Comparison of Artiﬁcial Intelligence and Physical Models for Forecasting Photosynthetically-Active Radiation

: Different kinds of radiative transfer models, including a relative sunshine-based model (BBM), a physical-based model for tropical environment (PBM), an efﬁcient physical-based model (EPP), a look-up-table-based model (LUT), and six artiﬁcial intelligence models (AI) were introduced for modeling the daily photosynthetically-active radiation (PAR, solar radiation at 400–700 nm), using ground observations at twenty-nine stations, in different climatic zones and terrain features, over mainland China. The climate and terrain effects on the PAR estimates from the different PAR models have been quantitatively analyzed. The results showed that the Genetic model had overwhelmingly higher accuracy than the other models, with the lowest root mean square error (RMSE = 0.5 MJ m − 2 day − 1 ), lowest mean absolute bias error (MAE = 0.326 MJ m − 2 day − 1 ), and highest correlation coefﬁcient (R = 0.972), respectively. The spatial–temporal variations of the annual mean PAR (APAR), in the different climate zones and terrains over mainland China, were further investigated, using the Genetic model; the PAR values in China were generally higher in summer than those in the other seasons. The Qinghai Tibetan Plateau had always been the area with the highest APAR (8.668 MJ m − 2 day − 1 ), and the Sichuan Basin had always been the area with lowest APAR (4.733 MJ m − 2 day − 1 ). The PAR datasets generated by the Genetic model, in this study, could be used in numerous PAR applications, with high accuracy.


Introduction
Solar radiation is the most important energy sources, driving the sources and sinks of energy between the earth surface and atmosphere [1]. Ninety-nine percent of the solar energy concentrated in the wavelength of 0.25 µm-4.0 µm, which can be divided into three broadbands-ultraviolet spectrum (0.25-0.40 µm), visible spectrum (0.40-0.70 µm), and near infrared spectrum (0.70-4 µm). Among them, almost 45% of the solar radiation concentrated in the visible spectrum, namely photosynthetically-active radiation (PAR) [2]. PAR is of vital importance in many biological and physical processes, such as chlorophyll synthesis and plant photosynthesis [3][4][5]. Thus, in a large number of studies accurate observations and estimations of the PAR at the given location, are required [6,7], including concentrating solar power (CPV), meteorology, agriculture, land surface ecosystem, and sustainable development. However, due to the difficulties in calibration, construction, estimating PAR in China. The spatial and temporal variations and related causes of PAR in different climate zones and terrain features, across China, were further analyzed in detail.

Observation Data
Daily PAR measurements at twenty-nine CERN stations, throughout China, were used for the model calibrations and validations. Figure 1 shows the spatial distributions of the CERN and CMA stations used in this study. Table 1 shows the general climatic patterns of these CERN stations, Figure 2 also presents the annual mean air temperature, relative humidity, air pressure at sea-level and the sunshine duration (the hours when solar irradiance is greater than 120 Wm −2 ) in China. It was clear that these CERN and CMA stations spread across most areas of China, with complicated geomorphology and distinctive climatic features. a is altitude, pre-precipitation, ps-surface pressure, rh-relative humidity, sh-sunshine duration, at-air temperature, ws-wind speed, vis-visibility, trise-sunrise time, tset-sunset time.

Observation Data
Daily PAR measurements at twenty-nine CERN stations, throughout China, were used for the model calibrations and validations. Figure 1 shows the spatial distributions of the CERN and CMA stations used in this study. Table 1 shows the general climatic patterns of these CERN stations, Figure  2 also presents the annual mean air temperature, relative humidity, air pressure at sea-level and the sunshine duration (the hours when solar irradiance is greater than 120 Wm −2 ) in China. It was clear that these CERN and CMA stations spread across most areas of China, with complicated geomorphology and distinctive climatic features. a is altitude, pre-precipitation, ps-surface pressure, rh-relative humidity, sh-sunshine duration, at-air temperature, ws-wind speed, vis-visibility, trise-sunrise time, tset-sunset time.

