Water Resour Manage (2014) 28:99–113 DOI 10.1007/s11269-013-0474-1

Estimation of Monthly Mean Reference Evapotranspiration in Turkey Hatice Citakoglu & Murat Cobaner & Tefaruk Haktanir & Ozgur Kisi Received: 18 December 2012 / Accepted: 5 November 2013 / Published online: 22 November 2013 # Springer Science+Business Media Dordrecht 2013

Abstract Monthly mean reference evapotranspiration (ET0) is estimated using adaptive network based fuzzy inference system (ANFIS) and artificial neural network (ANN) models. Various combinations of long-term average monthly climatic data of wind speed, air temperature, relative humidity, and solar radiation, recorded at stations in Turkey, are used as inputs to the ANFIS and ANN models so as to calculate ET0 given by the FAO-56 PM (PenmanMonteith) equation. First, a comparison is made among the estimates provided by the ANFIS and ANN models and those by the empirical methods of Hargreaves and Ritchie. Next, the empirical models are calibrated using the ET0 values given by FAO-56 PM, and the estimates by the ANFIS and ANN techniques are compared with those of the calibrated models. Mean square error, mean absolute error, and determination coefficient statistics are used as comparison criteria for evaluation of performances of all the models considered. Based on these evaluations, it is found that the ANFIS and ANN schemes can be employed successfully in modeling the monthly mean ET0, because both approaches yield better estimates than the classical methods, and yet ANFIS being slightly more successful than ANN. Keywords ANFIS . ANN . Hargreaves . Ritchie . Evapotranspiration . Modelling 1 Introduction For water resources engineering problems related to soil water budget and determination of irrigation water demand, calculation of reference evapotranspiration (ET0) with a reasonable H. Citakoglu : M. Cobaner (*) : T. Haktanir Civil Engineering Department, Erciyes University, 38039 Kayseri, Turkey e-mail: [email protected] H. Citakoglu e-mail: [email protected] T. Haktanir e-mail: [email protected] O. Kisi Canik Basarî University, Samsun, Turkey e-mail: [email protected] M. Cobaner Erciyes University, Tomarza Mustafa Akincioglu Vocational Collage, Kayseri, Turkey

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accuracy is very important. Because evaporation and transpiration occur simultaneously, there is no easy way of distinguishing between the two processes (Allen et al. 1998). Evaporation, passage of water from liquid to gaseous state, takes place from open water body surfaces, like lakes and rivers, and also from wet ground surfaces and vegetation. Water molecules in the plant tissues evaporate from surfaces of leaves by a process called transpiration. Evapotranspiration is the total water transferred to the air from a field of vegetation by both transpiration from the existing plantation and evaporation from the surface of the underlying soil (McCuen 2004). Reference evapotranspiration (ET0) is the amount of evapotranspiration which will take place from a field of standard grass whose soil is saturated close to its field capacity. Once ET0 is known, the evapotranspiration of any other plant, whether cultivated or natural, is easily calculated as a function of ET0, because relationships between transpirations of many plants and that from grass are already determined with high precision as a result of century-old experimental research. Many empirical or semi−empirical equations have been developed for estimating ET0 as a function of meteorological data. Both the United Nations Food and Agriculture Organization (FAO) and the World Meteorological Organization (WMO) recommend the Penman–Monteith (PM) model as the standard method of calculating ET0. The PM method indeed gives highly accurate estimates for ET0, but it requires detailed meteorological data. The recent version of this method is known as the FAO-56 PM model as described in the FAO’s Irrigation and Drainage Paper No. 56 (Allen et al. 1998). Some comparison studies strongly suggest that the PM equation be preferred to other empirical models (e.g., Jensen et al. 1990). On the other hand, because it is a physically based causal model, the FAO–56 PM method requires quite a few climatic parameters as independent variables, such as daily maximum temperature (Tmax), daily minimum temperature (Tmin), solar radiation (Rs), relative humidity (RH), and wind speed (U2). And, necessitating so many data is a serious shortcoming of this method, simply because records of such weather variables are often incomplete or not always available for many locations. Therefore, although highly accurate, the FAO–56 PM model cannot be used for sites where sufficient or reliable data are not available, and in those cases the Hargreaves equation can be used as suggested, for example, by Allen et al. (1998). In the past decades, the artificial neural network (ANN) approach has been used to model reference evapotranspiration (e.g., Kumar et al. 2002; Sudheer et al. 2003; Trajkovic et al. 2003; Kisi 2006a, b, 2007; Rahimikhoob 2008, 2010). A comprehensive review of ANN applications in evapotranspiration modeling can be seen in Kumar et al. (2011), who showed that most of the developed models generally depend on a few meteorological stations having recorded weather data for a certain time period. For ET0 estimation, it is not practical to train ANNs for every station in a large region, and therefore, it is necessary to develop regional ANN models using data from many stations. And, application of soft computing techniques to many meteorological stations and different climatic conditions on modeling evapotranspiration is limited in the literature. Dai et al. (2009) developed ANN models for ET0 in three different climatic areas with 40, 60, and 35 stations in arid, semi-arid, and sub-humid climate areas, respectively, in north of China using the available climatic data at all those stations. They compared the models with respect to different input combinations and different climatic conditions. In their study, they used the monthly average values of 30–year–long records (1970–2000) for every climate factor for training and testing the ANN models (Dai et al. 2009). ANFIS provides an efficient way of handling the uncertainty for complex systems lacking sufficient data or having vague information (Ross 1995; Cox 1999). However, the application of the ANFIS technique to evapotranspiration modeling is limited in the literature. Kisi and Ozturk (2007) investigated the accuracy of ANFIS for modeling of ET0 obtained using the standard FAO–56 PM equation. Dogan (2009) examined the potential of ANFIS in ET0 estimation. He also determined the degree of effectiveness of the climatic variables on ET0.

