplot of statistical indicators for the prediction of R_d by the coupling model based on ground weather station data.

3.4. Model Performance Based on Cross-Station Application

When areas lacking basic data for simulating R_d were identified, such areas were replaced by data from adjacent regions that have the required data, which was described as “cross-station application”. In China and many developing countries, where local meteorological data are missing or insufficient, satellite data are often used to establish models for the simulation of R_d. However, in certain remote areas of China, ground meteorological data are often missing and there is a lack of full coverage of satellite remote sensing. In the traditional simulation of R_d values of a station, the ground weather station data of adjacent stations are often used. In the present study, the satellite data of adjacent stations were replaced to explore the universality of satellite remote sensing data in remote areas around the world. An assumption was made that there were four stations (Harbin, Ejinaqi, Beijing, and Wuhan stations) missing several significant data used to simulate R_d. Therefore, the meteorological data of one station were replaced with the Himawari-7 data obtained from the station closest to the four stations, and the four aforementioned coupling models were used to simulate the R_d. The R_d value of the station was simulated based on satellite data of the adjacent station (see Table 8).

As shown in Table 8, different station data adapted to different models. The XGBoost_GWO13 model performed optimally at Harbin and Beijing stations, and the RMSE values were 1.2–13.1% and 0.4–27.4% lower than the other models, respectively. The XGBoost_DE model and the XGBoost_FPA model exhibited resembling simulation level, but were obviously inferior to the XGBoost_GOA model and the XGBoost_GWO model. For Harbin station, the MAE, MBE, and RMSE values of the former were 13.5%, 6.4%, and 8.8% lower than the latter, respectively. The XGBoost_GOA model (average RMSE = 1.752 MJ·m⁻²·d⁻¹) was only slightly better than the XGBoost_GWO model (average RMSE = 1.787 MJ·m⁻²·d⁻¹) at the Wuhan station. Scatter plots were drawn of the R_d simulated using the four coupled models in cross-station application at these four stations (Figure 6). Figure 6 clearly illustrated that the scatter distribution of the model established at each station had a certain linear relationship. The scatter distribution at the Wuhan station was the most uniform, and the model showed the most accurate simulation trend. The dispersion degrees of the scatter plot at the Beijing and Harbin stations were slightly higher than that at the Wuhan station, while the scatter distribution at the Ejinaqi station deviated greatly from the fitting line. Further, the fitting degree of the XGBoost_GWO model was markedly higher than that of the others. In general, each model exhibited ideal results in cross-station applications, especially the XGBoost_GWO model. The simulation performance was the most optimal, and thus, use of the adjacent station data to replace the local station data in the absence of satellite data is feasible.

Different combinations used at different stations in the same model can also lead to differences in model simulation capabilities. Table 8 shows that at Harbin, Beijing, and Wuhan stations, the performance of these models’ input combination of S7 was better than that of the combination of S8. Taking Harbin station as an instance, the average RMSE of the former was 0.2 % lower than that of the latter, while at Ejinaqi station, the average RMSE of the former was 2.8 % higher than that of the latter. The XGBoost_DE model reveled the best simulation performance at Harbin, Ejinaqi, and Wuhan stations for the input combination of S8 (mean RMSE = 1.67 MJ·m⁻²·d⁻¹, R² = 0.64, MAE = 1.33 MJ·m⁻²·d⁻¹, MBE = −0.29 MJ·m⁻²·d⁻¹) compared with S7 (mean RMSE = 1.57 MJ·m⁻²·d⁻¹, R² = 0.68, MAE = 1.26 MJ·m⁻²·d⁻¹, MBE = −0.37 MJ·m⁻²·d⁻¹). At the four stations, the XGBoost_GOA model input combination of S7 was better than the input combination of S8. As such, increasing the input of RH_s reduced the simulation performance of the model, which could be attributed to the large difference in relative humidity caused by the excessive number of influencing factors, thereby reducing the accuracy of the data. Figure 7 shows the boxplots of the statistical indicators of these coupling models using the satellite data to detect the R_d values. In terms of RMSE, the accuracy levels of these models were as follows: XGBoost_GWO > XGBoost_GOA > XGBoost_FPA > XGBoost_DE. In terms of MBE, when the combination of S8 was input into the XGBoost_DE model, the model was significantly underestimated, which indicates that the accuracy of RH_s was insufficient, which made the model less stable.

