Solar radiation prediction using different techniques: model evaluation and comparison

Renewable and Sustainable Energy Reviews 61 (2016) 384–397

Contents lists available at ScienceDirect

Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Solar radiation prediction using different techniques: model evaluation and comparison Lunche Wang a,n, Ozgur Kisi b, Mohammad Zounemat-Kermani c, Germán Ariel Salazar d, Zhongmin Zhu e,f, Wei Gong f,g a

Laboratory of Critical Zone Evolution, School of Earth Sciences, China University of Geosciences, Wuhan 430074, China Canik Basari University, Faculty of Architecture and Engineering, Civil Engineering Department, Samsun, Turkey c Department of Water Engineering, Shahid Bahonar University of Kerman, Kerman, Iran d Department of Physics, School of Exact Sciences, National University of Salta, Bolivia Avenue #5150, 4408 FVY Salta Capital, Argentina e Huazhong University of Science and Technology Wuchang Branch, Wuhan 430064, China f State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, Hubei Province 430079, China g Collaborative Innovation Center for Geospatial Technology, Wuhan 430079,China b

art ic l e i nf o

a b s t r a c t

Article history: Received 27 December 2015 Received in revised form 12 March 2016 Accepted 7 April 2016 Available online 22 April 2016

Daily observations of meteorological parameters, air temperature, air pressure, relative humidity, water vapor pressure and sunshine duration hours observed at 12 stations in different climatic zones during 1961–2014 are reported for testing, validating and comparing different solar radiation models. Three types of Artificial Neural Network (ANN)methods, Multilayer Perceptron (MLP), Generalized Regression Neural Network (GRNN) and Radial Basis Neural Network (RBNN) are applied in this study for predicting the daily global solar radiation (Hg) using above meteorological variables as model inputs. The BristowCampbell model has also been improved by considering the factors influencing the incoming solar radiation, such as relative humidity, cloud cover, etc. The results indicate that there are large differences in model accuracies for each model at different stations, the ANN models can estimate daily Hg with satisfactory accuracy at most stations in different climate zones, and MLP and RBNN models provide better accuracy than the GRNN and IBC models, for example, the MAE and RMSE values range 1.53–2.29 and 1.94-3.27 MJ m
2 day
1, respectively for MLP model. The model performances also show some differences at different stations for each model, for example, the RMSE values from MLP model are 1.94 and 3.27 MJ m
2 day
1at NN and HZ stations, respectively. Meanwhile, ANN models underestimate few high radiation values at some stations, which may due to the differences in training and testing data ranges and distributions of the stations. Finally, the differences in model performances from different solar radiation models have been further analyzed. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Solar radiation Generalized regression neural network Multilayer perceptron Radial basis neural network Improved Bristow-Campbell model Model evaluation

Contents 1. 2.

3.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 2.1. Sites and data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 2.2. Solar radiation prediction models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 2.2.1. Multilayer perceptron neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 2.2.2. Radial basis neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 2.2.3. Generalized regression neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 2.2.4. Improved Bristow–Campbell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Model applications and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 3.1. Comparisons of measures of fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 3.2. Model performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

Corresponding author. Tel.: þ 86 13349889828. E-mail addresses: [email protected], [email protected] (L. Wang).

http://dx.doi.org/10.1016/j.rser.2016.04.024 1364-0321/& 2016 Elsevier Ltd. All rights reserved.

L. Wang et al. / Renewable and Sustainable Energy Reviews 61 (2016) 384–397

4. Discussion . . . 5. Conclusion . . . Acknowledgments . References . . . . . . .

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1. Introduction Solar radiation reaching the Earth's surface plays an important role in the energy balances of numerous physical, chemical, and biological processes [1–3]. The changes in the amount of solar radiation greatly influences the fluxes of sensible and latent heat, the hydrological cycle, terrestrial ecological ecosystems and the climate [4,5]. Meanwhile, the solar energy has a much lower environmental pollution than the conventional sources like fossil fuels [6], and it is the most abundant of all renewable and sustainable energy resources at places around the world, which can be harnessed for commercial uses through large solar array farms to meet the global energy challenges [7,8]. Thus, accurate determination and clear understanding of the spatial-temporal variability of solar radiation is of great importance to meteorological and hydrological processes, photosynthesis, ecological functions, agricultural and industrial production, energy development and utilization [9,10]. Though Meteonorm version 6.0 is a global climatological database designed for planners of active solar systems like PV plants or solar thermal systems, which contains monthly mean values of Hg of several databases [11,12], the radiation data has not been routinely observed at most meteorological stations around the world due to the high instrument cost and technical requirements [13], for example, the ratio between stations observing solar radiation and those observing Ta is lower than 1:100 in America [14]. Therefore, developing and applying proper methods to estimate solar radiation has been the focus of numerous studies in locations without direct radiation measurements in recent years [15,16]. One of the most widely used methods is to establish the relationships between solar radiation and other measured meteorological parameters such as Ta, h and water vapor contents [17,18], for example, Yacef et al. [19] estimated the daily Hg from Ta in Algeria; Li et al. [20] calculated the Hg in Tibet, China from h. Among the temperature-based models, the BC model can relate diurnal air temperature range (TM
Tm) to incoming solar radiation, which has been widely used for modeling solar energy [21], for example, Almorox et al. [22] estimated the daily Hg from measured Ta at Cañada de Luque, Córdoba, Argentina. Due to the effects of geographical, meteorological and terrestrial factors (albedo, aerosol, cloudiness, etc.), the amount of solar radiation reaching the surface are greatly affected, above empirical models should be recalibrated [23], for example, the Ångström-Prescott model has been modified to the quadratic, cubic, exponential and logarithmic forms in many places of the world [24]. The physical radiation models take into considerations of radiative transferring process (aerosol absorption and scattering), which is proved as an effective method for predicting solar radiation around the world, for example, Pyrina et al. [25] investigated the cloud effects on the shortwave, longwave and all-wave radiation budget of the Mediterranean basin. Gueymard et al. [26] developed an atmospheric transmittance model for calculating the clear-sky beam, diffuse and global photosynthetically active radiation. Yang et al. [27] estimated the hourly, daily and monthly solar radiation by importing global data sets using a hybrid model, which was also validated as one of the best broadband radiation models [28]. Hybrid models that coupled both the physical and empirical aspects have also been developed over the years as

