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  • 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 195 ARTIFICIAL NEURAL NETWORK MODELS FOR ESTIMATING REFERENCE EVAPOTRANSPIRATION IN RAJENDRANAGAR REGION K. CHANDRASEKHAR REDDY Professor, Department of Civil Engineering & Principal, Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India ABSTRACT Artificial Neural Networks (ANNs) are effective tools to model non linear systems and require fewer inputs. The goal of this study is to develop artificial neural network (ANN) models for estimating daily, weekly and monthly reference evapotranspiration (ET0) in Rajendranagar region of Andhra Pradesh. The climatic parameters influencing mostly the ET0 in the region of study area have been identified through multiple and partial correlation analysis using observed climatic data and ET0 estimated by FAO-56 Penman-Monteith (PM) method (PM ET0). The ANN models with these input nodes (temperature, wind velocity, sunshine hours and relative humidity) varying the number of nodes in the hidden layer have been tried to obtain optimal architectures. The performance of the models was evaluated with respect to PM ET0 by the performance indicators such as regression coefficients (slope and intercept of scatter plots), Root Mean Square Error (RMSE), Coefficient of Determination (R2 ) and Efficiency Coefficient (EC). The optimal ANN (4-3-1) model showed a satisfactory performance in the daily, weekly and monthly ET0 estimation. These ANN models may therefore be adopted for estimating ET0 in the study area with reasonable degree of accuracy. Keywords: Artificial Neural Network, Reference Evapotranspiration, Multiple and Partial Correlation Coefficients. 1. INTRODUCTION Efficient use of water resources in agriculture is becoming an important issue in India because of the depletion of freshwater resources due to the rapid increase of industries and population. Reliable and consistent estimates of reference evapotranspiration (ET0) are a key element of managing water resources efficiently. It is desirable to have a method that estimates reasonably the reference Evapotranspiration (ET0). Most of the studies have shown that the FAO-56 Penman- Monteith (PM) equation (Allen et al., 1998)[1] is widely used in recent times for ET0 estimation and it gives very accurate ET0 estimates in different environments. However, under limited climatic data, INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2014): 7.9290 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME
  • 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 196 the simple empirical methods giving good results comparable with PM ET0 may be selected at regional level for reasonable estimation of ET0. Most of the ET0 estimation methods do not effectively represent the complete nonlinear dynamics inherent in the ET0 process. Artificial Neural Networks (ANNs) are capable of representing complex and nonlinear process effectively extracting the relation between the inputs and outputs of a process without the physics being explicitly provided to them. ANNs also identify the underlying rule even if the data is noisy and contaminated with errors (ASCE Task committee, 2000a[2] and 2000b[3] ) and which may not be always possible with the application of traditional statistical techniques. ANNs are therefore used in recent times as a successful soft computing tool in ET0 modelling. Although ANNs belong to the class of data driven approaches, it is important to determine the dominant network model inputs as this not only reduces the training time but also increases the generalization ability of the network for a given data set. The present study examines several aspects associated with the use of ANN structure including the type of input data, number of hidden layers and nodes in each hidden layer to be included in the network in the ET0 estimation. Khoob (2008)[4] tested the ANNs, for converting pan evaporation data to estimate ET0 as a function of the maximum and minimum air temperatures in semiarid climate. While comparing with PM method, it was concluded that the ANN methods are better ET0 estimates than the conventional methods. Landeras et al. (2008)[6] evaluated the ANN models for daily ET0 estimation