In summary, the XGBoost_GWO13 model performed optimally in simulating R_d. The model is most suitable for cross-station applications at Harbin and Beijing stations, while the XGBoost_GOA13 model had better simulation performance at Wuhan station. In addition, the relative humidity obtained by the Himawari-7 satellite is not suitable for model simulations. In the present study, only a few groups of stations were adopted as representatives to prove the applicability of cross-station applications for simulating R_d. In the future, a more suitable model should be explored and established, higher-precision satellite remote sensing data should be used, and more groups of stations should be selected for cross-station applications, so as to estimate the level of each model to predict R_d values using satellite remote sensing data at stations in different climate zones.

Table 8. Statistical results of XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for simulating R_d in Mohe, Urumqi, Shengyang, and Zhengzhou stations based on satellite data at Harbin, Ejinaqi, Beijing, and Wuhan stations.

Stations	Models	Combinations/Statistical Indicators	RMSE	R2	MAE	MBE
Harbin	XGBoost_DE13	S7	1.569	0.789	1.211	−0.651
	XGBoost_DE14	S8	1.496	0.790	1.129	−0.526
	XGBoost_FPA13	S7	1.457	0.805	1.055	−0.599
	XGBoost_FPA14	S8	1.516	0.785	1.153	−0.392
	XGBoost_GOA13	S7	1.401	0.810	1.009	−0.520
	XGBoost_GOA14	S8	1.407	0.784	1.016	−0.200
	XGBoost_GWO13	S7	1.363	0.807	0.982	−0.357
	XGBoost_GWO14	S8	1.380	0.794	1.001	−0.246
Ejinaqi	XGBoost_DE13	S7	1.551	0.342	1.278	0.593
	XGBoost_DE14	S8	1.419	0.410	1.196	0.508
	XGBoost_FPA13	S7	1.452	0.393	1.238	0.568
	XGBoost_FPA14	S8	1.427	0.389	1.162	0.446
	XGBoost_GOA13	S7	1.499	0.372	1.298	0.622
	XGBoost_GOA14	S8	1.510	0.342	1.263	0.548
	XGBoost_GWO13	S7	1.452	0.413	1.266	0.593
	XGBoost_GWO14	S8	1.436	0.418	1.185	0.535
Beijing	XGBoost_DE13	S7	1.839	0.763	1.365	0.589
	XGBoost_DE14	S8	1.942	0.837	1.519	−1.144
	XGBoost_FPA13	S7	1.831	0.770	1.376	0.600
	XGBoost_FPA14	S8	1.725	0.784	1.316	0.247
	XGBoost_GOA13	S7	1.424	0.831	1.150	−0.106
	XGBoost_GOA14	S8	1.457	0.825	1.173	−0.226
	XGBoost_GWO13	S7	1.409	0.833	1.153	0.061
	XGBoost_GWO14	S8	1.415	0.834	1.161	−0.068
Wuhan	XGBoost_DE13	S7	1.886	0.799	1.506	−0.800
	XGBoost_DE14	S8	1.804	0.852	1.457	−1.081
	XGBoost_FPA13	S7	1.754	0.831	1.372	−0.844
	XGBoost_FPA14	S8	1.815	0.848	1.447	−1.072
	XGBoost_GOA13	S7	1.709	0.833	1.334	−0.756
	XGBoost_GOA14	S8	1.795	0.849	1.433	−1.050
	XGBoost_GWO13	S7	1.745	0.822	1.369	−0.744
	XGBoost_GWO14	S8	1.829	0.843	1.450	−1.070

Table 8. Statistical results of XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO models for simulating R_d in Mohe, Urumqi, Shengyang, and Zhengzhou stations based on satellite data at Harbin, Ejinaqi, Beijing, and Wuhan stations.