Satellite Products
The MODIS atmosphere and land products and the MTSAT data were used to derive the input parameters for the PAR models in this study. Atmospheric parameters, including liquid water and ice cloud optical depth (CPO), total column ozone amount (Ioz), total column precipitable water (w), liquid water path and ice water path (CWP), effective particle radius for liquid water clouds and ice water clouds (re), cloud fraction (TCP), solar zenith angle ( ), aerosol optical depth (aod) and surface pressure (PS) were derived from the MOD04/MYD04, MOD06/MYD06, and MOD07/MYD07. The ground albedo (α) was derived from the MOD09CMG and MYD09CMG. The top of atmosphere albedo (pg) was derived from the MTSAT data. Detailed information for MODIS and MTSAT products are presented in Table 2.

Satellite Products
The MODIS atmosphere and land products and the MTSAT data were used to derive the input parameters for the PAR models in this study. Atmospheric parameters, including liquid water and ice cloud optical depth (CPO), total column ozone amount (Ioz), total column precipitable water (w), liquid water path and ice water path (CWP), effective particle radius for liquid water clouds and ice water clouds (re), cloud fraction (TCP), solar zenith angle (θ), aerosol optical depth (aod) and surface pressure (PS) were derived from the MOD04/MYD04, MOD06/MYD06, and MOD07/MYD07. The ground albedo (α) was derived from the MOD09CMG and MYD09CMG. The top of atmosphere albedo (p g ) was derived from the MTSAT data. Detailed information for MODIS and MTSAT products are presented in Table 2. The BBM model is a physical-based broadband model, which was developed by Qin et al. [35], based on the clear-sky spectral transmittance parameterization. Considering the major radiative extinction processes between the surface and the atmosphere, the BBM model has been proved to be an efficient PAR model, with a high accuracy, at seven Surface Radiation Budget Network (SURFRAD) stations and seven hundred and sixteen CMA stations, which is expressed as following equations: where R all is the daily PAR under all-sky conditions, and R clr means the daily PAR under clear sky conditions. R clr b and R clr d are the beam and diffuse PAR under clear sky conditions, respectively. τ c means the transmittances due to cloud scattering and absorption; r represents the relative sunshine duration. R clr b and R clr d can be calculated using following equations: where θ is the solar zenith angle (degree); d 0 /d is the eccentricity correction factor for the mean sun-earth distance; R 0 is the spectral irradiance (400-700 nm) at the mean distance between the earth and the sun in PAR band. τ b is the beam transmittance in clear sky conditions; τ d is the diffuse transmittance in clear sky conditions. τ b and τ d can be calculated as follows: where τ g , τ R , τ w , τ o , and τ a are the transmittances for the mixed gasses absorption, Rayleigh scattering, water vapor absorption, ozone absorption, and the aerosol extinction, respectively. Where τ g , τ R , τ w , τ o , and τ a represent the transmittances for mixed gasses, Rayleigh transmittance, water vapor, ozone, and aerosol, respectively, which can be calculated from: where m represents the relative air mass; m means the pressure-corrected relative air mass; w is the precipitable water vapor (cm); l is the ozone thickness (cm); and β is the Ångström turbidity coefficient.

