Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks

Energy 36 (2011) 5356e5365

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Energy journal homepage: www.elsevier.com/locate/energy

Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks Alvaro Linares-Rodríguez, José Antonio Ruiz-Arias, David Pozo-Vázquez, Joaquín Tovar-Pescador* Department of Physics, University of Jaen, Building A3, Campus Lagunillas, 23071 Jaen, Spain

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 March 2011 Received in revised form 2 June 2011 Accepted 22 June 2011 Available online 24 July 2011

Four variables (total cloud cover, skin temperature, total column water vapour and total column ozone) from meteorological reanalysis were used to generate synthetic daily global solar radiation via artificial neural network (ANN) techniques. The goal of our study was to predict solar radiation values in locations without ground measurements, by using the reanalysis data as an alternative to the use of satellite imagery. The model was validated in Andalusia (Spain), using measured data for nine years from 83 ground stations spread over the region. The geographical location (latitude, longitude), the day of the year, the daily clear sky global radiation, and the four meteorological variables were used as input data, while the daily global solar radiation was the only output of the ANN. Sixty five ground stations were used as training dataset and eighteen stations as independent dataset. The optimum network architecture yielded a root mean square error of 16.4% and a correlation coefficient of 94% for the testing stations. Furthermore, we have successfully tested the forecasting capability of the model with measured radiation values at a later time. These results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates and forecasts. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Global solar radiation Artificial neural network Meteorological reanalysis Solar maps Prediction

1. Introduction Solar radiation is a required variable for the designers of solar systems. It is often provided as solar radiation maps, which is usually a preferable approach, more efficient and easy to handle. In order to build them, many procedures have been proposed. Most of them require knowing the solar radiation at many points spread wide across the region of interest. In addition, empirical, semiempirical, physical, neural networks, wavelets, fractals, etc. techniques must be assumed for the spatial prediction. Unfortunately, solar radiation is still a scarcely sampled variable with respect to other environmental variables as temperature or precipitation, and there is usually a small set of stations with available radiation measurements. This lack of information has been often avoided with satellite imagery [1e5]. The method we propose in this study consists in the combination of meteorological reanalysis and artificial intelligence techniques for spatial prediction. It involves a new approach given that these reanalysis do not provide direct information on downward shortwave solar flux.

* Corresponding author. Tel.: þ34 953212428; fax: þ34 953212838. E-mail addresses: [email protected] (A. Linares-Rodríguez), [email protected] (J.A. Ruiz-Arias), [email protected] (D. Pozo-Vázquez), [email protected] (J. TovarPescador). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.06.044

Therefore, this work describes a new form of exploitation of this meteorological dataset and a valid alternative to the use of satellite imagery. ANNs have been used in diverse applications in control, robotics, pattern recognition, forecasting, medicine, power systems, manufacturing, optimisation, signal processing, and social/ psychological sciences. They are particularly useful in system modelling, such as in implementing complex mapping and system identification. In the last years, neural network methods have been employed for the prediction of global solar radiation both in time and space. Comparative studies of ANNs and traditional regression approaches have been achieved [6e9], and it has been shown that ANN models are usually more efficient and less time consuming in modelling complex systems. A clear review of ANN applications for renewable energy systems has been reported by Kalogirous [10,11], and Mellit et al. [12] for photovoltaic systems. ANNs have been used in solar radiation modelling works for locations with different latitudes and climates (e.g., Saudi Arabia [13,14], Spain [15e18], Turkey [4,19e21], Greece [22], China [23]), using various internal topologies (e.g. [18,24e27]), different input variables (geographical and climatological, e.g. [14,16,28e30]), or several time scales (monthly, daily and hourly, e.g. [17,26,28,31]). Typically, these models were devised to forecast solar radiation (from ground data from earlier time), to estimate values at

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Nomenclature

4 J

sigmoidal activation function at the hidden layer linear activation function at the output layer w1(j,i) weigth between jth input and ith hidden layer neuron weigth between ith hidden layer neuron and the w2(i) output neuron bias term applied to the ith hidden layer neuron b1(i) bias term applied to the output layer neuron b2 N number of hidden neurons M number of input neurons ! x input vector jth element of the input vector xj response of the ith hidden neuron yi G measured daily global solar radiation ^ G predicted daily global solar radiation G mean measured daily global solar radiation global clear sky solar radiaton Gcs daily global solar radiation GD unsampled locations, or to remove/fill data gaps (e.g. [13,25,32e36]). In this work, ANNs with different topologies have been developed for spatial and time prediction of daily global solar radiation in Andalusia (Spain), using measured values at 83 ground stations over the region. 2. Methodology First, we trained the ANN with measured data at the 65 training stations from 1999/10/01 to 2008/12/31. Following, we tested the results against the measurements at the 18 testing stations. Finally, we also used the ANN to predict the period 2009/01/01e2009/09/ 30, which is out of the training period. 2.1. Artificial neural network architecture An ANN is characterized by its architecture, training or learning algorithm and activation function. The architecture describes the connections between the neurons. It consists of an input layer, an output layer and generally, one or more hidden layers in-between as depicted in Fig. 1. The architecture used in this work, shown in Fig. 1, has an input layer with eight inputs, one hidden layer with 25 neurons and a sigmoidal activation function, 4, defined by the logistic function: 4 ¼ 1/(1 þ exp(x)), x being the corresponding input. For the output layer, a linear activation function j was used in the implementation. ^ representing daily global solar The approximating function G, radiation, was defined as