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393 396 396 396

elaborated in Schmetz [29], Noia et al. [30], Pinker et al. [31] and Perez et al. [32]. Rigollier et al. [33] demonstrated a clear-sky model, which was developed in the framework of the new digital European Solar Radiation Atlas and compared with the Heliosat method. The above model was validated as one of the most accurate with respect to robustness and accuracy because it considered the Linke turbidity factor and the elevation of the sites. Kambezidis et al. [34] reported the recent improvements of the meteorological radiation model in predicting solar radiation under all-sky conditions at Athens, Greece, which indicated that the inclusion of the aerosol properties in the radiation model can significantly improve the estimations. Shamim et al. [35] presented an improved technique (Mesoscale meteorological model) that utilizes information from a numerical weather prediction model for determining the cloud cover index and solar radiation at Brue catchment situated in the southwest of England. The results clearly showed an improvement in the estimated Hg in comparison to the prevailing approach. Meanwhile, artificial intelligence is a particularly promising approach for modeling solar radiation variation in recent years [36,37], a number of ANN methods have been optimized for estimating solar radiation in different regions of the world [38,39]. Olatomiwa et al. [40] developed an adaptive neuro-fuzzy approach for predicting solar radiation in Nigeria using TM, Tm and h. Park et al. [8] tried to estimate the spatial distribution of solar radiation using topographic factor and h in South Korea. Aguiaret al. [41] proposed the Markov transitions matrix approach for estimating daily radiation values using only the clearness index as input. Aguiar and Collares-Pereira [42] also developed a time-dependent, autoregressive, Gaussian model for generating synthetic hourly radiation, which has been widely used and modified in predicting solar radiation [43]. Amrouche and Pivert [44] predicted daily G with satisfactory accuracy at two sites in France using combined spatial modeling and ANN techniques. Olatomiwa et al. [45] developed an efficient support vector machines firefly algorithm, ANN and Genetic Programming models for estimating solar radiation at the Iranian city. Linares-Rodríguez et al. [46] applied ANN for predicting solar radiation in Spain based on latitude, longitude, day of the year and general climatic parameters, and the results showed that RMSE values were in the range of 13.52–14.2%. Emad et al. [47] predicted the monthly average Hg using ANN model in Qena, Upper Egypt, the RMSE and R2 values were 115 Wh/m2 and 0.977, respectively. Shamshirband et al. [48] proposed a hybrid support vector machine-firefly optimization method for estimating monthly mean Hg in Iran, the results revealed that this method was greatly capable to give favorable predictions with much higher precision than other examined methods. Rizwan et al. [49] used fuzzy logic technique to estimate monthly mean Hg in four Indian stations using different input data. They reported that the developed model was accurate since the amounts of obtained errors are limited. Bhardwaj et al. [50] introduced a hybrid approach which includes hidden Markov models and generalized fuzzy models to prediction solar irradiation in India. The results indicated that the predicted values obtained using the proposed model are in favorable agreements with the measured data. Aguiar et al. [51] employed a library of Markov transition matrices, each corresponding to a specific interval in clearness indices, and explained how they were used

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Nomenclature ANN MLP GRNN RBNN BC IBC ANFIS Ta PA TM G0

Artificial Neural Network Multilayer Perceptron Generalized Regression Neural Network Radial Basis Neural Network Bristow-Campbell model Improved Bristow-Campbell model Adaptive network-fuzzy inference system Air temperature Air pressure Maximum air temperature extraterrestrial radiation

for generating radiation sequences. Mohanty et al. [52] reviewed and compared different models and techniques used for prediction of solar radiation using general climatic parameters. Mohammadi et al. [53] investigated the potential of ANFIS for predicting daily Hg by day of the year. Yadav and Chandel [54] reviewed different ANN techniques to identify suitable methods for forecasting solar radiation in literature. The results indicated that the prediction accuracy was dependent on input parameter combinations, training algorithm and architecture configurations. Moreover, satellite imagines are also widely used for studying the spatial-temporal variations of solar radiation around the world [55], for example, Hay [56] introduced the modeling approaches for satellite based estimates of solar irradiance at the Earth's surface. Cano et al. [57] proposed a method for determining Hg from meteorological satellite data. Cros et al. [58] simulated the Meteosat-7 broadband radiances using two visible channels of Meteosat-8. Polo et al. [59] estimated the solar radiation over India using Meteosat satellite images. Antonanzas-Torres et al. [60] conducted the comparative assessment of Hg from a satellite estimate model and on-ground measurements in Spain. Zhang et al. [61] also developed an integrated algorithm to estimate shortwave solar radiation on clear-sky days in rugged terrain using aerosol optical depth and precipitable water vapor from MODIS atmospheric products. Quesada-Ruiz et al. [62] developed an optimized ANN ensemble model to derive hourly Hg estimates from Meteosat Second Generation imagery, the results obtained with the proposed model reduced the RMSE value of the Heliosat2 model a 22% for all-sky conditions and a 42% for overcast conditions. Some researchers compared and analyzed the model performances for modeling solar radiation using different techniques, for example, Kumar et al. [63] compared the regression and ANN models for estimation of Hg; Rahimikhoob et al. [64] compared the statistical and ANN's methodologies for deriving Hg from NOAA satellite images; Polo et al. [65] analyzed the sensitivity of satellite-based methods for deriving solar radiation to different choice of aerosol input and models. Ahmad and Tiwari [66] reviewed different solar radiation models and it was found that the Collares-Pereira and Rabl model as modified by Gueymard provided the best accuracy for estimating mean hourly Hg under clear sky conditions for Indian regions, and the Ertekin and Yaldiz model yielded the best accuracy against measured data of Konya, Turkey. Citakoglu [67] also compared the accuracies of the ANFIS, ANN, and MLR models, and of Ångström, Abdalla, Bahel and Hargreaves-Samani empirical equations, the final results indicated that the ANN model generally performed superior to the ANFIS, MLR and the empirical equations in estimating monthly Hg at 163 stations in Turkey. Engerer and Mills [68] compared nine of the most prominent beam and global clear sky radiation models at 14