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Cobaner (2011) investigated the potential use of ANFIS models in estimation of ET0 whose inputs were the solar radiation and air temperature. Based on the RMSE values, Cobaner (2011) concluded that the ANFIS model performed better than the temperature-based ANN, Hargreaves, Ritchie methods and their calibrated versions. Its accuracy was found to be better than the CIMIS Penman method (Snyder and Pruitt 1985) and its calibrated version, also, whose input parameters were solar radiation, air temperature, relative humidity, and wind speed (Cobaner 2011). Recently, the genetic programming and wavelet transform techniques have been applied to evapotranspiration modeling. Traore and Guven (2012, 2013) used the genetic programming scheme for ET0 modeling in Burkina Faso. The results showed that the models developed by genetic programming can be alternative formulae to those of Hargreaves and Blaney-Criddle in Burkina Faso. Cobaner (2013) investigated the accuracy of the wavelet transform algorithm based on discrete wavelet transform and linear regression techniques for conversion of Class A pan evaporation to reference evapotranspiration at weather stations of Fresno and Bakersfield in California. The results of the developed models were compared with those of three panbased equations, namely the FAO-24 pan (Doorenbos and Pruitt 1977), Snyder ET0 (Snyder et al. 2005) and Ghare ET0 (Ghare et al. 2006) equations and their calibrated versions with FAO–56 PM model. He concluded that the wavelet regression technique is a promising alternative approach to estimate reference evapotranspiration based on Class A pan evaporation data in calculation of irrigation schedules. In the current study, the long-term monthly mean solar radiation (Rs), air temperature (AT), relative humidity (RH), and wind speed (U2) obtained from 275 stations in Turkey, are used as inputs to ANFIS and ANN models to estimate the monthly mean ET0 given by the FAO–56 PM equation. Root mean squared error (RMSE), mean absolute error (MAE), and determination coefficient (R2) statistics are used as evaluation criteria. In the first part of the study, various input combinations of the climatic variables are investigated using ANFIS and ANN models, and the best combination is selected according to the comparison criteria. In the second part, the results of the ANFIS and ANN models are compared with those of two empirical models, which are those by Hargreaves (Hargreaves and Samani 1985) and Ritchie (Jones and Ritchie 1990).

2 Adaptive Network Based Fuzzy Inference System Both ANN and fuzzy logic are implemented in a complementary way in an ANFIS model. Coupling of ANN with fuzzy logic provides acceleration of execution time, reduction in error tolerance, and improvement in adaptation. These combined models are able to solve problems having widely variable structures in a more efficient way than the sole ANN model. ANFIS consists of six layers, which are briefly summarized in the following. 1

Input layer: All input signals received from every node at this layer are transferred to the proceeding layers. 2. Fuzzification layer: The output of every node here consists of membership degrees which are dependent on input values and on the used membership function. The membership degrees resulting from the second layer are symbolized as μAj(X1) and μCj(X2). 3. Rules layer: The Sugeno fuzzy logic rules (Takagi and Sugeno 1985) and numbers are used at this layer as summarized below. μ1 ¼ μ A j  μ C j

ð1Þ

4. Normalization layer: All the values coming from the third layer are taken as input values by this layer which computes the normalized value of every rule. The

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outputs of this layer are called the firing level. The normalized firing level ðμι Þ is computed by Eq. (2) below. μ1 ¼

μ1 μ1 þ μ 2 þ μ 3 þ μ 4

ð2Þ

5. Defuzzification layer: The weighted output values of the rules given at each node are computed at this layer by Eq. (3) below. Ni ¼ μ1 ðp1 X1 þ q1 X2 þ r1 Þ