^ ! Gð xÞ ¼ j

N X

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Acronyms ANN artificial neural network ECMWF European Centre for Medium-Range Weather Forecasts ERA-Interim Reanalysis-interim from ECMWF TCC Total cloud cover SKT Skin temperature, i.e. surface temperature TCW Total column of water vapour TCO Total column of ozone MBE Mean bias error RMSE Root mean square error rRMSE Relative root mean square error subscript i neuron number of the hidden layer j neuron number of the input layer k time-step for ECMWF variables: k ¼ 1.4 corresponds to 00, 06, 12 18 UTC

minimizes a linear combination of squared errors and weights, and then uses Bayesian regularization to determine the correct combination that results in a network that generalizes satisfactorily. The number of hidden neurons in an ANN is a function of the problem’s complexity, the number of input and output parameters, and the number of training cases available. A trial and error process was used to determine the number of hidden neurons. After trying a number of different configurations, and repeating each training process ten times to avoid random errors, it was found that 25 neurons in the hidden layer yielded the best results with a reasonable computational effort. Before selecting this ANN model (multilayer perceptron feedforward neural network), we conducted several trials with different networks and architectures, specially radial basis function neural networks and some sort of ensemble networks. We found no significant improvement in the results, but higher computational cost. 2.2. Selection of ANN input variables As shown in Fig. 1, the variables selected as ANN inputs were geographical latitude and longitude, day of the year, clear-sky daily

! yi ,w2 ðiÞ þ b2

(1)

i¼1

where

1 0 M X ! yi ð x Þ ¼ 4@ xj ,w1 ðj; iÞ þ b1 ðiÞA

(2)

j¼1

For the training process of the ANN, a Bayesian regulation backpropagation algorithm was used. This algorithm is a supervised iterative training method that updates the weights and bias values according to LevenbergeMarquardt optimisation [37]. It

Fig. 1. Multilayer perceptron feed-forward neural network used in the study.

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Fig. 2. Region of study. The highlighted region shows the digital model of terrain (DEM) used.

radiation, and four variables from the ERA-Interim dataset: total cloud cover, skin temperature, total column water vapour and total column ozone. Following, we provide a detailed description of these variables. 2.2.1. Latitude, longitude, day of the year The first two ANN input variables were geographical variables of the ground stations: latitude and longitude. They would allow us to spatially extrapolate to the entire study region. Altitude of each station was not included as input variable because it was inserted into the clear sky model (Section 2.2.2). The third ANN input variable was the day of the year, which takes into account the seasonal trend. 2.2.2. Clear sky solar radiation model Daily clear sky global solar radiation plays an important role as input variable because it incorporates the atmospheric optical mass and, consequently the altitude [38,39]. Other meteorological variables, specially cloud data, were introduced as input variables to take into account all sky conditions. We used the clear sky model of the European Solar Radiation Atlas (ESRA) [40], which is based on the turbidity coefficient of Linke. Particularly, this parameter accounts for the climatic aerosols. We used representative averages of monthly Linke turbidity factors for the study region. The calculations were conducted with the module r.sun of the GRASS GIS platform, which also includes additional routines to account for the terrain influence [41]. The terrain was modelized with the SRTMv3 digital elevation model (DEM) [42] upscaled to 30 arc seconds (approximately 1 km at the study region latitudes). The grid of this DEM (a 418  788 matrix for the region of our study) was used as support for the subsequent interpolations. 2.2.3. Meteorological reanalysis The meteorological variables used as inputs in the ANN model were obtained from the ECMWF ERA-Interim dataset [43]. It is a reanalysis of the global atmosphere covering the data-rich period Table 1 Error values of the ANN model. MBE

RMSE 2

65 training stations (219,439 values) 18 testing stations (60,768 values) All stations (280,207 values) a

2

R a

MJ$m

MJ$m

%

4.11e07 0.47 0.10

2.59 2.88 2.65

14.29 16.41 14.75

Percentages of the mean measured daily global solar radiation value.