B Hg MAE RMSE R2 h OPp MLR RH PWV Tm w BP

biases Global solar radiation Mean absolute error Root mean square error Determination coefficient Sunshine durations occurrence of precipitation Multiple linear regression Relative humidity Water vapor pressure minimum air temperature weighting coefficient back-propagation

sites in Australia, the results showed that the Solis, Esra and REST2 approaches performed the best, while the Iqbal, Esra and REST2 methods are the most proficient clear skybeam models. Mghouchi et al. [69] compared and validated three solar radiation models under all sky conditions at Tetuan city in northern of Morocco, the results indicated that some models can be preferred to estimate the solar radiation intensities for the studied site and for other locations that have similar climate conditions. Wu and Wang [70] proposed a novel hybrid model for short term solar radiation prediction, which outperforms than the BP model and the Autoregressive Integrated Moving Average model. Despotovic et al. [71] used statistical analysis to evaluate performance of analyzed diffuse solar radiation models using long term measurements at 267 different sites around the world, which was visually presented by means of Taylor diagrams. Despotovic et al. [72] further conducted a detailed statistical analysis and comparison of Hg models, a total of 101 different radiation models were tested on long term meteorological data corresponding to 924 sites throughout the world, and the results showed wide range of calculated statistical indicators, from very poor to satisfactory. It can be seen from above analysis that the estimated results of solar radiation using remote sensing methods may not be as good as above empirical, physical and artificial intelligence methods, although it can provide the spatial distributions of solar radiation in regional or global scales [66,73]. The model performance may also differ greatly from different observation stations for each model, and there are relative less studies focusing on comparing the model accuracy for stations at different climates, so it is not able to scientifically and comprehensively evaluate the model performances with different input variables [74,75]. For instance, the coefficients for the origin BC model are site specific (local geographical and atmospheric conditions), which should be modified to expand its application by incorporating more meteorological data to derive the atmospheric transmissivity [21,76]. The aim of this study is to review recent studies related to application of artificial intelligence methods to Hg and to apply four different methods, including MLP, GRNN, RBNN and IBC, for modeling daily Hg in different climate zones (Plateau Climate, Cold-Temperate, Mid-Temperate, Warm-Temperate, Subtropical and Tropical climate zones, respectively). Daily observations of general meteorological parameters, Ta, PA, RH, PWV and h at 12 stations in different ecosystems of China during 1961–2014 are used for training and testing each solar radiation model. The information about model principles and operation steps will be described in detail and the model results will be evaluated through the measures of fit, RMSE, MAE and R2. The model accuracies will be further compared at different stations (and climate zones) for comprehensively evaluate different radiation

L. Wang et al. / Renewable and Sustainable Energy Reviews 61 (2016) 384–397

models, which might be helpful in selection of the most appropriate and accurate model for mapping solar energy in regional or global scale based on the available meteorological data.

2. Materials and methods 2.1. Sites and data processing In order to test the model performances (MLP, GRNN, RBNN and IBC model) at different climate zones, daily measurements of radiation and meteorological variables during 1961–2014 at 12 stations across China were selected, the geographical distributions of above stations can be seen in Fig. 1 and Table 1. LSA and GEM stations are located at the Qinghai-Tibet Plateau, the climate in this area belongs to the Plateau Climate Zone, which is characterized by extremely cold winters with large ranges between the annual TM and Tm. For example, the annual mean Ta, TM and Tm at LSA station is about 8.18, 15.95 and 1.78 °C, respectively; the RH and PWV at both LSA (RH and PWV are 43% and 5.15 hPa, respectively) and GEM stations (RH and PWV are 32% and 3.21 hPa, respectively) are the lowest among all the stations. The HEB station is located at the Cold-Temperate Zone, which is characterized by long and cold winter, short and cool summer; the annual Ta, TM and Tm at HEB station is 4.79, 10.66 and
0.89 °C, respectively. The ELHT, BJ, ALT and LZ stations are in Northern China (Mid-Temperate zone), which is hot in summer, cold in winter months. The detailed information about the meteorological conditions can be clearly seen in Table 1, for example, the annual Ta, TM, Tm, RH and PWV at BJ station are 12.64 °C, 18.50 °C, 7.22 °C, 54% and 10.34 hPa, respectively. HT station is located at the Warm-Temperate Zone, the annual mean daily h is about 7.88 h; the annual Ta, TM and Tm are 13.10, 19.69 and 7.33 °C, respectively, which is obviously higher than those at ALT station (Table 1) in Northwestern China. The WH, HZ and NN stations belong to the Subtropical Climate Zone, which is characterized by hot summer (with abundant rainfall) and warm winter; for example, the annual Ta, TM, Tm, RH and PWV at HZ station are 18.18 °C, 23.36 °C,14.13 °C, 72% and 17.20 hPa, respectively. The HK station is located in the Hainan Peninsula, and the climate here belongs to typical tropical zone, the annual Ta, RH