PBM
This PBM model is a physical-based PAR model taking into consideration the physical relations between PAR and the earth-atmospheric albedo with absorption and scattering atmospheric constituents [22]. The instantaneous PAR at the Earth's surface in PBM, was obtained from: where ρ B is the earth-atmospheric albedo in the PAR band; ρ g is the surface albedo; τ o means the ozone transmittance; α w , α aer , and α g denote the absorption coefficients of water vapor, aerosols, and mixed gasses, respectively; I TOA is the extraterrestrial solar irradiation at the top of atmosphere in the PAR band, which could be calculated using following equation: where R c is the solar constant in the PAR band; d n means the day number since the first day of the year; θ z is the solar zenith angle. The ozone transmittance τ o , absorption of water vapor (α w ), and mixed gasses (α g ) were calculated, using where I oλ is the extraterrestrial solar irradiance; τ oλ , τ wλ , and τ gλ are the spectral transmission coefficient for ozone, water vapor, and mixed gasses, respectively.
where k oλ , k wλ and k gλ denotes the spectral extinction coefficient for ozone, water vapor, and mixed gasses, respectively; m a represents the air mass; m r represents the relative air mass; l means the total ozone amount (cm); and w is the precipitable water vapor (cm).
where rh is the relative humidity; p s means the surface pressure (mbar); and T means the air temperature (K). The absorption and scattering (Daer) of aerosol was calculated using Equation (23). α aer was partitioned from Daer, the detailed descriptions for the estimation of α aer could be found in Reference [40,41].
where τ aerλ is aerosol transmission coefficient, calculated as β is the Ångström turbidity coefficient and α denotes the wavelength exponent. β was calculated as follows: where VIS is the visibility (km). It must be noted that Equation (25) was not correct in some situations, for example, when VIS was 15,16,17,18,19,20, and 21 km, β was −0.0035, −0.0126, −0.0179, −0.0194, −0.0171, −0.011 and −0.0011, respectively. Thus, we introduced the formula below for the β estimation [42], which was expressed as follows where θ is the latitude and z means the surface elevation.

EPP
This physical-based parameterization (EPP) was proposed by Tang et al. [8], based on the BBM and the cloud parameterization developed by Sun et al. [40]. PAR could be calculated using the following equation: where C w and C i are the cloud fractions for water cloud and ice cloud, respectively. R clr , R wc , and R ic represent PAR in clear sky conditions, water cloudy sky conditions, and ice cloudy sky conditions, respectively; ρ g is the surface albedo; ρ a,all denotes the atmospheric spherical albedo, which was calculated as follows where ρ a,clr , ρ a,wc , and ρ a,ic are the atmospheric spherical albedo for clear sky conditions, water cloudy sky conditions, and ice cloudy sky conditions, respectively. R clr , R wc , and R ic could be calculated using following equations: where τ b and τ d are beam and diffuse transmittance, respectively; τ wc and τ ic denote the global transmittance for water cloud and ice cloud, respectively.

LUT
The LUT method introduced in this study was developed by Zhang et al. [24]. First, the input parameters derived from the MODIS products were preprocessed (geometric correction, reprojection, and calibration). Second, the first look-up table was generated to connect atmospheric condition (visibility, cloud optical depth, water vapor amount, ozone amount, aerosol type, and cloud type, etc.) Remote Sens. 2018, 10, 1855 9 of 27 to the top of the atmosphere radiance (I TOA ). Then, the second look-up table was generated to connect the atmospheric condition to PAR. At last, the surface PAR was calculated using the look-up Tables 1 and 2. In this study, GLASS (Global land surface satellite) PAR datasets generated by Zhang et al. [24] were used for the PAR validation, across China (http://glass-product.bnu.edu.cn).

The AI models BP
The BP model is the most widely used AI models for estimating a solar radiation, with a strong learning ability and high accuracy [27]. The basic schematic architecture of the BP neural network was illustrated in Figure 3a. The BP model was formed by the input layer, the hidden layer, and the output layer. Each layer consisted of some neurons connected to each other. The basic idea of BP is to find a function that best maps a set of input parameters to the correct output values, using a gradient descent optimization algorithm, which minimizes the mean square error between the network's actual output and the expected output values. In this study, six parameters (rh, at, ps, sd, a, d n ) that were closely correlated with the PAR values were set as input parameters for the BP model; daily PAR measurements were set as the model output parameter. The PAR values could be calculated using following equation: where F g is the estimated PAR; Z(.) means the hidden transfer function; w i (t) means the weight; x i (t) means the input parameters indiscrete time space; and b means the neuronal bias.
Remote Sens. 2018, 10, x FOR PEER REVIEW 9 of 28 The BP model is the most widely used AI models for estimating a solar radiation, with a strong learning ability and high accuracy [27]. The basic schematic architecture of the BP neural network was illustrated in Figure3a. The BP model was formed by the input layer, the hidden layer, and the output layer. Each layer consisted of some neurons connected to each other. The basic idea of BP is to find a function that best maps a set of input parameters to the correct output values, using a gradient descent optimization algorithm, which minimizes the mean square error between the network's actual output and the expected output values. In this study, six parameters (rh, at, ps, sd, a, ) that were closely correlated with the PAR values were set as input parameters for the BP model; daily PAR measurements were set as the model output parameter. The PAR values could be calculated using following equation: where Fg is the estimated PAR; Z(. ) means the hidden transfer function; wi(t) means the weight; xi(t) means the input parameters indiscrete time space; and b means the neuronal bias.

