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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. 178-186 © IAEME 178 RECALIBRATION OF REFERENCE EVAPOTRANSPIRATION ESTIMATION METHODS K. CHANDRASEKHAR REDDY Professor, Department of Civil Engineering and Principal, Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India. ABSTRACT Reference evapotranspiration (ET0) estimates are often required in irrigation system design, crop yield simulation and water resources planning and management. Many reference evapotranspiration (ET0) estimation methods have been developed for different types of climatic data, and the accuracy of these methods varies with climatic conditions. In this study, the weekly ET0 values estimated from nine different ET0 equations are evaluated with ET0 estimated by FAO-56 Penman-Monteith(PM) equation in order to select an appropriate ET0 equation for the semi- aridNellore region of Andhra Pradesh, India. The evaluation is based on performance criteria namely, Root Mean Square Error (RMSE), Coefficient of Determination (R2 ) and Efficiency Coefficient (EC). Then the ET0 equations were recalibrated with respect to PM method for improving their weekly ET0 estimation capability in the region selected for the present study. The recalibrated Modified Penman and Blaney-Criddle methods showed satisfactory performance in the weekly ET0 estimation. However, the recalibrated Blaney-Criddle method can be adopted because of its simpler data requirements with reasonable degree of accuracy. Keywords: Reference Evapotranspiration, Recalibration, Performance Evaluation. 1. INTRODUCTION Evapotranspiration (ET) is the loss of water to the atmosphere by the combined processes of evaporation from soil and plant surfaces and transpiration from plants. It is one of the major components of the hydrologic cycle and its accurate estimation is essential for many studies such as hydrologic water balance, crop yield simulation, and water resources planning and management. Field measurement of evapotranspiration is rarely available and actual crop evapotranspiration (ETc) is generally calculated from reference evapotranspiration (ET0) using the crop factor method, which consists of multiplying ET0 with crop coefficients (Kc) to obtain ETc (i.e., ETc = ET0 x Kc). Several reports on the estimation of Kc are available. Allen et al., (1998)[2] and Jensen et al. (1990)[5] have INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © 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. 178-186 © IAEME 179 reported crop coefficients for many crops. These values are commonly used in places where the local data is not readily available. It is desirable to have a method that estimates reasonably the reference Evapotranspiration. According to the Food and Agricultural Organization (FAO), FAO-56 Penman-Monteith (PM) method, that requires numerous climatic parameters, achieves better agreement with the lysimeter ET0 measurements compared to all other known methods. However, under limited climatic data availability conditions, the simple empirical methods yielding results comparable with PM ET0 may be selected for reasonable estimation of ET0. Irmak et al.(2003)[4] , Berengena and Gavilan(2005)[3] , Alkaeed et al.(2006)[1] , Suleiman and Hoogenboom (2007)[8] , Trajkovic and Stojnic (2008)[9] have evaluated, compared and tested the applicability of various ET0 equations for different regions. The present study reports the performance evaluation of nine ET0 estimation methods based on their accuracy of estimation and these methods are recalibrated with PM method for Nellore region of Andhra Pradesh. 