ð3Þ

Here, the coefficients of Xi’s are referred to as the result parameters. 6. Summation (output) layer: The final output, which is formed as the summation of all signals coming from all of the nodes, is computed at this layer by Eq. (4) below. y¼

n X

μi ½pi X1 þ qi X2 þ ri 

ð4Þ

i¼1

3 Artificial Neural Network (ANN) Generally, the configuration of a multi-layer feed-forward neural network consists of many layers where each layer represents a set of parallel processing units (or nodes). The three-layer ANN structure used in this study contains only one intermediate (hidden) layer. Although a multi-layer ANN can have more than one hidden layers, many relevant studies so far have shown that a single hidden layer is sufficient for most problems. Nodes of the hidden layer allow the network to detect and capture the relevant patterns in the data and to create a complex non-linear mapping between input and output variables. The nodes of the input layer perform the sole task of relaying the external inputs to the neurons of the hidden layer. Hence, there are as many input nodes as the number of input variables. The final output of the network is produced by the last (output) layer after having received the outputs of the hidden layer. If there are too few hidden nodes allocated, then this too small network will have difficulty in learning the data, and conversely, a too complex network will have a poor generalization capability because it will tend to over-fit the training samples. Because there is not a formal method of determining the optimum number of hidden nodes prior to training, finding a model which accurately predicts the output with a parsimonious number of hidden nodes is critical in configuring an ANN structure. Therefore, as we also have done herein, the trial-and-error method is resorted to in designing an ANN model (e.g., Tokar and Johnson 1999). Detailed theoretical information about ANN can be found in Haykin (1998).

4 Case Study In the present study, ANFIS and ANN models are applied to long-term monthly mean climatic data of Turkey, which are obtained from the General Directorate of Turkish State Meteorological Service (TSMS). The long-term monthly mean climatic data records having lengths between 20 and 45 years at 275 stations scattered all over

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Turkey covering an area of about 800 thousand km2 are used. This geographical area is bounded between the longitudes of 26° and 45° E and the latitudes of 36° and 42° N. Temperature variation in the region is high due to the rough topographical terrain of Anatolian Peninsula surrounding the large inland plateau. The minimum temperature is recorded as –42.8 °C at Agri station in the northeast, while the maximum temperature is recorded as +46.8 °C at Sanliurfa station in the southeast. The average annual pan evaporation varies between 435 and 2,800 mm/year. The overall climate of the study area is semi-arid and the annual precipitation ranges from 318 mm/year at Konya in Central Anatolia up to 2,245 mm/year at Rize in the north at the seaward side of the Black Sea Mountains. The annual average precipitation of Turkey is 643 mm/year (TSMS 2012). Figure 1 shows the distribution of the gauging stations in the study area. Monthly mean statistical parameters of the climatic data and the ET0 values computed by the FAO–56 PM method using these data are shown in Table 1. Distributions of both the relative humidity and wind speed data are observed to show high skewnesses both for training and test phases. Although each data set has similar statistical peculiarities in general, the magnitudes of the kurtosis coefficient of relative humidity and wind speed being 0.07 and 3.28, and 1.06 and 1.51 in the training and testing stages, respectively, may cause difficulties in estimating the high ET0 values because of these wide differences.

5 Physically-Based (Causal) Models Many empirical equations are available for calculating the reference evapotranspiration (ET0) as a function of one or more climatic factors. The Food and Agricultural Organization (FAO) and the International Commission for Irrigation and Drainage (ICID) of the United Nations both have recommended the FAO–56 PM equation as the standard model for estimating ET0 and further recommended it as the reference for assessing other methods (Allen et al. 1994). Accordingly in this study also, the results of the Hargreaves (Hargreaves and Samani 1985), and Ritchie (Jones and Ritchie 1990) methods are compared with those of the FAO–56 PM

Fig. 1 Locations of the gauging stations ((white circle): stations used in training; (black circle): stations used in testing)

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Table 1 Statistical parameters of input and output variables for each data set Data set Training

Variable

Csx

Ck

xmaks

xmin

Range

Solar Radiation, ly/day

26.805

0.328

−0.17

−1.39

42.913

10.732

32.181

Air temperature, °F

12.784

0.680

−0.11

−0.79

34.400

−10.700

45.100

Relative humidity, %

63.745

0.167

−0.66

0.07

86.000

27.400

58.600

2.068 8.726

0.420 0.405

1.30 −0.06

3.28 −1.15

7.400 17.949

0.400 1.935

7.000 16.014

Wind speed, mi/hr FAO 56 PM ET0, mm/day Testing

Cv

xort

Solar radiation, ly/day

26.450

0.332

−0.15

−1.37

40.691

10.395

30.296

Air temperature, °F

14.222

0.606

−0.18

−0.62

32.900

−11.300

44.200 58.000

Relative humidity, %

64.262

0.166

−0.99

1.06

83.400

25.400

Wind speed, mi/hr

1.951

0.358

1.04

1.51

4.600

0.500

4.100

FAO 56 PM ET0, mm/day

8.705

0.395

−0.08

−1.14

16.553

2.062

14.491

Cv variation coefficient, Csx skewess coefficient, Ck kurtosis coefficient

method. Hence, it is deemed appropriate herein to give a brief summary of these methods in the following. 5.1 FAO–56 PM (Penman-Monteith) Method The FAO-56 PM method is fully described in paper #56 by FAO (Allen et al. 1998). The equation to compute ET0 is: ET 0 ¼

