ESTIMATION OF EVAPOTRANSPIRATION WITH ANN TECHNIQUE

Transcription

1 J. Indian Water Resour. Journal Soc., of Vol. Indian, Water No., Resources January, Society, Vol, No., January, ESTIMATION OF EVAPOTRANSPIRATION WITH ANN TECHNIQUE M. U. Kale, M. B. Nagdeve and S. J. Bagade ABSTRACT To identify the best alternative method to estimate reference evapotranspiration (ETo), performances of various ANN architectures and two climate based methods namely Penman Monteith (P-M) (FAO-) and Hargreaves-Samani (H-S) model, were compared with FAO- Pan evaporation model. Practical based pan evaporation method (FAO-) was taken as standard method. The ANN architectures formulated using varied input combinations of climatic variables, were trained using backpropagation algorithm i.e. Levenberg-Marquardt with sigmoid function. Performances of these methods were evaluated using the statistical indices i.e. mean standard error (MSE), root mean square error (RMSE) and the coefficient of determination (r). The results confirmed that when all climatic data is available, Penman-Monteith method is the best indirect method for daily ETo estimation. The ANN (--; input parameter - air temperature and wind speed only) with an r of.9 and RMSE of.8 mm day - estimated fairly accurate ETo. The climate based Hargreaves-Samani model overestimated the ETo by about %. Hence, ANN (--) topology should be used to estimate fairly accurate ETo when data pertaining to climatic parameters is insufficient to apply standard ETo estimation methods. Keywords: Evapotranspiration, Artificial Neural Network, Pan Evaporation, Penman- Monteith, Hargreaves-Samani INTRODUCTION Evapotranspiration (ETo) is key hydrological variable, which play an important role in irrigation scheduling. Evapotranspiration is a complex and non-linear process depending on several interacting meteorological factors. Methods for measuring evapotranspiration are based on micrometeorological techniques (aerodynamic method, eddy covariance etc.) or on the use of lysimeters. The direct methods for measuring evapotranspiration require complex and very costly instruments/devices. The direct methods are generally recommended only for specific research purposes (Allen et al. 998). The ETo is commonly estimated by indirect methods i.e. either physically-based equations (e.g. Penman, Penman-Monteith model etc.) or empirical relationships between meteorological variables (e.g. Hargreaves, Hargreaves-Samani, Blaney- Criddle model etc.) (Doorenbos and Pruitt, 9; Jensen et al., 99; Smith et al., 99; Kumar et al., 8). Empirical and semi-empirical models reported in literature are based on relationships between evapotranspiration and a limited number of meteorological variables. Some of these models are valid only under specific climatic and agronomic conditions, and they cannot be applied under other conditions, which are different from those they were originally developed for. For these reasons such models require local calibration to produce reliable estimates. Local calibration can be carried out by a multiple regression between meteorological variables and evapotranspiration determined using a standard method (lysimeter or combination methods) (Jensen et al., 99).. Assistant Professor, CAET, Department of Irrigation and Drainage Engineering,Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola (MS), kale9@gmail.com, -9. Chief Scientist, AICRP on Dryland Agriculture, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola (MS). Student, Department of Irrigation and Drainage Engineering, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola (MS) Manuscript No. The Food and Agriculture Organization (FAO) recommended a combined model of Penman-Monteith (P-M) as a sole standard method for determining ETo using meteorological data in all climates (Allen et al., 998). Several studies have proved the superiority of the P-M method across a wide range of climate conditions (Jensen et al. 99; Irmark et al. ; Itenfisu et al. ). The fundamental obstacle to widely applying the P-M method is the numerous required data that are not always available at many locations. To overcome this obstacle, few other methods like Hargreaves-Samani model were developed which required less climatic parameter data. The Hargreaves-Samani model was adopted for use by the FAO for areas where air temperature is the only available variable (Allen et al., 998, Hargreaves and Allen, ). Tiwane and Dhumal (8) reported that for estimation of ETo for Akola region Penman-Monteinth model is the best followed by Hargreaves Samani model. Artificial neural networks are black box models, which are quite perfect in modeling complex non-linear phenomenon. Majority of studies (Kumar et al. ; Sudheer et al. ; Trajkovic et al. ; Jain et al. ; Rahimikhoob 8) have proved that ANNs are capable of performing quite satisfactorily in evapotranspiration modelling. ANNs are effective tools for the modeling of nonlinear systems that require fewer inputs than conventional methods. Hence this study aimed to evaluate the potential of ANN for ETo estimation based only on limited climatic data set. MATERIALS AND METHODS The study was carried out on meteorological data collected from 99 to 8 by weather station located at Telhara (Maharashtra, India) in command area of Hanumansagar Reservoir Project at Wan (India). The measure quantities were: temperature (maximum and minimum), relative humidity (maximum and minimum), wind speed, solar radiation, actual sunshine hours and pan evaporation. Data were collected at 8 hrs and hrs during a day, and then summarized on daily basis. The brief description of the models used in the present study to estimate ETo using daily climatological data is as below.