ANFIS
The ANFIS is a hybrid intelligence system integrating the self-learning ability of the ANN and the reasoning ability of fuzzy logic [41]. The general structure of the ANFIS model is shown in Figure3b. The ANFIS model establishes the appropriate membership function of the input and the

ANFIS
The ANFIS is a hybrid intelligence system integrating the self-learning ability of the ANN and the reasoning ability of fuzzy logic [41]. The general structure of the ANFIS model is shown in Figure 3b. The ANFIS model establishes the appropriate membership function of the input and the output variables, by a set of fuzzy If-Then rules and forms output functions [42]. The rh, at, ps, sd, a, and d n were the input parameters for the ANFIS, the measured PAR value was the output value for ANFIS. There were five layers for ANFIS, including fuzzification, rules, normalization, defuzzification, and summation in this study.

LSSVM
LSSVM is a powerful AI model for solving nonlinear regression evolved from the Support Vector Machine (SVM) [43]. The procedure of LSSVM in this study is shown in Figure 3c. Given a set of inputs a i (meteorological parameters) and output y i (PAR values), the LSSVM could reveal the nonlinear relationship between the input and the output values. The nonlinear function of LSSVM could be briefly expressed as: where ω, δ, and bt are the m-dimensional weight vector, mapping function, and bias term, respectively. In this study, daily rh, at, ps, sd, a, d n and PAR records at twenty-nine CERN stations were used for training and testing the LSSVM model. More detailed information about the LSSVM model could be found in Kisi [44].

Genetic
The Genetic algorithm is a heuristic algorithm inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms [45]. The Genetic algorithm is commonly used to generate high-quality solutions to optimization and search problems. The Genetic model was used to improve the model accuracy for predicting the PAR values. The Genetic models for estimating PAR were conducted as the following setups ( Figure 3d): (1) Initialize the random population: The basic structure of the BP neural network in this study was 6-10-1 (Figure 3a) with six input layers, ten hidden layers, and one output layer. Thus, the number of weights was 6 × 10 + 10 × 1 = 70; the number of thresholds was 10 + 1 = 11. So, the encoding length was 70 + 11 = 81. (2) Selection operation: The new individuals with the high-fitness values would be selected from old individuals using a roulette selection method. The selection probability for individuals were calculated as the following equation: where P i is the selection probability; g i is the fitness value, which could be calculated as: where N is the number of input layers of Genetic; y i is the i-th expected output value; o i is the i-th predicted output values.
(3) Crossover operation: The crossover operation was conducted using the arithmetic crossover algorithm: where a cj and a dj are the c-th and d-th chromosome at j position, respectively; c2 is a constant with the range of 0-1. (4) Mutation operation: The mutation operation was conducted using following equations: where a max and a min are the maximum and minimum values for a i,j , respectively; r is a random number [0,1]; rr is the random number; g is the number of iterations; and G max is maximum evolution times.

M5Tree
The M5Tree was first developed by Quinlan [46], based on a binary decision tree. The M5Tree could be used to reconstruct the quantitative relationship between the input and the output values. The M5Tree contains three steps [47,48]: (1) Splitting data into subsets to create decision trees; (2) generating the model tree; (3) building the linear regression model. In this study, the rh, at, ps, sd, a, d n , and the PAR measurements were used for training and testing M5Tree model for predicting the PAR values.

