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    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 81 REFERENCE EVAPOTRANSPIRATION ESTIMATION BY RADIATION BASED METHODS K. Chandrasekhar Reddy Professor and Principal, Department of Civil Engineering, Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India ABSTRACT Most of the studies have shown that the FAO-56 Penman-Monteith (PM) method gives very accurate estimation of reference evapotranspiration(ET0) in different environments. However, under limited climatic data availability conditions, the simple empirical methods yielding results comparable with PM ET0 may be selected at regional level for reasonable estimation of ET0. This study deals with the evaluation of monthly reference evapotranspiration(ET0) estimation using radiation based methods of Priestley-Taylor(PT), FAO-24 Radiation(RA) and Makkink(MK) by comparing their performance with that of PM method, developing relationships between PM and other methods and recalibrating the methods with respect to PM method. Tirupati region of Andhra Pradesh, India is selected as the study area and its meteorological data was collected from the India Meteorological Department, Pune. It is observed that the RA method improved its performance significantly on recalibration when compared to other two methods. Therefore, RA method may be used for reasonable ET0 estimation in similar climatic regions as that of the study area. Keywords: Radiation based methods, Penman-Monteith, Recalibration, Reference evapotranspiration. 1. INTRODUCTION Evapotranspiration(ET) is the loss of water into the atmosphere by the combined processes of evaporation from the soil and plant surface and transpiration from plants.[1] Field measurement of evapotranspiration is rarely available and actual crop evapotranspiration(ETc) is usually calculated from estimated reference crop 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 in Doorenbos and Pruitt (1977)[5] , Allen et al. (1998)[1] . Doorenbos and Kassam (1979)[4] and Jensen et al. (1990) [8] have reported crop coefficients for many crops. These values are commonly used in places where the local data is not available. Reference crop evapotranspiration or Reference evapotranspiration (ET0) is defined as the rate of evapotranspiration from a hypothetical reference crop with an assumed crop height of 0.12 m, INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND TECHNOLOGY (IJCIET) ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2014): 3.7120 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 82 a fixed surface resistance of 70 s m−1 , and an albedo of 0.23, closely resembling the evapotranspiration from an extensive surface of green grass of uniform height, actively growing, completely shading the ground, and not short of water.[1] Its accurate estimation is vital in irrigation system design, crop yield simulation and water resources planning and management. It is desirable to have a method that estimates reasonably the reference Evapotranspiration (ET0). The amount of ET0 is calculated by meteorological data based methods. However, choosing the best method for ET0 estimation from the described methods is difficult. Therefore, the International Commission for Irrigation and Drainage and the Food and Agriculture Organization of the United Nations (FAO) Expert Consultation on revision of FAO methodologies for crop water requirements have recommended the FAO56 Penman-Monteith (PM) equation, which was presented in FAO 56[1] , to be used as the standard method to estimate ET0. Many researchers thereafter took it as a standard to modify other methods that required less input data. Er-Raki et al. (2010)[6] shown, under arid and semi-arid climates, radiation based models may perform poorly. Bois et al. (2005)[2] studied that use of locally calibrated equations can make them more accurate than temperature based and even combination type ones. Denmirtas et al. (2007)[3] developed regional relationships between ET and that estimated by various climatological methods and concluded that PM method gives the best results followed by Penman, Radiation and Blaney-Criddle methods. Irmak et al. (2003)[7] recommended solar radiation and net radiation based ET0 equations over the other commonly used temperature and radiation based methods by comparing their performance with PM method. The present study reports the performance evaluation of commonly used radiation based ET0 estimation methods based on their accuracy of estimation and development of inter-relationships between the PM and the other climatological variables. And also, these methods are recalibrated with reference to PM method for Tirupati region of Andhra Pradesh, India. 2. MATERIALS AND METHODS Tirupati region, located in Chittoor district of Andhra Pradesh, India, with global coordinates of 130 05’N latitude and 790 05’ E longitudes, has been chosen as the study area. The meteorological data of the study area for the period 1992-2001 was collected from IMD, Pune. Data from 1992 to 1998 is used for the purpose of training the model and that of 1999 to 2001 for testing the model. The details of the methods selected for the present study are presented in Table 1. Table1: Details of reference evapotranspiration estimation methods Method Basic reference Equation Input data Primary Secondary FAO 56 Penman- Monteith (PM) Method Allen et al., (1998)[1] ET0 = )34.01( )( 273 900 )(408.0 2 '' '' 2 '''' u eeu T GR as mean n ++∆ − + +−∆ γ γ Tmax, Tmin, RHmax, RHmin, u2, n …. Radiation based methods 1.Priestley- Taylor (PT) Priestley- Taylor (1972)[12] ( )G− + = n0 R γ∆ ∆ 26.1ET Tmax, Tmin, n --- 2.FAO-24 Radiation (RA) Doorenbos and Pruitt (1977)[5] ET0 = c (W.Rs) Where c = 1.066 – 0.00128 RHmean + 0.045 ud – 0.0002 RHmean ud + 0.0000315 (RHmean) 2 – 0.00103 (ud)2 Tmax, Tmin, n RHmax, RHmin, u2, ud/un 3.Makkink(MK) Makkink (1957)[10] Tmax, Tmin, n --- Rs γΔ Δ 65.0ET0 + =