under the situations of presence of only temperature and relative humidity data. ANNs showed better performance over traditional ET0 equations. Kumar et al. (2009)[5] developed generalized artificial neural network (GANN) based reference crop evapotranspiration models corresponding to Turc, FAO-56 Penman-Monteith, FAO-24 Radiation and FAO-24 Blaney-Criddle methods. It was concluded that the GANN models can be used directly to predict ET0 under the arid conditions since they performed better than the conventional ET0 estimation methods. The study reports the identification of most influencing climatic parameters in ET0 estimation, development of ANN models for estimation of daily, weekly and monthly ET0 for Rajendranagar region of Andhra Pradesh. 2. MATERIALS AND METHODS Rajendranagar region, located in Rangareddy district of Andhra Pradesh, India, has been chosen as the study area. The meteorological data in the region for the period 1978-1993 were collected from India Metrological Department, Pune. Data from 1978 to 1988 is used for the purpose of training the model and that of 1989 to 1993 for testing the model. A brief description of region selected for the present study is given in Table 1. Table 1: Brief description of the Rajendranagar region Longitude Latitude Altitude Mean daily relative humidity Mean daily temperature Mean daily wind velocity Mean daily sunshine hours Mean daily vapour pressure Mean annual rainfall (0 E) (0 N) (m) (%) (0 C) (kmph) (hr) (mm of Hg) (mm) 780 23′ 170 19′ 536.0 61.8 26.2 7.3 8.0 14.9 920 2.1 Artificial Neural Network (ANN) model development A standard multilayer feed forward ANN with logistic sigmoid function was adopted for the present study. A constant value of 0.1 for learning rate and a constant value of 0.9 for momentum factor were considered. The input data were normalized in the range of (0.1, 0.9) to avoid any saturation effect. Error back propagation which is an iterative nonlinear optimization approach based on the gradient descent search method (Rumelhart, 1996)[9] was used during calibration. The
  • 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 197 calibration set was used to minimize the error and validation set was used to ensure proper training of the neural network employed such that it does not get over-trained. The performance of the model was checked for its improvement on each iteration to avoid over-learning. The optimal network corresponding to minimum mean squared error was obtained through trial and error process. Care was taken to avoid too few and too many neurons which can respectively cause difficulties in mapping each input and output in the training set and increases the training time, in the process of determination of optimal number of hidden layers and nodes in each hidden layer to arrive at the optimal neural network. The entire process was carried out using MATLAB routines. 3. PERFORMANCE EVALUATION CRITERIA The performance evaluation criteria used in the present study are the Coefficient of Determination (R2 ), the Root Mean Square Error (RMSE) and the Efficiency Coefficient (EC). 3.1 Coefficient of Determination (R2 ) It is defined as the square of the correlation coefficient (R) and the correlation coefficient is expressed as Where O and P are observed and estimated values, O and P are the means of observed and estimated values and n is the number of observations. This parameter measures the degree of association between the observed and estimated values and indicates the relative assessment of the model performance in dimensionless measure. 3.2 Root Mean Square Error (RMSE) It yields the residual error in terms of the mean square error and is expressed as (Yu et al., 1994)[10] n op RMSE ii n i 2 1 )( − = ∑= 3.3 Efficiency Coefficient (EC) It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[8] . It is a better choice than RMSE statistic when the calibration and verification periods have different lengths (Liang et al., 1994)[7] . It measures directly the ability of the model to reproduce the observed values and is expressed as ( ) ( )∑ ∑ = = − − −= n i i n i ii oo po EC 1 2 1 2 1 2/1 1 2 1 2 1 )()( ))((     ∑ −∑ − −−∑ = == = n i i n i i ii n i ppoo ppoo R