2 J. Indian Water Resour. Soc., Vol., No., January, Conventional Methods I. Pan evaporation model (Epan, FAO-) Evaporation from pan provides a measurement of combined effect of temperature, humidity, wind speed and sunshine hours on the reference crop evapotranspiration (Doorenbos and Pruitt, 9). This method is also known as FAO Pan Evaporation (-PAN) method. The data from USWB-class A pan was used for analysis. ET O = E pan x K p. () ETo = Reference evapotranspiration, (mm day - ) E pan = Pan evaporation, (mm day - ) K p = Pan coefficient (.) II. Penman Monteith model (FAO - ) The FAO version of the Penman-Monteith model is so accurate that it is recommended as the sole method of calculating ET O if data is available (Allen et al., 998). The Penman Monteith (FAO - ) equation is given as: 9.8 +ϒ ET = O ( Rn G) µ ( es ea) T + +ϒ ( +.µ ). () = Slope of vapour pressure curve, (k Pa - C - ) Ra = Daily extraterrestrial radiation (MJm - day - ) G = Soil heat flux density, (MJm - day - ) γ = Psychometric constant, (k Pa - C - ) T = Mean daily air temperature at m height, ( C) µ = Wind speed at m height, (m s - ) e s e a e s e a = Saturation vapour pressure, (k Pa) = Actual vapour pressure, (k Pa) = Saturation vapour pressure deficit, (k Pa) III. Hargreaves-Samani (H-S) model This model is computationally simple and applicable to a variety of climates using commonly available meteorological data. The Hargreaves-Samani model was adopted for use by the FAO, for areas where air temperature is the only available variable (Allen et al., 998, Hargreaves and Allen, ). The form of the Hargreaves-Samani model presented in FAO- by Allen et al. (998) is as: ETo =. (Tmean+.8)(Tmax-Tmin). Ra. () Tmean = Mean air temperature, ( C) Tmax = Daily maximum temperature, ( C) Tmin = Daily minimum temperature, ( C). Artificial Neural Network Artificial Neural Network (ANN) is data driven model commonly used for modeling complex non-linear phenomenon. Among the different types of ANNs, multilayer perceptron (MLP) neural networks are quite popular and were used in the present study. Multi-layer perceptrons are feedforward networks with one or more hidden layers. The architectures with only one hidden layer were adopted in this study based on the fact that an ANN with only one hidden layer is enough to represent the nonlinear relationship between the climatic elements and the corresponding evapotranspiration (Kumar et al., ; Arca et al., ). Given a training set of input-output data, the most common learning rule (supervised learning) for multi-layer perceptrons is the back propagation algorithm. A neural network with such type of learning algorithms is usually referred as back propagation network (BPN). Specifically the Levenberg-Marquardt algorithm was used in this study. The activation function used in this study was a sigmoid function [ f( x) = ]. The number of ( ) + exp x nodes in the input and the output layers depend on the number of input and output variables, respectively. The performance of the ANN depends on the number of nodes in the hidden layer. As no specific guidelines exist for choosing the optimum number of hidden nodes for a given problem, this network parameter was optimized using a combination of empirical rules and trial and error method. Methodology Daily ETo was estimated with conventional methods using MS Excel based computational procedure. Artificial Neural Network model was constituted with ETo determined with pan evaporation (FAO ) model as a desired output, while the input parameters included five climatological parameters (maximum temperature, minimum temperature, maximum relative humidity, minimum relative humidity and wind speed) that influences evapotranspiration. The various ANN architectures were formulated by excluding input parameters one by one on the basis of easy availability, so as to obtain the best possible combination of minimum input parameters that gives fairly accurate estimate of ETo. To avoid overtraining and undertraining, split sampling