Stations	Models	Combinations/Statistical Indicators	RMSE	R2	MAE	MBE
Harbin	XGBoost_DE13	S7	1.569	0.789	1.211	−0.651
	XGBoost_DE14	S8	1.496	0.790	1.129	−0.526
	XGBoost_FPA13	S7	1.457	0.805	1.055	−0.599
	XGBoost_FPA14	S8	1.516	0.785	1.153	−0.392
	XGBoost_GOA13	S7	1.401	0.810	1.009	−0.520
	XGBoost_GOA14	S8	1.407	0.784	1.016	−0.200
	XGBoost_GWO13	S7	1.363	0.807	0.982	−0.357
	XGBoost_GWO14	S8	1.380	0.794	1.001	−0.246
Ejinaqi	XGBoost_DE13	S7	1.551	0.342	1.278	0.593
	XGBoost_DE14	S8	1.419	0.410	1.196	0.508
	XGBoost_FPA13	S7	1.452	0.393	1.238	0.568
	XGBoost_FPA14	S8	1.427	0.389	1.162	0.446
	XGBoost_GOA13	S7	1.499	0.372	1.298	0.622
	XGBoost_GOA14	S8	1.510	0.342	1.263	0.548
	XGBoost_GWO13	S7	1.452	0.413	1.266	0.593
	XGBoost_GWO14	S8	1.436	0.418	1.185	0.535
Beijing	XGBoost_DE13	S7	1.839	0.763	1.365	0.589
	XGBoost_DE14	S8	1.942	0.837	1.519	−1.144
	XGBoost_FPA13	S7	1.831	0.770	1.376	0.600
	XGBoost_FPA14	S8	1.725	0.784	1.316	0.247
	XGBoost_GOA13	S7	1.424	0.831	1.150	−0.106
	XGBoost_GOA14	S8	1.457	0.825	1.173	−0.226
	XGBoost_GWO13	S7	1.409	0.833	1.153	0.061
	XGBoost_GWO14	S8	1.415	0.834	1.161	−0.068
Wuhan	XGBoost_DE13	S7	1.886	0.799	1.506	−0.800
	XGBoost_DE14	S8	1.804	0.852	1.457	−1.081
	XGBoost_FPA13	S7	1.754	0.831	1.372	−0.844
	XGBoost_FPA14	S8	1.815	0.848	1.447	−1.072
	XGBoost_GOA13	S7	1.709	0.833	1.334	−0.756
	XGBoost_GOA14	S8	1.795	0.849	1.433	−1.050
	XGBoost_GWO13	S7	1.745	0.822	1.369	−0.744
	XGBoost_GWO14	S8	1.829	0.843	1.450	−1.070

Figure 6. Scatter plot of R_d predicted by the coupling models based on Himawari-7 data at other stations in cross-station application.

Figure 6. Scatter plot of R_d predicted by the coupling models based on Himawari-7 data at other stations in cross-station application.

Figure 7. Boxplot of statistical indicators for the prediction of R_d predicted by the coupling models based on Himawari-7 data at other stations in cross-station application.

Figure 7. Boxplot of statistical indicators for the prediction of R_d predicted by the coupling models based on Himawari-7 data at other stations in cross-station application.

4. Discussion

R_d is a significant parameter in the design of various solar devices, and various techniques have been developed due to the inconsistency of the frequencies at which R_d is measured [28,29]. Owing to scarce ground weather stations and uneven distribution of meteorological data in time and space, satellite remote sensing data are often used by researchers to simulate R_d due to the wide coverage and continuous advantages in time and space. As an example, for mapping with data from four ground weather stations in Thailand, Charuchittipan et al. [30] used data from the multi-functional transport satellite (Himawari-6) for 2006–2015 and the Himawari-8 satellite for 2016 to design a semi-empirical model for R_d estimation. The results revealed that the estimated values of the developed semi-empirical model agreed well with the measured values. To improve the empirical model of monthly and daily R_d in northern China, Feng et al. [31] used the aerosol optical depth measured by the MODIS satellite and the solar radiation measured by a ground weather station. The improved model was found to have improved the estimation accuracy of R_d compared with the existing model. Bakirci [32] compared the R_d value obtained from the NASR-SSE database with the R_d value calculated by the model in two cities in Turkey to examine the ability of these models. The statistical results revealed that the optimal model could maintain good prediction accuracy using the R_d value obtained from the NASA-SSE database. To evaluate the European Centre for Medium-Range Weather Prediction fifth-Generation Reanalysis (ERA5) data and JiEA Satellite Retrieval Centre (JiEA) for R_d in East Asia, Jiang et al. [33] used ground weather station measurements from 39 stations of the World Radiation Data Centre (WRDC) and the China Meteorological Administration. The results showed that JiEA was in good agreement with the measurements, while ERA5 significantly underestimated the R_d. Such research has indicated that satellite data had certain accuracy in simulating R_d. In the present study, four heuristic algorithms were proposed for optimizing the machine learning model and simulating R_d based on satellite data, with the aim of evaluating the performance of these models. An observation can be made from Figure 2 that the models based on Himawari-7 data revealed a good fitting trend, which was consistent with the research results.