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 83 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), systematic RMSE, unsystematic RMSE and the efficiency coefficient (EC). 3.1 Coefficient of Determination (R2 ) It 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 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)[13] 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( − = ∑= 2/1 1 2 1 2 1 )()( ))((     ∑ −∑ − −−∑ = == = n i i n i i ii n i ppoo ppoo R
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 84 3.5 Efficiency Coefficient (EC) It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[11] . It is a better choice than RMSE statistic when the calibration and verification periods have different lengths (Liang et al., 1994)[9] . 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 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 percentage deviations of ET0 values estimated by PT, RA and MK methods with reference to PM method are presented in Table 2. It may be observed that the deviations are significant for all the methods. Fig.1 showing the comparison of ET0 estimates with those of PM ET0 also exhibit similar observations. Table 2 Percentage deviations in the monthly average ET0 values estimated by radiation based methods with PM method Percentage deviation PT RA MK -39.4 to 13.4 -11.6 to 75.6 -51.6 to -2.6 Fig.1 Comparison of monthly average ET0 values estimated by radiation based methods with PM method 4.1 Development of inter-relationships between PM method and radiation based methods The ET0 values estimated using PT, RA and MK methods plotted against PM ET0 are shown in Fig.2 for study area. The performance indicators of the relationships developed between PM method and these methods are presented in Table 3. The large deviations of the slope from one and intercept from zero can be observed from the scatter plots. Low values of R2 & EC and high values of RMSE indicate unsatisfactory performance of the relationship. High values of systematic RMSE and unsystematic RMSE represent the scope for recalibration. It indicates the unsatisfactory performance of relationships between PM and radiation based methods. Therefore, it may be tried to improve these methods’ performance by suitably recalibrating them against PM method using the observed climatic data. Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 1 11 21 31 41 51 61 71 81 91 101 Months ETo(mm/day) PM PT RA MK
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 85 Fig.2 Scatter plots of monthly average ET0 values estimated by radiation based methods against PM method Table 3 Performance indicators of radiation based methods with reference to PM method Method Relationship R2 RMSE (mm) RMSES (mm) RMSEU (mm) EC (%) PT PM = 1.4215 PT – 1.0428 0.5980 0.86 0.55 0.67 59.80 RA PM = 0.8174 RA – 0.4955 0.5164 0.95 0.66 0.68 51.64 MK PM = 1.3083 MK + 0.1970 0.4610 1.00 0.73 0.68 46.10 4.2 Recalibration of radiation based ET0 estimation methods It has been emphasized in the above section that radiation based methods selected for the present study have not performed satisfactorily in the regional ET0 estimation. The relationships developed between PM method and these methods to estimate ET0 comparable with PM method in the region as presented in the above section also showed unsatisfactory performances, though there was an improvement over the original methods. Therefore, before applying these methods to other regions, it is necessary to recalibrate them based on the locally collected lysimeter measured ET0 data accompanied by meteorological data such that they can be used in the region of the study area for reliable ET0 estimation. However, in the absence of lysimeter data, the competent PM method is usually adopted as the standard method of comparison for recalibration of the other methods. Since lysimeter measured ET0 data is not available in most of the regions, the methods were recalibrated with respect to PM method. The PT, RA and MK methods selected for the present study were recalibrated with reference to PM method. The recalibrated equations derived for the study area are presented along with original equation in Table 4. The performance indicators of recalibrated equations in the estimation of ET0 for both training and testing periods are given in Table 5. The scatter and comparison plots of ET0 values estimated by these methods with those of PM ET0 during the testing period are shown in Fig.3 and Fig.4 respectively. It may be observed from Table 5 that the RA method yielded the least RMSE and high R2 & EC values resulting in ET0 comparable with that from PM method. The RA method outperformed these methods in terms of performance evaluation criteria which may be due to the fact that the method takes into account not only the effects of humidity and wind velocity in the form of secondary input in addition to the primary input of radiation but also adjusts on recalibration over the other methods. The slope and intercept respectively close to one and zero also indicate an improved performance of the method with recalibrated coefficients. From the above discussion, it may be concluded that the RA method with recalibrated coefficients may be used for reasonable ET0 estimation in the study area. Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by PT, mm/day ETobyPM,mm/day Ideal line Best fit line Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by RA, mm/day ETobyPM,mm/day Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by MK, mm/day ETobyPM,mm/day
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 86 Table 4 Recalibrated radiation based ET0 equations Method Original Equation Recalibrated Equation 1.Priestley- Taylor (PT) 2.FAO-24 Radiation(RA) ET0 = c (W.Rs) Where c = 1.066 – 0.00128 RHmean + 0.045 ud – 0.0002 RHmean ud + 0.0000315 (RHmean) 2 – 0.00103 (ud)2 ET0 = c (W.Rs) Where c = 0.325 + 0.00198 RHmean + 0.303 ud – 0.0026 RHmean ud + 0.000007 (RHmean) 2 – 0.000034 (ud)2 3.Makkink(MK) Table 5 Performance indices of recalibrated radiation based ET0 methods Method Slope of the scatter plots Intercept of the scatter plots R2 RMSE (mm) EC (%) Training Period Testing period Training period Testing period Training period Testing period Training Period Testing period Training period Testing period PT 1.1933 1.1260 -0.8720 0.1894 0.6082 0.5668 0.85 0.88 60.82 56.68 RA 0.9390 1.0087 0.3052 0.1894 0.9528 0.9610 0.30 0.26 95.28 96.10 MK 0.9468 0.9445 0.2995 0.1501 0.4582 0.4459 1.00 0.99 45.82 44.59 Fig.3 Scatter plots of monthly average ET0 values estimated by recalibrated radiation based methods against PM ET0 values during testing period Fig.4 Comparison of monthly average ET0 values estimated by recalibrated radiation based methods with those estimated by PM method during testing period Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by PT, mm/day ETobyPM,mm/day Ideal line Best fit line Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by RA, mm/day ETobyPM,mm/day Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 ETo by MK, mm/day ETobyPM,mm/day Tirupati 0 1 2 3 4 5 6 7 8 9 10 11 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 Months ETo(mm/day) PM PT RA MK Rs γΔ Δ 89.0ET0 + =Rs γΔ Δ 65.0ET0 + = )GRn(52.1ET0 − γ+∆ ∆ =)GRn(26.1ET0 − γ+∆ ∆ =
    • International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME 87 5. CONCLUSION The percentage deviations of ET0 values estimated by PT, RA and MK methods with reference to PM method are significant. The PT and MK methods underestimated and RA method overestimated ET0 even after developing inter-relationships with PM methods, which is unsatisfactory. The RA method improved its performance significantly on recalibration over the other methods. Hence, the recalibrated RA method may be recommended for reasonable ET0 estimation in the study area. 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. pp.326. [2] Bois, B., Pieri, P., Van Leeuwen, C., Gaudillere, J.P. (2005): XIV International GESCO Viticulture Congress, Geisenheim, Germany, 23–27 August, 2005. pp.187–193 [3] Denmirtas, C., Buyukcangaz, H., Yazgan, S., Candogan.B.N. (2007), Evaluation of Evapotranspiration Estimation Methods for Sweet Cherry Trees (Prunus avium) in Sub-humid Climate. Pakistan Journal of Biological Sciences, Vol.10 (3), pp. 462-469. [4] Doorenbos, J. and Kassam, A.H. (1979). Yield Response to Water. FAO Irrigation and Drainage, Paper No 33. Rome, Italy. [5] Doorenbos, J. and Pruitt, W.O. (1977), Guidelines for predicting crop water requirements. FAO Irrigation and Drainage Paper No.24, FAO, Rome, Italy. [6] Er-Raki, S., Chehbouni, A., Khabba, S., Simonneaux, V., Jarlan, L., Ouldbba, A., Rodriguez, J.C., Allen, R. (2010): Assessment of reference evapotranspiration methods insemi-arid regions: Can weather forecast data be used as alternate of ground meteorological parameters? Journal of Arid Environments, Vol. 74. pp.1587–1596. [7] Irmark, 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, ASCE, Vol.129, No.5. pp. 336-347. [8] 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 [9] 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. [10] Makkink, G. F. (1957). “Testing the Penman formula by means of lysimeters.”, International Journal of Water Engineering, Vol.11, No.3, pp.277-288. [11] 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. [12] Priestley, C. H. B. and Taylor, R. J. (1972). “On the assessment of surface heat flux and evaporation using large-scale parameters.” Monthly Weather Review, Vol.100, No.2, pp. 81-92. [13] 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. [13] 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. [14] P.C.Madhuraj and J.Sudhakumar, “Assessment of Transient Hygroscopic Behaviour for Design of Passive Solar Building Envelope for Hot-Humid Regions”, International Journal of Civil Engineering & Technology (IJCIET), Volume 1, Issue 1, 2010, pp. 46 - 54, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.