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Around 15% of India's gross domestic product comes from agriculture, which is the foundation of the country's economy. India's economic development and efforts to combat poverty have already benefited greatly from its agricultural sector. Sustainable management of water resources can increase agricultural productivity. The study was performed in the Paliganj distributary, a part of the Sone canal system in south Bihar, India. The Paliganj distributary command area lies wholly in the Gangetic plain. The estimation of crop evapotranspiration was carried out using the Modified Penman–Monteith equation for the period 1980 to 2015. The crop coefficient of the crops has been estimated by using a single crop coefficient and a dual crop coefficient. The crop water requirement, irrigation water requirement, and irrigation scheduling of crops grown in the study area were determined using CROPWAT 8.0 software. The results conclude that the maximum, minimum, and average values of ET0 were found to be 7.65 mm/day, 1.31 mm/day, and 3.86 mm/day respectively. The crop water requirement and irrigation requirement of crops grown in Kharif, Rabi, hot weather, and annual seasons in the study area were lower by using dual crop coefficient.

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  • To assess the suitability of FAO-56 suggested coefficients for the specified crops.

  • To compare ETc results with the computed amount using single- and dual-Kc techniques.

  • To assess the suitability of the single and dual crop coefficients (single-Kc and dual-Kc) techniques presented in FAO-56 for estimating the crop evapotranspiration (ETc) of the predominant crops.

crop coefficient, irrigation scheduling, reference evapotranspiration
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The water required for the cultivation of crops is not only for its healthy growth during its lifetime, but also for land preparation including leaching (WALMI 1988, 1989). According to scientists and policymakers, freshwater shortage is the second most important environmental concern of the 21st century, behind climate change (IPCC 2014; Ray et al. 2022, 2023; Shah et al. 2021). The measurement of the evapotranspiration is very difficult (Douville et al. 2021). According to Pereira et al. (2021), Pereira et al. (2015) and Pereira et al. (2020), who studied the FAO56 (Allen et al. 1998) proposal, one of the most widely used computational techniques that remains still in use, the FAO technique utilizes the Kc–ET0 procedure, in which the grass reference evapotranspiration (ET0) is multiplied by a crop coefficient (Kc) to determine the crop evapotranspiration (ETc) (Allen et al. 1998; Pereira et al. 1999). Reference evapotranspiration represents mainly weather-induced effects on the rate of evapotranspiration of the grass reference crop. Crop coefficient impacts on ETc due to variations in aerodynamic and surface resistances between the studied crop and the reference grass crop over the crop growing season are taken into account by multiplying the reference ET0 with the Kc. The reference surface is a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m−1 and an albedo of 0.23 (Allen et al. 1998).

Crop coefficients for several crops have been given by Doorenbos & Kassam (1979). These Kc values are frequently utilized in locations where local data are unavailable. Because crop coefficients are dependent on a variety of factors, including soil characteristics, crop characteristics, irrigation techniques, and climate conditions. Allen et al. (1998) have proposed that the values of crop coefficients should be empirically determined for each crop, using lysimetric data and local climate conditions. The ETc is estimated using the single crop coefficient (single-Kc) and dual crop coefficient (dual-Kc) approaches. The single crop coefficient only represents the time-averaged (multi-day) impacts of crop evapotranspiration since soil evaporation might vary daily as a result of rainfall or irrigation. In the dual crop coefficient approach, the impacts of soil evaporation and crop transpiration are calculated separately. The basal crop coefficient (Kcb), which describes plant transpiration, and the soil water evaporation coefficient (Ke) (Solangi et al. 2022a, b). The dual-Kc approach is significantly more complicated and time-consuming than the single-Kc method. However, a few studies conducted in dry and semiarid locations found that the dual-Kc technique outperformed the single one in terms of ETc estimation accuracy (Fan & Cai 2002). Thus, there are not numerous studies that compare, assess, and quantify the accuracy of the dual-Kc and single-Kc approaches for estimating ETc in agricultural systems. The present study will compare the single and dual crop coefficients since precise ETc values are necessary for the study area real-time irrigation scheduling.

Irrigation scheduling intends to provide plants with the appropriate amount of water at the proper time to encourage plant development and achieve high yield and/or quality. For agricultural purposes, the amount of water delivered and its timing are both crucial factors in irrigation scheduling (Ragab et al. 2017a, b).

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The study area

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In the plains of south Bihar, the Sone canal is a 120-year-old diversion irrigation scheme. The Sone irrigation program was begun in 1871. But in 1879, it was put to systematic use for irrigation. To meet the growing demand for water for irrigation, the government thought of increasing irrigation supplies. Consequently, the 1,410-m long barrier at Indrapuri was constructed in 1968 (Praveen & Roy 2022). The index map of the Sone command area and the detailed canal network are shown in Figure 1.
Figure 1
Index map of the Sone command area canal system (source: Masood et al. 2014).
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Index map of the Sone command area canal system (source: Masood et al. 2014).

Figure 1
Index map of the Sone command area canal system (source: Masood et al. 2014).
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Index map of the Sone command area canal system (source: Masood et al. 2014).

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The Paliganj distributary is one of the parts of the Sone Canal System in South Bihar. The total length of the distributary is 27.4 km. The total Paliganj command area is 14,867 ha (Praveen & Roy 2021a, b). The Paliganj command area is shown in Figure 2.
Figure 2
The Paliganj distributary command area (source: Praveen & Roy 2022).
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The Paliganj distributary command area (source: Praveen & Roy 2022).

Figure 2
The Paliganj distributary command area (source: Praveen & Roy 2022).
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The Paliganj distributary command area (source: Praveen & Roy 2022).

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Figure 3
Generalized crop coefficient curve for the single crop coefficient approach (source: Allen et al. 1998).
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Generalized crop coefficient curve for the single crop coefficient approach (source: Allen et al. 1998).

Figure 3
Generalized crop coefficient curve for the single crop coefficient approach (source: Allen et al. 1998).
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Generalized crop coefficient curve for the single crop coefficient approach (source: Allen et al. 1998).