900 U2 ðea −ed Þ T þ 273 Δ þ γð1 þ 0:34U 2 Þ

0:408ΔðRn −GÞ þ γ

ð5Þ

where, ET0 is reference evapotranspiration in (mm day−1), Δ is slope of the saturation vapor pressure function at air temperature T in (kPa °C−1), Rn is net solar radiation in (MJ m−2day−1), G is soil heat flux density in (MJ m−2 day−1), γ is psychometric constant in (kPa °C−1), T is mean air temperature in (°C), U2 is average 24-hour wind speed at 2 m height above ground surface in (m s−1), ea is saturation vapor pressure in (kPa), and ed is actual vapor pressure in (kPa). Trajkovic and Kolakovic (2009) examined the potential of FAO-56 PM equation in estimating ET0 under humid conditions where weather data were limited, and they concluded that the minimum and maximum air temperatures and local wind speed were the minimum data requirements to successfully use the FAO-56 PM equation under humid conditions. 5.2 Hargreaves Method The Hargreaves equation is one of the most accurate equations to calculate ET0 while having a simple analytical expression (Jensen et al. 1997; Zhai et al. 2009), which is (Hargreaves and Samani 1985), which is:   pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T max þ T min ð6Þ ET 0 ¼ ð0:0023ÞRa þ 17:8 T max −T min 2 where, ET0 is reference evapotranspiration in (mm day−1), Tmax and Tmin are maximum and minimum air temperatures in (°C), and Ra is extraterrestrial radiation in (mm day−1).

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5.3 Ritchie Method ET0 by the Ritchie method, as described by Jones and Ritchie (1990) is computed by:   ET 0 ¼ α1 3:87  10−3 Rs ð0:6T max þ 0:4T min þ 29Þ

ð7Þ

where, ET0 is reference evapotranspiration in (mm day−1), Tmax and Tmin are maximum and minimum air temperatures in (°C), and Rs is solar radiation in (MJ m−2 day−1). α1 in this equation is computed as a function of Tmax by: 9 α1 ¼ ð0:01Þ⋅exp½ð0:18Þ⋅ðT max þ 20Þwhen T max < 5 C = α1 ¼ 1:1 when 5 C < Tmax < 35 C ; α1 ¼ 35 C < T max

ð8Þ

6 Applications and Results In the current study, the data of the monthly mean solar radiation (Rs), air temperature (T), relative humidity (RH), and wind speed at 2 m above the ground surface (U2) measured at 275 stations in Turkey are used as inputs to ANFIS and ANN models to estimate the values of reference evapotranspiration (ET0) given by the FAO–56 PM equation. Root mean squared error (RMSE), mean absolute error (MAE), and determination coefficient (R2) are used as evaluation criteria. R2 measures the degree to which two variables are linearly related. RMSE and MAE provide different types of information about the prediction ability of the models. RMSE indicates the goodness–of–fit relevant to high values whereas MAE yields a more balanced perspective of the goodness–of–fit at moderate values (Karunanithi et al. 1994). The RMSE and MAE used in this study are defined as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X  2 ð9Þ ET 0measured;i −ET 0predicted;i RMSE ¼ t N i¼1

MAE ¼

N  1 X  ET 0measured;i −ET 0predicted;i  N i¼1

ð10Þ

where, N is the number of data, ET0measured,i is the standard ET0 value of the i’th station computed by the FAO–PM equation and ET0predicted,i is ET0 value of the i’th station computed by one of the models considered herein. Next, two different applications are employed. First, various input combinations are investigated using ANFIS and ANN models, and the best combination is selected according to the comparison criteria. And, in the second, the accuracy of the ANN and ANFIS models are compared with those of the empirical models, which are Hargreaves and Ritchie methods. In the first part of the study, different input combinations including various monthly mean climatic data, which are: solar radiation (SR), air temperature (AT), relative humidity (RH), and wind speed (U2), are used in ANN and ANFIS models to estimate the reference evapotranspiration (ET0). The available data consisting of 36 years (1974–2010) are separated into two parts as training and testing data sets. The training set includes the randomly chosen 2,640 data records, which is 80% of the total data. In order to make more reliable comparisons, the

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Table 2 RMSE, MAE, and R2 statistics of ANFIS models in training and testing phases Input combinations

Membership function Input

Output

Number of Epoch Training set membership function MAE RMSE R2

Testing set MAE RMSE R2

i.