0.95 0.94 0.95

since 1989, and continuing in real time. The ERA-Interim data assimilation system contains many improvements both in the forecasting model and analysis methodology relative to ECMWF’s previous reanalysis, ERA-40, including the use of 4-dimensional variational analysis, a revised humidity analysis, the use of variational bias correction for satellite data, and other improvements in data handling [44]. The atmospheric model and reanalysis system is configured with 60 levels in the vertical (the top level at 0.1 hPa), a grid spacing of 0.7 (Gaussian grid N128) and data every 6 h. However, we retrieved the dataset from the server interpolated at 0.25  0.25 (roughly 25 km of grid spacing at the study site latitudes). ERA-Interim products are already used extensively at ECMWF for research and diagnostic studies, and for many other purposes such as developing the seasonal forecasting system, and providing climatology for operational verification. Reanalysis products are used increasingly in many fields that require an observational record of the state of either the atmosphere or its underlying land and ocean surfaces. 2.2.4. Selection of climatological variables Among the variety of instantaneous surface and single level parameters saved on the model’s Gaussian grid, we selected the following ones:    

TCC: total cloud cover (0e1) SKT: skin temperature (K) (i.e. surface temperature) TCW: total column water vapour (kg m2) TCO: total column ozone (kg m2)

As expected, the most important variable in the performance of the ANN was TCC. The other variables have been used in the literature as input variables for a variety of models (empirical, neural networks, etc. [12]), and they also improve the accuracy of this model. The data cover the period from October 1999 to October 2009. Moreover, the ERA-Interim reanalysis is available in near real time. 2.2.5. Daily averaging The ERA-Interim data assimilation system produces four analyses per day, at 00, 06, 12 and 18 UTC. In order to obtain a single daily value for each variable, we averaged these four analyses for each day. To take into account the different hourly influence on radiation, we integrated the four values by a weighted sum, according with Equation (3) (as variable we have considered TCC, but the same equation was used for the others variables: SKT, TCW and TCO):

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because, obviously, it has no influence in the daily global solar radiation. 2.3. ANN output variable Daily global solar radiation was selected as the only output of the model. Training and testing of the network continued until no improvement in the output was achieved (i.e. minimum error between ANN output values and measured data) or after a predetermined number of epochs, which was set at 1000. In this case, minimum error was achieved before maximum epoch had been reached. 3. Study region and experimental dataset The study was carried out throughout the region of Andalusia, in the southern part of the Iberian Peninsula, between the latitudes 37 and 42 N (Fig. 2). The region comprises the southern-most part of the European continent, in the western facade of the Mediterranean basin. It covers an extension of about 87,000 km2 with 917 km of coastlines. The region is located in the transition zone from temperate to warm climates. Geographically, Andalusia is in a key region to play an important strategic role in the implementation of renewable energy technology in Europe, as well as providing sufficient energy for its own needs and even exporting such projects to other countries [45]. It is worth mentioning that Spain has the greatest amount of available sunshine of any country in Europe and has a very abundant solar resource (1200e1800 kWh m2 year1). Furthermore, Spain is one of the largest manufacturers in the world of solar power technology. 3.1. Measured daily global solar radiation data

Fig. 3. A comparison between measured and predicted data a) at Baena training station, and b) at Jerez testing station.

The Andalusian Regional Office of Agriculture and Fishing records the daily global solar radiation on horizontal surface by means of two different networks: the Alert and Phytosanitary Information Network, with 86 stations, and the Agroclimatic Network, with 102 stations. Data are measured with Kipp & Zonen CM-5 pyranometers. An instrumental error of 5% is expected in the best case. However, despite the stations are regularly maintained and calibrated, typically, it is more realistic to assume a 7%. The networks were deployed to provide information of, mainly, agroclimatical interest. Therefore, the radiometric stations are clustered around the principal agricultural areas of the region. The range of elevations above mean sea level goes from 4 m to 1212 m, with a mean elevation of 345 m. The selected period ranges from 1999/ 10/01 to 2009/09/30. Due to the long time period used in our work, the number of stations with available data was largely reduced. 3.2. Quality control

TCCday ¼

4 X

wk ,TCCk

(3)

k¼1

where the weights wk are:

wk ¼ Gcs;k =

4 X

Gcs;k

(4)

k¼1

The subscript k indicates the kth time-step (k ¼ 1 corresponds to 00 UTC, k ¼ 2 to 06 UTC, and so on). Thus, the higher the clear sky radiation (Gcs,k), the greater the weight of that value. With this method, for instance, the cloudness at 00 UTC is neglected when averaging the TCC over the whole day