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Climate

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The climate of the command area is tropical humid to sub-humid type. The normal average rainfall of the command area is about 1,000 mm. Paliganj distributary lies in Patna District. Patna district receives an annual average rainfall of 1,000 mm. For this project, meteorological data for the period of 1980–2015 have been used. About 85% of total rainfall occurs during southwest monsoon (June to October). The maximum temperature recorded is 41 °C. Average maximum and minimum relative humidity are 86 and 24% respectively. The average monthly meteorological data (1980–2015) for the Patna station is given in Table 1.

Table 1

Average climatological data of Patna during the period 1985–2015

MonthMin. tempa (°C)Max. tempa (°C)Humidity (%)Wind speed (km/day)Sunshine (h)Radiation (MJ/m²/day)EToa (mm/day)
January 9.3 22.5 75 59 6.9 13.7 1.95 
February 12 26 63 77 7.7 16.7 2.75 
March 16.7 32.2 48 93 8.6 20.3 4.19 
April 22.1 37.2 42 135 8.3 21.7 5.83 
May 25 37.4 52 165 8 22 6.3 
June 26.7 36.4 66 146 6.3 19.5 5.38 
July 26.3 33 80 125 4 16 3.98 
August 26.3 32.9 80 125 4.6 16.3 3.97 
September 25.5 32.5 80 112 5.1 15.8 3.76 
October 21.5 31.9 74 63 6.8 16.1 3.44 
November 15.1 29 72 41 7.5 14.8 2.63 
December 10.5 24.5 76 41 5 11 1.8 
MonthMin. tempa (°C)Max. tempa (°C)Humidity (%)Wind speed (km/day)Sunshine (h)Radiation (MJ/m²/day)EToa (mm/day)
January 9.3 22.5 75 59 6.9 13.7 1.95 
February 12 26 63 77 7.7 16.7 2.75 
March 16.7 32.2 48 93 8.6 20.3 4.19 
April 22.1 37.2 42 135 8.3 21.7 5.83 
May 25 37.4 52 165 8 22 6.3 
June 26.7 36.4 66 146 6.3 19.5 5.38 
July 26.3 33 80 125 4 16 3.98 
August 26.3 32.9 80 125 4.6 16.3 3.97 
September 25.5 32.5 80 112 5.1 15.8 3.76 
October 21.5 31.9 74 63 6.8 16.1 3.44 
November 15.1 29 72 41 7.5 14.8 2.63 
December 10.5 24.5 76 41 5 11 1.8 

aMin. temp., minimum temperature; Max. temp., maximum temperature.

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Cropping pattern

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The cropping pattern for the command area was taken from the report of the second Bihar state irrigation commission, 1994. The seasonal cropping pattern of the study area is given in Table 2.

Table 2

Cropping pattern in the study area

Sl. No.SeasonCropPercentage (%)
1. Kharif (June to end of October) Paddy 74 
2. Rabi (mid-November to April) Wheat 51 
Barley 1.5 
Maize 3 
Pulses 4 
Oilseeds – Mustard 4 
Vegetables 6 
Miscellaneous 1.5 
3. Hot Weather (March to May) Paddy (Nursery) 8 
Maize & Millets 2 
Pulses 2 
Oilseeds 0.5 
Vegetables 3 
Miscellaneous 0.5 
4. Annual Sugarcane 2 
Sl. No.SeasonCropPercentage (%)
1. Kharif (June to end of October) Paddy 74 
2. Rabi (mid-November to April) Wheat 51 
Barley 1.5 
Maize 3 
Pulses 4 
Oilseeds – Mustard 4 
Vegetables 6 
Miscellaneous 1.5 
3. Hot Weather (March to May) Paddy (Nursery) 8 
Maize & Millets 2 
Pulses 2 
Oilseeds 0.5 
Vegetables 3 
Miscellaneous 0.5 
4. Annual Sugarcane 2 

Source: Report of the Second Bihar State Irrigation Commission, 1994.

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The cropping intensity during kharif is 74%, during rabi is 71%, and during hot weather season is 16%, which is very low and shows that the resources are currently not utilized to their full potential. Sugarcane is the annual crop in the area.

Land use pattern

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The land use pattern of the study area is classified into nine categories. The percentage area wise category is shown in Table 3.

Table 3

Land use pattern in the Sone command area

Sl. No.DescriptionArea in haPercentage (%)
1. Reporting area (total of items 2–10) 796,157 100 
2. Forest 3,179 0.4 
3. Barren lands 17,664 2.2 
4. Land put to non-agricultural use 88,426 11.1 
5. Permanent pastures 956 0.1 
6. Land under mice tree crops 2,241 0.3 
7. Culturable waste land 3,587 0.4 
8. Current fallow 30,904 3.9 
9. Other fallow 5,251 0.7 
10. Net sown area 643,949 80.9 
11. Area sown more than once 343,812  
12. Gross area sown (10 + 11) 987,761  
Sl. No.DescriptionArea in haPercentage (%)
1. Reporting area (total of items 2–10) 796,157 100 
2. Forest 3,179 0.4 
3. Barren lands 17,664 2.2 
4. Land put to non-agricultural use 88,426 11.1 
5. Permanent pastures 956 0.1 
6. Land under mice tree crops 2,241 0.3 
7. Culturable waste land 3,587 0.4 
8. Current fallow 30,904 3.9 
9. Other fallow 5,251 0.7 
10. Net sown area 643,949 80.9 
11. Area sown more than once 343,812  
12. Gross area sown (10 + 11) 987,761  
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The crop growth period and the date of plantation of all crops grown in the study area are shown in Table 4.

