Irrig Sci (2008) 26:169–175 DOI 10.1007/s00271-007-0083-y
ORIGINAL PAPER
Evaluation of pan coefficient for reference crop evapotranspiration for semi-arid region H. G. Gundekar Æ U. M. Khodke Æ S. Sarkar Æ R. K. Rai
Received: 26 April 2007 / Accepted: 29 June 2007 / Published online: 24 July 2007 Springer-Verlag 2007
Abstract Pan coefficient (Kpan) is the important factor for computation of reference evapotranspiration (ETo) from pan evaporation (Epan). In this paper, the approaches proposed by Cuenca (Irrigation system design: an engineering approach. Prentice-Hall, Englewood Cliffs, 1989), Snyder (J Irrig Drain Eng 118(6):977–980, 1992), Orang (Potential accuracy of the popular non-linear regression equations for estimating pan coefficient values in the original and FAO24 tables. Unpublished Report, Calif. Dept. of Water Resources, Sacramento, 1998), Raghuwanshi and Wallender (J Irrig Drain Eng 118 (6):977–980, 1998) and Pereira et al. (Agric Water Manage 76:75–82, 1995) were evaluated for a semi-arid region. By comparing with the FAO 56 Penman-Monteith (F-PM) method the Snyder (J Irrig Drain
Communicated by J. Ayars. H. G. Gundekar (&) S. Sarkar Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India e-mail:
[email protected] S. Sarkar e-mail:
[email protected] U. M. Khodke Department of Irrigation and Drainage Engineering, Marathwada Agricultural University, Parbhani, Maharashtra, India e-mail:
[email protected] R. K. Rai Department of Irrigation, State Water Resources Agency, Ground-floor WALMI Bhawan, Utrethia, 226 026 Lucknow, Uttar Pradesh, India e-mail:
[email protected]
Eng 118(6):977–980, 1992, 1992) approach was best suited for the semi-arid region. Introduction Process of evaporation and evapotranspiration are the major components of the hydrologic cycle which play a vital role in agricultural and hydro-meteorological studies as well as in the operation of reservoirs, design of irrigation and drainage systems, and irrigation scheduling. Estimation of evapotranspiration from the pan evaporation data is commonly practiced. Since Class-A pan (USWB) evaporimeters are widely available, in the estimation of reference crop evapotranspiration, Pan coefficient (Kpan) is used as a multiplicative factor to convert Pan evaporation to ETo. Therefore, a reliable estimate of Kpan is required. To determine ETo other methods are available in the literatures, which use climatic parameters such as solar radiation, temperature, wind speed and relative humidity (Pruitt 1966; Doorenbos and Pruitt 1977; Burman et al. 1980; Snyder 1992; Smith et al. 1996, so on) but these parameters are scarce in developing countries. Also, these methods require a good computational skill. On the other hand, estimation of ETo directly from the pan evaporation data can easily be done. Many researchers reported a high correlation between Epan and ETo, when evaporation pans are properly maintained (Jensen et al. 1961; Pruitt 1966; Doorenbos and Pruitt 1975). Therefore, a study was conducted to determine which method is best for estimation of Kpan values in the semi-arid region of India. Methodology There is a high correlation between Epan and ETo, and the expression can be given as follows (Snyder 1992).