SR

Trimf

Lineer

5

1

0.977

1.583 0.873 0.906

1.358 0.886

ii.

AT

Trimf

Lineer

5

1

1.594

3.731 0.701 1.646

4.001 0.678

iii. iv.

RH U2

Trimf Trimf

Constant Lineer

3 5

3 1

2.192 7.236 0.420 2.274 7.381 0.377 2.939 11.430 0.083 2.882 11.033 0.064

v.

SR and AT

Gaussmf Lineer

3

5

0.593

0.613 0.951 0.538

vi.

SR, AT, and RH Trimf

Lineer

2

1

0.603

0.631 0.949 0.543

0.489 0.960

Trimf

Lineer

3

5

0.356

0.211 0.980 0.366

0.235 0.980

viii. SR, AT, RH, and U2 Gaussmf Lineer

2

1

0.334

0.187 0.985 0.345

0.198 0.985

vii. SR, AT, and U2

0.486 0.960

models are evaluated by the testing data set which is not used during the training phase. The testing set consists of the remaining 660 data records, which is 20% of the total data. In order to investigate the effect of monthly mean climatic data on ET0, each input variable, which are: (i) SR, (ii) AT, (iii) RH, (iv) U2, is used to estimate ET0, one by one, and, the degree of effect of each variable on ET0 is evaluated with respect to the reduction in error statistics. Next, four additional combinations are generated as: (v) SR and AT; (vi) SR, AT, and RH; (vii) SR, AT, and U2; and (viii) SR, AT, RH, and U2. The output layer has one neuron for the monthly mean value of ET0. The optimum ANFIS and ANN structures used for each input combination are given in Tables 2 and 3. Optimum membership functions are found for the ANFIS inputs and output by trial and error. As can be seen from Table 2, the triangular and linear membership functions are found to be optimal for the inputs and output, respectively. For the ANN models (Table 3), by trial and error, the number of nodes in the hidden layer is varied between 1 and 6. For example, ANN(4,6,1) comprises four input nodes, six hidden nodes, and one output node, as the input layer has

Table 3 RMSE, MAE and R2 statistics of ANN models in training and testing phases Input combinations

Activation functions Hidden Output layer layer

Training set Number of hidden layer units MAE RMSE

Testing set R2

MAE

RMSE

R2

i.

SR

Tansig

Pureline

1

1.002

1.652

0.868

0.934

1.419

0.881

ii.

AT

Tansig

Pureline

1

1.603

3.745

0.700

1.656

4.033

0.676

iii.

RH

Tansig

Pureline

1

2.190

7.117

0.429

2.294

7.408

0.375

iv.

U2

Tansig

Pureline

4

2.962

11.581

0.071

2.907

11.171

0.053

v.

SR and AT

Tansig

Pureline

5

0.740

0.950

0.924

0.651

0.725

0.939

vi. vii.

SR, AT and RH SR, AT and U2

Tansig Tansig

Pureline Pureline

6 6

0.749 0.648

0.993 0.741

0.920 0.941

0.682 0.639

0.787 0.709

0.934 0.940

viii.

SR, AT, RH and U2

Tansig

Pureline

6

0.555

0.527

0.958

0.553

0.507

0.957

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SR, AT, RH, and U2, and the output layer consists of ET0. Training of ANN is terminated after 50,000 iterations. In the hidden and output layers, the tangent and logarithmic sigmoid and linear transfer functions are used, respectively. The estimation results of the ANN and ANFIS models by means of RMSE, MAE, and R2 statistics are given in Tables 2 and 3, which indicate that the ANN and ANFIS models comprising only U2 (input combination (iv)) perform the worst. However, adding wind speed into the input combination (input combinations (vii) and (viii)) increases the models’ performances. This may be due to the advection effect of U2 on ET0. Kisi (2006a) also found similar results, which indicated that adding wind speed into the solar radiation, air temperature, and relative humidity inputs increased the model performance a little bit. Similarly, in this study, adding wind speed into the input combination (v) whose inputs are solar radiation and air temperature slightly increase the model performance by reducing RMSE and MAE by 52% and 32% and increasing R2 by 2% for the weather stations of Turkey. Among the four variables considered in this study, the solar radiation (SR) has turned out to be the most effective one in estimation of ET0. It can be seen from Tables 2 and 3 that the ANN and ANFIS models having SR, AT, RH, and U2 altogether as input variables yield the lowest RMSE’s (0.198 and 0.507). According to the test results, the ANFIS models give slightly better estimation than the ANN models. In the second part of the study, the results by the ANFIS and ANN models are compared with the results of two empirical models, which are Hargreaves (Hargreaves and Samani 1985) and Ritchie (Jones and Ritchie 1990) methods. Aside from their original forms, these two empirical models are also calibrated based on the training data using the standard ET0’s given by the FAO-56 PM equation. Allen et al. (1998) recommend that the empirical formulas be calibrated using the standard FAO–56 PM method by determining the empirical coefficients of a and b as defined below: ET 0 ðPMÞ ¼ a þ b⋅ðET 0 Þ