387

and PWV (25.22 °C, 82% and 26.68 hPa, respectively) in this area are the highest among all the stations. It is reported that two different types of the radiometers have been used for observing solar radiation in China before 1994 and afterwards, respectively, so the daily observations of Hg at above stations should be checked to ensure the data quality [77,78]. The radiation data are controlled by following principles: the measured radiation should not exceed the G0 and not less than the lower bound; the surface observed Hg should not exceed the clearsky daily solar radiation too much; the data with evident systematic and operational errors are further removed to exclude the likely noisy data [79]. After the quality control, the remaining data are used for model development and validation in this study. The monthly variations of h, Ta, RH, Hg, TM-Tm and PWV at each station are shown in Fig. 2, it is clear that most of the meteorological variables (h, Ta, Hg and PWV) are higher in summer and lower in winter months, for example, the monthly mean Hg at ALT station is 25.25 and 5.69 MJ m
2 day
1 in June and December, respectively; the monthly mean values of Ta at GEM station is 18.22 °C in July, while this value decreases to
9.19 °C in January. There are also obvious differences at different stations for each meteorological variable, for example, the monthly Hg is generally higher at LSA and GEM stations (larger than 15 MJ m
2 day
1 for most months) and the lower values of Hg are observed at HEB and HZ stations (lower than 18 MJ m
2 day
1 for most months); the highest monthly mean PWV is observed at HK and NN stations, which are generally higher than 12 hPa throughout the year, while the largest monthly PWV at GEM, LSA and ELHT stations are lower than 12 hPa; the monthly mean Ta at HK station is generally higher than other stations throughout the year and the lowest Ta is observed at ALT station; the monthly h is highest at ALT and ELHT stations and the lowest values are observed at NN and HZ stations. However, the monthly values of (TM
Tm) at some stations are lower in summer months, for example, the highest monthly (TM
Tm) at BJ station is 12.97 °C in May, while the lowest values are observed in August (9.48 °C). Similar phenomenon has also been observed at other stations except HK station: the monthly (TM
Tm) is higher in spring and lower in winter months at HK station, and the values of (TM
Tm) are generally lower than 8 °C during the year. This relative small temperature differences between day and night are associated with the larger specific heat

Fig. 1. Spatial distribution of the solar radiation observation stations.

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L. Wang et al. / Renewable and Sustainable Energy Reviews 61 (2016) 384–397

Table 1 The geographical locations of each radiation station and its annual mean meteorological parameters. Station

Lon

Lat

Altitude (m)

Hs (h)

Tmean (°C)

Tmax (°C)

Tmin ( °C)

RH (%)

PwvG (hPa)

ALT BJ ELHT GEM HEB HK HT HZ LSA LZ NN WH

88°050 E 116°280 E 111°580 E 94°540 E 126°460 E 110°210 E 79°560 E 120°100 E 91°080 E 103°530 E 108°130 E 114°080 E

47°440 N 39°480 N 43°390 N 36°250 N 45°450 N 20°020 N 37°080 N 30°140 N 29°400 N 36°030 N 22°380 N 30°370 N

735.30 31.3 964.7 945.4 142.30 13.9 1374.5 41.7 3648.7 1035.3 121.6 23.1

8.89 8.09 9.01 8.58 7.46 6.90 7.88 6.79 8.26 7.7 6 7.35

5.35 12.64 4.39 5.26 4.79 25.22 13.10 18.18 8.18 9.30 23.62 18.39

11.78 18.50 11.99 13.01 10.66 29.56 19.69 23.36 15.95 16.61 28.97 23.72


0.69 7.22
2.31
1.39
0.89 22.32 7.33 14.13 1.78 3.51 19.94 14.09

56 54 47 32 64 82 41 72 43 56 78 74

6.05 10.34 4.86 3.21 8.10 26.68 6.69 17.20 5.15 7.52 23.41 17.67

16.22 15.58 17.52 19.31 13.85 16.39 16.85 15.29 20.47 15.90 15.65 15.58

The unit of G is MJ m
2 day
1.

Fig. 2. Monthly variations of metrological parameters for each station.

capacity of water at HK station, in which is surrounded by the sea. Meanwhile, the monthly RH at subtropical and tropical stations are relatively stable during the year, however, the RH values are generally lower at stations in Mid-Temperate or Qinghai-Tibet Plateau (HT, GEM and ELHT), which may be associated with the Mongolia and Siberian high pressure system. 2.2. Solar radiation prediction models Fig. 3. Schematic architecture of a MLP neural network.