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Irrig Sci (2008) 26:169–175
ETo ¼ Epan Kpan
ð1Þ
The locations of evaporation pans influence the proper interpretation of pan evaporation data (Howell et al. 1983). The Kpan accounts for the upwind fetch of low-growing vegetation, mean daily wind speed, and relative humidity effects on the difference between Epan and ETo (Jensen 1974; Doorenbos and Pruitt 1977). Since the location (i.e. climate) is important for converting EPan to ETo (Howell et al. 1983), a study was conducted to identify a method to determine the KPan values for semi-arid climatic conditions. The following five approaches were considered. Cuenca (1989) Frevert et al. (1983) proposed the following relationship as a function of daily mean relative humidity, wind speed and upwind fetch distance. The relationship was then modified by Cuenca (1989) and was given as follows. Kpan ¼ 0:475 ð0:245 103 U2 Þ þ ð0:516 102 RHÞ þ ð0:118 102 FÞ ð0:16 104 RH2 Þ
Raghuwanshi and Wallender (1998) Raghuwanshi and Wallender (1998) presented another equation for Kpan using indicator regression approach. In this approach, the categorical (wind run and relative humidity) and quantitative fetch length data were used rather than the average or particular values within a range. Kpan ¼ 0:5944 þ 0:0242X1 0:0583X2 0:1333X3 0:2083X4 þ 0:0812X5 þ 0:1344X6
ð5Þ
where X1 = ln(F); X2, X3 and X4 = wind run categories of 175–425, 425–700, and > 700 km/day, respectively, and were assigned values of one or zero depending upon their presence. A zero value for these variables represented a wind run of < 175 km/day. Similarly, X5 and X6 = relative humidity categories of 40–70% and ‡ 70%, respectively. Again the value of one or zero were assigned depending on the presence of the relative humidity category, and a zero value for these variables represented a relative humidity of £ 40%. Pereira et al. (1995)
ð0:101 105 F 2 Þ ð0:8 108 RH2 U2 Þ ð0:1 107 RH2 FÞ
ð2Þ
where U2 = daily mean wind speed measured at 2 m height (km/day), RH = daily mean relative humidity (%), and F = upwind fetch distance of low-growing vegetation (m). Snyder (1992) Snyder (1992) reported that the Kpan relationship proposed by Cuenca (1989) was complex, and gave unsatisfactory results for some climatic conditions when compared with the original coefficients published by Doorenbos and Pruitt (1977). The following relationship for Kpan values was suggested. Kpan ¼ 0:482 þ ½0:24 lnðFÞ ð0:000376 U2 Þ þ ð0:0045 RHÞ
ð3Þ
Orang (1998) Orang (1998) developed a equation for Kpan using interpolation between fetch distances and based on the data used to develop FAO 24 Kpan values (Doorenbos and Pruitt 1977). Adopting linear regression techniques similar to Snyder (1992) he proposed the following equation. Kpan ¼ 0:51206 0:000321U2 þ 0:002889H þ 0:031886lnðFÞ 0:000107HlnðFÞ
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ð4Þ
Pereira et al. (1995) developed the following relationship for KPan based on temperature and the psychometric constant. Kpan ¼ 0:85 ðD þ cÞ=½D þ c ð1 þ 0:33 U2 Þ
ð6Þ
where D = Slope of the saturation vapour pressure curve (kPa C–1) and c = Psychometric constant (i.e. 0.0642 kPa C–1). Equations (2) through (6) require testing or calibration when they are used under different climatic conditions. The accuracy and reliability of these equations may differ from one location to another because some assumptions might have been made that could limit the application in a particular climate (Irmark et al. 2002). To our knowledge Eqs. (2) through (6) were not evaluated for arid and semiarid sub-tropical regions. Different studies have reported dissimilar results for varying climatic conditions. Conceicao (2002) recommended Eq. (3) for warm and mild climate of Northwest Brazil. On the other hand Eq. (2) gave better results in humid conditions (Irmark et al. 2002). The reliability and accuracy of these relationships need to be carefully tested and/or calibrated for the local climate in order to obtain more reliable and accurate estimates of ETo from Kpan data for semi-arid conditions. The F-PM method was used in this study to test the accuracy of the ETo estimated from Kpan equations, because the comparative studies (Jensen et al. 1990; Itenfisu et al. 2000; Allen et al. 1994a, 1994b, 1998, 2000; Smith
Irrig Sci (2008) 26:169–175
171
et al. 1996; Walter et al. 2000; Gundekar 2004, so on) have confirmed the superior performance of F-PM method. Also, It has been accepted as a standard method for estimating ETo by the ASCE Task Committee on standardization of ETo. The F-PM method computed ETo using the following relationship along with other auxiliary equations presented in Allen et al. (1998). ETo ¼
900 0:408DðRn GÞ þ c Tþ273 U2 ðes ea Þ D þ cð1 þ 0:34 U2 Þ
ð7Þ
where, ETo = reference crop evapotranspiration (mm day–1); T = mean daily air temperature measured between 1.5 and 2 m height (C) [=(Tmax + Tmin)/2]; Rn = net radiation over well-watered, cool-season grass (MJ m–2 day–1); G = soil heat flux density (MJ m–2 day–1); U2 = wind speed at 2 m height (ms–1); es = saturation vapor pressure (kPa); ea = actual vapor pressure (kPa); (es – ea) = vapor pressure deficit (kPa); D = slope of the evaporation vapour pressure curve (kPa C–1); and c = psychometric constant (= 0.0642 kPa C–1). The various terms present in the above equation were computed on daily basis and the ETo was estimated as per procedure outlined in FAO 56 (Allen et al. 1998).