ð11Þ

where, ET0 (PM) is the reference evapotranspiration calculated by FAO–56 PM equation, and ET0 is the reference evapotranspiration estimated by another method. The a and b coefficients calibrated by Eq. (11) are 2.3856 and 1.2327 for Hargreaves equation, and 2.6117 and 1.0285 for Ritchie equation, respectively. As mentioned before, the Hargreaves and Ritchie methods require only two meteorological variables, SR and AT. The FAO-56 PM method is a physically based, more comprehensive

Table 4 Magnitudes of evaluation statistics for each model Model

Model inputs

MAE

RMSE

R2

Hargreaves

SR, AT

3.408

12.744

0.930

CAL_ Hargreaves Ritchie

SR, AT SR, AT

0.742 2.602

0.881 7.986

0.930 0.881

CAL_ Ritchie

SR, AT

1.509

0.953

0.881

ANFIS1

SR, AT, RH, and U2

0.345

0.198

0.985

ANFIS2

SR, AT

0.538

0.486

0.960

ANN1

SR, AT, RH, and U2

0.553

0.507

0.957

ANN2

SR, AT

0.651

0.725

0.939

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Table 5 The estimated ET0 amounts (mm year-1) in the test phase Region of Central Anatolia Empirical models FAO-56 PM 71 Relative error (%)

Hargreaves 39

CAL_Hargreaves 68

Ritchie 45

CAL_Ritchie 68

−45.07

−4.22

36.62

−4.22 ANN2

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

71

71

70

70

71

Relative error (%)

0.00

−1.41

−1.41

0.00

Region of Eastern Anatolia FAO-56 PM

Empirical models Hargreaves

CAL_Hargreaves

Ritchie

CAL_Ritchie

66

37

64

43

65

−43.94

−3.03

−34.85

−1.51 ANN2

Relative error (%)

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

66

67

67

67

69

Relative error (%)

1.51

1.51

1.51

4.54

Region of Southeast Anatolia Empirical models FAO-56 PM

Hargreaves

CAL_Hargreaves

Ritchie

CAL_Ritchie

66

40

66

49

69

Relative error (%)

−39.39

0.00

−25.75

4.54 ANN2

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

66

66

66

66

64

0.00

0.00

0.00

−3.03

Relative error (%) Region of Black Sea

Empirical models FAO-56 PM

Hargreaves

CAL_Hargreaves

Ritchie

CAL_Ritchie

66

41

70

46

68

Relative error (%)

−37.80

6.06

−30.30

3.03

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

ANN2

66 Relative error (%)

64 −3.03

65 −1.51

67 1.51

67 1.51

Region of Mediterranean Empirical models FAO-56 PM

Hargreaves

CAL_Hargreaves

Ritchie

CAL_Ritchie

71

46

76

53

75

Relative error (%)

−35.21

7.04

−25.35

5.63

Artificial intelligence models FAO-56 PM 71

ANFIS1 71

ANN1 70

ANFIS2 74

ANN2 72

Relative error (%)

0.00

−1.41

4.22

1.41

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Table 5 (continued) Region of Marmara Empirical models FAO-56 PM 68

Hargreaves 43

CAL_Hargreaves 72

Ritchie 50

CAL_Ritchie 72

Relative error (%)

−36.76

5.88

−26.47

5.88 ANN2

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

68

68

68

70

70

Relative error (%)

0.00

0.00

2.94

2.94

Region of Agean FAO-56 PM

Empirical models Hargreaves

CAL_Hargreaves

Ritchie

CAL_Ritchie

73

45

75

53

75

Relative error (%)

−38.36

2.74

−27.40

2.74 ANN2

Artificial intelligence models FAO-56 PM

ANFIS1

ANN1

ANFIS2

73

73

73

73

71

Relative error (%)

