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Use of the ‘modified Hargreaves’ equation (Droogers & Allen 2002) for calculating ET0 under limited data conditions is a very popular one and derives better result than Penman–Monteith when information is uncertain. In our study, we have calculated ET0 using the normal Hargreaves (Hargreaves et al. 1985; Hargreaves 1994), modified Hargreaves, and Hamon (Hamon 1961) equations and have observed that in certain months the modified Hargreaves equation is not applicable in five gauge stations in Tungabhadra River Basin (up to Haralahalli gauge station) as the term (TD - 0.0123*P) (where TD = difference of mean daily maximum and mean daily minimum temperature, P = precipitation) is generating negative value which is not feasible, but the other two methods are applicable for all the months. Whereas in the case of the second study sub-area, the Sutlej River Basin (up to Kasol gauge station), modified Hargreaves and the other two equations run smoothly there. A comparative study among the three methods (Table 7) shows that the use of modified Hargreaves method for calculating ET0 in the Sutlej River Basin, generates the best result as compared to the other two methods. In the case of the Tungabhadra River Basin, use of modified Hargreaves method along with normal Hargreaves method (only where the modified Hargreaves method is not applicable) generates the best result. Therefore, the values of ET0 calculated using modified Hargreaves method along with normal Hargreaves method (only where the modified Hargreaves method is not applicable) in the case of Tungabhadra River Basin and using modified Hargreaves equation in the case of Sutlej River Basin have been used. In Figure 6, the months along with their corresponding monthly precipitation (P) and TD (difference between mean daily maximum and mean daily minimum temperatures) are highlighted when the modified Hargreaves method is not applicable in the corresponding gauge stations. In Figure 6, it is shown that in the case of Tungabhadra River Basin (up to Haralahalli gauge station), modified Hargreaves is not applicable mainly in the months of June, July, and August. The months and their corresponding values of mean annual precipitation (P), mean monthly maximum (Tmax) and minimum temperature (Tmin), and difference between Tmax and Tmin, i.e., TD when the modified Hargreaves method is not applicable, are shown in Table 8.
Table 7

Comparative study among three ET0 calculation methods for both catchments

 Water yield (m3/sec)
% Error
Model outputObserved value
Sutlej River Basin Modified Hargreaves method 378.95 355.14 6.7 
Normal Hargreaves method 381.58 355.14 7.44 
Hamon's method 506.65 355.14 42.66 
Tungabhadra River Basin Modified Hargreaves method along with normal Hargreaves method (only where modified Hargreaves is not applicable) 157.49 219.16 −28.14 
Normal Hargreaves method 153.69 219.16 −29.87 
Hamon's method 295.66 219.16 34.91 
 Water yield (m3/sec)
% Error
Model outputObserved value
Sutlej River Basin Modified Hargreaves method 378.95 355.14 6.7 
Normal Hargreaves method 381.58 355.14 7.44 
Hamon's method 506.65 355.14 42.66 
Tungabhadra River Basin Modified Hargreaves method along with normal Hargreaves method (only where modified Hargreaves is not applicable) 157.49 219.16 −28.14 
Normal Hargreaves method 153.69 219.16 −29.87 
Hamon's method 295.66 219.16 34.91 
Table 8

Statistics of climatic parameters of the months when modified Hargreaves method is not applicable in Tungabhadra River Basin (up to Haralahalli gauge station)

