Modeling Reference Evapotranspiration in aSemiarid Area Using Data-driven Techniques: ACase Study in Lower Cheliff plain, AlgeriaMohammed ACHITE  ( m.achite@univ-chlef.dz )

Hassiba Benbouali University of Chlef: Universite Hassiba Benbouali de ChlefMuhammad Taghi Sattari 

: University of Tabriz Faculty of AgricultureAbderrezak Kamel Toubal 

Hassiba Benbouali University of Chlef: Universite Hassiba Benbouali de ChlefAndrzej Wałęga 

Krakow University Faculty in Tychy: Krakowska Akademia Wydzial Zamiejscowy w TychachNir Krakauer 

City College of the City University of New York: The City College of New YorkParveen Sihag 

Shoolini UniversityQuoc Bao Pham 

Ton Duc Thang University

Research Article

Keywords: Reference Evapotranspiration, FAO-56 Penman-Monteith, Data Driven Models, Lower Cheliff,Algeria

Posted Date: August 10th, 2021

DOI: https://doi.org/10.21203/rs.3.rs-773420/v1

License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

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Modeling reference evapotranspiration in a semiarid area using data-

driven techniques: A case study in Lower Cheliff plain, Algeria

Mohammed Achite1*, Mohammad Taghi Sattari2, Abderrezak Kamel Toubal1, Andrzej Wałęga3, Nir

Krakauer4, Parveen Sihag5 and Quoc Bao Pham6,7

1Faculty of Nature and Life Sciences, Laboratory of Water & Environment, University Hassiba Benbouali of Chlef, Chlef, P.B 78C, Ouled Fares, Chlef 02180, Algeria; m.achite@univ-chlef.dz 2Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran; mtsattar@gmail.com 3Department of Sanitary Engineering and Water Management, University of Agriculture in Krakow, Mickiewicza 24/28 Street, 30-059 Krakow, Poland; andrzej.walega@urk.edu.pl 4Department of Civil Engineering and NOAA-CREST, the City College of New York, New York 10031, NY, USA; nirkrakauer@gmail.com 5Department of Civil Engineering, Shoolini University, Solan, Himachal Pradesh, India; parveen12sihag@gmail.com Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, 6

pbquoc92@gmail.com; Ho Chi Minh City, Vietnam 7Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

*Corresponding author: m.achite@univ-chlef.dz

Abstract: Evapotranspiration (ET) is an important part of the hydrologic cycle, especially

when it comes to irrigated agriculture. For the estimation of reference evapotranspiration

(ET0), direct methods either pose difficulties or call for many inputs that may not always be

available from weather stations. This study compares Feed Forward Neural Network (FFNN),

Radial Basis Function Neural Network (RBFNN). and Gene Expression Programming (GEP)

approachs for the estimation of daily ET0 in a weather station in Lower Cheliff plain

(northwest Algeria), over a 6-year period (2006–2011). Firstly, measured air temperature,

relative humidity, wind speed, solar radiation and global radiation was used to calculate ET0

using FAO-56 Penman-Monteith equation as the reference. Then, the calculated ET0 using

FAO-56 Penman-Monteith was considered as output for data driven models, while the

measured meteorological data were considered as input of the models. The coefficient of

determination (𝑅2), root mean square error (RMSE) and Nash Sutcliffe efficiency coefficient

(EF) were used to evaluate the developed models. The results of the developed models were

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compared with the Penman-Monteith evapotranspiration using these performance criteria. The

FFNN model proved to yield the best performance compared to all the developed data-driven

models, while the RBF-NN and GEP models also demonstrated potential for good

performance.

Key words: Reference Evapotranspiration, FAO-56 Penman-Monteith, Data Driven Models,

Lower Cheliff, Algeria

INTRODUCTION

Given increases in the global population, adequately and reliably meeting people’s nutritional

needs in arid and semi-arid climates is one of the most immediate problems of management in

water and agriculture sectors. Since water resources are very limited in climates with varying

degrees of aridity, there is an inevitable need to use existing water resources as optimally as

possible (Nairizi 2017). Evapotranspiration (ET) is one of the most important component of

the hydrology cycle and influences runoff, soil water storage, groundwater recharge,

biodiversity, and the global climate system (Amatya et al. 2018, Sun et al. 2011).

Determining the amount of ET is necessary in water resource management, irrigation

planning, watershed management, and the design of drainage systems.

To calculate the amount of ET for an agricultural system, the reference evapotranspiration

(ET0) is calculated first. However, estimating ET0 is known to be very complex. ET0 is either

measured directly (e.g. by lysimeter or pan setups) or complex physics-based experimentally

validated equations are used. It is clear that direct measurements are very costly and time

consuming. Physics-based equations (e.g.,Thornthwaite 1948; Blaney and Criddle 1950;

Makkink 1957; Turc 1961; Priestley and Taylor 1972; Hargreaves and Samani 1985),

including the FAO-56 Penman Monteith (Allen et al. 1998) are complex in that they involve

multiple parameters which may not all be known from local observations. Nevertheless, the

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FAO-56 Penman Monteith method has been accepted as a standard and used by scientists in

different climates. A high correlation is observed between the ET0 values obtained from FAO-

56 Penman Monteith method and direct measurements even in different climatic conditions.

Therefore, scientists have considered the values computed using the FAO-56 Penman

Monteith method as the desired output of data-based artificial intelligence methods and

different combinations of meteorological variables as inputs for such methods for accurately

estimating ET0 (Kumar et al. 2008; Eslamian et al. 2012; Mohawesh 2011; Citakoglu et al.