Table 4

Crop growth period and date of plantation

Sl. No.Growth stageInitial (days)Dev (days)Mid (days)End (days)TotalDate
Kharif Rice 20 30 40 30 120 11 July 
Rabi Wheat 20 35 45 30 130 11 Nov 
Barley 15 25 50 30 120 21 Nov 
Maize 20 30 40 30 120 21 Nov 
Pulses (Gram) 20 25 30 30 105 1 Nov 
Oilseed (Mustard) 20 30 40 30 120 15 Oct 
Veg (Potato) 20 20 30 20 90 1 Nov 
(Onion) 15 25 40 25 105 1 Nov 
Hot Weather Paddy (Nursery)      21 June 
Maize 20 30 40 30 120 1 Apr 
Millet 15 25 40 25 105 20 Feb 
Pulses (Lentil) 10 15 20 15 60 1 Mar 
Oilseed (Sunflower) 25 35 45 25 130 1 Apr 
Veg (Eggplant) 30 40 40 20 130 1 Apr 
(Tomato) 30 40 40 25 135 1 Apr 
Sl. No.Growth stageInitial (days)Dev (days)Mid (days)End (days)TotalDate
Kharif Rice 20 30 40 30 120 11 July 
Rabi Wheat 20 35 45 30 130 11 Nov 
Barley 15 25 50 30 120 21 Nov 
Maize 20 30 40 30 120 21 Nov 
Pulses (Gram) 20 25 30 30 105 1 Nov 
Oilseed (Mustard) 20 30 40 30 120 15 Oct 
Veg (Potato) 20 20 30 20 90 1 Nov 
(Onion) 15 25 40 25 105 1 Nov 
Hot Weather Paddy (Nursery)      21 June 
Maize 20 30 40 30 120 1 Apr 
Millet 15 25 40 25 105 20 Feb 
Pulses (Lentil) 10 15 20 15 60 1 Mar 
Oilseed (Sunflower) 25 35 45 25 130 1 Apr 
Veg (Eggplant) 30 40 40 20 130 1 Apr 
(Tomato) 30 40 40 25 135 1 Apr 
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Estimation of reference evapotranspiration

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The crop evapotranspiration can be calculated from the reference evapotranspiration by multiplying it by crop coefficient (Allen et al. 1998, 2006):
(1)
where ETc indicates crop evapotranspiration; ET0 indicates reference evapotranspiration; Kc indicates crop coefficient.

Penman–Monteith equation

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The FAO 56 Modified Penman–Monteith equation recommended the use of this equation for the estimation of reference evapotranspiration (Allen et al. 1998, 2006). This method overcomes the problem of regional dependence shown by the other methods and gives accurate results.

The relationship recommended is expressed as,
(2)
where ET0 indicates reference evapotranspiration (mm/day), Rn indicates net radiation at the crop surface (MJ/m2day), G indicates soil heat flux density (MJ/m2/day), T indicates air temperature (°C), U2 indicates wind speed at 2 m height (m/s), es indicates saturation vapor pressure (kPa), ea indicates actual vapor pressure (kPa), (es – ea) indicates vapor pressure deficit (kPa), Δ = slope vapor pressure curve (kpa°C−1), γ is the psychometric constant (kPa°C−1), and 900 corresponds to a conversion factor.

The weather data required for the calculation of ET0 using Penman–Monteith equation include minimum and maximum temperature, minimum and maximum relative humidity, wind speed and, net radiation.

Estimation of crop coefficient

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The most fundamental definition of crop coefficient, Kc, is simply the ratio of the ET observed for the crop studied over that observed for the well-calibrated reference crop under the same conditions.

Single crop coefficient approach

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The influences of bare soil evaporation and crop transpiration are merged into a single coefficient in the single crop coefficient technique. The coefficient integrates differences in the soil evaporation and crop transpiration rate between the crop and the grass reference surface (Figure 3).

This technique is used to determine ETc for weekly or longer time periods, however computations may occur on a daily time step, as the single-Kc coefficient averages soil evaporation and transpiration. When the averaged effects of soil moisture are suitable and significant, the time-averaged single Kc is employed in planning studies and irrigation system design. This is valid for systems that use set sprinklers and surface irrigation where the gap between watering cycles is typically 10 days or more. The time-averaged single Kc is appropriate for traditional irrigation management.

The single crop coefficient values of crops grown in four seasons in the study area are used to determine the crop water requirement of crops using the single crop coefficient approach are given in Table 5 (Doorenbos & Pruitt 1977; FAO-24).

Table 5

Single crop coefficients (Kc) for the crops in the study area

Sl. No.SeasonCropKc
Initial stageDevelopment stageMid stageLate stage
1. Kharif Rice 1.1 By interpolation 1.05 0.95 
2. Rabi Wheat 0.39 1.1 0.225 
Barley 0.315 1.1 0.225 
Maize 0.345 1.2 0.35 
Lentil 0.345 1.1 0.275 
Potato 0.345 1.1 0.725 
Onion 0.345 1 0.775 
3. Hot weather Millet 0.23 1.05 0.275 
Maize 0.23 1.2 0.35 
Lentil 0.23 1.1 0.275 
4. Perennial Sugarcane 0.4 1.25 0.75 
Sl. No.SeasonCropKc
Initial stageDevelopment stageMid stageLate stage
1. Kharif Rice 1.1 By interpolation 1.05 0.95 
2. Rabi Wheat 0.39 1.1 0.225 
Barley 0.315 1.1 0.225 
Maize 0.345 1.2 0.35 
Lentil 0.345 1.1 0.275 
Potato 0.345 1.1 0.725 
Onion 0.345 1 0.775 
3. Hot weather Millet 0.23 1.05 0.275 
Maize 0.23 1.2 0.35 
Lentil 0.23 1.1 0.275 
4. Perennial Sugarcane 0.4 1.25 0.75 

Source: Doorenbos & Pruitt 1977 FAO-24.

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Dual crop coefficient approach

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The impacts of soil evaporation and crop transpiration are calculated separately in the dual crop coefficient technique. The basal crop coefficient (Kcb), which describes plant transpiration, and the soil water evaporation coefficient (Ke), which describes evaporation from the soil surface, are the two coefficients that are employed. The dual crop coefficient curves at different stages of crop are shown in Figure 4:
(3)
where Kcb is the basal crop coefficient and Ke is the soil water crop coefficient.
Figure 4
Dual crop coefficient curve at different stages of crop (source: Allen et al. 1998).
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Dual crop coefficient curve at different stages of crop (source: Allen et al. 1998).