The purpose of the data quality control was to eliminate spurious data and inaccurate or inconsistent measurements, caused by cosine response error of the pyranometers, large calibration drifts and other malfunctions. First, a quality assessment based on physical limits was applied: an upper limit of 0.8 for the atmospheric clearness, calculated as the daily measured solar radiation to the daily potential extraterrestrial, and a lower limit of 0.01 MJ m2. Following, the data were undergone to a visual inspection and 14 of the stations were ruled out since they presented suspicious trends. Overall, excluded values did not reach the 2%. After this quality control procedure, 83 candidate stations remained. However, the stations tend to be clustered around flat areas which, from the methodological point of view, might lead to

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Fig. 4. Comparison between results of the ANN trained with the whole dataset (global-ANN) and the ones trained only with data of a year (annual-ANN), focused on the testing dataset. Table 2 Error values of the ANN model, grouped by TCC values. ANN trained with the whole dataset (from 1999/10/01 to 2008/12/31) TCC * 10

Training dataset Number of input/output pairs

[0,1] [1,2] [2,3] [3,4] [4,5] [5,6] [6,7] [7,8] [8,9] [9,10]

99,681 14,953 10,939 10,531 11,474 12,100 10,694 9279 10,320 29,468

(45.4%) (6.8%) (5%) (4.8%) (5.2%) (5.5%) (4.9%) (4.2%) (4.7%) (13.4%)

Testing dataset MBE

RMSE

MJ$m2

MJ$m2

%

R

0.0083 0.0075 0.058 0.080 0.017 0.050 0.038 0.0061 0.021 0.018

1.77 2.52 2.76 2.99 3.13 3.20 3.27 3.35 3.51 3.19

7.97 13.06 15.34 17.61 19.68 20.98 22.38 24.18 27.02 30.88

0.97 0.94 0.92 0.90 0.89 0.88 0.88 0.87 0.85 0.85

Number of input/output pairs

27,963 3933 2858 2807 3098 3349 3052 2594 2905 8209

(46%) (6.5%) (4.7%) (4.6%) (5.1%) (5.5%) (5%) (4.3%) (4.8%) (13.5%)

Fig. 5. Fitted models for RMSE of the ANN based on TCC values.

MBE

RMSE

MJ$m2

MJ$m2

%

R

0.70 0.67 0.45 0.41 0.29 0.28 0.13 0.12 0.070 0.14

2.10 2.88 3.18 3.35 3.47 3.45 3.60 3.61 3.66 3.43

9.81 15.48 18.27 20.48 22.63 22.97 24.89 26.52 28.49 34.1

0.96 0.92 0.89 0.88 0.87 0.85 0.84 0.85 0.84 0.82

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Fig. 6. a) Daily global solar radiation map generated by ANN model. Next figures show input matrixes for each input variable of the ANN: b) TCC values, c) Global clear sky values, d) SKT values, e) TCW values and f) TCO values from ECMWF dataset.

wrong results by overweighting the areas with higher density of stations. Therefore, 18 of these stations (60,768 records) were carefully extracted, and reserved for independent validation of the results, trying to homogenize the spatial distribution of the stations. The remaining 65 stations were used for training the ANN (219,439 records). Fig. 2 shows the distribution of the training and validation datasets along the study region.

measured values of daily global radiation for training and testing datasets.Where

MBE ¼

n 1X Gs  GPs n s¼1

Table 3 Forecasting capability of the model. Error values of the ANN model, for data from 2009/01/01 to 2009/09/30.

4. Results and discussions Validation of the results was carried out by using the following statistical scores: mean bias error (MBE), root mean square error (RMSE), relative mean square error (rRMSE) and correlation coefficient (R) between the predicted and the

(5)

65 training stations (17745 values) 18 testing stations (4914 values) All stations (22659 values)

MBE

RMSE

MJ$m2

MJ$m2

%

R

0.14 0.49 0.22

2.83 3.016 2.87

13.52 14.20 13.67

0.94 0.93 0.94

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Fig. 7. Comparison between measured and predicted data a) for Jaen station (training station n. 42) and b) for Jerez station (testing station n. 2).

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX ^ s Þ2 =n RMSE ¼ t ðGs  G

(6)

s¼1

rRMSE ¼ RMSE*100=G R ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X X ^ s  GÞ2 = ðGs  GÞ2 ðG

(7) (8)

n being the number of input/output patterns. 4.1. Prediction of daily global solar radiation After successfully trained with data from 1999/10/01 to 2008/ 12/31, the ANN was ready to perform prediction with new input data. In order to judge its performance, we tested it using the independent dataset. A comparison between the results for training and testing dataset gives us an estimation of the ANN’s spatial extrapolating capability. Table 1 shows the error values of the ANN model. Fig. 3 shows a comparison between measured and predicted data a) at Baena training station, and b) at Jerez testing station.