2. MATERIALS AND METHODS Nellore region located in Nellore district of Andhra Pradesh, India, with global coordinates of 140 22’ N latitude and 790 59’ E longitudes, has been chosen as the study area. Meteorological data in the study area for the period 1983-2003 was collected from India Meteorological Department (IMD), Pune. A part of the data (1983-1997) was used for the purpose of developing recalibrated equations, while the rest of the data (1998-2003) was used to verify the performance of the recalibrated equations. The details of the methods selected for the present study are shown in Table 1. Table 1: Details of reference evapotranspiration estimation methods Method Equation Input data Primary Secondary Temperature based 1. FAO-24Blaney- Criddle(BC) method 2. Jensen-Haise (JH) method 3. FAO-56 Hargreaves (HR) method ET0 = a +b [p (0.46T + 8.13)] Where a = 0.0043 (RHmin) – n/N – 1.41 b = 0.82– 0.0041 (RHmin) + 1.07 (n/N)+ 0.066 (ud) – 0.006 (RHmin) (n/N)–0.0006 (RHmin) (ud) ET0 = Rs (0.025 Tmean + 0.08) ET0 = 0.0023 Ra (Tmean + 17.8) x (TD) 0.5 Tmax, Tmin Tmax, Tmin, n Tmax, Tmin, n RHmin, n, u2, ud/un --- --- Radiation based 1. Priestley-Taylor (PT) method 2. FAO-24 Radiation (RA) method 3.Makkink(MK) method ET0 = c (W.Rs) Where c = 1.066 – 0.00128 RHmean + 0.045 ud – 0.0002RHmeanud + 0.0000315 (RHmean) 2 – 0.00103 (ud)2 Tmax, Tmin, n Tmax, Tmin, n Tmax, Tmin, n --- RHmax, RHmin, u2, ud/un --- 0 Rs γΔ Δ 65.0ET + = )GRn(26.1ET0 − γ+∆ ∆ =
  • 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME 180 Physically based 1. FAO-24Modified- Penman(MP) method 2.FAO-56 Penman- Monteith(PM) method ET0 = C x       −+ +∆ + +∆ ∆ ))(01.00.1)(27.0( 2 asn eeUR γ γ γ Where C = 0.68 + 0.0028 (RHmax) + 0.018 (Rs) – 0.068 (ud) + 0.013 (ud/un) + 0.0097 (ud )(ud/un) + 0.000043 (RHmax) (Rs) (ud) ET0 = )34.01( )( 273 900 )(408.0 2 11 11 2 1111 u eeu T GR as mean n ++∆ − + +−∆ γ γ Tmax, Tmin, RHmax, RHmin, n Tmax, Tmin, RHmax, RHmin, u2, n u2, ud/un --- Pan Evaporation based 1. FAO-56 Pan Evaporation(PE) method 2.Christiansen(CS) method ET0 = Kp Epan where Kp = 0.108 – 0.0286 u2 + 0.0422 ln(FET) + 0.1434 ln(RHmean) – 0.000631 [ln(FET)]2 ln(RHmean) ET0 = 0.473 Ra CT CW CH CS CE CM where CT = 0.393 + 0.5592 (T/Tm) + 0.04756 (T/Tm)2 CW = 0.708 + 0.3276 (U2/U2m) – 0.036 (U2/U2m)2 CH = 1.25 – 0.212(RH/RHm) – 0.038(RH/RHm)5 CS = 0.542+0.64(sp/spm)–0.4992(sp/spm)2 +0.3174(sp/spm)3 CE = 0.970 + 0.030(E/Em) CM = ranges from 0.9 to 1.1depending on the latitude Epan --- FET, RHmax, RHmin, u2 Tmax, Tmin, u2, RHmax, RHmin, n, E 3. PERFORMANCE EVALUATION CRITERIA The performance evaluation criteria used in the present study are, namely, the coefficient of determination (R2 ), the root mean square error (RMSE), systematic RMSE, unsystematic RMSE and the efficiency coefficient (EC). 3.1 Coefficient of Determination (R2 ) Coefficient of Determination is 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. It measures the degree of association between the observed and estimated values and indicates the relative assessment of the model performance. 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. 178-186 © IAEME 181 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 Systematic RMSE (RMSEs) It measures the room available for local adjustment. It is expressed as, n op RMSE ii n i s 2 1 )ˆ( − = ∑= Where ii boap +=ˆ , a and b are the liner regression coefficients 3.4 Unsystematic RMSE (RMSEu) It shows the noise level in the model and is a measure of scatter about the regression line and potential accuracy. It is expressed as n pp RMSE ii n i u 2 1 )ˆ( − = ∑= 3.5 Efficiency Coefficient (EC) It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[7] . It is a better choice than RMSE statistic when the calibration and verification periods have different lengths (Liang et al., 1994)[6] . It measures directly the ability of the model to reproduce the observed values and it is expressed as ( ) ( )∑ ∑ = = − − −= n i i n i ii oo po EC 1 2 1 2 1 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 Reference evapotranspiration(ET0) was estimated using the climatic data for different methods with original values of empirical coefficients. The mean weekly values were compared with those estimated by PM method. The percentage deviations with respect to PM method are shown in Table 2. The positive deviation represents overestimation and negative deviation indicates