2014; Aparecido et al. 2017; Sattari et al. 2020).

The development of computing, software, informatics, and networking has facilitated

measurement and computational estimation of meteorological variables to a great extent. As a

result of these developments, data-based models are frequently used in modeling stochastic

and complex nonlinear dynamics in water resources engineering (Sattari et al. 2017;

Rouzegari et al. 2019; Shabani et al. 2020, Apaydın et al. 2020). For example, de Oliveira

Ferreira Silva et al. (2019) presented the R package "agriwater" for the spatial modelling of

actual evapotranspiration and radiation balance. Thorp et al. (2019) developed a methodology

for unbiased evaluation and comparison of three ET algorithms in the Cotton2K

agroecosystem model. Guven et al. (2008) successfully estimated he daily amount of ET0 in

California, USA, with a genetic programming. Rahimikhoob (2010) predicted ET0 values

with artificial neural networks using temperature and relative humidity parameters in an eight-

station region of Iran with a subtropical climate. The results obtained from the ANN method

were compated with the Hargreaves equation, and it was found that the ANN method was

successful in ET0 estimation. Ozkan et al. (2011) successfully estimated daily ET0 amounts

using artificial neural networks and bee colony hybrid method using the meteorological data

of two stations in California, USA. Cobaner (2013) estimated ET0 amounts in the USA using

wavelet regression (WR) and class A pan evaporation data. WR model results were found to

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give better results than FAO-56 Penman-Monteith equation. Ladlani et al. (2014) applied

Adaptive Neuro-Fuzzy Inference System (ANFIS) and Multiple Linear Regression (MLR)

models for daily ET0 estimation in the north of Algeria. According to the results of the study,

ANFIS yielded better results. Wen et al. (2015) calculated daily ET0 amounts using the

support vector machine (SVM) method in a region of China that was extremely arid. They

utilized limited meteorological variables as model input. It was observed that modeling is

sufficient in estimating daily ET0 based on maximum and minimum temperature. Gocić et al.

(2015) used genetic programming (GP), support vector machine-firefly optimization

algorithm (SVM-FFA), artificial neural network (ANN) and support vector machine-wavelet

(SVM-Wavelet) models for ET0 prediction in Serbia. This particular study took FAO-56

Penman-Monteith equation to be the basic method. The results pointed to SVM-Wavelet

being the best performing methodology for the estimation of ET0 under the given conditions.

Petković et al. (2016) estimated the amount of ET0 in Serbia between 1980 and 2010 using

particle swarm optimization, radial basic function network (RBFN-PSO), and back

propagation radial basic function network (RBFN-BP) methods. Pandey et al. (2017)

estimated daily ET0 by methods like ANN, support vector regression (SVR) and nonlinear

regression (NR). In this study, limited climatic parameters were used as model input. Daily

ET0 values calculated from FAO56PM method were compared to the model output. The

results pointed to the acceptability of the ANN model estimations. Fan et al. (2018) estimated

daily ET0 amounts using SVM, extreme learning machine (ELM) models, and four tree-based

ensemble methods in China’s different climatic conditions. The results pointed to the fact that

tree-based ensemble methods can yield appropriate results in different climates. Wu et al.

(2019) used cross-station and synthetic climate data to estimate the amount of ET0. They also

found that machine learning methods could perform successfully in the prediction process.

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In this study, the aim was to investigate the potential of Feed Forward Neural Network

(FFNN), Radial Basis Function Neural Networks (RBFNN) and the Gene Expression

Programming (GEP) models for the estimation of daily ET0 values using different

combinations of climatic variables in a semi-arid farmland area, namely Lower Cheliff plain

in northwest Algeria. This research made use of the well-known FAO-56 (PM56) equation as

the basic method. In this article, the role of climatic parameters in ET0 estimation in this semi-

arid region was also determined.

MATERIALS AND METHODS

Study area and meteorological data acquisition

The region in focus for this study was Lower Cheliff Plain in the northwest of Algeria (Figure

1), lying between latitudes 34°03′12′′ and 36°05′57′′ N and between longitudes 0°40 and

01°06′08′′ E, and occupying an area of 40,000 ha (Douaoui et al. 2006). This area is classified

as semi-arid. Average annual rainfall ranges from 320 mm to 250 mm. Temperature reach its

maximum in July and August and its minimum in January. The average annual temperature

along the Lower Cheliff plain ranges from 19.5 °C in the north to 25.3 °C in the south.