Study area and data To evaluate the qualitative as well as the quantitative analysis of Kpan for the semi-arid region, the data from Marathwada region of Maharashtra province of India was used. The region is located between 1945¢ to 2001¢ N latitude and 7324¢ to 7797¢ E longitude with an elevation of 409 m above msl. The climate is semi-arid and subtropical, and experiences average rainfall of 850 mm. About 75% of the total rainfall of the region is due to the onset of South-West Monsoon (June to September). The average annual temperature is 25.9C with a mean maximum 41.4C and a mean minimum 21.6C. The area experiences extreme cold during the month of December, and the maximum temperature is recorded in May. The yearly sunshine duration recorded over the region is between 3,212 and 4,429 h. The annual average evaporation is approximately 2,460 mm. The annual wind speed ranges from 72.5 to 335 km/day. Daily weather data from 1971 to 2002 were obtained from meteorological observatory located at Marathwada Agricultural University Parbhani, Maharashtra under India Meteorological Department. Meteorological variables included rainfall, maximum and minimum air temperature, relative humidity, wind speed as well as wind direction at 2 m height above ground surface, and (Class A) pan evaporation. The Class-A pan evaporimeter (USWB) is
surrounded by dry fallow land. Value of F used for the computation of Kpan is 1,000 m. The data were randomly divided into two sets. A 30-year data set (1971–2000) was used for the evaluation of Kpan, and a 2-year data-set (2001–2002) was used for verification. In addition to the 2001–2002 data sets, another 2 years of data were randomly selected from the 30-year calibration data set.
Results and discussion The analysis was completed using daily, monthly and annual ETo. Computation of daily ETo The 30-year mean daily Epan measured from Class A evaporimeter is given in Fig. 1d. The peak evaporation was experienced during the period of 15 April to 15 May, and the peak seems to be related to high temperature, low relative humidity, and increasing wind speeds (Fig. 1a–c). A large drop in Epan occurred when the air temperature decreased and relative humidity increased during late May. Daily values of Kpan were computed using Eqs. (2) through (6) and were plotted in Fig. 2. The computed daily values of Kpan were nearly similar for Eqs. (2) to (5), whereas Eq. (6) gave a lower value of Kpan. In particular, Eqs. (3) and (5) result in almost equal values of Kpan except during the Monsoon (i.e. mid-June to mid- October). Estimated monthly mean Kpan values (using Eqs. 2–6) were compared with the FAO-24 Kpan (Doorenbos and Pruitt 1977) and are given in Table 1. In Table 1 the Snyder (1992) approach gave the best agreement to the FAO-24 followed by Raghuwanshi and Wallender (1998) and Orang (1998). The Pereira et al. (1995) showed poor ability to predict Kpan which might be due to exclusion of the fetch distance (Conceicao 2002). The sequence of performance from the most to the least accurate methods are Snyder (1992), Raghuwanshi and Wallender (1998), Orang (1998), and Cuenca (1989). Because of the poor performance of Pereira et al. (1995), it is eliminated for further analysis. The Kpan values computed by Eqs. (2–5) were used to estimate daily ETo (using Eq. 1) and were compared with ETo computed by F-PM (i.e. Eq. 7). A comparison in Fig. 3 revealed that the daily F-PM ETo tended to be higher than ETo estimated from Epan using Eqs. (2–5). Computation of monthly and annual ETo The earlier stated analyses were also performed for the computation of monthly ETo. The root mean squared error (RMSE), mean absolute deviation (MAD) and percentage
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Irrig Sci (2008) 26:169–175
Fig. 1 Mean measured daily meteorological parameters averaged over 30 years: mean daily mean and maximum temperature (a), mean daily wind speed (b), mean daily mean and minimum RH (c), mean daily evaporation (d)
M ax
45
M ean
a
340
270
U 2 ( k m /d a y )
35
T em p ( o C )
b
305
40
30 25
235 200 165
20
130
15
95 60
10
80
M ean
Month
c
Min
14 12
60
10
E p a n ( m m /d a y )
70
R H (%)
50 40 30
d
8 6 4
20 10
2
0
0
N
D
O
S
J
A
J
M
A
M
J
F
J
F
M
A
M
Month
Eq. 2
0.9
Eq. 4
Eq. 5
Eq. 3
J
J
A
S
O
N
D
Month
Mean absolute deviation (MAD)
Eq. 6
0.8
MAD ¼
0.6
Kpan
D
Month
O
D
N
N
S
O
J
S
A
A
J
J
A
J
M
M
M
A
M
J
F
F
J
N 1X ETK;i ETo;i N i¼1
ð9Þ
0.5
Percentage error of estimate (PE) ETK;i ETo;i 100% PE ¼ ETo;i
0.3 0.2 0.0 F
J
M
A
M
J
J
A
S
O
N
D
Month
Fig. 2 Calculated daily Kpan values using Eqs. (2) to (6)
error (PE) were used to test the results using the following equations. Root mean squared error (RMSE) "
N 2 1X RMSE ¼ ETK;i ETo;i N i¼1
#1=2 ð8Þ
where, ETK, i and ETo, i are the ETo values based on Kpan and F-PM, respectively, and N is the number of observations.