  • 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME 182 underestimation of ET0 values. It may be observed that the percentage deviation between PM method and other methods varied between –14.9% and 55.3%. RA method estimated ET0 with largest deviation followed by JH method and, HR, PT, CS, and BC methods with minimum deviation. The performance indicators of the methods with original coefficients are presented in Table 3. The relatively more unsystematic RMSE components with the ET0 estimation methods except MP and BC methods indicate more noise level in the methods and scatter about the regression line. The temperature, radiation, physically and pan evaporation based methods selected for the present study were recalibrated with respect to PM method as presented in Table 4. The performance indicators of these empirical models with original and recalibrated coefficients in the estimation of ET0 are given in Table 5. The improved R2 , EC and reduced RMSE (Table 5) indicate the closeness of estimated weekly ET0 values and thereby reflect the appropriateness of recalibration. Though an improvement in the performance of ET0 estimation methods with recalibrated coefficients over these methods with original coefficients, in general, has been observed (Table 5), a significant improvement has been found in case of recalibrated MP and BC methods. However, out of these methods, recalibrated BC method may be adopted in the reasonable weekly ET0 estimation in the regions because of simpler data requirements. The scatter plots as shown in Figs.1 & 2 also depict similar observations. Table 2: Percentage deviations in the estimated mean weekly reference evapotranspiration with original coefficients Method PM BC JH HR PT RA MK MP PE CS ET0 (mm) 4.7 4.5 6.3 4.7 4.8 7.3 4 6.0 4.2 4.8 Percentage deviation … -4.3 34.0 0.0 2.1 55.3 -14.9 27.7 -10.6 2.1 Table 3: Performance indicators of various methods with original coefficients against PMM Method Slope(m) Intercept(c) R2 RMSE (mm) RMSES (mm) RMSEu (mm) EC (%) BC 0.9241 0.5012 0.9276 0.33 0.09 0.32 92.76 JH 0.7125 0.2030 0.7179 0.65 0.35 0.55 71.79 HR 0.9962 0.0369 0.7208 0.65 0.35 0.55 72.08 PT 1.0048 -0.1147 0.6270 0.75 0.46 0.60 62.70 RA 0.6193 0.1504 0.5384 0.83 0.57 0.62 53.84 MK 1.1337 0.1849 0.5434 0.83 0.57 0.62 54.34 MP 0.7606 0.0860 0.9673 0.22 0.04 0.22 96.73 PE 0.5933 2.1925 0.4745 0.89 0.65 0.61 47.45 CS 0.9184 0.2547 0.9024 0.38 0.12 0.36 90.24
  • 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME Table 4: ET0 estimation methods with original and recalibrated coefficients Method Original equation Recalibrated equation BC ET0 = a +b [p (0.46T + 8.13)] where a = 0.0043 (RHmin) – n/N – 1.41 b = 0.82 – 0.0041 (RHmin) + 1.07 (n/N) + 0.066 (ud) – 0.006 (RHmin) (n/N) – 0.0006 (RHmin) (ud) ET0 = a +b [p (0.46T + 8.13)] where a = – 0.0722 (RHmin) – 4.27 (n/N) + 4.70 b = – 0.36+ 0.0115 (RHmin) + 0.96 (n/N) + 0.215 (ud) + 0.004 (RHmin) (n/N) – 0.0027 (RHmin) (ud) JH ET0 = Rs (0.025 T + 0.08) ET0 = Rs (0.030 T – 0.29) HR ET0 = 0.0023 Ra (T + 17.8) x (TD) 0.5 ET0 = 0.0024 Ra (T +14.9) x (TD) 0.5 PT RA ET0 = c (W.Rs) where c = 1.066 – 0.00128 RH + 0.045 ud – 0.0002 RH ud + 0.0000315 (RH) 2 – 0.00103 (ud)2 ET0 = c (W.Rs) where c = 0.554 + 0.00185 RH + 0.346 ud – 0.0037 RH ud – 0.000015 (RH)2 – 0.00195 (ud)2 MK MP ET0 = C       −+ +∆ + +∆ ∆ ))(01.00.1)(27.0( 2 asn eeUR γ γ γ where C = 0.68 + 0.0028 (RHmax) + 0.018 (Rs) – 0.068 (ud) + 0.013 (ud / un) + 0.0097 (ud )(ud/un) + 0.000043 (RHmax) (Rs) (ud) ET0 = C       −+ +∆ + +∆ ∆ ))(01.00.1)(27.0( 2 asn eeUR γ γ γ Where C = 0.63+ 0.0012 (RHmax) + 0.011 (Rs) – 0.010 (ud) + 0.013 (ud / un) + 0.0097 (ud )(ud/un) – 0.000039 (RHmax) (Rs) (ud) PE ET0 = Kp Epan where Kp = 0.108 – 0.0286 u2 + 0.0422 ln(FET) + 0.1434 ln(RH) – 0.000631[ln(FET)]2 ln(RH) ET0 = Kp Epan where Kp = – 2.896 + 0.1260 u2 + 0.0422 ln(FET) + 0.8127 ln(RH) – 0.000631[ln(FET)]2 ln(RH) CS ET0 = 0.473 Ra CT CW CH CS CE CM where CT = 0.393 + 0.02796 T + 0.0001189 (T)2 CW = 0.708 + 0.00339 W – 0.0000038 (W)2 CH = 1.25 – 0.00369 RH – 6.1x10-11 (RH)5 CS = 0.542 + 0.80 sp – 0.78 (sp)2 + 0.62 (sp)3 CE = 0.970 + 0.0000984 E CM = ranges from 0.9 to 1.1depending on the latitude ET0 = 2.45 Ra CT CW CH CS CE CM where CT = 1.06 – 0.06791 T + 0.001343 (T)2 CW = 0.819 + 0.002999 W – 0.0000024 (W)2 CH = 1.01 – 0.00684 RH – 29.68x10-11 (RH)5 CS = 0.847 – 0.40 sp + 2.06 (sp)2 – 1.51 (sp)3 CE = 0.970 + 0.0000984 E CM = ranges from 0.9 to 1.1depending on the Latitude )GR(26.1ET n0 − γ+∆ ∆ = s0 R γΔ Δ 76.0ET + =s0 R γΔ Δ 65.0ET + = )GR(23.1ET n0 − γ+∆ ∆ =
