20120140503020
Upcoming SlideShare
Loading in...5
×
 

20120140503020

on

  • 155 views

 

Statistics

Views

Total Views
155
Views on SlideShare
155
Embed Views
0

Actions

Likes
0
Downloads
0
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

20120140503020 20120140503020 Document Transcript

  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 183 GENERALIZATION OF PAN EVAPORATION BASED METHODS FOR ESTIMATING REFERENCE EVAPOTRANSPIRATION K. CHANDRASEKHAR REDDY Professor, Department of Civil Engineering and Principal, Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India. ABSTRACT The main objective of this study is evaluation and generalization of the pan evaporation based methods of FAO-56 Pan Evaporation (PE) method and Christiansen (CS) method with reference to the standard FAO-56 Penman-Monteith (PM) method in Tirupati region of Andhra Pradesh, India for estimating monthly reference evapotranspiration (ET0). Meteorological data observed in Tirupati region was collected from the India Meteorological Department (IMD), Pune. The evaluation is based on performance criteria namely, Root Mean Square Error (RMSE), Coefficient of Determination (R2 ) and Efficiency Coefficient (EC). The relationships between PM method and the other methods were developed to obtain monthly ET0 estimates comparable with PM method. The ET0 equations were then generalized (recalibrated) with respect to PM method for improving their monthly ET0 estimation capability in the region selected for the present study. The recalibrated FAO- 56 Pan Evaporation (PE) method performed satisfactorily in the monthly ET0 estimation. So, it may be adopted for the study area because of its simpler data requirements with reasonable degree of accuracy. Keywords: Reference Evapotranspiration, Recalibration, Penman-Monteith, Pan Evaporation Based Methods. 1. INTRODUCTION A reliable estimation of Evapotranspiration (ET) is of critical importance in irrigation system design, crop yield simulation and water resources planning and management. Field measurement of evapotranspiration is rarely available and actual crop evapotranspiration (ETc) is usually 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)[1] and Jensen et al. (1990)[6] have reported crop coefficients for many crops. These values are commonly used in places where the local data is not available. INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) Volume 5, Issue 3, March (2014), pp. 183-190 © IAEME: www.iaeme.com/ijaret.asp Journal Impact Factor (2014): 7.8273 (Calculated by GISI) www.jifactor.com IJARET © I A E M E
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 184 It is desirable to have a method that estimates judicially the reference Evapotranspiration (ET0). 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, the simple empirical methods for yielding results comparable with PM ET0 may be selected at regional level for reasonable estimation of ET0 under limited climatic data availability conditions Grismer et al. (2002)[4] evaluated the use of FAO-24 table values of pan coefficients (Kp) and six different Kp equations. Use of Kp table slightly underestimated measured ET0 at coastal sites, while the Cuenca, Allen-Pruitt and Synder Kp equations most closely approximated the average measured ET0 at all other sites. Irmak et al. (2002)[5] evaluated the Kp equation developed by Frevert et al. (1983)[3] and Synder (1992)[9] using a 23 year climatic data of Gainesville, Florida to estimate ET0. The ET0 values estimated using Frevert et al.’s pan coefficients were in good agreement with FAO 56 PM method compared to Snyder’s equation. The present study reports the performance evaluation of commonly used pan evaporation based ET0 estimation methods based on their accuracy of estimation and development of inter- relationships with PM method. And also, these methods are recalibrated with PM method for Tirupati region of Andhra Pradesh. 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 at the region for the period 1992-2001 were collected from IMD, Pune. For the purpose of training the model, data from 1992 to 1998 is used and from 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) 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 --- Pan evaporation based methods 1.FAO-56 Pan Evaporation (PE) Allen et al. (1998)[1] 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) Epan FET, RHmax, RHmin, u2 2.Christiansen (CS) Christiansen (1968)[2] ET0 = 0.473 Ra CT CW CH CS CE CM where CT = 0.393 + 0.02796 T + 0.0001189 (T)2 CW = 0.708 + 0.003393 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 --- Tmax, Tmin, u2, RHmax, RHmin, n, E
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 185 3. PERFORMANCE EVALUATION CRITERIA The performance evaluation criteria used in the 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 it 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 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 it 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 and 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 (RMSE u) It shows the noise level in the model and it is a measure of scatter about the regression line and potential accuracy. It is expressed as 2/1 1 2 1 2 1 )()( ))((           −− −− = ∑∑ ∑ == = n i i n i i ii n i ppoo ppoo R
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 186 n pp RMSE ii n i u 2 1 )ˆ( − = ∑= 3.5 Efficiency Coefficient (EC) Efficiency Coefficient is used to assess the performance of different models (Nash and Sutcliffe, 1970)[8] and 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 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 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 pan evaporation based methods with reference to PM method are presented in Table 2. It may be observed that the deviations are significant for both the methods. PE method underestimated ET0 for most of the period. The performance of CS method is better. Further, both CS and PM methods consider similar climatic parameters; the significant deviations in CS ET0 may be due to inapplicability of the coefficients in the equation for the study area. Fig.1 shows 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 pan evaporation based methods with PM method Percentage deviation PE CS - 42.3 to 2.9 -19.0 to 16.2 Fig.1: Comparison of monthly average ET0 values estimated by pan evaporation based methods with PM method 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 PE CS