method was used. The available data was split in three separate data sets: () the training set, () the cross-validation set, and () the testing set. These data sets were then used for respective operation. The size of training set, validation set and testing set was %, % and % of total data set, respectively. Training constitutes the first stage in implementation of a neural network designed to identify the relationship between the independent and dependent variables of a given process. The training set data was used for training of ANN. Training is for evaluating the weights and biases, and for deciding when to stop the training. Training is achieved by adjusting (determining) the weights and biases of the neurons through an iterative algorithm that minimizes the error between the network predicted outputs and actual data. The stopping criterion used in this study was that the training should be

3 J. Indian Water Resour. Soc., Vol., No., January, stopped when the performance in the validation set starts to increase, despite the fact that the performance in the training set continues to decrease. The cross validation data set was used for this purpose. The third data set was used to validate the weights and biases, to verify the effectiveness of the stopping criterion and to estimate the expected network operation on new data sets. The ANN model implementation was carried out using NeuroSolutions for Excel software. Model Performance In addition to qualitative assessment with graphical displays using test set data, the model simulation results were evaluated quantitatively using statistical measures as a) Mean Square Error The Mean square error (MSE) of an estimator is one of the many ways to quantify difference between an estimator and the true value of the quantity being estimated. MSE measures the average of the square of the error. The error is the amount by which an estimator differs from a desired estimate. The MSE is determined by using following formula: ( P - O ) MSE = N i i. () N = Number of observations, P i = Estimated ETo O i = Observed ET O (estimated with Pan evaporation method), An MSE of zero, meaning that the estimator Pi predicts observation of the parameter Oi with perfect accuracy, is the ideal and forms the basis for least squares method of regression analysis. While particular values of MSE other than zero are meaningless in and of themselves, they may be used for comparative purpose only. The unbiased model with the smallest MSE is generally interpreted as best explaining the variability in the observation. b) Root Mean Square Error The root mean square deviation (RMSD) or root mean square error (RMSE) is a measure of the differences between values predicted by a model and observed values. RMSE is a good measure of accuracy. These individual differences are also called residuals, and the RMSE serves to aggregate them into a single measure of predictive power. RMSE was calculated by using following equation: N i = i i N RMSE = P Q. () ( ) c) Linear Regression Analysis A single linear regression was accomplished for each estimation by considering the ETo values from Pan and alternative methods as the independent variable and the dependent variable respectively. The results were analyzed by using the coefficients (b and r ) of the equations. The regression equation of Y on X is expressed as follows: Y= b + ax. () Y = dependent variable, X = independent variable, b = Y axis intercept, a = slope of regression line. It represents change in Y variable for a unit change in X variable. Such a line is known as the line of best fit. d) Coefficient of Correlation The value of the coefficient of correlation was determined by using following formula: P-P i O i -O r =. () P-P i O i -O = Average values for P i = Average values for O i The value of the coefficient of correlation obtained by the above formula shall always lie between to +. When r = +, it means there is perfect positive correlation between the variables. When r = -, it means