A first result, as shown in Table 1, was that the estimation of global solar radiation performs with an acceptable accuracy using ECMWF ERA-interim dataset. Taking into account the scale of our study area, it is worth noting that the MBE and RMSE values were better or similar to others reported in the literature, and also compared with satellite-derived irradiance models [2]. For testing stations, the overall RMSE was found to increase from 14.29% (training stations) to 16.41%. RMSE per each testing station varied from 13.94% to 21.42%. The last one was obtained for the easternmost station and, hence, the station with a greatest relative distance to the whole set of training stations. This result could be explained by the significant dependence of the accuracy with the distance between stations.

4.2. Yearly and seasonal dependence To further explore the performance of the ANN model, we built nine ANN models, one for each year from 2000 to 2008. Each annual-ANN was trained only with data within a year, e.g. ANN_2002 was trained with data from 2002/01/01 to 2002/12/31. The structure of each annual-ANN was exactly the same than the

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original ANN. The results for the testing dataset e in terms of MBE and RMSE e are shown in Fig. 4. Overall, the ANN trained with the whole dataset generated worse GD estimates for every single year than its corresponding annual-ANN model. Each annual-ANN was able to fit the data better for a year, and the climatic differences between years led to a loss of accuracy over the whole time period. On the other hand, each annual model lacked generalization and only generated accurate estimates for the trained year. In order to use the model to predict GD for future time periods, ANN should be trained with the whole dataset, because it takes into account all climatic trends over a decade. We also conducted a monthly evaluation of the ANN along the whole time period, and concluded that the worst estimates were obtained in winter (RMSE ¼ 24.52% in December) and the best ones in summer (8.27% in July). In Andalusia, summer is usually sunny and dry, and winter is cloudy and rainy. Despite using the four meteorological variables from ERA-Interim to train the ANN, and more specifically total cloud fraction (TCC), the model is very sensitive to the presence of clouds. Therefore, we evaluated the ANN model by TCC values (ranged from 0 to 1), dividing dataset into ten subsets according to the TCC value. The results are shown in Table 2. As expected, ANN led to highly accurate estimates in clear sky days (9.81% over 46% of the whole dataset), but lost accuracy in cloudy days. It is worth noting that both RMSE and rRMSE presents a well defined trend, which can be used as an error estimate of the ANN, using the TCC value. Consequently, we fitted the rRMSE (Fig. 5) against TCC (we have used 20 TCC subsets to improve accuracy). The model used for the empirical error is depicted in the figure.

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5. Conclusions The model for generation of synthetic series of solar radiation via ANN presented a good performance, demonstrating the viability of the methodology for generating daily global solar radiation in localities were there only exists meteorological information from ERA-Interim reanalysis. RMSE ranged from 13.94% to 21.42%. Spatial prediction of ANN estimates demonstrates to be distance dependent. If only a few stations are used for training the ANN, or these stations do not cover the whole area of study, the results can’t be extrapolated for a long distance. Therefore, solar maps could be generated with a reasonable accuracy only if many stations spread over the study region are available. Furthermore, ANN model is heavily dependent on presence of clouds. In order to improve the model, further research should be carried out to incorporate, for instance, more detailed cloud information. nce trained the ANN, its forecasting capability has been evaluated by predicting GD values for the first nine months of 2009, with a relative RMSE between ANN estimates and observed values ranged from 13.52% (for training stations) to 14.20% (for testing stations).

Acknowledgements This work was supported by the Spanish Ministry of Science and Technology (Project ENE2007-67849-C02-01) and the Andalusian Ministry of Science and Technology (Project P07-RNM-02872). The data were kindly provided by the regional office of Agriculture and Fishing of Andalusia.

4.3. Solar radiation maps Daily global solar radiation maps were generated using the annual-ANN models. For a given day, a 418  788 matrix for each variable (latitude, longitude, day of the year, daily clear sky global radiation, and four ERA-Interim variables) was used as input variable. Hence, a 418  788 matrix with GD estimates was generated as output of the model, covering the whole area of Andalusian with a spatial resolution of 30 arc seconds. Fig. 6 shows a sample of a solar radiation map and its corresponding input maps. The maps were generated for a day: 2005/10/ 12. Fig. 6 a) shows the daily global solar radiation generated by the ANN model, and next figures show input matrices for each input variable of the network: TCC, SKT, TCW and TCO values from ECMWF dataset e Fig. 6 b), def) respectively e and global clear sky values (Fig. 6c). 4.4. Forecasting capability The ANN trained with data from 1999/10/01 to 2008/12/31 was tested with data from 2009/01/01 to 2009/09/30 to evaluate the forecasting capability of the model. The results are shown in Table 3. It’s to be noted that the ANN even yields accurate estimates for future time period. It proves that ANN has successfully learnt the complex relationship between input variables and solar radiation, and it can be used to predict GD for any location within the study region, as there are input data for the entire region, even for future periods. Fig. 7 shows a comparison between predicted and measured data at one training station (a) and at one testing station (b). These results were a bit better than those obtained in Section 4.1. because the available time period didn’t include some of more cloudy months (octoberedecember 2009).