2.2.1. Multilayer perceptron neural network ANNs are information processing systems inspired from the biological neural network, which can be considered as a mathematical model developed by the concepts of neural biology. MLP neural networks are known as a class of nonlinear models with the ability to discover patterns, simulation and time series forecasting adaptively from the data [80,81]. The effort in an MLP is based on the intrinsic relationship established between data, nonlinear mapping between independent and dependent variables. Each

MLP model is consisted of input layer, hidden layer and output layer. In each hidden and output layer, there are several processing elements (also called as neurons or nodes). Each processor is associated and interconnected with all the processors in the next layer. The relationship between network layers is possible to investigate according to the weighting coefficients (w) and biases (B) for each processor and activation function (Fig. 3). After establishing the MLP architecture, the information given to MLP is

L. Wang et al. / Renewable and Sustainable Energy Reviews 61 (2016) 384–397

propagated from input layer to the output layer through hidden layer(s). The output can be regarded as assimilation of the network after the training process. In the training process it is necessary to adopt appropriate learning algorithm to reduce errors. It should be noted that the learning algorithms for a MLP model are based on BP technique which is normally a steepest gradient descent method. The main objective of the BP method is to reduce the amount of network error that can be calculated using [82]: e ¼ 0:5 

N X

ðok
t k Þ2

ð1Þ

k¼1

where N is the number of processors, ok is the network output in the kth processor and tk denotes the target value. 2.2.2. Radial basis neural network A RBNN model can be regarded as a type of MLP with a single hidden layer. The main differences between the MLP and RBF neural networks can be given as follows: (1) the connections between the input layer and the hidden layer for RBNN models are not weighted, and (2) the transfer (activation) functions on the nodes of the hidden layer are designed to be radically symmetrical. The most common transfer function which is designated to RBNN networks are Gaussian function, whilst and other options such as multiquadric, inverse quadric and polyharmonic spline functions might also be applied [83]. Fig. 4a indicates schematic diagram of a RBNN model with several inputs and one output neuron. RBNN parameters include the centers (Uj) and spread (σj) of the transfer functions in the hidden layer nodes and consist of synaptic weights w in the output layer node. Having the RBNN centers in each separate point in the input space is desirable, but practically a few entry points of the total available points might be selected through a process called clustering. For Xi as an input vector, jth hidden node shows the response of hj based on [84]: " #
‖Xi
Uj ‖ hj ¼ exp ð2Þ 2σ 2j here, ‖Xi
Uj ‖ represents the distance between Xi and the center of the jth hidden node to which is measured by a norm operator (e.g. Euclidean norm). Eventually, the output of RBNN model is provided in the kth output node via yik ¼

L X

hj wkj

ð3Þ

j¼1

2.2.3. Generalized regression neural network A GRNN model is a kind of RBNN which is based on kernel regression networks. Originally, GRNN model is proposed as an alternative to the BP training algorithm for MLP model, but unlike MLP, they do not require an iterative training procedures such as back-propagation algorithm. GRNNs have the ability to approximate any nonlinear function between input and output vectors in a direct function drawing from the training data [85]. Moreover, in GRNNs, the larger the size of the training set, the smaller the

389

estimation error would be. As shown in Fig. 4b, GRNN model consists of four layers: the input layer, pattern layer, summation layer and output layer. The number of entries in the input layer will depend on the total number of observed parameters. The first layer, in which each neuron presents a training pattern and provides its output, is connected to the pattern layer. Pattern layer is attached to the summation layer. The third layer (summation layer) consists two different types of summation including single division and summation units. The summation and output layers work together to normalize the output vector. In training process of network, linear and radial basis transfer functions are used in the output and hidden layers. Each neuron in the pattern layer is connected to both neurons in the summation layer (summation neurons of S and D). S-summation neuron calculates the sum of the weighted responses in pattern layer, whereas, D-summation neuron computes the unweighted output neuron in the pattern layer. The output layer just divides each S-summation neuron on 0 D-summation neuron and gives predicted Y i for an unspecified input vector and the value of x as the following expression [85,86]: n P

yi :exp½
Dðx; xi Þ 0 ; Y i ¼ i ¼ n1 P exp½
Dðx; xi Þ

Dðx; xi Þ ¼

m  X xi
xik 2 σ k¼1

ð4Þ

i¼1

yi denotes the weight relationship between neuron i-th in the pattern layer and S neuron in the summation layer. D is the Gaussian function, n and m stand for the number of training patterns and the number of elements of an input vector, respectively. xik is kth element of and xi, also, σ is the spread (smoothness) parameter whose optimal value can be experimentally evaluated. 2.2.4. Improved Bristow–Campbell model Bristow and Campbell [76] proposed a method for estimating the daily Hg from diurnal temperature range (TM
Tm), the atmospheric transmittance, the ratio between Hg and G0, is calculated as a function of (TM
Tm), which can be expressed as Hg ¼ A½1
expð
BðT M
T m ÞC Þ G0

ð5Þ

where A is the maximum radiation expected on a clear day, being distinctive for each location and depending on air quality and altitude; coefficients B and C control the rates at which A is approached as the temperature difference increases. The above BC model does not take into considerations of other factors influencing the incoming surface solar radiation, such as relative humidity, cloud cover, etc. So more meteorological variables [for example, TM, Tm, RH and OPp (binary value)] should be employed to represent the actual atmospheric transmittance in this study, the IBC model is proposed as follow

G0 ¼ 37:54 

  dm  ½ðH S Þ sin ϕ sin δ þ cos ϕ cos δ sin H S  d

Fig. 4. General structure of (a) RBNN and (b) GRNN models.

ð6Þ

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n  P

R2 ¼

i¼1

n  P i¼1

!2   Xmi
Xm Xoi
Xo

Xmi
Xm

n  2 P 2 Xoi
Xo

ð11Þ

i¼1

where N and bar respectively indicate the number of data and mean of the variable, Xm and Xo are the modeled and observed daily G. 3.2. Model performances

Fig. 5. Variation of spread constant vs RMSE for the GRNN model in ALT station.

