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GEP and MLR approaches for the prediction of reference evapotranspiration

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Abstract

In this study, reference evapotranspiration (ETo) is modeled as one of the major items of hydrological applications from different combinations of climatic variables using two different techniques: gene expression programming (GEP) and multiple linear regression (MLR). The data used in modeling were collected from weather stations in Egypt through the CLIMWAT database. The Penman–Monteith FAO-56 equation was considered as a reference target for ETo values depending on the entire climatic variables. The developed ETo models’ performances were compared and evaluated with regard to their predictive abilities using statistical criteria to identify the superiority of one modeling approach over the others and determine climatic variables which have a significant effect on ETo. The results indicated that GEP and MLR models’ contribution toward mean relative humidity and wind speed at 2 m height is greater compared to that of other variables. Meanwhile, when adding temperature data to models, solar radiation has a slight effect on increasing the accuracy of ETo estimate. Moreover, the lower statistical error criteria values of GEP models confirmed their better performance than MLR models and other empirical equations.

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Abbreviations

b i :

Estimated regression coefficients

b 0 :

Unknown intercept

C i :

GEP or MLR estimated ETo value

C sx :

Skewness coefficient of the applied data

\(\overline{C}\) :

Average GEP or MLR estimated value

e a :

Actual vapor pressure

e s :

Saturation vapor pressure

E i :

PMF-56 estimated ETo value

E n :

Minimum PMF-56 estimated value

ETo :

Reference evapotranspiration

E x :

Maximum PMF-56 estimated value

\(\overline{E}\) :

Average PMF-56 estimated value

G :

Soil heat flux

k x :

Kurtosis coefficient of the applied data

n :

Number of data points

RH:

Mean relative humidity

R a :

Extraterrestrial radiation

R n :

Net radiation

R s :

Solar radiation

S x :

Standard deviation of the applied data

T :

Mean air temperature

T max :

Maximum air temperatures

T min :

Minimum air temperatures

u 2 :

Wind speed at 2-m height

x i :

Independent variables

x max :

Maximum of the applied data

x mean :

Mean of the applied data

x min :

Minimum of the applied data

\(\mathop Y\limits^{ \wedge }\) :

Predicted value of the dependent variable

Δ :

Slope of the saturation vapor pressure–temperature curve at mean air temperature

λ :

Latent heat of vaporization

α 1 :

Intercept of fit line equation

α 0 :

Slope of fit line equation

γ :

Psychometric constant

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Acknowledgements

With sincere respect and gratitude, we would like to express our deepest gratitude to the Deanship of Scientific Research, King Saud University, and Agriculture Research Center, College of Food and Agriculture Sciences, for the financial support and encouragement.

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Correspondence to Mohamed A. Mattar.

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Mattar, M.A., Alazba, A.A. GEP and MLR approaches for the prediction of reference evapotranspiration. Neural Comput & Applic 31, 5843–5855 (2019). https://doi.org/10.1007/s00521-018-3410-8

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