Artificial neural network estimation of ReferenceEvapotranspiration from pan evaporation in a semi-

arid environment

Veena JadejaCivil Engineering Dept., S.S.E.C.

Shantilal Shah Engineering CollegeBhavnagar, India

Email: veena_jadeja@yahoo.co.in

Abstract— The objective of this study was to test an artificial neural network (ANN) for converting pan evaporation data (Ep) to estimate reference evapotranspiration (ETo) as a function of the maximum and minimum temperature. The conventional method that uses Pan (Kp) as a factor to convert Ep to ETo, is also considered for the comparison. The ANN has been evaluated under semi-arid conditions in Sabarmati river of Gujarat State, comparing daily estimates against those from the FAO-56 Penman–Monteith equation (PM), which was used as standard. ANN method gave better estimates than the conventional that requires wind speed and humidity data.

Keywords- Neural Networks, evapotranspiration,relative humidity,wind speed, solar radiation,

I. INTRODUCTION

Evapotranspiration (ET) is an important component of the hydrologic cycle. In many watersheds, the return of moisture to the atmosphere through the process of ET is a large proportion of the input precipitation. Accurate estimation of reference evapotranspiration (ETo) is needed for water resources management, farm irrigation scheduling, and environmental assessment. Evaporation pans (class A pan, US Weather Bureau) are used extensively throughout the world to estimate ETo. Evaporation pan (Ep) provides a measurement of the combined effect of temperature, humidity, wind speed and solar radiation on the reference crop evapotranspiration. This measurement can successfully be used to estimate ET0 with a reasonable accuracy (Irmak et al. 2002). Numerous studies have shown that a high correlation between Ep and ET0 can be obtained when evaporation pans are properly maintained (Jensen et al. 1961; Doorenbos and Pruitt 1977; Irmak et al. 2002). Pan coefficient (Kp) is used as a factor to convert Ep into ET0. Tabulated values or equations are available in the literatures to determine Kp which use fetch distance around the pan (F) and climatic parameters such as wind speed at 2 m height (U2) and air relative humidity (RH). Unfortunately, in many irrigated areas, class A pans are installed without the necessary instrumentation to measure U2 and RH. Under this

condition, simplified methods, which require readily available climatic data, should be considered. Evaporation is a function of temperature, windspeed and humidity, all of which are interdependent. Wind changes the humidity and if the humidity is low, the evaporation rate is higher. At the same time, air temperature influences humidity and surface temperature. All thesefactors contribute to evaporation with temperature likely being the dominant factor influencing evaporation. Because of maximum and minimum air temperature can be easily recorded at most weather stations world-wide, so it is desirable to have a method that converts Ep data to estimateET0 based on temperature data. A method that can be used for this purpose is the artificial neural network (ANN). Artificial neural networks (ANNs) are effective tools to model nonlinear systems and require fewer inputs. According to Sudheer et al. (2003), the main advantage of ANN methods over conventional methods is the ability for solving problems which are difficult to formalize. Numerous reference ET equations have been developed and are being used, depending upon the availability of weather data. These equations range in sophistication from empirical solar radiation- or temperature based equations, to complex methods based on physical processes such as the combination method of Penman (1948). The combination approach links evaporation dynamics with the flux of net radiation and aerodynamic transport characteristics of a natural surface. Based on the observations that latent heat transfer in plant stems is influenced not only by these abiotic factors, Monteith (1965) introduced a surface conductance term that accounted for the response of leaf stomata to its hydrologic environment. This modified form of the Penman equation is widely known as the Penman–Monteith (PM) equation. In order to validate the developed model, a comparison was made between the model and the conventional method that uses Kp for converting Ep to ET0. FAO-24 (Doorenbos and Pruitt 1977) described a method to convert pan evaporation to ET0. This method adjusts the measured pan evaporation by a coefficient (Kp) to estimate ET0. In this study, the performance of both ANN and the

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conventional method were compared with the FAO-56 Penman–Monteith method (PM). The PM method is the standard procedure when there is no measured lysimeter data (Irmak et al. 2003; Utset et al. 2004; Gavilan et al. 2006). Although in practice the best way to test the performance of the above-mentioned methods would be to compare their performances against the lysimeter-measured data, this type of data set is not available in the study area.