The historical data for this study was provided by the Hmadna station (SYNMET Automatic

Station), located at latitude 35°55’31” N and longitude 00°45’04” E. The instrument used for

measuring ET0 at the automatic meteorological station of Hmadna is shown in Figure 2. The

units and the measuring range of sensors are listed in Table 1.

2.2. Description of data

The meteorological data included daily observations of maximum, minimum and mean air

temperatures (Tmax, Tmin and Tmean), daily mean relative humidity (RH), wind speed (Ws),

sunshine duration (Sd) and global radiation (GR). The days with data that proved to be

inadequate were excluded from the patterns. The statistical parameters pertaining to the daily

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climatic data are given in Table 2, in which the Xmean, Xmax, Xmin, Sx and Cv stand for the

mean, maximum, minimum, standard deviation and coefficient of variation , respectively.

Evapotranspiration estimation method

The FAO Penman–Monteith method to calculate ET0 can be expressed following Allen et al.

(1998) as:

𝐸𝑇0 = 0.408𝛥(𝑅𝑛 − 𝐺) + 𝛾 900𝑇𝑚𝑒𝑎𝑛 + 273𝑈2 (1)

where ET0 is the reference crop evapotranspiration (mm day-1), Rn is the net radiation (MJ m-2

day-1), G is the soil heat flux (MJ m-2day-1), c is the psychrometric constant (kPa °C-1), es is

the pressure of saturation vapor (kPa), ea is the pressure of the actual vapor (kPa), D is the

slope of the curve for saturation vapor pressure–temperature (kPa.C-1), Ta is the average daily

air temperature (°C), and U2 is the mean daily wind speed at 2 m (m s-1). All the data needed

in the calculation of ET0 were computed on the basis of the procedures outlined in Chapter 3

of FAO-56 (Allen et al. 1998).

Artificial neural networks

Artificial neural networks (ANNs) are nonlinear mathematical models based on ideas about

the behavior of biological neural networks. An ANN consists of with a variety of layers of

interconnected nodes or neurons. Each neuron gets a linearly transformed combination of the

previous neuron’s outputs (∑wijxj), or (for the first layer) of the network inputs and returns a

nonlinear transformation of this quantity.

The weights (wij) are the parameters added to each source defining this linear combination

and typically also include an intercept term called the activation threshold (Shiri et al. 2012).

A nonlinear activation function is then applied to the linear output combination (f (∑wijxj)).

This activation function can be, for example, a sigmoid function, which constrains each

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neuron's output values to between two asymptotes. Once the activation function is applied,

each neuron’s output feeds into the outputs of the next layer. The most frequently used

architecture for an ANN consists of an input layer in which the data is introduced into the

ANN, a hidden layer(s) in which the data undergoes processing, and the output layer in which

the effects of the input generate a predicted output value(s) (Shiri et al. 2012).

Multi-Layer Perceptron (MLP)

The literature contains many kinds of neural networks that have been put to many uses. The

Multilayer Perceptron (MLP) is a commonly used ANN configuration utilized regularly in the

hydrological modelling field (Leahy et al. 2008) (Figure 3). This study assesses the usefulness

of neural MLP networks for the estimation of EP. The MLP is the most frequently used and

simplest neural network architecture (Haciismailoglu et al. 2009).

Radial Basis Function (RBF)

Another architecture used commonly in ANN is the Radial Basis Function (RBF). Multilayer

and feed-forward RBF is often used for multi-dimensional spatial interpolation. The word

"feed-forward" means the neurons in a layered neural network are arranged in layers (Lin et

al. 2004). The underlying architecture of a neural network with three layers is presented in

Figure 4. The RBF network comprises three layers, i.e. hidden, input, and output. The

activation function of each RBF neuron has the form of an RBF, generating a response only if

the inputs are close to some central value determined for that particular neuron.

Gene Expression Programming (GEP)

While ANNs are compicated models that typically do not capture the physical relationships

between different process components in an understandable way, GEP models have the

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capacity to express the relationship between dependent and independent variables explicitly

(Wang et al. 2015).

The procedure for modelling daily evapotranspiration (considered to be the dependent

variable) on the basis of weather variables (considered as the independent variables) involves

the following: selecting the fitness function; selecting terminals T and set of functions F for

creating chromosomes; selecting chromosome architecture; and selecting the link function

and genetic operators (Figure 5) (Shiri et al. 2012).