Appendix ^ As we explained in Section 2.1, the approximating function G, representing daily global solar radiation, was defined as

^ ! Gð xÞ ¼ j

N X

! yi ,w2 ðiÞ þ b2

(A1)

i¼1

where

1 0 M X ! yi ð x Þ ¼ 4@ xj ,w1 ðj; iÞ þ b1 ðiÞA

(A2)

j¼1

where, w1(j,i) is the weight between jth input and ith hidden layer neuronw2(i) is the weight between ith hidden layer neuron and the output neuron b1(i) is the bias term applied to the ith hidden layer neuron, b2 is the bias term applied to the output layer neuron f is the sigmoidal activation function at the hidden layer j is the linear activation function at the output layer We can rewrite these equations in matrix form:

^ ¼ jðW ,4ðW ,! G 2 1 x þ b1 Þ þ b 2 Þ

(A3)

where, W1 is a (25  8) matrix of weights between each input and every hidden neuron; W2 is a (1  25) matrix of weights between each hidden neuron and the output neuron; b1 is a (25  1) matrix of biases applied to the hidden neurons; b2 is the (1  1) bias term ! applied to the output layer neuron; x is the (8  1) input matrix After the ANN has been trained with data from 1999/10/01 to 2008/12/31 (Section 4.1), the resulting weights and biases matrices are as follows:

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1 2:0257 1:9248 0:7586 1:4803 0:1631 0:4961 0:4689 0:6478 B 0:2330 0:1080 0:1401 1:5124 0:7826 0:3000 2:0876 1:1004 C C B B 0:2307 0:1595 0:0831 1:0957 1:9995 1:2996 0:0886 0:1582 C C B B 0:5655 0:3750 2:3539 0:2324 0:0318 0:5526 0:0643 0:0605 C C B B 0:1955 0:0503 0:0827 0:6669 0:3227 0:3473 0:7569 2:3600 C C B B 2:6461 1:7188 0:5818 0:5587 0:0664 0:8964 0:1944 0:1704 C C B B 0:5492 0:6028 7:6980 7:5172 1:3690 2:4727 5:6944 8:5319 C C B B 0:2053 0:0500 0:1181 1:5136 0:9183 0:6013 1:9814 1:1070 C C B B 0:1608 0:1681 0:0545 0:6763 0:0847 0:4484 1:0025 1:1705 C C B B 1:3083 1:8669 0:1256 0:7478 0:4142 0:7585 1:3607 0:5081 C C B B 0:0410 0:1693 0:9740 2:3339 0:2737 4:0113 3:1594 0:6098 C C B B 0:1217 0:3213 0:1084 0:2088 0:5499 2:9931 2:4852 0:3022 C C B 1:6004 1:5183 0:4857 0:0625 0:5474 0:2376 0:3555 C W1 ¼ B C b1 ¼ B 2:7401 B 0:1228 0:2312 0:2868 0:5584 0:1637 0:4883 4:6352 1:1371 C C B B 0:1127 0:0351 0:8817 0:5817 0:3699 1:7828 1:1582 0:1986 C C B B 0:0531 0:2927 1:299 1:0223 0:2018 1:2167 0:7641 0:1107 C C B B 0:2493 0:4610 0:4273 0:0925 0:0784 0:5394 0:7257 0:0751 C C B B 0:1160 0:9436 7:6667 5:3694 0:8369 10:9933 4:9302 1:3692 C C B B 0:7542 1:0518 0:0318 0:6622 0:2627 1:5702 1:5699 0:1936 C C B B 0:2455 0:1530 1:9512 0:0565 0:0361 0:0777 0:1519 0:0501 C C B B 0:8175 2:7185 0:1531 0:2279 0:2831 0:5271 0:0300 0:2194 C C B B 0:3752 1:0697 0:2048 0:2343 0:1687 0:4285 0:6488 0:2495 C C B B 0:2324 0:0468 0:0237 1:7075 1:773 0:9947 2:3809 1:3326 C C B @ 8:8661 10:4886 0:0016 0:3271 0:2383 0:0206 0:0181 0:3630 A 0:0470 0:1515 0:1446 0:6034 1:2245 1:1459 0:5831 0:1880 W2 ¼ ð 0:2501 23:839 18:701 0:4960 0:4704 0:0929 0:0584 4:2625 0:4019 0