0.00

0.00

0.00

−2.74

approach which requires two more parameters than the others. So, ANFIS2 and ANN2 models, whose input variables are SR and AT (input combination (v)), are compared with the Hargreaves and Ritchie models, and with their calibrated versions, which are denoted as CAL_Hargreaves and CAL_Ritchie. The RMSE, MAE, and R2 statistics of four- and twoinput-variable ANFIS1 and ANN1 models in estimating ET0 are given in Tables 4. As can be seen from Table 4, the ANFIS and ANN models have superior performance as compared to the Hargreaves and Ritchie models and their calibrated versions. It can be clearly seen from Table 4 that additional meteorological variables (RH and U2) significantly increase the estimation accuracy. In the test phase, this yields a reduction in the RMSE (by 30% and 60%), a reduction in the MAE (by 15% and 36%) and an increase in R2 (by 1.8% and 2.5%) for the ANFIS1 and ANN1 models, respectively. Table 4 also reveals that calibrating the empirical models significantly increases their accuracy. It can be concluded from Tables 4 and 5 that the ANFIS models are superior to the ANN and to the empirical models. Among the two parameter empirical models, the CAL_Hargreaves model performs better than the CAL_ Ritchie model. The ET0 estimates of each model for stations in Turkey are presented in Figs. 2 and 3 in the form of scatter plots. It is obvious from R2’s of the fitted lines in the scatter plots and from the visual inspection of the scatter plots that the ANFIS1 estimates are closer to the observed ET0 values than those of the other models. It can be seen from the scatter plots that the estimates by the four–parameter ANFIS1 and ANN1 models are less scattered relative to the two-parameter models (Fig. 2). Among the empirical models, the CAL_Hargreaves model performs better than the others. The comparison of the ANFIS, ANN, and empirical models for estimation of ET0 amounts at seven different geographical regions of Turkey is given in Table 5. It is clear from this table that the ANFIS and ANN models give better estimates than those

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Fig. 2 ET0 estimated by ANFIS and ANN versus ET0 given by the FAO-56 PM equation

of the empirical models, and yet the ANFIS model performs a little better than the ANN model. ANFIS1 model catches the total FAO-56 PM ET0 values in five regions, Central Anatolia, Southeast Anatolia, Mediterranean, Marmara, and Aegean, while the ANN1 model catches in three regions, Southeast Anatolia, Marmara, and Aegean. Table 5 also indicates that calibrating empirical models significantly increases their accuracies in estimation of total ET0 amounts Overall, the ANFIS models are more accurate than the ANN, Hargreaves, and Ritchie models for the process of establishing a relationship between meteorological variables and ET0. The flexibility and capability of the ANN approach to model nonlinear relationships are the known advantage of them. A special ASCE Task Committee defines ANN as a universal approximator (ASCE Task Committee 2000). In recent times, modeling of nonlinear input– output systems by the ANN technique has become a promising research area leading to results applicable by practitioners. On the other hand, the neuro-fuzzy (NF) models couple the transparent and linguistic representation of a fuzzy system with the learning ability of the ANN approach. Hence, the NF models can be trained to produce an input/output mapping of the ANN model with an additional advantage of being able to provide the set of rules on which the model is based, which renders further insight into the modeled process (Sayed et al. 2003).

Estimation of Monthly Mean Reference Evapotranspiration in Turkey

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Fig. 3 ET0 estimated by the empirical models versus ET0 given by the FAO-56 PM equation

7 Conclusions The following conclusions can be drawn from this study:

&

& & &

The potential of ANFIS and ANN models for estimation of reference evapotranspiration (ET0) as a function of climatic variables is illustrated. The long-term monthly mean ET0 anywhere in Turkey can be successfully estimated by models developed using the ANN and ANFIS techniques. Both the ANFIS and ANN methods are superior to the classic Hargreaves and Ritchie methods in estimation of ET0. Yet, the ANFIS method slightly outperforms the ANN. Using only the wind speed as the input variable in ANFIS and ANN models is found to be insufficient for accurate estimation of ET0. Adding wind speed to the other input combinations, however, improve the estimation accuracy due to its advection effects on ET0. Using only the solar radiation as the input variable gives much better ET0 estimates than using the wind speed, relative humidity, and air temperature, individually. This result indicates the impact of solar radiation on ET0.

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The ANFIS model whose inputs are solar radiation, wind speed, relative humidity, and air temperature performs the best among the input combinations tried. This indicates that all these variables are needed for better ET0 estimations by the ANFIS model. Calibration is found to significantly increase accuracy of Hargreaves and Ritchie methods in estimating long-term monthly mean ET0.

Acknowledgments The authors wish to thank the Turkish State Meteorological Service (TSMS) for the supply of long-term monthly mean climatic variables.