Evaluation criteria

The performance of the models utilized in this study were evaluated by means of standard

criteria for statistical performance evaluation. The statistical measures taken into account

were coefficient of determination (𝑅2), root mean square error (RMSE) and Nash Sutcliffe

efficiency coefficient (EF) (Moriasi et al. 2007). The calculation of the three criteria was done

according to the following equations:

𝑅2 = 1 − ∑ (𝐸𝑇𝑖(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) − 𝐸𝑇𝑖(𝑚𝑜𝑑𝑒𝑙))𝑁𝑖=1∑ (𝐸𝑇𝑖(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) − 𝐸𝑇𝑚𝑒𝑎𝑛)𝑁𝑖=1 (2)

𝑅𝑀𝑆𝐸 = √1𝑁∑(𝐸𝑇𝑖(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) − 𝐸𝑇𝑖(𝑚𝑜𝑑𝑒𝑙))𝑁𝑖=1

(3)

𝐸𝐹 = 1 − ∑ (𝐸𝑇𝑖(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) − 𝐸𝑇𝑖(𝑚𝑜𝑑𝑒𝑙))2𝑁𝑖=1∑ (𝐸𝑇𝑖(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑) − 𝐸𝑇𝑚𝑒𝑎𝑛)2𝑁𝑖=1 (4)

where N is the number of observed ET data, ETi(observed) and ETi(model) are observed and model

estimations of ET, respectively, and ETmean is the mean of observed ET.

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RESULTS AND DISCUSSION

In this study, firstly, ET0 values were computed by Penman-Monteith method using climatic

data. Then the following equation was used to normalize the input (meteorological data) and

output (calculated ET0 by Penman-Monteith):

𝑋𝑛 = 2. 𝑋𝑜 − 𝑋𝑚𝑖𝑛𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛 − 1 (5)

where, Xn and XO stand for the normalized and original data, while Xmin and Xmax represent

the minimum and maximum values in the original data. Approximately 70% of the available

data period (from around 2006 to 2010) was selected for the training phase; the remaining

30% belonged to the year 2011 and was used for testing process. MATLAB was used for the

modeling process.

Application of MLP

In this study, FFNN algorithm was used with a single hidden layer. More details about the

parameters used for the FFNN-based model with one hidden layer are listed in Table 3. With

the input data playing a considerable role in model development, several input combinations

were used for model development. The performances of all MLP-based input combinations

are listed in Table 4 for training and testing stages. MLP-based model development is a trial

and error process. In this study, tangent sigmoid transfer function was used in the hidden layer

and linear transfer function was used for target. To achieve ideal performance with MLP

models, the number of neurons in the hidden layer has to be optimized. The results in Table 4

suggest that Model FFNN2 including Tmax, Tmean, (Tmax-Tmin), RH, I, Ws and GR performed

better than other FFNN-based input combination models with R2 values as 0.9903, 0.9921,

RMSE values as 0.2332, 0.2342 and E values as 0.9902, 0.9902 for both training and testing

stages, respectively. Nineteen neurons were used in the hidden layer to achieve this ideal

performance. The performance and agreement plot among actual and predicted values of

FFNN2 model for both training and testing stage are mapped out in Figure 6 which shows that

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max values lie very close to the line of 450 and follow the same pattern as the actual values in

both training and testing stages. If all the values lie on the line of 450 and follow the exact

same path, the model is ideal and predicts values similar to actual ones.

Performance evaluation results suggest than FFN2 model performed better than other input

combination based models. As to comparing various input combination based models with

one another, the results in Table 4 indicate that several other models are comparable in

performance to the best model (FFNN2), while having a lower number of required input

meteorolgical variables. Overall, going with the assessment in Table 4, the FFNN11 model

(Tmean, RH, Ws and GR) is suitable for predicting ET with R2 values as 0.9875, 0.9892,

RMSE values as 0.2656, 0.2623 and E values as 0.9873, 0.9877 for both training and testing

stages, respectively. The same number of neurons (19) is used in the single hidden layer for

achieving this performance similar to the FFNN2 model. The performance and agreement plot

among actual and predicted values of the FFNN11 model for both training and testing stage is

shown in Figure 7 which points to the fact that max values lie very close to the line of perfect

agreement and follow the same pattern as the actual values in both training and testing stages.

Application of RBF

For the RBF method as well, several input combinations were used for model development.

The performance of all input combination based RBF-NN models are listed in Table 5 for

training and testing stages. RBF-NN based model development is a trial and error process

similar to FFNN model development. In this study, the RBF models had a single hidden layer.

To achieve ideal performance with RBF-NN models, the value of the spread must be found

through a trial and error process. The results of Table 5 suggest that the RBF-NN5 model

including Tmin, Tmax, Tmean, RH, I, Ws and GR performs better than other input combination

RBF-NN based models with R2 values as 0.9907, 0.9911, RMSE values as 0.2270, 0.2374

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and E values as 0.9907, 0.9899 for both training and testing stages, respectively. The

performance and agreement plot among actual and predicted values of RBF-NN5 model for

both training and testing stages are shown in Figure 8 which shows that max values lie very

close to the line of 450 and follow the same pattern as the actual values in both training and

testing stages.