Figure 4
Dual crop coefficient curve at different stages of crop (source: Allen et al. 1998).
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Dual crop coefficient curve at different stages of crop (source: Allen et al. 1998).

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The ratio of ETc to ET0 when the soil top surface is dry but the average soil water content of the root zone is sufficient to support complete plant transpiration is known as the basal crop coefficient (Kcb). In the absence of the extra impacts of soil wetness by irrigation or precipitation, the Kcb reflects the baseline potential Kc (Allen et al. 1998):
(4)
where refers to the basal crop coefficient, refers to the value for Kcb mid or Kcb end (if 0.45) taken from Allen et al. 1998, U2 refers to the mean value for daily wind speed at 2 m height over grass during the mid- or late-season growth stage [m s–1] for 1 m s−1U26 m s−1, refers to the mean value for daily minimum relative humidity during the mid- or late-season growth stage [%] for 20%RHmin80%, H refers to the mean plant height during the mid- or late-season stage [m] for 20%RHmin80% taken from Allen et al. 1998.
The component of evaporation from the soil surface is described by the soil evaporation coefficient (Ke). Ke may be high if the soil is saturated from irrigation or rain. However, a maximum value, Kc max, defined by the energy available for evapotranspiration at the soil surface, cannot be reached by the sum of Kcb and Ke. Ke decreases when the soil surface dries out and reaches zero when there is no water left for evaporation. A daily water balance calculation is necessary for the assessment of Ke in order to determine how much water is left in the upper top surface soil:
(5)
where refers to the soil water crop coefficient, refers to the soil evaporation reduction coefficient, refers to the basal crop coefficient, refers to the fraction of the soil that is both exposed and wetted, and refers to the maximum value of Kc following rain or irrigation:
(6)

The dual crop coefficient values of crops grown in the study area are determined using the dual crop coefficient approach given in Table 6 (Allen et al. 1998).

Table 6

Dual crop coefficients (Kcb + Ke) for the crops in the study area

Sl. No.Crop SeasonCropInitial
Mid
Late
KcbKeKc = Kcb + KeKcbKeKc = Kcb + KeKcbKeKc = Kcb + Ke
1. Kharif Rice 1.00 0.02 1.02 1.15 0.01 1.05 0.60 0.10 0.70 
2. Rabi Wheat 0.15 0.17 0.32 1.10 0.02 1.03 0.25 0.17 0.42 
Maize 0.15 0.16 0.31 1.15 0.01 1.04 0.35 0.15 0.50 
Lentil 0.15 0.17 0.32 1.05 0.03 0.99 0.20 0.17 0.37 
Mustard 0.15 0.17 0.32 1.10 0.02 1.02 0.25 0.17 0.42 
Potato 0.15 0.17 0.32 1.10 0.02 1.05 0.65 0.10 0.75 
Onion (Dry) 0.15 0.17 0.32 0.95 0.05 0.94 0.65 0.10 0.75 
3. Hot weather Millet 0.15 0.16 0.31 0.95 0.05 0.88 0.20 0.16 0.36 
Maize 0.15 0.18 0.33 1.17 0.01 1.18 0.35 0.17 0.52 
Lentil 0.15 0.18 0.33 1.06 0.03 1.09 0.20 0.18 0.38 
4. Annual Sugarcane 0.15 0.16 0.31 1.20 0.001 1.06 0.70 0.07 0.77 
Sl. No.Crop SeasonCropInitial
Mid
Late
KcbKeKc = Kcb + KeKcbKeKc = Kcb + KeKcbKeKc = Kcb + Ke
1. Kharif Rice 1.00 0.02 1.02 1.15 0.01 1.05 0.60 0.10 0.70 
2. Rabi Wheat 0.15 0.17 0.32 1.10 0.02 1.03 0.25 0.17 0.42 
Maize 0.15 0.16 0.31 1.15 0.01 1.04 0.35 0.15 0.50 
Lentil 0.15 0.17 0.32 1.05 0.03 0.99 0.20 0.17 0.37 
Mustard 0.15 0.17 0.32 1.10 0.02 1.02 0.25 0.17 0.42 
Potato 0.15 0.17 0.32 1.10 0.02 1.05 0.65 0.10 0.75 
Onion (Dry) 0.15 0.17 0.32 0.95 0.05 0.94 0.65 0.10 0.75 
3. Hot weather Millet 0.15 0.16 0.31 0.95 0.05 0.88 0.20 0.16 0.36 
Maize 0.15 0.18 0.33 1.17 0.01 1.18 0.35 0.17 0.52 
Lentil 0.15 0.18 0.33 1.06 0.03 1.09 0.20 0.18 0.38 
4. Annual Sugarcane 0.15 0.16 0.31 1.20 0.001 1.06 0.70 0.07 0.77 

Source: Allen et al. 1998.

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Irrigation scheduling

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Irrigation scheduling intends to provide plants with the appropriate amount of water at the proper time to encourage plant development and achieve high yield and/or quality. For agricultural purposes, the amount of water delivered and its timing are both crucial factors in irrigation scheduling. In this study, the irrigation scheduling has been done using two components, frequency of irrigation and depth of irrigation. Water delivery frequency or the irrigation interval for a specific crop at specific stage can be calculated by the following relationship,
(7)
where i refers to the irrigation interval in days, P refers to the fraction of available soil water, permitting unrestricted evapotranspiration (fraction). It is also called management allowable depletion (MAD) of available soil moisture, Sa refers to the available soil water capacity, mm/m of soil depth. This can be determined experimentally or can be estimated for different soil textural groups reported in the literature, D refers to the rooting depth in m, ETc refers to the crop evapotranspiration in mm/day. It can be estimated by any standard method, e.g., the modified Penman Equation for different stages of crop.
The calculation of the scheduling program is based on a soil water balance, where basis the soil moisture status is determined on a daily accounting for all ingoing and outgoing water in the root zone (Gabr & Fattouh 2021), according to:
(8)
Here, SMDi refers to the soil moisture depletion at day i; ETa refers to the actual crop evapotranspiration; Peff refers to the effective rainfall; dirr refers to the net irrigation.