Station No.Month No.P (mm)Tmax (°)Tmin (°C)TD (°C)Station No.Month No.P (mm)Tmax (°C)Tmin (°C)TD (°C)
598.5 30.5 23.3 7.2 116 696.4 28.6 22.4 6.2 
32 692.3 28.1 23.1 126 1,077.8 30.5 22.9 7.6 
43 564.4 29.4 23.1 6.3 127 1,211.4 28.2 22.1 
44 586 28.3 22.8 5.6 128 486.2 27.6 22 5.6 
56 637.9 28 22.8 5.2 138 716.9 30.8 23 7.8 
57 461.8 27.3 22.3 139 1,283.1 28.1 22.8 5.3 
68 933.8 27.6 22.6 140 908 27.7 22.5 5.2 
69 454.8 27.7 22.4 5.2 150 1,347.4 30.8 23.8 7.1 
80 748.4 28.6 23 5.5 151 1,057.3 28.4 23.1 5.3 
81 573.5 27.9 22.7 5.2 152 815.8 28.7 23.1 5.6 
92 681.7 28.1 22.8 5.3 153 691.1 28.4 22.6 5.8 
103 682 29.2 23.3 5.8 162 1,427.1 28.6 22.6 
104 1,037.6 27.6 22.8 4.8 163 1,535.5 27.4 22.4 
105 426.3 27.8 22.8 174 1,176.8 28.8 22.9 5.9 
116 569.9 28 22.9 5.2 175 958.4 27.4 22 5.4 
128 620.2 28.6 22.8 5.8 176 989.9 27.8 22 5.8 
139 638 30.8 23.4 7.4 186 913.9 29.4 23.1 6.3 
140 813.5 28.7 23.3 5.4 187 850.3 27.7 22.4 5.3 
141 1,018.7 28.1 22.8 5.2 188 639.4 27.7 22.2 5.5 
152 498.6 28.9 23.5 5.5 198 1,175.9 29.6 23 6.6 
163 637.8 29 22.9 200 610.3 27.6 21.8 5.8 
164 1,099.4 27.8 22.8 210 1,255.9 30.9 23.1 7.8 
176 800 27.7 22.4 5.3 211 1,271.7 28.2 22.3 5.9 
188 466.9 28.1 22.8 5.2 212 779.7 28.7 22.2 6.4 
201 455.6 28 22.6 5.4 222 714.9 29.3 22.4 6.9 
225 593.9 28.1 22.3 5.8 223 775.3 28.5 21.8 6.7 
235 581.7 30.8 23.7 7.1 224 653.1 27.6 21.5 6.2 
236 1,453.9 28.4 22.8 5.6 234 928 30.2 23.1 7.1 
237 607.4 28.4 22.5 5.9 235 1,236.2 27.9 22.2 5.8 
238 685.6 28.5 22.3 6.2 236 517.8 28.2 22.1 6.1 
235 812.5 30.2 22.3 237 539.2 28.3 21.9 6.3 
885.4 30 22.9 7.1 235 1,047.8 27.7 20.6 7.2 
 709.6 28 22.3 5.7 633.5 26 19.8 6.2 
 820.1 27.4 21.4  31 709.5 26.3 20.6 5.8 
 18 1,041.5 29.9 22.9  43 736.3 26.4 20.2 6.2 
 19 569.7 28.8 23.1 5.7  44 514.1 25.6 19.9 5.7 
 20 797 28.4 22.6 5.7  55 573.3 25.6 19.8 5.8 
 30 1,045.3 29.8 23.1 6.7  56 649.4 25 19.8 5.2 
 31 1,225.7 27.7 22.7 5.1  67 792.3 25.4 19.9 5.6 
 32 1,133.2 27.7 22.5 5.2  68 500.9 25.3 19.7 5.6 
 33 706.2 28.5 22.5 6.1  78 680.2 28.1 21.1 
 42 1,209.9 29 22.6 6.4  79 532.7 26.2 20.6 5.7 
 43 793.3 28.1 22.2 5.9  80 693.7 25.8 20.5 5.3 
 44 763.9 27.3 21.8 5.5  91 601.7 26.1 19.9 6.1 
 54 956.5 28.8 22.6 6.2  102 816.1 26.7 20.6 6.1 
 55 1,066.3 27.4 22 5.4  103 1,617.6 25.5 20.1 5.4 
 56 950.3 26.8 21.7 5.1  104 641.9 26 20.1 
 66 757.3 29.9 23.4 6.6  115 748.6 25.8 20.2 5.6 
 67 1,719.6 27.3 22.1 5.2  127 575 26.6 20 6.6 
 68 785.9 27.2 21.8 5.4  139 708.8 26.1 20.6 5.5 
 78 1,062.7 30.2 23 7.2  140 692.2 26.1 20.4 5.7 
 79 1,046.4 28 22.6 5.4  151 754.1 26.5 21 5.5 
 80 839.6 27.4 22.2 5.2  163 979.7 25.8 20.5 5.3 
 91 1,402.4 27.6 22 5.6  175 637.6 26 20.2 5.8 
 92 529.6 27.7 21.9 5.8  176 522.4 26.3 20.3 5.9 
 102 892.2 28.6 22.8 5.8  187 474.9 25.9 20.4 5.5 
 103 1,211.1 27.1 22.2 4.9  234 625.3 28.6 21.1 7.5 
 104 713.2 27.4 22.2 5.2  235 1,258.3 26.4 20.4 
 114 858.8 30.8 23.6 7.2  236 564.9 26.5 20.2 6.3 
 115 1,593.1 27.5 22.3 5.2 235 1,152.8 27.4 19.8 7.5 
Station No.Month No.P (mm)Tmax (°)Tmin (°C)TD (°C)Station No.Month No.P (mm)Tmax (°C)Tmin (°C)TD (°C)
598.5 30.5 23.3 7.2 116 696.4 28.6 22.4 6.2 
32 692.3 28.1 23.1 126 1,077.8 30.5 22.9 7.6 
43 564.4 29.4 23.1 6.3 127 1,211.4 28.2 22.1 
44 586 28.3 22.8 5.6 128 486.2 27.6 22 5.6 
56 637.9 28 22.8 5.2 138 716.9 30.8 23 7.8 
57 461.8 27.3 22.3 139 1,283.1 28.1 22.8 5.3 