The performance evaluation results suggest than the RBF-NN5 model performs better than

other input combination based models. On inter comparison among various input combination

based models, the results in Table 5 indicate that the performance of several other models was

comparable to the best model (RBF-NN5) and involved a lower number of inputs. Overall,

the assessment mapped out on Table 5 shows that the RBF-NN11 model (Tmean, RH, Ws and

GR) is suitable for predicting the ET with R2 values as 0.9886, 0.9892, RMSE values as

0.2514, 0.2551 and E values as 0.9886, 0.9884 for both training and testing stages,

respectively. A lower rate of spread (Table 5) was used in the development of this model than

in the case of the RBF-NN5 model. The performance and agreement plot among actual and

predicted values of the RBF-NN11 model for both training and testing stages are shown in

Figure 9 which shows that max values lie very close to the line of perfect agreement and

follow the same pattern as the actual values in both training and testing stages.

Application of GEP

The details of parameters used in the GEP model are listed in Table 6. The performance of all

input combination based GEP models are listed in Table 7 for training and testing stages. GEP

based model development is also a trial and error process similar to the model development

typical of FFNN and RBF-NN based models. For the performance of GEP models under

different input combinations, for the training phase, the R2 ranged between 0.6973 – 0.9664,

RMSE ranged 0.4830–1.3112 mm day−1 and EF ranged 0.6895- 0.9579. So, for the test phase,

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the R2 ranged between 0.8057– 0.9775, RMSE ranged 0.3701–1.1224 mm day−1 and E ranged

0.7744 - 0.9755 (Table 7). It is clear that the presence or absence of critical meteorological

variables in the input combinations significantly affected GEP model performance. The

results of Table 7 suggest that the GEP11 model including Tmean, RH, Ws and GR

parameters in the input combination performed better than other input combination and

GEP based models with R2 values as 0.9606, 0.9775, RMSE values as 0.4830, 0.3701 and E

values as 0.9579, 0.9755 for the training and testing stages, respectively. The performance

and agreement plot among actual and predicted values of the GEP11 model for both training

and testing stages are shown in Figure 10 which indicates that max values lie very close to the

line of 450 and follow the same path as the actual values in both training and testing stages.

Table 7 concludes that the GEP11 model is the best performing model with optimum input

combinations.

Inter comparison among best and optimum input combination based models

Table 8 shows that the FFNN2 based model works better than the RBF-NN and GEP based

models. Figure 11 indicates that predicted values using FFNN2-based model lie closer to the

line of perfect agreement than the values predicted by the RBF-NN and GEP based models.

The overall performance of the FFNN2 based model is reliable and suitable for the prediction

of ET0. So Tmax, Tmean, (Tmax-Tmin), RH, I, Ws and the GR input combination based FFNN

model could be used for the prediction of ET0. However, the results mapped out in Table 9 of

single factor ANOVA suggest that there is no significant difference among observed and

predicted values using FFNN, RBF-NN and GEP best combination based models.

Figure 12 displays box plots for prediction errors for the best input combination based models

using the test period. The values of descriptive statistic of prediction errors for the best input

combinations are listed in Table 10. According to Table 10 and Figure 11, the FFNN2 model

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followed the corresponding observed values with lower minimum error (-0.8840), lower

maximum error (1.4199), and the width of 1st quartile is less than other best input

combination based models.

The Taylor diagram of the observed and predicted ETo by different best input combination

based models over the test period is depicted by Figure 13. It is clear that the representative

points of all the applied models have nearly the same position. The FFNN2 model is located

nearest to the observed point with lower value of RMSE and SD and higher value of

coefficient of correlation, which picks out this model as the superior model.

Table 11 proposes that the RBF-NN11-based model works better than FFNN and GEP based

models. Figure 14 indicates that predicted values using the RBF-NN11-based model lie closer

to the line of perfect agreement than the values predicted by the FFNN and GEP based

models. The overall performance of the RBF-NN11 based model is reliable and suitable for

the prediction of ET0, which suggests that Tmean, RH, Ws and GR input combination based

RBF-NN model could be used for the prediction of ET0. The results in Table 12 of single

factor ANOVA suggest that there is no significant difference among observed and predicted

values using FFNN, RBF-NN and GEP optimum input combination based models.

Figure 15 displays the Box Plot for the prediction errors for the optimum input combination

based models using the test period. The descriptive statistical values of prediction errors for

the optimum input combinations are listed in Table 13. According to the Table 13 and Figure

15, the RBF-NN11 model has followed the corresponding observed values with lower

maximum error (1.3700) and the width of the 1st quartile (-0.0952) is less than other optimum

input combination based models.

The Taylor diagram of the observed and predicted ETo by different optimum input

combination based models over the test period is depicted by Figure 16. It is clear that, the

representative points of all the applied models have nearly the same position. The RBF-NN11

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model is located nearest to the observed point with lower value of RMSE, SD and higher

value of coefficient of correlation, making this model emerge as a superior model with

optimum number of input parameters.

CONCLUSIONS

This study aimed to investigate the potential of FFNN, RBFNN and GEP to estimate daily

evapotranspiration in a semi-arid region in Algeria. Different input combinations of

meteorological variables were tried in these models. The results pointed to the fact that both

the neural network (i.e. FFNN and RBFNN) and GEP models make for optimal levels of

agreement with the ET0 obtained by the FAO PM method. They yielded reliable estimations

for the semi-arid area in question. The study also found that modeling ET0 by means of the

ANN technique leads to better estimates than the GEP model.