MARS
MARS is a non-parametric regression technique, which could be used to predict the values of a continuous dependent or outcome variable from a set of independent or predictor variables, without any assumption about the underlying functional relationship between the dependent and the independent variables [49,50]. The MARS model for estimating PAR is given as: where Y is the estimated PAR values as a function of the input parameters (rh, at, ps, sd, a, d n ); β m is the weight; h m (X) is the basis functions; X is the input parameters. Further details of MARS can be found in Sharda et al. [51].

Preprocesses for PAR Measurements
The equipment and operation-related errors would degrade the accuracy of the PAR measurements. In this study, the quality control process for the PAR measurements at the CERN stations was conducted following two principles: (1) The ratio between PAR (mol m −2 s −1 ) and SSR (MJ m −2 day −1 ) must be in the range of 1.3-2.8 mol MJ −1 ; (2) each measured PAR should not exceed the PAR at the top of the atmosphere (G 0 ), at the same geographical location. Moreover, the instantaneous PAR is typically expressed as the photon flux density (mol m −2 s −1 ) [3,27]. Dye [52] considered that the ratio of energy flux density to the photosynthetic photon flux density was 1/4.57 (MJ mol −1 ). Therefore, in our study, the unit of PAR measurement was unified to the energy flux density by multiplying 1/4.57.

The Statistical Indicators Representing Model Accuracy
In this study, a total of 70% of the database, during the whole study period, were used to train these PAR models, and the remaining datasets were used for testing these models. The model accuracies were validated using the following statistical indicators: The mean absolute bias error (MAE), the mean bias error (MBE), the root mean square error (RMSE), and the correlation coefficient (R): where N is the sample number; P est and P obs represent the estimated and observed PAR, respectively; P est and P obs represent mean values of the estimated and the observed PAR, respectively.

Validation of Daily PAR Estimations at CERN Stations
The model accuracies of these ten PAR models were evaluated at twenty-nine CERN stations over mainland China. More than twenty-five thousand six hundred and sixty-six data samples were used for the training phases of six AI models. Figure 4 shows the model performance of these AI models, in the training phases. All the estimated PAR showed good agreements with the PAR measurements. Among these AI models, the Genetic model performed superior to the other AI models. Then, another eleven thousand data samples were used to validate the model performance of all ten PAR models that were used in this study. Figure  Taylor diagrams were introduced to visualize the model accuracies. Figure 6 shows the Taylor diagrams used to visualize the model accuracies for all PAR models in each month of the year, respectively. It was clear that the model accuracies for all models were subject to seasonal climatic characteristics. The physical models (BBM, EPP, PBM and LUT) showed better performances in winter than those in summer, due to the abundant water vapor and large cloud cover in summer. The smallest RMSE for all physical-based models were in January, the smallest MAE were also in January; the largest RMSE for all physical-based models were also in June, the largest MAE were in June. In contrast, the estimated PAR by the AI models (BP, ANFIS, M5Tree, MARS, Genetic and LSSVM) showed better agreements with the PAR measurements in each month, due to their strong adaptability to the fluctuation of input parameters. The model performances for the Genetic model, throughout the year, were more stable than the other models, the largest RMSE (0.679 MJ m −2 day −1 ) and MAE (0.460 MJ m −2 day −1 ) for the Genetic were found in April; the smallest RMSE (0.239 MJ m −2 day −1 ) and MAE (0.153 MJ m −2 day −1 ) were found in July. PBM was not as accurate as other PAR models for estimating PAR values throughout a year, with distinct seasonal variations, and had high RMSE and MAE values, in each month. models. Then, another eleven thousand data samples were used to validate the model performance of all ten PAR models that were used in this study. Figure 5 illustrates the statistical indicators representing model accuracies of all PAR models. All methods produced PAR estimates that positively correlated with the measurements at the CERN stations. The R values for the BBM, EPP, PBM, LUT, BP, ANFIS, M5Tree, Genetic, MARS, and LSSVM were 0.947, 0.872, 0.900, 0.787, 0.955, 0.970, 0.967, 0.987, 0.955, and 0.961, respectively. All AI models (BP, ANFIS, M5Tree, Genetic, MARS, and LSSVM) showed overwhelming superiority than the BBM, EPP, PBM, LUT, owing to their strong learning. The     Taylor diagrams were introduced to visualize the model accuracies. Figure 6 shows the Taylor diagrams used to visualize the model accuracies for all PAR models in each month of the year, respectively. It was clear that the model accuracies for all models were subject to seasonal climatic characteristics. The physical models (BBM, EPP, PBM and LUT) showed better performances in winter than those in summer, due to the abundant water vapor and large cloud cover in summer. The smallest RMSE for all physical-based models were in January, the smallest MAE were also in January; the largest RMSE for all physical-based models were also in June, the largest MAE were in June. In contrast, the estimated PAR by the AI models (BP, ANFIS, M5Tree, MARS, Genetic and LSSVM) showed better agreements with the PAR measurements in each month, due to their strong adaptability to the fluctuation of input parameters. The model performances for the Genetic model, throughout the year, were more stable than the other models, the largest RMSE (0.679 MJ m −2 day −1 ) and MAE (0.460 MJ m −2 day −1 ) for the Genetic were found in April; the smallest RMSE (0.239 MJ m −2 day −1 ) and MAE (0.153 MJ m −2 day −1 ) were found in July. PBM was not as accurate as other PAR models for estimating PAR values throughout a year, with distinct seasonal variations, and had high       In all, the AI models were more accurate and stable than the BBM, EPP, PBM and LUT. BBM, EPP, PBM and LUT were more susceptible to weather conditions than the AI models, which may be attributed to the uncertainties of satellite signals caused by cloud cover and precipitable water vapor. Compared with the AI models, larger spatial and temporal variations of statistical indicators were observed for the BBM, EPP, PBM and LUT. The Genetic showed better accuracies and robustness than the other PAR models, at all selected CERN stations, without significant seasonal variations, due to its strong learning ability and optimized weight and thresholds, for the neural network.