123
ð10Þ
The monthly mean estimated values of RMSE, MAD, and PE along with the computed values of ETo (i.e. ETK) are given in Table 2. It is clear from Table 2 that Snyder’s (1992) method (Eq. 3) gave best agreement to the F-PM method. The sequential performance was observed as follows: Eq. (3) > Eq. (5) > Eq. (4) > Eq. (2). Annual mean daily ETo estimates from Eqs. (2) to (5) were slightly lower than F-PM ETo (Table 2), but RMSE value on the order of 0.5 mm/day (i.e. Eq. 3) is sufficiently accurate for irrigation applications. Investigation of equations on individual years Four randomly selected data sets (i.e. 1983, 1996, 2001, and 2002) having different weather patterns than the 30year averaged data were used to verify the Kpan relationships (i.e. Eq. 2 to 5) for the estimation of ETo. The annual
Irrig Sci (2008) 26:169–175
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Table 1 Monthly mean Kpan coefficients obtained from Eqs. (2) to (6) and FAO-24 (Doorenbos and Pruitt 1977)
Eq. 4
Eq. 5
Eq. 3
F-PM
8.0
Pan coefficients (Kpan) Eq. (2)
Eq. (3)
Eq. (4)
Eq. (5)
Eq. (6)
FAO 24
January
0.68
0.73
0.69
0.72
0.40
0.75
February
0.64
0.68
0.66
0.69
0.37
0.75
March
0.60
0.63
0.63
0.65
0.38
0.65
April
0.58
0.60
0.61
0.63
0.38
0.65
May
0.58
0.60
0.60
0.62
0.31
0.60
June
0.65
0.69
0.65
0.67
0.26
0.70
July August
0.69 0.71
0.75 0.78
0.69 0.71
0.70 0.72
0.25 0.27
0.75 0.75
September
0.72
0.79
0.72
0.73
0.35
0.85
October
0.70
0.76
0.71
0.73
0.41
0.75
November
0.69
0.74
0.70
0.73
0.40
0.75
December
0.69
0.74
0.70
0.73
0.41
0.75
ETo (mm/day)
Month
Eq. 2
9.5
6.5
5.0
3.5
2.0 D
N
O
S
A
J
J
M
A
M
F
J
M onth
Fig. 3 Calculated daily ETo by F-PM method and using Eqs. (2) to (5)
evaluated for estimating ETo in the semi-arid region of India using the 32 years of data. From this study following conclusions can be drawn. 1.
totals are summarised in Table 3, whereas sample results of computed monthly ETo values for year 2001 and 2002 are plotted in Fig. 4. The monthly and annual analysis showed that Eq. (3) provided closer agreement with the F-PM method followed by Eqs. (5) and (4), whereas Eq. (2) consistently underestimated ETo.
2.
3. Conclusions The approaches for the estimation of Kpan proposed by Cuenca (1989), Snyder (1992), Orang (1998), Raghuwanshi and Wallender (1998), and Pereira et al. (1995) were
4.