  • 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 198 A value of EC of 90% generally indicates a very satisfactory model performance while a value in the range 80-90%, a fairly good model. Values of EC in the range 60-80% would indicate an unsatisfactory model fit. 4. RESULTS AND DISCUSSION The analysis of multiple linear correlation between FAO-56 Penman-Monteith reference evapotranspiration (PM ET0) and the climatic parameters was carried out by omitting one of the climatic factors each time. While carrying out the analysis, the data period was divided into training and testing periods. The training period data set was used to identify the parameters influencing the region and to develop linear ET0 models in terms of these parameters. The verification of applicability of the models developed was checked using the testing period data set. The multiple linear correlation coefficients and partial correlation coefficients between PM ET0 and climatic parameters for the regions selected for the present study were computed for both training and testing periods are presented in Table 2 and 3. Table 2: Multiple correlation co-efficients Time step Multiple correlation co-efficient Independent variable omitted ---- T S W RH VP R Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Daily 0.9643 0.9689 0.8684 0.8533 0.9099 0.9134 0.8865 0.8487 0.9531 0.9657 0.9642 0.9687 0.9643 0.9687 Weekly 0.9755 0.9804 0.8816 0.8584 0.9521 0.9544 0.9161 0.8967 0.9697 0.9783 0.9753 0.9804 0.9754 0.9803 Monthly 0.9900 0.9886 0.9209 0.8884 0.9805 0.9775 0.9509 0.9387 0.9872 0.9869 0.9899 0.9884 0.9900 0.9884 Table 3: Partial correlation co-efficients Time step Partial correlation co-efficient T S W RH VP R Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Daily 0.8455 0.8802 0.7697 0.7940 0.8201 0.8838 0.4842 0.3030 0.0524 0.0793 0.0000 0.0793 Weekly 0.8847 0.9233 0.6945 0.7513 0.8360 0.8955 0.4348 0.3095 0.0894 0.0000 0.0634 0.0709 Monthly 0.9322 0.9447 0.6962 0.7003 0.8901 0.8996 0.4665 0.3592 0.0993 0.1309 0.0000 0.1309
  • 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 199 From Tables 2 and 3, it may be observed that the influence of Temperature (T), Sunshine hours (S), Wind velocity (W) and Relative humidity (RH) is relatively more on ET0 in the region of the study area irrespective of the time step. Further, no significant effect of Vapour Pressure (VP) and Rainfall (R) on ET0 is found in the region. This may be due to the fact that the region lies in the semi-arid zone, mostly experienced by high temperature and radiation. The ANN models with these input nodes (T, S, W and RH) varying the number of nodes in the hidden layer have been tried to obtain optimal architectures. The performance indicators of these ANN models are presented in Table 4. The high values of EC represent the satisfactory performance of ANN (4-4-1) models for Rajendranagar region. The low RMSE values also indicate that the models proposed estimate ET0 satisfactorily. The scatter plots as shown in Fig.1 also depict similar results. The nearly unit slope and zero intercept of scatter plots indicate that ANN models predict ET0 comparable with that of FAO-56 Penman-Monteith method. The models proposed may therefore be adopted for ET0 estimation in the selected regions of the study area with reasonable degree of accuracy. Table 4: Performance indices of Artificial Neural Network (ANN) models Time step ANN Architecture Slope of the scatter plot Intercept of the scatter plot R2 RMSE (mm) EC (%) Training period Testing period Training period Testing period Training period Testing period Training period Testing period Training period Testing period Daily 4-3-1 1.0014 0.9132 -0.0059 0.2641 0.9822 0.9739 0.23 0.24 98.22 97.39 3-4-1 1.0003 0.9495 -0.0015 0.2042 0.9240 0.9000 0.47 0.47 92.40 90.00 2-5-1 0.9998 1.1050 0.0006 -0.1308 0.7887 0.6988 0.78 0.82 78.87 69.88 1-5-1 1.0000 0.6923 -0.0004 1.3734 0.4119 0.1752 1.30 1.36 41.19 17.52 Weekly 4-3-1 1.0007 1.0016 -0.0009 -0.0052 0.9876 0.9888 0.17 0.14 98.76 98.88 3-4-1 1.0016 0.9209 -0.0074 0.8793 0.9655 0.8290 0.28 0.55 96.55 82.90 2-5-1 1.0004 0.9516 -0.0018 0.7923 0.8726 0.7469 0.53 0.67 87.26 74.69 1-5-1 1.0001 0.6675 -0.0004 1.8909 0.4848 0.2130 1.07 1.19 48.48 21.30 Monthly 4-3-1 1.0007 1.0017 -0.0034 -0.0075 0.9956 0.9953 0.09 0.09 99.56 99.53 3-4-1 1.0001 0.9933 -0.0009 0.2268 0.9884 0.8995 0.15 0.41 98.84 89.95 2-5-1 1.0021 0.7954 -0.0094 1.0130 0.9455 0.8062 0.32 0.57 94.55 80.62 1-5-1 1.0022 0.5864 -0.0108 2.0349 0.5220 0.1727 0.95 1.18 52.20 17.27