Validation of PAR Models in Various Climate Zones and Terrains
Many radiation extinction processes occur when solar radiation passes through the atmosphere and is eventually reflected back to space. These extinction processes would vary with time and locations. Temperature was directly proportional to surface solar radiation, without radiation-damping processes in the atmosphere. Table 3 showed the statistical errors for all PAR models in different temperate zones over China, the largest errors were found in temperature zone in the plateau (HII), due to the strong heating atmosphere. The mean RMSE and MAE for all models in the HII were 1.25 and 0.994 MJ m −2 day −1 , respectively. It was clear that the Genetic performed superior to other PAR models, in different temperate zones, the largest RMSE (0.540 MJ m −2 day −1 ) and MAE (0.368 MJ m −2 day −1 ) for the Genetic were observed in the HII, while the smallest RMSE (0.324 MJ m −2 day −1 ) and MAE (0.215 MJ m −2 day −1 ) were in VII. PBM was not as accurate as the other models, in most temperate zones. The underlying surface properties would have significant effects on the accuracy of the PAR estimations. In this study, seven types of underlying surfaces, including grassland, city, lake, desert, farmland, forest, and water were considered to reveal the effects of the underlying surfaces on the model accuracies. Table 4 shows the RMSE and MAE, in different underlying surfaces, for all PAR models. Wetland was a land area that permanently or seasonally saturated with water, thus, the radiation processes in wetlands were more complicated than the other ecosystems, which made it more difficult to estimate PAR [43]. The mean RMSE and MAE in wetlands were 1.306 and 1.043 MJ m −2 day −1 , respectively. The surfaces in the city had considerable influences on PAR balances, thus, modeling PAR in the city was also complicated. The mean RMSE and MAE in the city areas were 1.229 and 0.996 MJ m −2 day −1 , respectively. It was obvious that the Genetic model showed much higher accuracy than the other models in all underlying surfaces, the RMSE for the Genetic in wetland, desert, lake, forest, farmland, city, and grassland were 0.