Among the five approaches Pereira et al. (1995) gave a poor performance under the semi-arid climatic conditions. Based on the visual comparison as well as from the statistical criteria, ETo computed from Snyder (1992) gave closer agreement with the F-PM method for daily, monthly, and annual estimates as compared to other approaches. The sequential performance of the approaches were: Snyder (1992) > Raghuwanshi and Wallender (1998) > Orang (1998) > Cuenca (1989) for semi-arid climatic conditions. Using the simple Eq. (3) methodology avoids the use of Table Look-up procedure (Doorenbos and Pruitt
Table 2 Statistical test for comparison of estimated monthly mean and annual mean ETo using Eqs. (2) to (5) and F-PM method Month
F-PM Eq. (2) ETk
RMSE MAD PE
Eq. (3)
Eq. (4)
Eq. (5)
ETk
ETk
ETk
RMSE MAD PE
RMSE MAD PE
RMSE MAD PE
January
3.57
2.98 0.76
0.65
16.30 3.16 0.52
0.38
4.99 3.02 0.74
0.62
15.39 3.15 0.65
0.44
11.61
February
4.41
3.79 0.77
0.63
14.18 3.99 0.50
0.36
3.94 3.87 0.71
0.56
12.28 4.00 0.62
0.45
9.21
March
5.32
4.75 0.86
0.77
10.59 4.85 0.46
0.28
3.94 4.97 0.67
0.59
6.49 5.18 0.51
0.43
2.51
April
6.82
6.04 0.70
0.68
11.45 6.53 0.34
0.38
0.08 6.34 0.51
0.49
6.96 6.60 0.44
0.39
3.18
May
7.54
6.77 1.21
1.07
10.25 6.92 0.56
0.55
5.49 6.95 1.08
0.94
7.77 7.23 0.88
0.75
4.11
June
6.02
4.89 1.13
1.07
18.65 5.25 0.61
0.53
8.30 4.85 1.17
1.10
19.38 5.05 1.00
0.93
15.99
July
4.28
3.61 0.84
0.80
15.61 3.69 0.42
0.36
7.02 3.56 0.89
0.86
16.98 3.66 0.79
0.76
14.63
August
3.89
3.08 0.86
0.78
20.70 3.30 0.47
0.39
7.09 3.04 0.89
0.82
21.71 3.10 0.84
0.77
20.19
September 4.18
3.47 0.79
0.72
16.93 3.63 0.39
0.32
4.81 3.45 0.81
0.75
17.51 3.52 0.75
0.68
15.87
October
4.15
3.47 0.80
0.71
16.45 3.66 0.46
0.34
4.33 3.49 0.78
0.69
15.96 3.60 0.69
0.59
13.25
November
3.74
3.17 0.73
0.54
15.12 3.37 0.43
0.37
2.84 3.20 0.72
0.52
14.48 3.33 0.64
0.44
10.99
December
3.46
2.67 0.82
0.56
22.59 3.02 0.51
0.39
6.06 2.70 0.80
0.54
21.94 2.81 0.72
0.44
18.65
Average
4.78
4.06 0.86
0.75
15.74 4.28 0.47
0.39
4.91 4.12 0.81
0.71
14.74 4.27 0.71
0.59
11.68
F-PM, ETk, RMSE, MAD are in mm/day and PE in %
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Irrig Sci (2008) 26:169–175
Table 3 Annual ETo (mm) and PE (%) of estimates using Eqs. (2) to (5) for randomly selected years
Year
F-PM
Eq. (2)
ETo
ETo
PE
ETo
PE
ETo
1983
1813.2
1481.9
18.27
1672.70
7.75
1798.36
1996
1812.4
1559.7
13.94
1737.60
4.13
1605.74
2001 2002
1685.8 1614.02
1567.5 1320.0
7.02 18.22
1664.1 1508.1
1.29 6.56
1579.28 1509.65
6.32 6.47
Average
14.36
F-PM
Eq.2
Eq. 3
Eq. 4
ETo (m m /m onth)
4.93
Eq. (5) PE
ETo
PE
0.82
1871.51
3.22
11.40
1667.61
7.99
1610.13 1543.70
4.49 4.36
6.25
5.01
Eq. 5
250
2001
200 150 100 50 0
ec
ov
D
N
ct
O
p Se
l
ug
A
Ju
n
Ju
ay M
pr
A
ar M
b Fe
n
Ja
Month 300
F-PM
Eq.2
Eq. 3
Eq. 4
Eq. 5
250
ETo (m m /m onth)
Eq. (4)
References
300
2002
200 150 100 50 0
ec
D
ct
ov
N
O
p Se
ug
A
l
n
Ju
Ju
pr
ay M
A
ar M
n
b Fe
Ja
Month
Fig. 4 Comparison of monthly ETo calculated from F-PM and using Kpan from Eq. (2) to Eq. (5) for two randomly selected years (2001– 2002)
5.
Eq. (3)
1977), and it provides fast and reliable computation of ETo. The performance of Raghuwanshi and Wallender (1998) approach was also acceptable for estimating the ETo.
Acknowledgments The authors are thankful to the Department of Agro-meteorology, Marathwada Agricultural University Parbhani, Maharashtra, India for providing the data to carry out this study. Authors wish to thank the anonymous reviewers for their constructive suggestions to improve the quality.
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