The irrigation schedule of all crops grown in four seasons is calculated by using CROPWAT 8.0 software.

Irrigation requirements (In) are determined by WALMI (1989):
(9)

For normal irrigation planning and management purposes, e.g. irrigation scheduling, hydrological water balance studies, the single crop coefficients are relevant and more convenient than Kc captured on a daily time step using a separate crop and soil coefficients. Only when values of Kc are needed on a daily basis for specific fields of crops and for specific years, separate transpiration and evaporation coefficient (i.e. Kab + Kc) must be considered.

The dual crop coefficient approach is more complicated and computationally intensive than the single crop coefficient approach. The solution consists of splitting Kc into two separate coefficients, one for crop transpiration, i.e. basal crop coefficient (Kcb) and one for soil evaporation (Ke).

The dual crop coefficient is determined on a daily basis and is intended for applications using computers. It is recommended that this approach be followed when improved estimations for (Kc) are needed; for example, schedule irrigations for individual fields on a daily basis.

Dependable rainfall

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The 75% dependable rainfall is the value of the rainfall that can be expected to be equal to or exceeded 75% times. Thus, 75% dependable monthly rainfall means the value of rainfall in the monthly rainfall time series that has the probability of exceedance (P = 0.75), i.e. the rainfall data are arranged in decreasing order. Similarly, 75% dependable evapotranspiration is the value of evapotranspiration that can be expected to equal or not exceed 75% times. Thus, 75% dependable monthly evapotranspiration means the value of evapotranspiration in the monthly evapotranspiration time series that has the probability of non-exceedance (P = 0.75), i.e. the evapotranspiration data are arranged in descending order.

The 75% dependable rainfall and dependable Penman–Monteith ET0 is determined by using the Weibull plotting position:
(10)
where, m refers to the rank number, N refers to the number of records, P refers to the probability.

The calculation of 75% dependable rainfall of the study area is given in Table 7. The reference evapotranspiration of the study area is determined using Allen et al. 1998, Penman–Monteith equation for the meteorological data of Patna for the period from 1980 to 2015. Similarly, the calculation of 75% dependable reference evapotranspiration of the study area from 1980 to 2015 is given in Table 8. 75% dependable monthly Penman–Monteith ET0 has been used for the calculation of crop water requirement and irrigation water requirement and the data are given in Table 9.

Table 7

Calculation of 75% dependable rainfall (mm) of the Patna meteorological station during the year 1980–2015