68 933.8 27.6 22.6 140 908 27.7 22.5 5.2 
69 454.8 27.7 22.4 5.2 150 1,347.4 30.8 23.8 7.1 
80 748.4 28.6 23 5.5 151 1,057.3 28.4 23.1 5.3 
81 573.5 27.9 22.7 5.2 152 815.8 28.7 23.1 5.6 
92 681.7 28.1 22.8 5.3 153 691.1 28.4 22.6 5.8 
103 682 29.2 23.3 5.8 162 1,427.1 28.6 22.6 
104 1,037.6 27.6 22.8 4.8 163 1,535.5 27.4 22.4 
105 426.3 27.8 22.8 174 1,176.8 28.8 22.9 5.9 
116 569.9 28 22.9 5.2 175 958.4 27.4 22 5.4 
128 620.2 28.6 22.8 5.8 176 989.9 27.8 22 5.8 
139 638 30.8 23.4 7.4 186 913.9 29.4 23.1 6.3 
140 813.5 28.7 23.3 5.4 187 850.3 27.7 22.4 5.3 
141 1,018.7 28.1 22.8 5.2 188 639.4 27.7 22.2 5.5 
152 498.6 28.9 23.5 5.5 198 1,175.9 29.6 23 6.6 
163 637.8 29 22.9 200 610.3 27.6 21.8 5.8 
164 1,099.4 27.8 22.8 210 1,255.9 30.9 23.1 7.8 
176 800 27.7 22.4 5.3 211 1,271.7 28.2 22.3 5.9 
188 466.9 28.1 22.8 5.2 212 779.7 28.7 22.2 6.4 
201 455.6 28 22.6 5.4 222 714.9 29.3 22.4 6.9 
225 593.9 28.1 22.3 5.8 223 775.3 28.5 21.8 6.7 
235 581.7 30.8 23.7 7.1 224 653.1 27.6 21.5 6.2 
236 1,453.9 28.4 22.8 5.6 234 928 30.2 23.1 7.1 
237 607.4 28.4 22.5 5.9 235 1,236.2 27.9 22.2 5.8 
238 685.6 28.5 22.3 6.2 236 517.8 28.2 22.1 6.1 
235 812.5 30.2 22.3 237 539.2 28.3 21.9 6.3 
885.4 30 22.9 7.1 235 1,047.8 27.7 20.6 7.2 
 709.6 28 22.3 5.7 633.5 26 19.8 6.2 
 820.1 27.4 21.4  31 709.5 26.3 20.6 5.8 
 18 1,041.5 29.9 22.9  43 736.3 26.4 20.2 6.2 
 19 569.7 28.8 23.1 5.7  44 514.1 25.6 19.9 5.7 
 20 797 28.4 22.6 5.7  55 573.3 25.6 19.8 5.8 
 30 1,045.3 29.8 23.1 6.7  56 649.4 25 19.8 5.2 
 31 1,225.7 27.7 22.7 5.1  67 792.3 25.4 19.9 5.6 
 32 1,133.2 27.7 22.5 5.2  68 500.9 25.3 19.7 5.6 
 33 706.2 28.5 22.5 6.1  78 680.2 28.1 21.1 
 42 1,209.9 29 22.6 6.4  79 532.7 26.2 20.6 5.7 
 43 793.3 28.1 22.2 5.9  80 693.7 25.8 20.5 5.3 
 44 763.9 27.3 21.8 5.5  91 601.7 26.1 19.9 6.1 
 54 956.5 28.8 22.6 6.2  102 816.1 26.7 20.6 6.1 
 55 1,066.3 27.4 22 5.4  103 1,617.6 25.5 20.1 5.4 
 56 950.3 26.8 21.7 5.1  104 641.9 26 20.1 
 66 757.3 29.9 23.4 6.6  115 748.6 25.8 20.2 5.6 
 67 1,719.6 27.3 22.1 5.2  127 575 26.6 20 6.6 
 68 785.9 27.2 21.8 5.4  139 708.8 26.1 20.6 5.5 
 78 1,062.7 30.2 23 7.2  140 692.2 26.1 20.4 5.7 
 79 1,046.4 28 22.6 5.4  151 754.1 26.5 21 5.5 
 80 839.6 27.4 22.2 5.2  163 979.7 25.8 20.5 5.3 
 91 1,402.4 27.6 22 5.6  175 637.6 26 20.2 5.8 
 92 529.6 27.7 21.9 5.8  176 522.4 26.3 20.3 5.9 
 102 892.2 28.6 22.8 5.8  187 474.9 25.9 20.4 5.5 
 103 1,211.1 27.1 22.2 4.9  234 625.3 28.6 21.1 7.5 
 104 713.2 27.4 22.2 5.2  235 1,258.3 26.4 20.4 
 114 858.8 30.8 23.6 7.2  236 564.9 26.5 20.2 6.3 
 115 1,593.1 27.5 22.3 5.2 235 1,152.8 27.4 19.8 7.5 

P = precipitation, Tmax = mean monthly maximum, Tmin = mean monthly minimum temperature, TD = difference of Tmax and Tmin.

Figure 6

(a) Variation of mean monthly precipitation (P) with the corresponding months when modified Hargreaves is not applicable. (b) Variation of TD with the corresponding months when modified Hargreaves is not applicable in Tungabhadra River Basin (up to Haralahalli gauge station) for 1986–2005.

Figure 6

(a) Variation of mean monthly precipitation (P) with the corresponding months when modified Hargreaves is not applicable. (b) Variation of TD with the corresponding months when modified Hargreaves is not applicable in Tungabhadra River Basin (up to Haralahalli gauge station) for 1986–2005.

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