W ¼ 2πj=365 and j is the Julian day. The solar radiation at the top of the atmosphere can be calculated as Hg ¼ ðb0 þ b1 sin ðWÞ þ b2 cos ðWÞ þ b3 RH þ b4 OPpÞ G0 b6

½1
expð
b5 ðT M
T m Þ Þ

ð7Þ

dm d

is known as the correction factor for the Sun-Earth distance, which can be obtained from

In present work, the accuracies of above four different methods, MLP, GRNN, RBNN and IBC models, were compared for modeling daily Hg in different climate zones (Plateau Climate, Cold-Temperate, Mid-Temperate, Warm-Temperate, Subtropical and Tropical climate zones, respectively). Daily meteorological parameters, Ta, PA, RH, PWV and h at 12 stations in China during 1961-2014 were used as model inputs to the applied models for estimating solar radiation. 70% of the entire dataset was used for training and remaining 30% was used for testing phases. Before applying MLP, GRNN and RBNN methods to the data, the input and output values were standardized using the accompanying mathematical statement c1

xi
xmin þ c2 xmax
xmin

where xmin and xmax indicate the extreme values of the dataset; xi is the observed value of the variable at time i. Scaling elements c1 and c2 can take distinctive values. In this study, 0.8 and 0.2 were allotted for the c1 and c2, respectively; in this way, training data were scaled in the reach [0.2, 0.8].

dm pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1:00011 þ 0:034221 cos ξ þ 0:034221 sin ξ þ0:000719 cos 2ξ þ 0:000077 sin 2ξ d

The daily angle (ξ, in rad) is calculated as a function of the Julian day (ξ ¼ 2πðj
1Þ=365); Hs and δ are the solar angle at sunset and solar declination, respectively. Then, the coefficients of the IBC model (b0, b1, b2, b3, b4, b5 and b6) can be obtained by minimizing the sums of the squares of deviations between observed and expected values. These derivatives are numerically computed using finite differences, the Newton-Raphson algorithm is used for multivariate nonlinear optimization, which is conducted in the SPSS 22.0 software. The detailed procedures for calculating the model parameters for IBC model can be seen in Meza et al. [21] and Pan et al. [23].

3. Model applications and results 3.1. Comparisons of measures of fit The measures of fit used in the present study includes RMSE, MAE and R2, which can be expressed as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X ðXmi
Xoi Þ2 RMSE ¼ t Ni¼1

MAE ¼

n 1X jXmi
Xoi j Ni¼1

ð9Þ

ð10Þ

ð12Þ

ð8Þ

For the GRNN models, distinctive spread constants were attempted and the ideal values that gave the lowest RMSE values were obtained for each model. As a sample, the variety of spread constant versus RMSE for the GRNN model at ALT station is illustrated in Fig. 5. Diverse number of hidden nodes was tried for the MLP models and the ideal ones were achieved for each station. As an illustration, the variety of hidden node number versus RMSE for the MLP model at ALT station is shown at Fig. 6. For the RBNN models, the ideal spread constants and hidden node numbers were obtained by trial and error method for each station. As an illustration, the variety of hidden node number and spread constant versus RMSE for the RBNN model at ALT station is given in Fig. 7. Comparisons of ideal ANN and IBC models are made in Table 2 for above 12 stations. For the GRNN, IBC, MLP and RBNN models, the RMSE values range 2–3.29, 3.13–4.58, 1.94-3.27, 1.96-3.25 MJ m
2 day
1, respectively. For the GRNN, MLP and RBNN model, the most extreme RMSE values (3.29, 3.27 and 3.25 MJ m
2 day
1) were found for the station HZ. For the IBC model, however, the most extreme RMSE value (4.58 MJ m
2 day
1) was obtained for the ALT station. The best accuracy for GRNN (RMSE¼ 2 MJ m
2 day
1), MLP (RMSE¼1.94MJ m
2 day
1) and RBNN (RMSE¼1.96 MJ m
2 day
1) model was found at the NN station while the IBC model (RMSE¼3.13 MJ m
2 day
1) gave the best accuracy at HT station. It is clear from Table 2 that each ANN model generally performs superior to the IBC models in forecasting global solar radiation in different climate zones. The MLP model produces the highest accuracy in seven of twelve stations (ALT, BJ, ELHT, HT, HZ, LSA and LZ station). The RBNN model also brings higher model

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391

Table 2 The test statistics of different models in predicting the solar radiation Training

Fig. 6. Variation of hidden node number vs RMSE for the MLP model in ALT station.

Fig. 7. Variation of hidden node number and spread constant vs RMSE for the RBNN model in ALT station.

performances at four stations (GEM, HEB, HK and NN) while the GRNN model only produces high accuracy at only one station in China. The MAE values given in Table 2 range 1.58–2.34, 2.32–3.41, 1.53– 2.29, 1.54–2.32 MJ m
2 day
1 for the GRNN, IBC, MLP and RBNN models, respectively. Like the RMSE criterion, the lower MAE values (1.58, 1.53 and 1.54 MJ m
2 day
1, respectively) of the GRNN, MLP and RBNN models were found at NN station while the minimum MAE value (2.32 MJ m
2 day
1) for the IBC model was obtained for HT station. Furthermore, the larger MAE values for GRNN (MAE ¼ 2.34 MJ m
2 day
1), MLP (MAE¼2.29 MJ m
2 day
1) and RBNN (MAE ¼ 2.32 MJ m
2 day
1) model was obtained at HZ station while the IBC model (MAE¼3.41 MJ m
2 day
1) is demonstrated as the worst method at ALT station. Table 2 clearly shows that the ANN models generally outperform the IBC model with respect to MAE statistics. It is observed that the MLP model produces the best accuracy in seven of twelve stations (ALT, BJ, ELHT, HT, HZ, LSA and LZ) with respect to MAE and R2 values. The RBNN and MLP models gave similar statistical indices at four stations (GEM, HEB, HK and NN stations) while the RBNN model was observed to be superior to the