there is perfect negative correlation between the variables. When r =, it means there is no relationship between the two variables. e) Coefficient of Determination Coefficient of determination (r ) will give some information about the goodness of fit of a model. It is determined by using following formula: r = N ( Pi P)( Oi O) i= N N ( Pi P) ( Oi O) i= i=. (8) In regression, coefficient of determination (r ) is a statistical measure of how well the regression line approximates the real data points. An r of. indicates that the regression line perfectly fit the data. RESULTS AND DISCUSSION In order to find out the best ANN architecture yielding fairly accurate estimation of evapotranspiration with limited climatic data, first of all, the optimum number of nodes in hidden layer for each ANN architecture were found by trial and error method. To evaluate the performance of these ANN topologies, the evapotranspiration estimates provided by these

4 J. Indian Water Resour. Soc., Vol., No., January, topologies for test data were compared with the estimates provided by the FAO- pan evaporation model. The statistical analysis of the performance is summarized in Table. Daily evapotranspiration estimated with empirical methods and ANN architecture -- is summarized on monthly basis and shown in Figure. Table Statistical evaluation of neural network architectures. ANN architecture Inputs Tmax, Tmin, RH, RH, U Tmax, Tmin, U Tmax, Tmin, Ra Tmax, Tmin, Tmax, U No. of neurons Input Hidden Output Nodes in hidden layer MSE RMSE r r * Tmax = Daily maximum temperature, ( C); Tmin = Daily minimum temperature, ( C); RH = Maximum relative humidity, %; RH = Minimum relative humidity; U = Wind speed at m height, (m s - ); and Ra = Daily extraterrestrial radiation (MJm - day - ) ETo, mm - day ETopm EToHs EToANN Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Fig.: Variation in evapotranspiration estimates with different models The ANN architecture -- estimated evapotranspiration with maximum accuracy, i.e. RMSE =. mm day - ; MSE =. mm day - and r =.9. But, this topology requires five input parameters. While the ANN architecture -- requires only two input parameters i.e., maximum temperature and wind speed, and provided evapotranspiration estimate fairly accurate with less error i.e., RMSE =.8 mm day -, MSE =. mm day - and r =.9. Therefore, ANN architecture -- was chosen for comparison with other empirical methods of evapotranspiration estimation. All models, with exception of the Hargreaves-Samani model (ETo HS ), showed evapotranspiration estimate in close conformity with each other. Hargreaves-Samani model overestimated the evapotranspiration by about %. The result is in conformity with that reported by Rahimikhoob, 8 and Saghravanhi et al., 9. The variation in the ETo estimated by P-M model (ETo PM ) was approximately.%,

5 Sr. No ETo estimation method. Pan evaporation model (FAO-). Penman Monteith (P-M) (FAO-) Hargreaves-Samani (H-S) model ANN (Architecture - --) J. Indian Water Resour. Soc., Vol., No., January, Table Comparison of ETo estimation methods Average ETo estimated, mm day - MSE, mm day - RMSE, mm day - r R (regression line) b (Y intercept) EToHS y =.x +.8 R² =. EToHS trendline + percent error - percent error 8 9 Fig. a: Scatter plot of ETHs with respect to ETopm 8 y =.8x +. R² =.98 8 Fig. b: Scatter plot of ETpm with ETo-PM trendline + percent error - percent error

6 J. Indian Water Resour. Soc., Vol., No., January, EToANN 9 8 y =.8x +. R² =.89 8 Fig. c: Scatter ETo ANN with respect to ETo pan EToANN trendline + percent error - percent error while ANN architecture (--) (ETo ANN ) on an average, underestimate the value of ETo by about.