  • 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 200 Training period Testing period Fig.1: Scatter plots of ET0 values estimated using Artificial Neural Network (ANN) models with those estimated by Penman-Monteith (PM) method
  • 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME 201 5. CONCLUSION The effect of climatic parameters on ET0 at Rajendranagar region is brought out through multiple and partial correlation analysis. The sunshine hours, wind velocity, temperature and relative humidity mostly influenced ET0 in the study area. The ANN ET0 models comparable with FAO-56 Penman-Monteith method for the region have been developed in terms of the influencing climatic parameters. The performance ANN models developed was verified based on the evaluation criteria. The slope and intercept of scatter plots nearly equal to one and zero respectively, high values of R2 and EC and low values of RMSE indicate satisfactory performance of the models. The ANN(4-4-1) model showed better performance for all time steps in ET0 estimation. This ANN(4-4-1) model may therefore be adopted for estimating ET0 in the study area and also the other regions of similar climatic conditions with reasonable degree of accuracy. REFERENCES [1] Allen, R. G., Pereira, L. S., Raes, D. and Smith, M. (1998), Crop evapotranspiration - Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56, FAO, Rome. [2] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (2000a). Artificial neural networks in hydrology. I: Preliminary concepts. Journal of Hydrologic Engineering, ASCE, Vol.5, No.2, pp.115-123. [3] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (2000b). Artificial neural networks in hydrology. II: Hydrologic applications.Journal of Hydrologic Engineering, ASCE, Vol.5, No.2, pp.124-137. [4] Khoob, A.R. (2008). Artificial neural network estimation of reference evapotranspiration from pan evaporation in a semi-arid environment. J. Irrig. Sci., 27(1), 35-39. [5] Kumar, M., Raghuwanshi, N. S., & Singh, R. (2009). Development and validation of GANN model for evapotranspiration estimation. J. Hydrol. Eng., ASCE, 14(2). 131-233. [6] Landeras, G., Barredo, A. O., & Lopez, J. J. (2008). Comparison of artificial neural network models and empirical and semi-empirical equations for daily reference evapotranspiration estimation in the Basque Country (Northern Spain). Agricultural Water Management, 95(5), 553-565. [7] Liang, G. C., O-Connor, K. M. and Kachroo, R. K. (1994), a multiple-input single-output variable gain factor model. Journal of Hydrology, Vol.155, No.1-2, pp.185-198. [8] Nash, J. E. and Sutcliffe, J. V. (1970), River flow forecasting through conceptual models part I: A discussion of principles. Journal of Hydrology, Vol.10, No.3, pp.282-290. [9] Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1996). Learning international representations by error propagation, partial distributed processing. MIT press, Cambridge, MA, 1, 318-362. [10] Yu, P. S., Liu, C. L. and Lee, T. Y. (1994), Application of transfer function model to a storage runoff process. In Hipel K. W., McLeod A.I. and Panu U.S. (Ed.), Stochastic and Statistical Methods in Hydrology and Environmental Engineering, Vol.3, pp.87-97. [11] K. Chandrasekhar Reddy, “Reference Evapotranspiration Estimation By Radiation Based Methods” International Journal of Civil Engineering & Technology (IJCIET), Volume 5, Issue 2, 2014, pp. 81 - 87, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. [12] Sameer Ul Bashir, Younis Majid and Ubair Muzzaffer Rather, “Effect of Rapidite on Strength of Concrete in Warm Climates”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 6, 2013, pp. 126 - 133, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. [13] K. Chandrasekhar Reddy, “Evaluation And Calibration of Temperature Based Methods For Reference Evapotranspiration Estimation In Tirupati Region” International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 5, Issue 2, 2014, pp. 87 - 94, ISSN Print: 0976-6480, ISSN Online: 0976-6499.