0

1 4:1383 B 2:3164 C B C B 4:4779 C B C B 0:9265 C B C B 2:0277 C B C B 0:6465 C B C B 4:3481 C B C B 2:0885 C B C B 0:4099 C B C B 0:9875 C B C B 0:5224 C B C B 0:5272 C B C B 0:5684 C B C B 1:7027 C B C B 0:0919 C B C B 0:1643 C B C B 1:0887 C B C B 5:7082 C B C B 0:2262 C B C B 0:5533 C B C B 1:7158 C B C B 0:9279 C B C B 2:1184 C B C @ 9:6670 A 2:4298 0:0479

0:0753  0:1605  0:0897 0:0492 0:2806 0:3394  1:1515 0:0707  0:0747 1:0657 0:1044  0:5509 1:6801 0:0426 1:2570Þ b2 ¼ 1:0396

References [1] Perez R, Seals R, Zelenka A. Comparing satellite remote sensing and ground network measurements for the production of site/time specific irradiance data. Solar Energy 1997;60(2):89e96. [2] Perez R, Ineichen P, Moore K, Kmiecik M, Chain C, George R, et al. A new operational model for satellite-derived irradiances: description and validation. Solar Energy 2002;73(5):307e17. [3] Rubio M, Lopez G, Tovar J, Pozo D, Batlles F. The use of satellite measurements to estimate photosynthetically active radiation. Physics and Chemistry of the Earth, Parts A/B/C 2005;30(1e3):159e64. [4] S¸enkal O. Modeling of solar radiation using remote sensing and artificial neural network in Turkey. Energy 2010;35(12):4795e801. [5] Lu N, Qin J, Yang K, Sun J. A simple and efficient algorithm to estimate daily global solar radiation from geostationary satellite data. Energy 2011;36(5): 3179e88. [6] Reddy K. Solar resource estimation using artificial neural networks and comparison with other correlation models. Energy Conversion and Management 2003;44(15):2519e30. [7] Tymvios F, Jacovides C, Michaelides S, Scouteli C. Comparative study of Angström’s and artificial neural networks’ methodologies in estimating global solar radiation. Solar Energy 2005;78(6):752e62. [8] Elminir H, Azzam Y, Younes F. Prediction of hourly and daily diffuse fraction using neural network, as compared to linear regression models. Energy 2007; 32(8):1513e23. [9] Jiang Y. Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models. Energy 2009;34(9):1276e83. [10] Kalogirou SA. Artificial neural networks in renewable energy systems applications: a review. Renewable and Sustainable Energy Reviews 2001;5: 373e401. [11] Kalogirou SA. Applications of artificial neural networks for energy systems. Applied Energy 2000;67:17e35. [12] Mellit A, Kalogirou S. Artificial intelligence techniques for photovoltaic applications: a review. Progress in Energy and Combustion Science 2008; 34(5):574e632. [13] Mohandes M, Rehman S, Halawani TO. Estimation of global solar radiation using artificial neural networks. Renewable Energy 1998;14(1e4):179e84. [14] Rehman S, Mohandes M. Artificial neural network estimation of global solar radiation using air temperature and relative humidity. Energy Policy 2008; 36(2):571e6.