Sl. NoPro.JanFebMarAprMayJuneJulyAugSepOctNovDec
1 0.03 36.10 69.2 58.9 36.4 155 364.8 605.1 594.9 372.7 148 43.5 110 
2 0.06 35.00 56.9 51.6 39.5 97.5 297 542.1 434.5 304.4 131 29.5 41.2 
3 0.09 32.30 49.7 43.8 38.6 91 285.2 514 350.6 303.1 121 28.7 40.4 
4 0.13 28.50 41.1 33.6 27.2 77.5 281.5 497.6 347.7 287.6 121 23.7 32.2 
5 0.16 24.90 29 27.8 26.6 75.7 223.5 449.5 341.1 271.7 94 14.7 8.5 
6 0.19 23.00 27 12.3 25.3 75 223.3 442.5 333.5 256.6 84.7 11 7.1 
7 0.22 22.40 26.9 9.7 24.3 74.1 216.2 431.8 330.1 233.7 79.3 6.5 6 
8 0.25 21.10 14 7.9 22.8 67.9 210.8 369.1 322.2 232.7 71.7 2.9 5.4 
9 0.28 19.70 13.8 6.8 21 67.9 205 359.9 321.1 227.8 61.3 2.3 5 
10 0.31 17.20 13.5 6.4 19.9 61.5 203.5 356.4 307 220 41.6 1.2 3.8 
11 0.34 15.40 12.1 5.8 18.1 59.6 165.1 342.8 294 206.7 41.6 0.3 2.4 
12 0.38 25.05 32.1 24.1 26.3 82.1 243.3 446.4 361.5 265.2 90.4 14.9 23.9 
13 0.41 12.20 8.2 5.8 16.8 56.8 149.6 335.1 279.9 201.7 41.6 0 1.6 
14 0.44 11.20 7.9 5.4 15.1 44.2 143.9 329 275.4 198.9 38.9 0 1 
15 0.47 9.90 7.5 4.4 12.7 39.4 137.1 316.6 275.2 183 36.3 0 0.8 
16 0.50 9.20 5.8 3.6 8.8 36.2 98.3 293 271.9 178 36.1 0 0 
17 0.53 9.10 4.1 3.5 3 36.2 96.8 285.6 248.4 172.8 28.7 0 0 
18 0.56 9.00 3.4 2 2.7 35.7 92.9 282.1 247.9 159.9 20.6 0 0 
19 0.59 7.60 3.2 1.2 1.3 31.2 92.9 264.1 210.4 156.9 14.5 0 0 
20 0.63 7.30 3.2 1.1 1.2 28.9 91.1 259.8 207.3 151.2 9.5 0 0 
21 0.66 7.10 2.3 0.4 0.8 25.9 82 259.1 204.1 148.1 8.8 0 0 
22 0.69 6.40 1.1 0.2 0.4 22.2 80.1 258.8 201.4 139.4 8.5 0 0 
23 0.72 3.30 0.8 0.1 0.3 14.7 78.1 246.1 198.1 139.3 6.4 0 0 
24 0.75 1.50 0.8 0 0 13.7 76.4 230 198 128.1 3.6 0 0 
25 0.78 1.10 0.4 0 0 13 61.1 223.5 190.8 127.3 3.4 0 0 
26 0.81 0.80 0.4 0 0 11.8 58.6 211.2 186 116.6 3 0 0 
27 0.84 0.30 0.2 0 0 8.9 51.9 159.6 184.9 79.4 0.4 0 0 
28 0.88 0.10 0 0 0 0 48.6 130.9 184 77.4 0 0 0 
29 0.91 0.00 0 0 0 0 20.2 88.2 124 50.3 0 0 0 
30 0.94 0.00 0 0 0 0 31.5 116.5 135.5 67.1 0 0 0 
31 0.97 0.00 0 0 0 0 38.7 119 163.8 72.7 0 0 0 
Sl. NoPro.JanFebMarAprMayJuneJulyAugSepOctNovDec
1 0.03 36.10 69.2 58.9 36.4 155 364.8 605.1 594.9 372.7 148 43.5 110 
2 0.06 35.00 56.9 51.6 39.5 97.5 297 542.1 434.5 304.4 131 29.5 41.2 
3 0.09 32.30 49.7 43.8 38.6 91 285.2 514 350.6 303.1 121 28.7 40.4 
4 0.13 28.50 41.1 33.6 27.2 77.5 281.5 497.6 347.7 287.6 121 23.7 32.2 
5 0.16 24.90 29 27.8 26.6 75.7 223.5 449.5 341.1 271.7 94 14.7 8.5 
6 0.19 23.00 27 12.3 25.3 75 223.3 442.5 333.5 256.6 84.7 11 7.1 
7 0.22 22.40 26.9 9.7 24.3 74.1 216.2 431.8 330.1 233.7 79.3 6.5 6 
8 0.25 21.10 14 7.9 22.8 67.9 210.8 369.1 322.2 232.7 71.7 2.9 5.4 
9 0.28 19.70 13.8 6.8 21 67.9 205 359.9 321.1 227.8 61.3 2.3 5 
10 0.31 17.20 13.5 6.4 19.9 61.5 203.5 356.4 307 220 41.6 1.2 3.8 
11 0.34 15.40 12.1 5.8 18.1 59.6 165.1 342.8 294 206.7 41.6 0.3 2.4 
12 0.38 25.05 32.1 24.1 26.3 82.1 243.3 446.4 361.5 265.2 90.4 14.9 23.9 
13 0.41 12.20 8.2 5.8 16.8 56.8 149.6 335.1 279.9 201.7 41.6 0 1.6 
14 0.44 11.20 7.9 5.4 15.1 44.2 143.9 329 275.4 198.9 38.9 0 1 
15 0.47 9.90 7.5 4.4 12.7 39.4 137.1 316.6 275.2 183 36.3 0 0.8 
16 0.50 9.20 5.8 3.6 8.8 36.2 98.3 293 271.9 178 36.1 0 0 
17 0.53 9.10 4.1 3.5 3 36.2 96.8 285.6 248.4 172.8 28.7 0 0 
18 0.56 9.00 3.4 2 2.7 35.7 92.9 282.1 247.9 159.9 20.6 0 0 
19 0.59 7.60 3.2 1.2 1.3 31.2 92.9 264.1 210.4 156.9 14.5 0 0 
20 0.63 7.30 3.2 1.1 1.2 28.9 91.1 259.8 207.3 151.2 9.5 0 0 
21 0.66 7.10 2.3 0.4 0.8 25.9 82 259.1 204.1 148.1 8.8 0 0 
22 0.69 6.40 1.1 0.2 0.4 22.2 80.1 258.8 201.4 139.4 8.5 0 0 
23 0.72 3.30 0.8 0.1 0.3 14.7 78.1 246.1 198.1 139.3 6.4 0 0 
24 0.75 1.50 0.8 0 0 13.7 76.4 230 198 128.1 3.6 0 0 
25 0.78 1.10 0.4 0 0 13 61.1 223.5 190.8 127.3 3.4 0 0 
26 0.81 0.80 0.4 0 0 11.8 58.6 211.2 186 116.6 3 0 0 
27 0.84 0.30 0.2 0 0 8.9 51.9 159.6 184.9 79.4 0.4 0 0 
28 0.88 0.10 0 0 0 0 48.6 130.9 184 77.4 0 0 0 
29 0.91 0.00 0 0 0 0 20.2 88.2 124 50.3 0 0 0 
30 0.94 0.00 0 0 0 0 31.5 116.5 135.5 67.1 0 0 0 
31 0.97 0.00 0 0 0 0 38.7 119 163.8 72.7 0 0 0 

Bolded values indicate 75% dependable rainfall (mm) of the Patna meteorological station.

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Table 8

Calculation of 75% dependable reference evapotranspiration (mm/day) of Patna meteorological station during the year 1980–2015