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 187 4.1 Development of inter-relationships between PM method and pan evaporation based methods The ET0 values estimated using PE and CS methods plotted against PM ET0 are shown in Fig.2 for the study area. The performance indicators of the relationships developed between PM method and these methods are presented in Table 3. It may be observed from the scatter plots and performance indices that both the methods have improved their performance. The results are fairly comparable with PM method. However, the high values of unsystematic RMSE indicate more scatter about the regression line and considerably high values of systematic RMSE indicate the room for local adjustment of the coefficients for improving their performance. Fig.2: Scatter plots of monthly average ET0 values estimated by pan evaporation based methods against PM method Table 3: Performance indicators of pan evaporation based methods with reference to PM method Method Relationship R2 RMSE (mm) RMSES (mm) RMSEU (mm) EC (%) PE PM = 1.1804 PE + 0.4006 0.9211 0.38 0.11 0.37 92.11 CS PM = 0.9617 CS + 0.1254 0.8457 0.54 0.21 0.49 84.57 4.2 Recalibration of pan evaporation based ET0 estimation methods It has been emphasized in the above section that pan evaporation 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 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. 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 PE, 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 CS, mm/day ETo byPM,mm/day
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 188 The PE and CS methods selected for the present study were recalibrated with reference to PM method. The recalibrated equations derived for the region of the study area are presented along with original equation in Table 4. From this table it may be observed that there is a significant variation on recalibration of coefficients compared to the original values. 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. There was a marginal improvement in terms of R2 and EC of the recalibrated Christiansen equation. However, the large deviation of regression coefficients of scatter plots (slope and intercept) from one and zero indicates the significant amount of scatter around the regression line. This may be due to inapplicability of the coefficients, even after recalibration, in the equation for the study area. Further, the performance of the recalibrated PE method is better than the recalibrated CS method. From the above discussion, it may be concluded that recalibrated PE method may be used for the reasonable estimation of ET0 in the study area. Table 4: Recalibrated pan evaporation based ET0 equations Method Original Equation Recalibrated Equation 1.FAO-56 Pan Evaporation (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 = – 0.07 – 0.0082 u2 + 0.0422 ln(FET) + 0.2231 ln(RH) – 0.000631[ln(FET)]2 ln(RH) 2.Christiansen (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 + 0.003393 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 = 2.07 Ra CT CW CH CS CE CM where CT = 1.069 – 0.07119 T + 0.0015029 (T)2 CW = 0.609 + 0.006977 W – 0.0000119 (W)2 CH = 1.01 – 0.00848 RH – 17.7x10-11 (RH)5 CS = 0.884 – 0.38 sp + 1.01 (sp)2 – 0.52 (sp)3 CE = 0.970 + 0.0000984 E CM = ranges from 0.9 to 1.1depending on the latitude Table 5: Performance indices of recalibrated pan evaporation 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 PE 0.9350 0.9047 0.3272 0.6076 0.9434 0.9171 0.32 0.38 94.34 91.71 CS 0.6106 0.5674 2.3143 2.3668 0.9439 0.9468 0.32 0.31 94.39 94.68
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 189 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 CS, mm/day ETo byPM,mm/day Fig.3: Scatter plots of monthly average ET0 values estimated by recalibrated pan evaporation based methods against PM ET0 values during testing period Fig.4: Comparison of monthly average ET0 values estimated by recalibrated pan Evaporation based methods with those estimated by PM method during testing period 5. CONCLUSION The percentage deviations of ET0 values estimated by PE and CS methods with reference to PM method are significant. Both the methods slightly improved their performance over inter- relationships in terms of evaluation criteria in the region. There was a marginal improvement in terms of R2 and EC of the recalibrated Christiansen equation. However, the large deviation of regression coefficients of scatter plots (slope and intercept) from one and zero indicates the significant amount of scatter around the regression line. The performance of recalibrated PE method is better than that of the other method and it requires less climatic parameters as input. Hence, recalibrated PE method may be used for 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 PE, mm/day ETo byPM,mm/day Ideal line Best fit line 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 PE CS
  • International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME 190 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] Christiansen, J. E. (1968), Pan evaporation and evapotranspiration from climatic data. Journal of Irrigation and Drainage, ASCE, Vol.94, No.2, pp.243-265. [3] Frevert, D. K., Hill, R. W. and Braaten, B. C. (1983), Estimation of FAO evapotranspiration coefficients. Journal of Irrigation and Drainage Engineering, ASCE, Vol.109, No.2, pp.265- 270. [4] Grismer, M. E., Orang M., Snyder R. and Matyac R. (2002), Pan evaporation to reference evapotranspiration conversion methods. Journal of Irrigation and Drainage Engineering, ASCE, Vol.128, No.3, pp.180-184. [5] Irmak, S., Haman, D. Z. and Jones, J. W. (2002), Evaluation of class A pan coefficients for estimating reference evapotranspiration in humid location. Journal of Irrigation and Drainage Engineering, ASCE, Vol.128, No.3, pp.153-159. [6] 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. [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] Snyder, R. L. (1992), Equation for evaporation pan to evapotranspiration conversions. Journal of Irrigation and Drainage Engineering, ASCE, Vol.118, No.6. pp.977-980. [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.