Spatial and Temporal Variations of PAR in China
The annual and monthly mean PAR, during 1955-2015, were calculated to reveal the spatial and temporal variations of PAR across China, based on the Genetic model, using meteorological measurements at eight hundred and thirty-nine CMA stations. Figure 10 illustrates the mean PAR values during 1955-2015, the annual PAR values presents a clear decreasing trend at the rate of −0.003 MJ m −2 day −1 /year during 1955-2015. Figure 11 shows the spatial distributions of the annual mean estimated PAR (APAR) over mainland China. Generally, the PAR was higher in Western China than that in the Southern and Northeastern China, the Tibetan Plateau has always been an area with the highest PAR, over mainland China, due to the small atmospheric extinction effects, the maximum APAR was about 8.668 MJ m −2 day −1 in the Tibetan Plateau. In contrast, the Sichuan Basin in Southern China had always been an area with the lowest PAR, due to the perennial cloudy weather and strong atmospheric extinctions [34], the annual mean PAR was about 4.733 MJ m −2 day −1 in the Sichuan Basin. The Northeastern China was also an area with low PAR, owing to the relatively short sunshine durations and humid weather there. Figure 12 illustrates the monthly variation of PAR over mainland China, PAR values were generally higher in the summer than that in other seasons, because of higher solar zenith angle and longer sunshine duration, in the summer than that in other seasons. solar zenith angle and longer sunshine duration, in the summer than that in other seasons. The monthly mean PAR values from January to December were 3.676, 4.697, 6.112, 7.610, 8.570, 8.754, 8.795, 8.281, 6.965, 5.523, 4.202, and 3.468 MJ m −2 day −1 , respectively. The Qinghai Tibetan plateau has always been an area with the highest monthly mean PAR values throughout the year. The largest monthly mean PAR values for the Qinghai Tibetan plateau from January to December were 6.718, 7.975, 9.482, 10.893, 11.917, 12.550, 11.580, 10.727, 9.877, 8.762, 7.261, and 6.373 MJ m −2 day −1 , respectively. In contrast, the Sichuan Basin has always been an area with the lowest monthly mean PAR values. The largest monthly mean PAR values in the Sichuan Basin from January to December were 1.359, 2.619, 3.616, 4.645, 5.495, 5.943, 5.516, 6.368, 4.058, 3.129, 1.656, and 0.991 MJ m −2 day −1 , respectively.

Conclusions
The aim of this research was to make a comparative study on the model accuracies of ten models for estimating PAR over mainland China. The performances of the Genetic model, together with other nine PAR models, were evaluated in different climate zones and terrain features, using long-

Conclusions
The aim of this research was to make a comparative study on the model accuracies of ten models for estimating PAR over mainland China. The performances of the Genetic model, together with other nine PAR models, were evaluated in different climate zones and terrain features, using long-term continuous meteorological and radiation measurements at twenty-nine CERN stations and satellite signals. The spatial and temporal variations of PAR values, during 1955-2015, over mainland China, were further investigated.
Generally, the AI models showed better performances than the BBM, EPP, PBM and LUT. Among all PAR models, the Genetic performed superior to the other PAR models at all CERN stations in terms of RMSE, MAE and R. The model performances for Genetic were more stable than the other PAR models, throughout the year, without large monthly variations. The largest RMSE (0.679 MJ m −2 day −1 ) and MAE (0.460 MJ m −2 day −1 ) for the Genetic were found in April; the smallest RMSE (0.0.239 MJ m −2 day −1 ) and MAE (0.153 MJ m −2 day −1 ) were found in July.
Meanwhile, the climate and terrain effects on the PAR estimation for all PAR models were investigated. PAR models showed different performances in different ecosystems, the largest mean RMSE (1.306 MJ m −2 day −1 ) and MAE (1.043 MJ m −2 day −1 ) for all PAR models were found in wetlands, due to the complicated radiation processes. The model deviations were also larger in city ecosystems with RMSE and MAE of 1.229 and 0.996 MJ m −2 day −1 , respectively. In all, the Genetic model performed better than the other PAR models, with strong robustness in different climate zones and terrain features.