In the condition of simulating R_d based on satellite data, the input of different meteorological factors had different effects on the model. The input of P_s was found to have a more significant improvement than RH_s when using the XGBoost_FPA model. Zhou et al. [34] revealed that the introduction of precipitation could efficiently improve the underestimation of R_d. In humid areas, the correlation between precipitation and R_d was stronger than that of relative humidity, and similar results were obtained in this study. Yang et al. [35] selected data from 17 stations from 2000 to 2017 to build 18 R_d models and found that models with a combination of relative humidity, air temperature, and two other parameters (clearness index and relative sunshine hours) performed optimally among all models, which is consistent with the discoveries of the present study that using the XGBoost_DE and XGBoost_GWO models with a combination of relative humidity as an input could improve model performance. There were few studies on the simulation of diffuse solar radiation using the same machine learning model and heuristic optimization algorithm as this study, but some researchers used similar techniques to simulate diffuse solar radiation. For example, Fan et al. [15] proposed three new hybrid support vector machines to simulate diffuse solar radiation. The results showed that the coupled models (i.e., SVM-WOA, SVM-PSO, and SVM-BAT) further improved the prediction accuracy compared with the SVM model, which indicated that the use of heuristic algorithms to optimize the machine learning model could significantly improve the prediction results. It confirmed the feasibility of the coupling model method in this study.

Since certain areas are outside the satellite radiation range, the corresponding meteorological data could not be obtained. However, use of the available satellite data of adjacent stations as the training set of the model to simulate local R_d has become a widely used and effective method [36,37,38,39]. In most prior studies, the method of cross-station application was used to estimate ET₀, rather than R_d. For instance, Shiri et al. [40] collected meteorological data from the Basque Country (humid region) and Valencia Country (non-humid region) in Spain to train a neuro-fuzzy model. The results revealed that the GNF model successfully estimated the ET0 value in Iran. In this study, four coupling models were selected to conduct cross-station applications at four similar groups of stations, showing high simulation accuracy. The R_d values at four stations were also successfully estimated, which indicated that the cross-station application method was feasible in many fields including the direction of R_d.

In investigating R_d, most previous researchers used the data of ground weather stations, and there was a lack of significant meteorological factors. Therefore, the selection of satellite products with high accuracy of measurement data and the improvement of satellite data with low accuracy were used to promote the performance of the model, which is of considerable significance in the simulation of R_d. In this study, four coupling models were selected to input different parameter combinations to simulate R_d based on satellite data and meteorological data of 14 stations. At the same time, cross-station applications were conducted on four groups of stations in terms of R_d, in accordance with the experiences of previous researchers. The present study can provide certain reference value for exploring the performance of the four coupling models in the assessment of R_d and the regional applicability of cross-station applications in mainland China. In a follow-up study, better heuristic algorithms and models based on the data of other satellite products should be used to conduct cross-station applications in other countries with different climates to overcome the low accuracy of the meteorological parameters input in this study and the limited number of stations.

5. Conclusions

The performances of four coupled models (XGBoost_DE, XGBoost_FPA, XGBoost_GOA, and XGBoost_GWO) in simulating R_d based on satellite data and ground weather station data were evaluated, as well as the performances in terms of cross-station applications based on satellite data at four stations (Harbin-Mohe, Ejina-Urumqi, Beijing-Shenyang, and Wuhan-Zhengzhou).

The results show that: (1) the model based on Himawari-7 data was markedly promoted compared with the satellite original R_d data; (2) among the models based on satellite and ground weather station data, the XGBoost_GOA model performed optimally, slightly better than the XGBoost_GWO model, and the XGBoost_GWO model had the optimal simulation performance in cross-station application; and (3) in the case of satellite data, the input of P_s and Rd_s could improve the performance of the XGBoost_FPA and XGBoost_GWO models. In the case of ground weather station data, the input of relative humidity was beneficial for improving the performance of the XGBoost_FPA and XGBoost_GWO models, and the input of precipitation was beneficial for improving the performance of XGBoost_GOA model, both of which were not suitable for the input of the XGBoost_DE model.

The present study can contribute a scheme for the global prediction of R_d in the absence of ground weather station and satellite data. In future research, more parameters and different algorithms can be introduced to simulate R_d, and adjacent stations in the same climate zone can be selected for cross-station application to avoid the impact of regional differences on data integrity.