References Allen RG, Smith M, Perrier A, Pereira LS (1994) An update for the calculation of reference evapotranspiration. ICID Bull 43(2):35–92 Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration guidelines for computing crop water requirements, FAO irrigation and drainage, paper no. 56. Food and Agriculture Organization of the United Nations, Rome ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000) Artificial neural networks in hydrology II: hydrologic applications. J Hydrol Eng ASCE 5(2):124–137 Cobaner M (2011) Evapotranspiration estimation by two different neuro-fuzzy inference systems. J Hydrol 398(3–4):292–302 Cobaner M (2013) Reference evapotranspiration based on Class A pan evaporation via wavelet regression technique. Irrig Sci 31:119–134 Cox E (1999) The fuzzy systems handbook, 2nd edn. Academic, California Dai X, Shi H, Li Y, Ouyang Z, Huo Z (2009) Artificial neural network models for estimating regional reference evapotranspiration based on climate factors. Hydrol Process 23:442–450 Dogan E (2009) Reference evapotranspiration estimation using adaptive neuro-fuzzy inference systems. Irrig Drain 58:617–628 Doorenbos J, Pruitt WO (1977) Crop water requirements. FAO ırrigation and drainage paper 24. FAO, Rome Ghare AD, Porey PD, Ingle RN (2006) Discussion of ‘Simplified estimation of reference evapotranspiration from pan evaporation data in California’ by Snyder, R. L., Orang, M., Matyac S., and Grismer, M. E. J Irrig Drain Eng 132(5):519–520 Hargreaves GH, Samani ZA (1985) Reference crop evapotranspiration from temperature. Appl Eng Agric 1(2): 96–99 Haykin S (1998) Neural networks—a comprehensive foundation, 2nd edn. Prentice-Hall, Upper Saddle River, pp 26–32 Jensen ME, Burman RD, Allen RG (1990) Evapotranspiration and irrigation water requirements. ASCE manuals and reports on engineering practices no. 70. ASCE, New York Jensen DT, Hargreaves GH, Temesgen B, Allen RG (1997) Computation of ET0 under nonideal conditions. J Irrig Drain Eng 123(5):394–400 Jones JW, Ritchie JT (1990) In: Hoffman GJ, Howel TA, Solomon KH (eds) ASAE monograph no.9. ASAE, St. Joseph, pp 63–89 Karunanithi N, Grenney WJ, Whitley D, Bovee K (1994) Neural networks for river flow prediction. J Comp Civ Eng ASCE 8(2):201–220 Kisi O (2006a) Evapotranspiration estimation using feed-forward neural networks. Nord Hydrol 37(3):247–260 Kisi O (2006b) Generalized regression neural networks for evapotranspiration modeling. Hydrol Sci J 51(6): 1092–1105 Kisi O (2007) Evapotranspiration modelling from climatic data using a neural computing technique. Hydrol Process 21:1925–1934 Kisi O, Ozturk O (2007) Adaptive neurofuzzy computing technique for evapotranspiration estimation. J Irrig Drain Eng ASCE 133(4):368–379 Kumar M, Raghuwanshi NS, Singh R, Wallender WW, Pruitt WO (2002) Estimating evapotranspiration using artificial neural network, ASCE. J Irrig Drain Eng 128(4):224–233

Estimation of Monthly Mean Reference Evapotranspiration in Turkey

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Kumar M, Raghuwanshi NS, Singh R (2011) Artificial neural networks approach in evapotranspiration modeling: a review. Irrig Sci 29(1):11–25 McCuen RH (2004) Hydrologic analysis and design, 3rd edn. Prentice-Hall, Upper Saddle River 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(3):253–259 Rahimikhoob A (2010) Estimation of evapotranspiration based on only air temperature data using artificial neural Networks for a subtropical climate in Iran. Theor Appl Climatol 101(1–2):83–91 Ross TJ (1995) Fuzzy logic with engineering applications. McGraw Hill Co., New York Sayed T, Tavakolie A, Razavi A (2003) Comparison of adaptive network based fuzzy inference systems and bspline neuro-fuzzy mode choice models. J Comput Civ Eng ASCE 17(2):123–130 Snyder R, Pruitt W (1985) Estimating reference evapotranspiration with hourly data. Chpt. VII. In: R. Snyder et al. (ed.) California irrigation management information system final report. Univ. of California-Davis. Land, air and water resources paper #10013 Snyder RL, Orang M, Matyac S, Grismer ME (2005) Simplified estimation of reference evapotranspiration from pan evaporation data in California. J Irrig Drain Eng 131(3):249–253 Sudheer KP, Gosain AK, Ramasastri KS (2003) Estimating actual evapotranspiration from limited climatic data using neural computing technique. ASCE J Irrig Draın Eng 129(3):214–218 Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132 Tokar AS, Johnson PA (1999) Rainfall-runoff modeling using artificial neural networks. J Hydrologic Eng 4(3): 232–239 Trajkovic S, Kolakovic S (2009) Estimating reference evapotranspiration using limited weather data. J Irrig Drain Eng 135(4):443–449 Trajkovic S, Todorovic B, Stankovic M (2003) Forecasting reference evapotranspiration by artificial neural networks. ASCE J Irrıg Draın Eng 129(6):454–457 Traore S, Guven A (2012) Regional-specific numerical models of evapotranspiration using gene-expression programming interface in Sahel. Water Resour Manag 26:4367–4380 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 31:1–10 TSMS (2012) Turkish state meteorological service, http://www.mgm.gov.tr/veridegerlendirme/yillik-toplamyagis-verileri.aspx Zhai L, Feng Q, Li Q, Xu C (2009) Comparison and modification f equations for calculating evapotranspiration (ET) with data from Gansu Province, Northwest China. Irrig Drain. doi:10.1002/ird.502