The current results suggested that the FFNN based model 2 outperformed all other applied

models. Another major conclusion was that the RBF-NN based model 11 performed better

than other applied models with a smaller number of required meteorological inputs. ANN and

GEP based models suggest that Tmean, RH, Ws and GR parameters are the optimum

parameters for the estimation of daily evapotranspiration in the semi-arid region of Algeria.

The overall performance of all applied models is satisfactory, as there is no significant

difference among actual and predicted values using the optimum number of input parameters

in the models.

Conflict of interest: The authors declare that they have no conflict of interest

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REFERENCES

Allen RG, Pereira LS, Raes, D, Smith, M (1998) Crop evapotranspiration: guidelines for

computing crop water requirements. FAO Irrigation and Drainage Paper No. 56. Rome

(Italy): FAO. p. 300

Alves WB, Rolim GS & Aparecid LEO (2017) Reference evapotranspiration forecasting. J. of

Eng. Agric.v37, p1116-1125. Doi : 10.1590/1809-4430

Amatya, D.M., Muwamba, A.,Panda, S., Callahan, T., Harder, S., Pellett, A. 2018.

Assessment of Spatial and Temporal Variation of Potential Evapotranspiration Estimated

by Four Methods for South Carolina. J. of South Carolina Water Resources, 5(1), 3-24

Apaydin, H., Feizi, H., Sattari, M. T., Colak, M. S., Shamshirband, S., & Chau, K.-W. (2020).

Comparative Analysis of Recurrent Neural Network Architectures for Reservoir Inflow

Forecasting. Water, 12(5), 1500. https://doi.org/10.3390/w12051500

Blaney HF and Criddle WD (1950) Determining Water Requirements in Irrigated Areas from

Climatological and Irrigation Data. US Soil Conservation Service,TP 96.

Citakoglu H, Cobaner M & Haktanir T & Kisi O. (2014) Estimation of Monthly Mean

Reference Evapotranspiration in Turkey. Water Resour Manage (2014) 28:99–113. Doi

10.1007/s11269-013-0474-1

Cobaner, M. (2013). Reference evapotranspiration based on Class A pan evaporation via

wavelet regression technique. Irrigation Science, 31(2), 119–134.

https://doi.org/10.1007/s00271-011-0297-x

de Oliveira Ferreira Silva, C., de Castro Teixeira, A., H., Manzione, R.L. 2019. agriwater: An

R package for spatial modelling of energy balance and actual evapotranspiration using

satellite images and agrometeorological data. Environmental Modelling & Software 120,

104497, DOI: 10.1016/j.envsoft.2019.104497

16

Douaoui A, Walter Ch, Gaouar A. et Hammoudi S (2001) Assessment of the topsoil structural

degradation of the Lower Cheliff Valley (Algeria) -Application of multivariate Analysis.

4th conference of the Working Group on Pedometrics (WG-PM), Ghent, 19-21 september.

Douaoui AEK, Nicolas H and Walter C (2006) Detecting salinity hazards with in a semiarid

Context by means of combining soil and remote-sensing data. Geoderma134 (1): 217–230.

Doi: 10.1016/j.geoderma.2005.10.009

Eslamian SS, Gohari SA Zareian MJ & Firoozfar A (2012) Estimating Penman–Monteith

Reference Evapotranspiration Using Artificial Neural Networks and Genetic Algorithm: A

Case Study. Arab J Sci Eng (2012) 37:935–944. Doi : 10.1007/s13369-012-0214-5

Fan, J., Yue, W., Wu, L., Zhang, F., Cai, H., Wang, X., Lu, X., & Xiang, Y. (2018).

Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily

reference evapotranspiration using limited meteorological data in different climates of

China. Agricultural and Forest Meteorology, 263, 225–241.

https://doi.org/10.1016/j.agrformet.2018.08.019

Gocić, M., Motamedi, S., Shamshirband, S., Petković, D., Ch, S., Hashim, R., & Arif, M.

(2015). Soft computing approaches for forecasting reference evapotranspiration.

Computers and Electronics in Agriculture, 113, 164–173.

https://doi.org/10.1016/j.compag.2015.02.010

Guven, A., Aytek, A., Yuce, M. I., & Aksoy, H. (2008). Genetic Programming-Based

Empirical Model for Daily Reference Evapotranspiration Estimation. CLEAN - Soil, Air,

Water, 36(10–11), 905–912. https://doi.org/10.1002/clen.200800009

Haciismailoglu MC, Kucuk I, Derebasi N (2009) Prediction of dynamic hysteresis loops of

nano-crystalline cores. Expert Syst Appl 36:2225–2227

17

Hargreaves GH and Samani ZA (1985) Reference crop evapotranspiration from temperature.

Appl. Eng. Agr. 1:96–99. Doi:10.13031/2013.26773

Kisi O (2007) The potential of different ANN techniques in evapotranspiration modeling.