ALT ALT ALT ALT BJ BJ BJ BJ ELHT ELHT ELHT ELHT GEM GEM GEM GEM HEB HEB HEB HEB HK HK HK HK HT HT HT HT HZ HZ HZ HZ LSA LSA LSA LSA LZ LZ LZ LZ NN NN NN NN WH WH WH WH

GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN GRNN IBC MLP RBNN

Testing

MAE

RMSE

R2

Mean

MAE

RMSE

R2

Mean

1.87 2.18 1.97 2.06 1.82 2.37 1.87 1.96 1.85 2.3 1.97 2.04 1.75 2.35 1.83 1.88 2.19 2.34 2.26 2.23 2.3 2.88 2.26 2.28 1.56 1.99 1.61 1.68 2.2 2.64 2.1 2.28 2.6 2.67 2.66 2.74 1.82 2.34 1.95 1.99 1.97 2.4 2 2.03 2.49 2.92 2.44 2.45

2.43 3.16 2.59 2.68 2.35 3.08 2.43 2.51 2.49 3.24 2.67 2.73 2.28 3.14 2.39 2.44 2.91 3.27 2.99 2.98 2.96 3.63 2.92 2.94 2.02 2.67 2.08 2.17 2.82 3.41 2.71 2.91 3.34 3.45 3.44 3.52 2.53 3.20 2.68 2.72 2.57 3.05 2.61 2.63 3.21 3.76 3.16 3.18

91 85 90 89 88 79 87 86 89 82 87 87 90 82 88 88 83 80 82 83 75 63 75 75 90 82 89 88 80 69 82 79 67 66 65 63 89 82 87 87 79 66 78 78 76 65 77 77

16.26 16.6 16.26 16.26 15.81 15.81 15.81 15.81 17.52 17.6 17.52 17.52 19.56 19.62 19.56 19.56 13.81 14.1 13.81 13.81 16.04 17.26 16.04 16.04 16.97 16.99 16.97 16.97 15.02 16.17 15.02 15.02 20.55 20.37 20.55 20.55 15.9 15.77 15.9 15.9 15.52 16.59 15.52 15.52 15.61 16.27 15.61 15.61

2.15 3.41 2.08 2.16 1.83 2.93 1.80 1.87 2.09 3.02 1.97 2.00 1.97 2.51 1.75 1.77 2.26 3.19 2.22 2.21 2.03 3.35 2.02 2.03 2.06 2.32 1.92 1.97 2.34 3.11 2.29 2.32 2.13 2.86 1.83 1.89 2.02 3.19 1.89 1.93 1.58 2.85 1.53 1.54 2.10 3.03 1.98 1.94

2.72 4.58 2.64 2.74 2.27 3.86 2.02 2.28 2.76 4.14 2.62 2.68 2.43 3.45 2.19 2.19 2.92 4.16 2.86 2.85 2.59 4.15 2.59 2.59 2.69 3.13 2.53 2.58 3.29 4.02 3.27 3.25 2.63 3.76 2.30 2.36 2.56 4.26 2.41 2.45 2.00 3.62 1.94 1.96 2.76 3.96 2.61 2.59

89 70 90 89 88 66 89 88 87 70 88 87 90 77 92 92 83 63 83 84 82 53 82 82 85 77 87 87 72 64 73 72 77 52 81 80 86 64 88 87 86 55 86 86 78 61 81 81

16.15 15.35 16.15 16.15 15.05 15.04 15.05 15.05 17.53 17.35 17.53 17.53 18.72 18.56 18.72 18.72 13.93 13.26 13.93 13.93 17.21 14.36 17.21 17.21 16.58 16.54 16.58 16.58 15.92 13.25 15.92 15.92 20.29 20.71 20.29 20.29 15.89 16.21 15.89 15.89 15.97 13.47 15.97 15.97 15.51 13.98 15.51 15.51

The unit of MAE, RMSE and Mean are MJ m
2 day
1.

alternate models at only one station. For the GRNN, IBC, MLP and RBNN models, the most compelling determination coefficients R2 are 90, 77, 92 and 92% at GEM station, respectively. The minimum determination coefficient values were found to be 72, 73 and 72% for the GRNN, MLP and RBNN models at HZ station while the IBC model has the lowest R2 (52%) at LSA station. It is clearly seen from Table 2 that all the ANN models produce more accurate results than the IBC models, for example, the GRNN, MLP and RBNN model estimate the annual mean global solar radiation (16.22 MJ m
2 day
1) as 16.15 MJ m
2 day
1 with underestimations of 0.43% while the IBC model results in 15.35 MJ m
2 day
1 with an underestimation of 5.4% at ALT station; similar model performances were also obtained for other stations. The observed and predicted global solar radiation values by GRNN, MLP and RBNN models in training and testing stages are plotted in Figs. 8–10. It is clear from the figures that the higher solar radiation values ( 430 MJ m
2 day
1) were significantly underestimated for the stations ALT, ELHT, HK and HZ. The main

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Fig. 8. Comparison between daily measured solar radiation and estimates using GRNN model during the training (a) and validation (b) period for each station.

reason may be the high differences in training and testing data ranges and the distributions for these stations. All the models gave the least scattered estimates at NN station, which is also confirmed by the various statistics provided in Table 2. Comparisons between above three ANN methods indicate that the MLP and RBNN models generally give better accuracy than the GRNN model. This can also

be clearly seen from the fit line equations and R2 statistics. Fig. 11 illustrates the estimates of IBC model both in training and testing stages, model comparisons between IBC and ANN methods indicate that the IBC model generally provide higher scattered estimates and the fit lines of the ANN models are closer to the ideal line (45° line) than those of the IBC model.