[15] Hontoria L, Aguilera J, Zufiria P. An application of the multilayer perceptron: solar radiation maps in Spain. Solar Energy 2005;79(5):523e30. [16] Lopez G, Batlles FJ, Tovar-Pescador J. Selection of input parameters to model direct solar irradiance by using artificial neural networks. Energy 2005;30(9): 1675e84. [17] Bosch J, Lopez G, Batlles F. Daily solar irradiation estimation over a mountainous area using artificial neural networks. Renewable Energy 2008;33(7): 1622e8. [18] Siqueira AN, Tiba C, Fraidenraich N. Generation of daily solar irradiation by means of artificial neural net works. Renewable Energy 2010;35(11): 2406e14. [19] Sozen A. Use of artificial neural networks for mapping of solar potential in Turkey. Applied Energy 2004;77(3):273e86. [20] Sozen A, Arcaklioglu E, Ozalp M, Caglar N. Forecasting based on neural network approach of solar potential in Turkey. Renewable Energy 2005;30(7): 1075e90. [21] S¸enkal O, Kuleli T. Estimation of solar radiation over Turkey using artificial neural network and satellite data. Applied Energy 2009;86(7e8):1222e8. [22] Moustris K, Paliatsos A, Bloutsos A, Nikolaidis K, Koronaki I, Kavadias K. Use of neural networks for the creation of hourly global and diffuse solar irradiance data at representative locations in Greece. Renewable Energy 2008;33(5): 928e32. [23] Lam J, Wan K, Yang L. Solar radiation modelling using ANNs for different climates in China. Energy Conversion and Management 2008;49(5):1080e90. [24] Mohandes M, Balghonaim A, Kassas M, Rehman S, Halawani TO. Use of radial basis functions for estimating monthly mean daily solar radiation. Solar Energy 2000;68:161e8. [25] Dorvlo ASS, Jervase JA, Al-Lawati A. Solar radiation estimation using artificial neural networks. Applied Energy 2002;71:307e19. [26] Cao J, Lin X. Study of hourly and daily solar irradiation forecast using diagonal recurrent wavelet neural networks. Energy Conversion and Management 2008;49(6):1396e406. [27] Mubiru J. Estimation of monthly average daily global solar irradiation using artificial neural networks. Solar Energy 2008;82(2):181e7. [28] Behrang MA, Assareh E, Ghanbarzadeh A, Noghrehabadi AR. The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data. Solar Energy 2010;84(8): 1468e80. [29] Sozen A. Estimation of solar potential in Turkey by artificial neural networks using meteorological and geographical data. Energy Conversion and Management 2004;45(18e19):3033e52.

A. Linares-Rodríguez et al. / Energy 36 (2011) 5356e5365 [30] Mellit A, Benghanem M, Hadj Arab A, Guessoum A. Solar Energy 2005;79(5): 469e82. [31] Zervas P, Sarimveis H, Palyvos J, Markatos N. Prediction of daily global solar irradiance on horizontal surfaces based on neural-network techniques. Renewable Energy 2008;33(8):1796e803. [32] Cao J, Cao S. Study of forecasting solar irradiance using neural networks with preprocessing sample data by wavelet analysis. Energy 2006;31(15): 3435e45. [33] Hocaoglu F, Gerek O, Kurban M. Hourly solar radiation forecasting using optimal coefficient 2-D linear filters and feed-forward neural networks. Solar Energy 2008;82(8):714e26. [34] Mubiru J. Predicting total solar irradiation values using artificial neural networks. Renewable Energy 2008;33(10):2329e32. [35] Mellit A, Pavan AM. A 24-h forecast of solar irradiance using artificial neural network: application for performance prediction of a grid-connected PV plant at Trieste, Italy. Solar Energy 2010;84(5):807e21. [36] Voyant C, Muselli M, Paoli C, Nivet M- L. Optimization of an artificial neural network dedicated to the multivariate forecasting of daily global radiation. Energy 2011;36(1):348e59. [37] Foresee FD, Hagan MT. Gauss-Newton approximation to Bayesian regularization. In: Proceedings of the 1997 International Joint Conference on Neural Networks; 1997. p. 1930e5.

5365

[38] Batlles F, Bosch J, Tovar-Pescador J, Martinez Durban M, Ortega R, Miralles I. Determination of atmospheric parameters to estimate global radiation in areas of complex topography: generation of global irradiation map. Energy Conversion and Management 2008;49(2):336e45. [39] Ruiz-Arias JA, Tovar-Pescador J, Pozo-Vazquez D, Alsamamra H. A comparative analysis of DEM-based models to estimate the solar radiation in mountainous terrain. International Journal of Geographical Information Science 2009;23(8): 1049e76. [40] Rigollier C, Bauer O, Wald L. On the clear sky model od the ESRA European Solar Radiation Atlas with respect to the Heliosat method. Solar Energy 2000; 68(1):33e48. [41] Hofierka J, Súri M. A New GIS-based solar radiation model and its application to photovoltaic assessments. Transactions in GIS 2004;8(2):175e90. [42] Jarvis A, Reuter HI, Nelson A, Guevara E. Hole-filled seamless SRTM data V3. Int Cent Trop Agric (CIAT), Retrieved from: http://srtm.csi.cgiar.org. (last access: 07.03.2011). [43] http://data.ecmwf.int (last access: 07.03.2011). [44] Simmons A, Uppala S, Dee D, Kobayashi S. ERA-Interim: new ECMWF reanalysis products from 1989 onwards; 2007. [45] Ramos Ridao A, Hontoria Garcia E, Moreno Escobar B, Zamorano Toro M. Solar energy in Andalusia (Spain): present state and prospects for the future. Renewable and Sustainable Energy Reviews 2007;11(1):148e61.