II. STUDY AREA AND DATA AVAILABILITY

Daily measured weather data for an 8 year (from 2001 to 2008) of Sabarmati river were obtain from Dharoi dam. The climate in the study area is semi-arid with an average annual rainfall of 230 mm, approximately 80% of which occurs during June to September . The minimum and maximum air temperature range from 24 to 400C and 12 to 220C in summer and winter months, respectively. Daily mean relative humidity ranges from 13 to 92% with an annual average of 54%. The highest wind speed of approximately 259 km d-1 usually occurs in June. The meteorological data used in this study consisted of daily observations of maximum and minimum air temperature (Tmax and Tmin), daily mean relative humidity (RHmean), wind speed (U2), bright sunshine hours (n) and class A pan evaporation (EP). The days with inadequate data were removed from the patterns. The temperature data (Tmax and Tmin) and Ep data were adopted as input variables for the ANN. The basic form of the conventional method as described by FAO-24 (Doorenbos and Pruitt 1977) is ET0 = Kp x Ep. Values of Kp are function of RH, U2, and F and were first published by Jensen (1974) and subsequently tabulated by FAO-24. This study used original table FAO-24 to calculate daily values of Kp coefficient. In the Kp calculations, F was taken as 200 m since the weather station was surrounded by several hundred hectares of agricultural crops.

A. ANN Model Development

An ANN has the ability to learn from examples, to recognize a pattern in the data, to adapt solutions, and to process information rapidly. Owing to these advantages, ANNs been used in numerous real-world applications. In this study, an ANN of the multilayer perceptron (MLP) type with one-input layer, hidden layer and output layer was used. The transfer function in the networks was logsigmoid for this paper. Networks with a single hidden logsigmoid layer are by far the most frequently used network topology, probably because they are capable of approximating any function with a finite number of discontinuities (Cybenko 1989; Hornik et al. 1989), as long as sufficient training is performed. Feedforward Backpropagation (BP) algorithm was employed to train the MLP neural network. Levenberg–Marquardt (LM) algorithm was used with an early stopping criterion to improve the network training speed and efficiency. For the criterion, all the data were divided into three sets (Coulibaly et al. 2000).

The first set is the training set for determining the weights and biases of the network. The second set is the validation set for evaluating the weights and biases and for deciding when to stop training. The last data set is for validating the weights and biases to verify the effectiveness of the stopping criterion and to estimate the expected network operation on new data sets. In this study, pan evaporation data with maximum and minimum air temperature were employed as input variables. For training the network, data from the data set were divided into two parts: The first part (2058 patterns, from 2001 to 2006) was used for network training and the second part (538 patterns, from 2007 to 2008) was used for testing the trained network. A total of 70% of the training set was randomly reserved for training the ANN and the other 30% was used to validate the training. Since the purpose of this study was the estimation of ET0, the ANN has only one output variable. The PM estimated daily ET0 values were employed as substitute for measured ET0 data and used as target output. The number of hidden nodes in the ANN was determined empirically by trial and error, considering the need to derive reasonable results. In order to suit the consistency of the model, all source data were first normalized in the range from 0.0 to 1.0 .

III. FAO -56 PENMAN MONTEITH METHOD

As described in the Irrigation and Drainage Paper 56 (Allen et al., 1998), the FAO has adopted the PM equation (named here FAO56-PM) as the standard technique to compute reference ET. The FAO56-PM can be used for hourly or daily time steps. For hourly time steps, the equation is stated as (Allen et al., 1998):

where ET0 is grass reference ET in mm h-1, Rn is the net radiation at the grass surface in MJ m-2 h-1, G is the soil heat flux density in MJ m-2 h-1, T is the mean hourly air temperature in °C, u2 is the mean hourly wind speed at 2 m height in m s-1, e 0(Thr) is the saturation vapour pressure in kPa at air temperature Thr , ea is the actual hourly vapour pressure in kPa ,Δ is the slope of vapour pressure versus temperature

curve in kPa °C-1, and is the psychrometric constant in kPa °C-1. Allen et al. (1998) described the procedure and steps for the application of the PM equation for various time step sizes. The data used for the testing of neural network (daily weather data from 538 patterns; 2007–2008) were used for comparison of the selected ANN and the conventional method. This comparison was done by using three statistical indices: determination coefficient (R2), root mean square error (RMSE) and the ratio between average estimated ETo values and observed ETo values (R). The R2 measures the degree to which two variables are linearly related and should optimally be one. The RMSE is a measure of the residual standard