Sl. No.Prob.JanFebMarAprMayJunJulAugSepOctNovDec
1. 0.03 1.32 2.08 3.09 4.28 4.79 4.34 3.57 3.58 3.4 2.92 1.93 1.31 
2. 0.05 1.38 2.09 3.18 4.29 5.07 4.62 3.64 3.61 3.62 3.15 2.25 1.42 
3. 0.08 1.47 2.31 3.32 4.3 5.19 4.79 3.7 3.66 3.65 3.28 2.35 1.6 
4. 0.11 1.54 2.31 3.44 4.38 5.25 4.9 3.78 3.66 3.65 3.32 2.44 1.64 
5. 0.14 1.66 2.36 3.44 4.63 5.38 4.93 3.79 3.77 3.67 3.33 2.45 1.68 
6. 0.16 1.72 2.37 3.46 4.73 5.51 5.01 3.8 3.84 3.67 3.34 2.45 1.74 
7. 0.19 1.72 2.38 3.58 4.81 5.54 5.02 3.82 3.88 3.69 3.36 2.48 1.76 
8. 0.22 1.73 2.46 3.59 4.91 5.58 5.02 3.85 3.9 3.71 3.36 2.49 1.78 
9. 0.24 1.74 2.47 3.67 5.06 5.6 5.08 3.85 3.9 3.72 3.37 2.5 1.78 
10. 0.27 1.78 2.49 3.76 5.08 5.63 5.12 3.88 3.91 3.73 3.38 2.51 1.81 
11. 0.30 1.78 2.49 3.78 5.09 5.76 5.18 3.89 3.93 3.74 3.38 2.52 1.82 
12. 0.32 1.79 2.52 3.78 5.15 5.92 5.19 3.9 4.03 3.79 3.39 2.53 1.84 
13. 0.35 1.81 2.58 3.83 5.21 5.97 5.22 3.9 4.04 3.86 3.41 2.54 1.84 
14. 0.38 1.81 2.58 3.9 5.39 6.07 5.23 3.93 4.04 3.91 3.41 2.55 1.85 
15. 0.41 1.81 2.61 3.96 5.45 6.13 5.23 3.95 4.04 3.91 3.42 2.56 1.85 
16. 0.43 1.83 2.64 4.01 5.51 6.14 5.24 3.96 4.07 3.93 3.43 2.58 1.86 
17. 0.46 1.84 2.64 4.09 5.53 6.15 5.27 3.96 4.09 3.94 3.43 2.59 1.86 
18. 0.49 1.86 2.64 4.15 5.53 6.16 5.29 3.96 4.17 3.94 3.43 2.6 1.87 
19. 0.51 1.86 2.64 4.16 5.64 6.19 5.39 3.99 4.19 3.96 3.44 2.6 1.88 
20. 0.54 1.86 2.66 4.18 5.82 6.25 5.42 4 4.2 3.97 3.51 2.6 1.9 
21. 0.57 1.9 2.66 4.2 5.88 6.35 5.44 4.01 4.22 3.99 3.51 2.62 1.9 
22. 0.59 1.9 2.67 4.2 5.92 6.35 5.45 4.06 4.23 4.02 3.52 2.65 1.91 
23. 0.62 1.95 2.7 4.2 5.92 6.44 5.46 4.1 4.3 4.07 3.54 2.65 1.93 
24. 0.65 2.06 2.73 4.26 6.18 6.48 5.5 4.23 4.3 4.09 3.55 2.66 1.94 
25. 0.68 2.07 2.75 4.32 6.2 6.51 5.52 4.25 4.31 4.09 3.66 2.66 1.96 
26. 0.70 2.08 2.76 4.44 6.25 6.67 5.56 4.33 4.36 4.11 3.66 2.67 1.96 
27. 0.73 2.08 2.86 4.45 6.51 6.82 5.68 4.34 4.39 4.12 3.66 2.7 1.97 
28. 0.75 2.09 2.95 4.53 6.6 6.88 5.98 4.35 4.41 4.12 3.68 2.7 1.97 
29. 0.78 2.09 2.96 4.6 6.63 6.88 6.03 4.46 4.43 4.14 3.69 2.73 1.98 
30. 0.81 2.1 3.01 4.62 6.65 6.94 6.03 4.47 4.45 4.15 3.71 2.76 2 
31. 0.84 2.1 3.14 5.03 6.65 7.14 6.08 4.53 4.45 4.15 3.75 2.76 2.01 
32. 0.86 2.11 3.22 5.12 6.72 7.29 6.22 4.53 4.53 4.17 3.78 2.77 2.03 
33. 0.89 2.21 3.33 5.13 6.9 7.35 6.22 4.55 4.53 4.18 3.84 2.84 2.09 
34. 0.92 2.23 3.38 5.22 6.94 7.47 6.23 4.68 4.56 4.2 3.86 2.9 2.12 
35. 0.95 2.24 3.53 5.31 7.42 7.62 6.49 4.69 4.57 4.21 3.92 2.93 2.12 
36. 0.97 2.33 3.82 5.51 7.44 7.65 6.93 4.82 4.64 4.31 3.97 3.09 2.13 
Sl. No.Prob.JanFebMarAprMayJunJulAugSepOctNovDec
1. 0.03 1.32 2.08 3.09 4.28 4.79 4.34 3.57 3.58 3.4 2.92 1.93 1.31 
2. 0.05 1.38 2.09 3.18 4.29 5.07 4.62 3.64 3.61 3.62 3.15 2.25 1.42 
3. 0.08 1.47 2.31 3.32 4.3 5.19 4.79 3.7 3.66 3.65 3.28 2.35 1.6 
4. 0.11 1.54 2.31 3.44 4.38 5.25 4.9 3.78 3.66 3.65 3.32 2.44 1.64 
5. 0.14 1.66 2.36 3.44 4.63 5.38 4.93 3.79 3.77 3.67 3.33 2.45 1.68 
6. 0.16 1.72 2.37 3.46 4.73 5.51 5.01 3.8 3.84 3.67 3.34 2.45 1.74 
7. 0.19 1.72 2.38 3.58 4.81 5.54 5.02 3.82 3.88 3.69 3.36 2.48 1.76 
8. 0.22 1.73 2.46 3.59 4.91 5.58 5.02 3.85 3.9 3.71 3.36 2.49 1.78 
9. 0.24 1.74 2.47 3.67 5.06 5.6 5.08 3.85 3.9 3.72 3.37 2.5 1.78 
10. 0.27 1.78 2.49 3.76 5.08 5.63 5.12 3.88 3.91 3.73 3.38 2.51 1.81 
11. 0.30 1.78 2.49 3.78 5.09 5.76 5.18 3.89 3.93 3.74 3.38 2.52 1.82 
12. 0.32 1.79 2.52 3.78 5.15 5.92 5.19 3.9 4.03 3.79 3.39 2.53 1.84 
13. 0.35 1.81 2.58 3.83 5.21 5.97 5.22 3.9 4.04 3.86 3.41 2.54 1.84 
14. 0.38 1.81 2.58 3.9 5.39 6.07 5.23 3.93 4.04 3.91 3.41 2.55 1.85 
15. 0.41 1.81 2.61 3.96 5.45 6.13 5.23 3.95 4.04 3.91 3.42 2.56 1.85 
16. 0.43 1.83 2.64 4.01 5.51 6.14 5.24 3.96 4.07 3.93 3.43 2.58 1.86 
17. 0.46 1.84 2.64 4.09 5.53 6.15 5.27 3.96 4.09 3.94 3.43 2.59 1.86 
18. 0.49 1.86 2.64 4.15 5.53 6.16 5.29 3.96 4.17 3.94 3.43 2.6 1.87 
19. 0.51 1.86 2.64 4.16 5.64 6.19 5.39 3.99 4.19 3.96 3.44 2.6 1.88 
20. 0.54 1.86 2.66 4.18 5.82 6.25 5.42 4 4.2 3.97 3.51 2.6 1.9 
21. 0.57 1.9 2.66 4.2 5.88 6.35 5.44 4.01 4.22 3.99 3.51 2.62 1.9 
22. 0.59 1.9 2.67 4.2 5.92 6.35 5.45 4.06 4.23 4.02 3.52 2.65 1.91 
23. 0.62 1.95 2.7 4.2 5.92 6.44 5.46 4.1 4.3 4.07 3.54 2.65 1.93 
24. 0.65 2.06 2.73 4.26 6.18 6.48 5.5 4.23 4.3 4.09 3.55 2.66 1.94 
25. 0.68 2.07 2.75 4.32 6.2 6.51 5.52 4.25 4.31 4.09 3.66 2.66 1.96 
26. 0.70 2.08 2.76 4.44 6.25 6.67 5.56 4.33 4.36 4.11 3.66 2.67 1.96 
27. 0.73 2.08 2.86 4.45 6.51 6.82 5.68 4.34 4.39 4.12 3.66 2.7 1.97 
28. 0.75 2.09 2.95 4.53 6.6 6.88 5.98 4.35 4.41 4.12 3.68 2.7 1.97 
29. 0.78 2.09 2.96 4.6 6.63 6.88 6.03 4.46 4.43 4.14 3.69 2.73 1.98 
30. 0.81 2.1 3.01 4.62 6.65 6.94 6.03 4.47 4.45 4.15 3.71 2.76 2 
31. 0.84 2.1 3.14 5.03 6.65 7.14 6.08 4.53 4.45 4.15 3.75 2.76 2.01 
32. 0.86 2.11 3.22 5.12 6.72 7.29 6.22 4.53 4.53 4.17 3.78 2.77 2.03 
33. 0.89 2.21 3.33 5.13 6.9 7.35 6.22 4.55 4.53 4.18 3.84 2.84 2.09 
34. 0.92 2.23 3.38 5.22 6.94 7.47 6.23 4.68 4.56 4.2 3.86 2.9 2.12 
35. 0.95 2.24 3.53 5.31 7.42 7.62 6.49 4.69 4.57 4.21 3.92 2.93 2.12 
36. 0.97 2.33 3.82 5.51 7.44 7.65 6.93 4.82 4.64 4.31 3.97 3.09 2.13 

