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Daily total global solar radiation modeling from several meteorological data

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Abstract

This paper investigates the modeling of the daily total global solar radiation in Adana city of Turkey using multi-linear regression (MLR), multi-nonlinear regression (MNLR) and feed-forward artificial neural network (ANN) methods. Several daily meteorological data, i.e., measured sunshine duration, air temperature and wind speed and date of the year, i.e., monthly and daily, were used as independent variables to the MLR, MNLR and ANN models. In order to determine the relationship between the total global solar radiation and other meteorological data, and also to obtain the best independent variables, the MLR and MNLR analyses were performed with the “Stepwise” method in the Statistical Packages for the Social Sciences (SPSS) program. Thus, various models consisting of the combination of the independent variables were constructed and the best input structure was investigated. The performances of all models in the training and testing data sets were compared with the measured daily global solar radiation values. The obtained results indicated that the ANN method was better than the other methods in modeling daily total global solar radiation. For the ANN model, mean absolute error (MAE), mean absolute percentage error (MAPE), correlation coefficient (R) and coefficient of determination (R 2) for the training/testing data set were found to be 0.89/1.00 MJ/m2 day, 7.88/9.23%, 0.9824/0.9751, and 0.9651/0.9508, respectively.

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Abbreviations

ANN:

Artificial neural network

b :

Bias

BP:

Back-propagation

D :

Day of the month

FFNN:

Feed-forward neural network

GRNN:

Generalized regression neural network

H :

Global solar radiation (MJ/m2 day)

LM:

Levenberg–Marquardt

LR:

Linear regression

MAE:

Mean absolute error (MJ/m2 day)

MAPE:

Mean absolute percentage error (%)

MLR:

Multi-linear regression

MNLR:

Multi-nonlinear regression

M :

Month of the year

m :

Measured value

n :

Total number of data

p :

Predicted value

R :

Correlation coefficient

R 2 :

Coefficient of determination

RBNN:

Radial basis neural network

S :

Sunshine duration (h)

SPSS:

Statistical packages for the social sciences

t j :

Target output of the node j

T :

Atmospheric temperature (°C)

TSMS:

Turkish State Meteorological Service

x :

Net input of the weighted values of the individual inputs (\( p_{1} ,p_{2} , \ldots ,p_{3} \))

X :

Independent variable

X N :

Normalized value

X min :

Minimal value

X max :

Maximal value

VIF:

Variation inflation factor

w :

Weight

w S :

Measurement accuracy of sunshine duration (h)

w T :

Measurement accuracy of air temperature (°C)

w W :

Measurement accuracy of wind speed (m/s)

w H :

Uncertainty amount of solar radiation (±%)

W :

Wind speed (m/s)

y j :

Output of the node j

Y :

Dependent variable

α :

Equation parameter for nonlinear regression; momentum factor

β :

Equation parameter for linear regression

η :

Learning rate

δ k :

Error term of the output layer

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Acknowledgments

The author, Muammer Ozgoren, would like to thank the Coordinatorship of Selcuk University’s Scientific Research Office (BAP). The authors would like to thank the Turkish State Meteorological Service for providing data.

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Authors and Affiliations

  1. Electric and Energy Department, Adana Vocational High School, Cukurova University, 01160, Adana, Turkey

    Mehmet Bilgili

  2. Mechanical Engineering Department, Faculty of Engineering and Architecture, Selcuk University, Konya, Turkey

    Muammer Ozgoren

Authors
  1. Mehmet Bilgili
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  2. Muammer Ozgoren
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Correspondence to Mehmet Bilgili.

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Responsible editor: L. Gimeno.

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Bilgili, M., Ozgoren, M. Daily total global solar radiation modeling from several meteorological data. Meteorol Atmos Phys 112, 125–138 (2011). https://doi.org/10.1007/s00703-011-0137-9

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  • DOI: https://doi.org/10.1007/s00703-011-0137-9

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