  • 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME 184 Table 5: Performance evaluation of ET0 estimation methods with original and recalibrated coefficients against PM method Method Slope (m) Intercept (c) R2 RMSE (mm) EC (%) Original recalibrated Original recalibrated Original recalibrated Origina l recalibrated Original recalibrated training testing training testing training testing training testing training testing BC 0.9241 0.9999 1.0112 0.5012 0.0004 -0.0764 0.9276 0.9824 0.9882 0.33 0.15 0.15 92.76 98.24 98.82 JH 0.7125 0.8220 0.9462 0.2030 0.8726 0.2645 0.7179 0.7552 0.9132 0.65 0.57 0.42 71.79 75.52 91.32 HR 0.9962 0.9290 1.1888 0.0369 0.3448 -0.6678 0.7208 0.6977 0.8212 0.65 0.64 0.60 72.08 69.77 82.12 PT 1.0048 0.9473 1.2879 -0.1147 0.2409 -1.2627 0.6270 0.5793 0.7788 0.75 0.75 0.67 62.70 57.93 77.88 RA 0.6193 0.8238 0.7765 0.1504 0.7530 0.8841 0.5384 0.9221 0.9688 0.83 0.32 0.25 53.84 92.21 96.88 MK 1.1337 0.8745 1.2695 0.1849 0.6091 -1.2098 0.5434 0.4774 0.7476 0.83 0.84 0.71 54.34 47.74 74.76 MP 0.7606 1.0075 1.0141 0.0860 -0.0366 -0.0861 0.9673 0.9961 0.9967 0.22 0.07 0.08 96.73 99.61 99.67 PE 0.5933 0.5629 0.9029 2.1925 1.9086 1.1276 0.4745 0.5415 0.7645 0.89 0.78 0.69 47.45 54.15 76.45 CS 0.9184 0.6584 0.6254 0.2547 1.7254 1.8174 0.9024 0.8931 0.8674 0.38 0.38 0.48 90.24 89.31 86.74 Fig. 1: Scatter plots of weekly ET0 estimated by various methods with original coefficients against ET0 estimated using PM method
  • 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME 185 Fig. 2 Scatter plots of weekly ET0 estimated by various methods with recalibrated coefficients against ET0 estimated using PM method during testing period CONCLUSIONS The BC, JH and HR (temperature based), PT, RA and MK (radiation based), MP(physically based), PE and CS (pan evaporation based) reference evapotranspiration estimation methods have been recalibrated with respect to FAO-56 Penman-Monteith (PM) method and their performance in the weekly ET0 estimation was evaluated based on the performance criteria(R2 , RMSE and EC). All these ET0 estimation methods, in general, showed an improved performance with recalibrated coefficients. The recalibrated MP method and BC method have performed well in the weekly ET0 estimation. However, recalibrated Blaney-Criddle (BC) method may be applied for the reasonable estimation of weekly reference evapotranspiration (ET0) in the region because of simpler data requirements.
  • 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME 186 REFERENCES [1] Alkaeed, O., Flores, C., Jinno, K., and Tsutsumi, A. 2006. Comparison of several reference evapotranspiration methods for Itoshima Peninsula area, Fukuoka, Japan. Memoirs of the Faculty of Engineering, Kyushu University, 66(1), 1-14. [2] 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. [3] Berengena, J. and Gavilan, P. 2005. Reference evapotranspiration estimation in a highly advective semiarid environment Journal of Irrigation and Drainage Engineering, 131(2), 147-163. [4] Irmak, S., Irmak, A., Allen, R. G., and Jones, J. W.(2003). Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. Journal of Irrigation and Drainage Engineering, 129(5), 336-347. [5] Jensen, M.E., Burman, R.D. and Allen, R.G. (1990), Evapotranspiration and Irrigation water requirements. ASCE Manuals and Reports on Engineering Practice, No 70, New York, pp.332. [6] 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. [7] 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. [8] Suleiman, A. A. and Hoogenboom, G. 2007. Comparison of Priestley-Taylor and FAO-56 Penman-Monteith for daily reference evapotranspiration estimation in Georgia. Journal of Irrigation and Drainage Engineering, 133(2), 175-182. [9] Trajkovic, S. and Stojnic, V. 2008. Simple daily ET0 estimation techniques. Facta Universitatis. Series: Architecture and Civil Engineering, 6(2), 187 – 192. [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] 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. [12] 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. [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.

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