%. The results of statistical analysis of the ETo estimates of all models are summarized in Table. A single linear regression (y=b+ax) for each estimation was also accomplished by plotting the scatter plot for the test data and is depicted in Figures a to c. A close relationship between the ETo values obtained using the Penman Monteith model and those using pan model is evident by less scattering, higher coefficient of correlation (.9), less RMSE value (. mm day - ) and less value of y intercept (.). It is followed by ANN model with.9 coefficient of correlation and.8 mm day - RMSE. These results are in conformity with those reported by Arca et al., and Jain et al.,. While Hargreaves-Samani (H-S) model, estimated evapotranspiration with high error i.e. RMSE =.8 mm day -, less correlation coefficient i.e.. and large scattering, and hence not recommended for estimation of ETo for command area of Hanumansagar Reservoir at Wan (India). CONCLUSION When all climatic parameter data is available Penman Monteith (P-M) (FAO-) method is the best for indirect estimation of evapotranspiration, while ANN (architecture: - -, input parameters- temperature maximum and wind speed) method yields fairly accurate results under constraints of limited climatic parameter data for command area of Hanumansagar Reservoir at Wan (India). REFERENCES. Allen, R. G., Pereira L. S., Raes D. and Smith M., 998. Crop evapotranspiration, guidelines for computing crop water requirements, FAO Irrigation and Drainage Paper, No., FAO, Rome, Italy.. Arca, B., Beniscasa and Vincenzi M.,. Evaluation of neural network techniques for estimating evapotranspiration, National Research Council Research Institute for the Monitoring of Agroecosystems (IMAes), via Funtana di Lu Colbu /A, Sassari, Italy.. Doorenbos, J. and Pruitt W. O., 9. Guidelines for predicting crop water requirements, FAO Irrigation and Drainage Paper, No., FAO, Rome, Italy.. Hargreaves, G. H., and Allen R.G.,. History and evaluation of Hargreaves evapotranspiration equation, J. Irrig. Drain. Eng., 9(), -.. Irmak, S., Irmak A., Allen R. G. and Jones J. W.,. Solar and Net radiation-based equation to estimate reference evapotranspiration in humid climates, J. Irrig. and Drain. Eng., 9(), -.. Itenfisu, D, Elliott R. L., Allen R. G., and Walter I. A.. Comparison of reference evapotranspiration calculations as part of the ASCE standardization effort, J. Irrig. Drain. Eng., 9(), -8.. Jain, S. K., Nayak P. C., and Sudheer K. P.,. Models for estimating evapotranspiration using artificial neural network, and their physical interpretation, Hydrological Processes, (), Jensen, M. E., Burman R. D. and Allen R. G., 99. Evapotranspiration and irrigation water requirements, ASCF Manual and Report of Engineering practice No. New York, ASCE. 8

7 J. Indian Water Resour. Soc., Vol., No., January, 9. Kumar, M., Raghuvanshi N. S., Singh R., Wallender W. W. and Pruitt W. O.,. Estimation of evapotranspiration using Artificial Neural Network, J. Irrig. and Drain. Eng., 8(), -.. Kumar, M., Raghuvanshi N. S., and Singh R., 8. Comparative study of conventional and artificial neural network-based ETo estimation models, Irrigation science,, -.. Rahimikhoob, Ali, 8. Artificial Neural Network estimation of reference evapotranspiration from pan evaporation in a semi arid environment, Irrigation science. (), -9.. Saghravani, S. R., Mustapha S., Ibrahim S., and Randjbaran E., 9. Comparison of daily and Monthly Results of Three Evaporatranspiration Models in Tropical Zone: A Case Study, Ammerican Journal of Environmnetal Sciences (), Sudheer, K. P., Gosain A. K. and Ramasastri K. S.,. Estimating actual evapotranspiration from limited climatic data using neural computing technique, J. Irrig. and Drain. Eng., (), -8.. Smith, M., Allen R. G., Moonteith J. L., Perrier A., Pereira, L., and Segren A., 99. Expert consultation on revision of FAO methodologies for crop water requirements, Land and Water Development Division, Food and Agricultural Organization of the United Nations, Rome.. Tiwane, A. P. and Dhumal C. V., 8. Estimation of reference evapotranspiration at Akola using different models, Unpublished Thesis, CAET, Dr. PDKV, Akola.. Trajkovic, S., Todorovic B. and Stankovic M.,. Forecasting of reference of reference evapotranspiration by artificial neural networks, J Irrig. and Drain. Eng. 9(), -. 9