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deviation and should be as small as possible (optimally 0). The R shows under (R<1) or over (R>1) estimation prediction. The R2, RMSE and R are defined as:

where N is the number of observations, Pi is the estimated (using the ANN and conventional methods), Oi is the observed ETo (calculated with the PM method), �P and �Oare the average value for Pi and Oi.

IV. RESULT AND DISCUSSION

The neural networks were trained with 1–20 hidden nodes and after each training run; RMSE, R2 and R were calculated using only the test data set to find the optimal number of hidden nodes. Figure 1 shows the effect of changing the number of nodes in hidden layer on the network accuracy. It is clear that this factor had a significant bearing on the network accuracy. The variation of R2 oscillated less than the RMSE and R. However, the best R2 (almost 0.92), wasfound with six nodes. The best RMSE and R (0.8 and 0.99 mm d-1, respectively) values also were found with six nodes. Hence, the network using six nodes in the hidden layer is selected for daily ETo estimation in this study. The data used for the testing of neural network (daily weather data from 538 patterns; 2007–2008) were used for comparison of the selected ANN and PM methods. Figure 2a shows the comparison between daily ET0 values estimated by PM method and those calculated by the selected ANN model (ET_ANN) for both years under testing of neural network. Evolution is similar and one line is practically superimposed over the other..

(a)

(b) (c)Fig. 1 Relation between accuracy of neural network and the

number of nodes for estimating ET0. (a) R2,(b) RMSE and (c)R

Figure 2a presents the regression analysis of daily values calculated from PM estimations. The selected ANN model performs very well compared to PM estimations. The slope of the fitted line is nearly close to one (lying on 1:1 line). This shows that the ET_ANN model produces well for estimating ET0 for the data sets studied. Figure 3b shows the regression analysis of daily ET0 values calculated by conventional and PM estimations. The regression line has a slope of 0.80 and R2

of 0.84, which indicates the poor performance of this method.

(a)

(b)

13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India

National Conference on Recent Trends in Engineering & Technology

Fig. 2 Comparison of the daily ET0 estimated by ANN model and Epan X Kp equation to PM values, during the test period

Daily ET_PM values were compared with calculations from

ET_ANN and the conventional (Ep x Kp) methods. This comparison was conducted from 538 observations from both years that selected for testing of the neural network. Table 1 shows the results of simple regression analysis and presents the calculation of errors. The selected ANN model showed very good performance when compared to ET_PM values. This model with a RMSE of 0.8 mm d-1, a R2 of 0.91 produces a small underestimation (1%). The Epan x Kp equation over estimated the daily ET0 by 19% with a R2 value of 0.84 and RMSE of 1.46 mm d-1. From the above discussion, it was inferred that the selected ANN model gives better result of ETo estimation than the conventional (Ep x Kp) method. Although the ET_ANN method does not require wind speed and humidity data, it did provide more accurate estimates of ETo than the conventional Epan x Kp equation.Further research is required to evaluate the ANN method proposed in this study in other climate regions and other fetch distance.

TABLE IETO EVALUATION OF ET_ANN AND CONVENTIONAL METHOD

V CONCLUSION

For the semi-arid environment, the potential of the ANN model for converting Ep to estimate ETo using temperature data has been illustrated in this paper. The ANN model containing only three inputs, the Tmax and Tmin (0C) and Ep (mm d-1) were developed and compared with the conventional method that uses Kp. The study demonstrated that modeling of daily ETo through the use of ANN technique gave better estimates than the conventional method that also require wind speed and humidity data. However, it would be suitable to consider for more humid and fetch distance to confirm this result.