Hydrol Process. 22(14):2449–2460. Doi:10.1002/hyp.6837

Kumar M, Raghuwanshi NS, Singh R, Wallender WW and Pruitt WO (2002) Estimating

evapotranspiration using artificial neural network. J. Irrig Drainage E-ASCE. 128 (4):224–

232. Doi:10.1061/(ASCE)0733-9437(2002)128:4(224

Kumar M, Bandyopadhyay A, Raghuwanshi NS & Singh R (2008) Comparative study of

conventional and artifcial neural network-based ETo estimation models. Irrig Sci, 26:531–

545. Doi 10.1007/s00271-008-0114-3

Kumar M, Raghuwanshi NS and Singh R (2011) Artifcial neural networks approach in

evapotranspiration modeling: a review. Irrig Sci (2011) 29:11–25. Doi :10.1007/s00271-

010-023 0-8

Laaboudi A, Mouhouche B and Draoui B (2012) Neural network approach to reference

evapotranspiration modeling from limited climatic data in arid regions. Int J Biometeorol

(2012) 56:831–841. DOI:10.1007/ss00484-011-0485-7

Ladlani I, Houichi L, Djemili L, Heddam S and Belouz K (2012) Modeling daily reference

evapotranspiration (ET0) in the north of Algeria using generalized regression neural

networks (GRNN) and radial basis function neural networks (RBFNN): a comparative

study, Meteorol Atmos Phys (2012) 118:163–178. Doi:10.1007/s00703-012-0205-9

Leahy P, Kiely G & Corcoran G (2008) Structural optimization and input selection of an

artificial neural network for river level prediction. J Hydrol 355:192–201. Doi:

10.1016/j.jhydrol.2008.03.017

18

Lin F and Chen LH (2004) A Non-Linear Rainfall-Runoff Model Using Radial Basis

Function Network,” Journal of Hydrology, Vol. 289, No. 1-4, pp. 1-8.

Doi: 10.1016/j.jhydrol.2003.10.015

Makkink GF (1957) Testing the Penman formula by means of lysimeters. J. Inst. Water Eng.

11 (3), 277–288.

Mohawesh OE (2011) Artificial neural network for estimating monthly reference

evapotranspiration under arid and semi-arid environments, Archives of Agronomy and Soil

Science, Doi:10.1080/03650340.2011.603126

Marti P, González-Altozano P, López-Urrea R. & Mancha LA & Shiri J (2015) Modeling

reference evapotranspiration with calculated targets. Assessment and implications.

Agricultural Water Management 149:81-90. Doi: 10.1016/j.agwat.2014.10.028

Moriasi, D.N., Arnold, J.G., Van Liew, M.W., Bingner, R.L., Harmel, R.D. , Veith, T.L.,

2007. Model evaluations guidelines forsystematic quantification of accuracy in watershed

simulations. Trans. of the ASABE. 50(3), 885-900.

Nairizi S. (Eds.) 2017. Irrigated Agriculture Development under Drought and Water Scarcity

Irrigated Agriculture Development under Drought and Water Scarcity. International

Commission on Irrigation and Drainage, India

Pandey, P. K., Nyori, T., & Pandey, V. (2017). Estimation of reference evapotranspiration

using data driven techniques under limited data conditions. Modeling Earth Systems and

Environment, 3(4), 1449–1461. https://doi.org/10.1007/s40808-017-0367-z

Petković, D., Gocic, M., Shamshirband, S., Qasem, S. N., & Trajkovic, S. (2016). Particle

swarm optimization-based radial basis function network for estimation of reference

evapotranspiration. Theoretical and Applied Climatology, 125(3–4), 555–563.

https://doi.org/10.1007/s00704-015-1522-y

19

Priestley CHB and Taylor RJ (1972) On the assessment of surface heat flux and evaporation

using large-scale parameters. Mon. Weather Rev. 100 (2), 81–92

RahimiKhoob A (2008) Comparative study of Hargreaves’s and artificial neural network’s

methodologies in estimating reference evapotranspiration in a semiarid environment. Irrig

Sci. 26:253–259. Doi: 10.1007/s00271-007-0090-z

Rahimikhoob, A. (2010). Estimation of evapotranspiration based on only air temperature data

using artificial neural networks for a subtropical climate in Iran. Theoretical and Applied

Climatology, 101(1–2), 83–91. https://doi.org/10.1007/s00704-009-0204-z

RahimiKhoob A (2014) Comparison between M5 Model Tree and NeuralbNetworks for

Estimating Reference Evapotranspiration in an Arid Environment. Water Resour Manage

28:657–669. Doi: 10.1007/s11269-013-0506-x

Rouzegari, N., Hassanzadeh, Y., & Sattari, M. T. (2019). Using the Hybrid Simulated

Annealing-M5 Tree Algorithms to Extract the If-Then Operation Rules in a Single

Reservoir. Water Resources Management, 33(10), 3655–3672.

https://doi.org/10.1007/s11269-019-02326-4

Sattari MT, Pal M, Yurekli K & Ünlukara A (2013a) M5 model trees and neural network

based modelling of ET0 in Ankara, Turkey. Turk J Eng Environ Sci 37:211–219.