L. Wang et al. / Renewable and Sustainable Energy Reviews 61 (2016) 384–397

393

Fig. 9. Comparison between daily measured solar radiation and estimates using MLP model during the training (a) and validation (b) period for each station.

4. Discussion The model results at above 12 stations in diverse ecosystems indicate that all the ANN models performed superior to the IBC model. Scientifically, an ANN model can be acknowledged as a universal approximator [87], which has already become a

promising research area due to the simplicity of utilization and straightforward definition [88]. Among the ANN methods, the MLP and RBNN models were found to have preferred accuracies over the GRNN model in predicting global solar radiation. This outcome is consistent with the relevant literatures, for example, Kisi [89] investigated the accuracies of MLP, RBNN and GRNN models in

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Fig. 10. Comparison between daily measured solar radiation and estimates using RBNN model during the training (a) and validation (b) period for each station.

estimating daily suspended sediment concentration and the results showed that the MLP and RBNN methods gave preferable results over the GRNN model. The capability of above three distinctive ANN techniques are also investigated in modeling reference evapotranspiration by Kisi [90], the GRNN model gave the second rate results when compared with MLP and RBNN models.

Seckin et al. [91] predicted the flood peaks of different return periods at ungauged sites and the model performances further indicated that the MLP and RBNN performed superior to the GRNN method. Pinar et al. [92] analyzed the performances of MLP, RBNN and GRNN models in evaluating backwater through arched bridge constrictions with normal and skewed crossings, and the MLP and

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395

Fig. 11. Comparison between daily measured solar radiation and estimates using IBC model during the training (a) and validation (b) period for each station.

RBNN models produced more accurate forecasts than the other methods. The primary focal points of MLP contrasted to RBNN model are (1) the MLP model makes global approximations, while the RBNN model estimates locally nonlinear input-output relationships; (2) MLP model may require less number of parameters than the

RBNN for obtaining the same precision [93]. Despite its inferior results, the GRNN model might likewise be favored rather than the MLP method in view of the accompanying points of interest: (1) The MLP precision is highly sensitive to randomly assigned initial weight values while this issue is not confronted in GRNN model [94]; (2) The GRNN model does not require an iterative

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training procedure as that in the MLP model [95]; (3) The local minima issue is not confronted in GRNN model.

5. Conclusion The applicability of three ANN models, MLP, GRNN and RBNN models in modeling daily surface solar radiation at different climatic regions was investigated. The major contribution is the use of routine meteorological parameters as inputs to overcome the lack of rarely measured radiation database. Long-term continuously observations of meteorological data, i.e.: h, Ta, RH, Hg, TM
Tm and PWV at 12 stations were used in the present study for analyzing their variation characteristics and solar radiation model development, validation and comparisons. An improved Bristow–Campbell (IBC) model has been applied by considering the influencing factors of surface solar radiation, for example, TM, Tm, RH and OPp have been used to represent the actual atmospheric transmittance. The model performances have been evaluated and compared through the statistical indices RMSE, MAE and R2 for each model. The results indicate that the MLP and RBNN models generally provide better accuracies than the GRNN and IBC models in predicting daily solar radiation, for example, the RMSE values range 2–3.29, 3.13–4.58, 1.94–3.27, 1.96–3.25 MJ m
2 day
1 for GRNN, IBC, MLP and RBNN models, respectively, and the most extreme RMSE values (3.29, 3.27 and 3.25 MJ m
2 day
1 for the GRNN, MLP and RBNN models) were found for the HZ station; the MAE values given in Table 2 range 1.58–2.34, 2.32–3.41, 1.53–2.29, 1.54–2.32 MJ m
2 day
1 for the GRNN, IBC, MLP and RBNN models, respectively. The statistical results also show differences at different stations for each model, for example, the higher accuracy for GRNN (RMSE¼2 MJ m
2 day
1), MLP (RMSE¼ 1.94 MJ m
2 day
1) and RBNN (RMSE¼1.96 MJ m
2 day
1) models were found at the NN station while the IBC model (RMSE¼3.13 MJ m
2 day
1) gave the best accuracy at HT station. Meanwhile, it is observed that the ANN models underestimated high radiation values (430 MJ m
2 day
1) at some stations and the IBC model generally provided higher scattered estimates, which may due to the differences in training and test data ranges and distribution for the stations. From above, it can be concluded that the MLP and RBNN models are more accurate in estimating solar radiation at different climatic zones in China, which is of vital importance for surface energy budget, climate change and energy applications. Certainly, the models should be further applied and tested at other places in the world for extending the international applicability. More attentions will be paid on the atmospheric radiative transferring mechanism and mapping the regional and global radiation distributions using remote sensing techniques.

Acknowledgments This work was financially supported by the Special Fund for Basic Scientific Research of Central Colleges, China University of Geosciences, Wuhan (No. CUG150631), and the Fundamental Research Funds for the Central Universities (No. 2042016kf0165). We would like to thank the China Meterological Administration (CMA) for providing the meteorological and radiation data.

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