ACKNOWLEDGMENT

Author wants to acknowledge the help and the assistance received from the Department of Civil Engineering of the University

REFERENCES

[1] Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration. Guidelines for computing crop water requirements. Irrigation and Drainage Paper No. 56. FAO, Rome

[2] Bruton JM, Mcclendon RW, Hoogenboom G (2000) Estimating daily pan evaporation with artificial neural networks. Trans ASAE43(2):491–496

[3] Coulibaly P, Anctil F, Bobee B (2000) Daily reservoir inflow using artificial neural networks with stopped training approach. J Hydrol 230(3–4):244–257

[4] Cybenko G (1989) Approximation by superposition of a sigmoidal function. Math Control Signal Syst 2:303–314

[5] Doorenbos J, Pruitt WO (1977) Guidelines for prediction of crop water requirements. FAO Irrig Drain. Paper No. 24, Rome

[6] Gavilan P, Lorite IJ, Tornero S, Berengena J (2006) Regional calibration of Hargreaves equation for estimating reference ET in a semiarid environment. Agric Water Manage 81:257–281

[7] Hornik K, Stinchcombe M, White H (1989) Multilayer feedforwardnetworks are universal approximators. Neural Netw 2:359–366Irmak S, Haman D, Jones W (2002) Evaluation of class A pan coefficients for estimating reference evapotranspiration in humid location. J Irrig Drain Eng 128(3):153–159

[8] Irmak S, Allen RG, Whitty EB (2003) Daily grass and alfalfareference evapotranspiration estimates and alfalfa-to-grass evapotranspiration ratios in Florida. J Irrig Drain Eng 129(5):360–370

[9] Jensen ME (ed) (1974) Consumptive of water and irrigation water requirements. Irrig Drain Div ASCE, p 227

[10] Jensen MC, Middleton JE, Pruitt WO (1961) Scheduling irrigation from pan evaporation. Circular 386, Washington Agricultural Experiment Station

[11] Keskin ME, Terzi O (2006) Artificial neural network models of daily pan evaporation. J Hydrol Eng 11(1):65–70

[12] Kisi O (2006) Daily pan evaporation modelling using a neuro-fuzzy computing technique. J Hydrol 329(3–4):636–646

[13] Kumar M, Raghuwanshi NS, Singh R, Wallender WW, Pruitt WO (2002) Estimating evapotranspiration using artificial neural network. J Irrig Drain Eng 128(4):224–233

[14] Odhiambo LO, Yoder RE, Hines JW (2001) Optimization of fuzzy evapotranspiration model through neural training with inputoutput examples. Trans ASAE 44(6):1625–1633

[15] Silva AF (2002) Previsa˜o da evapotranspirac¸a˜o de refereˆncia utilizando redes neurais. Dissertac¸a˜o de Mestrado, Univ. Federal de Vic¸osa, Vic¸osa, Minas Gerais, Brazil

[16] Sudheer KP, Gosain AK, Ramasastri KS (2003) Estimating actual evapotranspiration from limited climatic data using neural computing technique. J Irrig Drain Eng 29(3):214–218

[17] Trajkovic S, Todorovic B, Stankovic M (2003) Orecasting of reference evapotranspiration by artificial neural networks. J Irrig Drain Eng 129(6):454–457

[18] Utset A, Farre I, Martinez-Cob A, Cavero J (2004) Comparing Penman–Monteith and Priestley–Taylor approaches as referenceevapotranspiration inputs for modeling maize wateruse under Mediterranean conditions. Agric Water Manage 66(3):205–219

[19] Zanetti SS, Sousa EF, Oliveira VPS, Almeida FT, Bernard S (2007) Estimating evapotranspiration using artificial neural network and minimum climatological data. J Irrig Drain Eng 133(2):83–89 Irrig Sci (2008) 27:35–39 39 123

Method R2 RMSE(mmd-1)

Oave(mm d-1)

Pave(mmd-1)

Pave/Oa

ve

ET_ANN 0.91 0.8 5.16 5.13 0.99Conventional (EpX Kp )

0.84 1.46 5.16 4.16 0.81

13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India

National Conference on Recent Trends in Engineering & Technology