Doi: 10.3906/muh-1212-5

Sattari, M. T., Mirabbasi, R., Sushab, R. S., & Abraham, J. (2017). Prediction of Level in

Ardebil Plain Using Support Vector Regression and M5 Tree Model. Groundwater.

https://doi.org/10.1111/gwat.12620

20

Sattari, M. T., Apaydin, H., & Shamshirband, S. (2020). Performance Evaluation of Deep

Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating

ETo by Using Limited Meteorological Variables. Mathematics, 8(6), 972.

https://doi.org/10.3390/math8060972

Shabani, S., Samadianfard, S., Sattari, M. T., Mosavi, A., Shamshirband, S., Kmet, T., &

Várkonyi-Kóczy, A. R. (2020). Modeling Pan Evaporation Using Gaussian Process

Regression K-Nearest Neighbors Random Forest and Support Vector Machines;

Comparative Analysis. Atmosphere, 11(1), 66. https://doi.org/10.3390/atmos11010066

Shiri J, Kisi Ö, Anderas G, López JJ, Nazemi AH and Stuyt LCPM (2012) Daily reference

evapotranspiration modeling by using genetic programming approach in the Basque

Country (Northern Spain, Journal of Hydrology 414–415 (2012) 302–316.

Doi:10.1016/j.jhydrol.2011.11.004.

Shiri J, Sadraddini A, Nazemi AH, Kisi O, Landeras G, Fakheri Fard A, Marti P (2014)

Generalizability of gene expression programming-based approaches for estimating daily

reference evapotranspiration in coastal stations of Iran. J Hydrol 508:1–11

Sudheer KP, Gosain AK and Ramasastri KS (2003) Estimating Actual Evapotranspiration

from Limited Climatic Data Using Neural Computing Technique. J. Irrig. Drain Eng.

129:214-218. Doi: 10.1061/~ASCE/0733-9437~2003!129:3~214

Sun G, Alstad K, Chen J, Chen S, Ford CR., Lin G, Zhang Z. 2011. A general predictive

model for estimating monthly ecosystem evapotranspiration. Ecohydrology. 4(2): 245–

255. doi:10.1002/eco.194

Thornthwaite, C.W., 1948. An approach toward a national classification of climate. Geogr.

Rev. 38 (1), 55–94.

21

Thorp, K.R., Marek, G.W., DeJonge, K.C., Evett, S.R., Lascano, R.J. 2019. Novel

methodology to evaluate and compare evapotranspiration algorithms in an agroecosystem

model. Environmental Modelling & Software 119, 214-227. DOI:

10.1016/j.envsoft.2019.06.007

Traore S, Guven A (2013) New algebraic formulations of evapotranspiration extracted from

gene-expression programming in the tropical seasonally dry regions of West Africa. Irrig

Sci 31(1):1–10

Wang S., Fu Z, Chen H, Nie Y & Wang K (2015) Modeling daily reference ET in the karst

area of northwest Guangxi (China) using gene expression programming (GEP) and

artificial neural network (ANN). Theor Appl Climatol. Doi: 10.1007/s00704-015-1602-z

Wen, X., Si, J., He, Z., Wu, J., Shao, H., & Yu, H. (2015). Support-Vector-Machine-Based

Models for Modeling Daily Reference Evapotranspiration With Limited Climatic Data in

Extreme Arid Regions. Water Resources Management, 29(9), 3195–3209.

https://doi.org/10.1007/s11269-015-0990-2

Wu, L., Peng, Y., Fan, J., & Wang, Y. (2019). Machine learning models for the estimation of

monthly mean daily reference evapotranspiration based on cross-station and synthetic data.

Hydrology Research, 50(6), 1730–1750. https://doi.org/10.2166/nh.2019.060

Figures

Figure 1

Lower Cheliff Plain situation

Figure 2

Automatic meteorological station of Hmadna

Figure 3

MLP architecture

Figure 4

RBF architecture

Figure 5

General GEP model implementation and general structure (Shiri et al., 2012).

Figure 6

Performance of the best performing FFNN M2 model for both training and testing stages

Figure 7

Performance of the optimum combination of inputs based best model FFNN M11 model for both trainingand testing stages

Figure 8

Performance of the best performing RBF-NN M5 model for both training and testing stages

Figure 9

Performance of the optimum combination of inputs based best model RBF-NN M11 model for bothtraining and testing stages

Figure 10

Performance of the optimum combination of inputs/ best input combination based model GEP M11model for both training and testing stages

Figure 11

Scatter plot among observed and predicted values using best input combination based models usingtesting data set

Figure 12

Box Plot for best performing models.

Figure 13

Taylor diagram for best performing models.

Figure 14

Scatter plot among observed and predicted values using optimum input combination based modelsusing testing data set

Figure 15

Box Plot for best performing optimum number of input combination based models.

Figure 16

Taylor diagram for best performing optimum number of input combination based models