Bolded values indicte 75% dependable reference evapotranspiration (mm/day) of Patna meteorological station.

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Table 9

75% Dependable rainfall (mm) and dependable Penman–Monteith ET0 during the period 1980–2015

Month75% dependable rainfall (mm)Average rainfall (mm)75% dependable Penman–Monteith ET0 (mm/day)Average Penman–Monteith ET0 (mm/day)
January 1.5 12.80 2.09 1.88 
February 0 14.02 2.95 2.72 
March 0 10.20 4.53 4.15 
April 0 11.76 6.60 5.71 
May 13.7 45.29 6.88 6.25 
June 76.4 143.51 5.98 5.45 
July 230 315.01 4.35 4.10 
August 198 268.56 4.41 4.14 
September 128.1 184.85 4.12 3.93 
October 3.6 43.40 3.68 3.51 
November 0 5.78 2.70 2.60 
December 0 9.34 1.97 1.86 
Month75% dependable rainfall (mm)Average rainfall (mm)75% dependable Penman–Monteith ET0 (mm/day)Average Penman–Monteith ET0 (mm/day)
January 1.5 12.80 2.09 1.88 
February 0 14.02 2.95 2.72 
March 0 10.20 4.53 4.15 
April 0 11.76 6.60 5.71 
May 13.7 45.29 6.88 6.25 
June 76.4 143.51 5.98 5.45 
July 230 315.01 4.35 4.10 
August 198 268.56 4.41 4.14 
September 128.1 184.85 4.12 3.93 
October 3.6 43.40 3.68 3.51 
November 0 5.78 2.70 2.60 
December 0 9.34 1.97 1.86 
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The computer program CROPWAT and the climatic database CLIMWAT are used to determine crop water requirements, irrigation water requirements, and irrigation scheduling for a range of crops at different climatological stations throughout the entire world. The Water Development and Management Unit and the Climate Change and Bioenergy Unit of FAO jointly published CLIMWAT 2.0 for CROPWAT. In the event that local climate data are unavailable, CLIMWAT offers information on over 5,000 stations worldwide. A computer program called CROPWAT 8.0 for Windows is used to determine crop water requirements and irrigation needs based on information about the soil, climate, and crops. Furthermore, the program facilitates the creation of irrigation schedules tailored to various farming situations and the computation of water requirements for various cropping patterns.

Readily available moisture

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This refers to the amount of soil moisture that plants can easily extract from the soil without experiencing water stress. It is the portion of water between the field capacity (the amount of water the soil can hold after excess water has drained away) and the wilting point (the point at which plants can no longer extract water). Readily available moisture (RAM) is often defined as a percentage of the available water capacity. It is commonly assumed that 50–60% of the available moisture is readily available for plants.

Total available moisture

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This refers to the total amount of water available to plants in the soil, usually measured between field capacity and the permanent wilting point. It is the full range of water that plants can potentially use.

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By analyzing crop water requirement and irrigation requirement of maize and wheat by using both single and dual crop coefficients, the dual crop coefficient gives the lower irrigation requirement. For maize, crop water requirement and irrigation requirement using single crop coefficient are 291.4 and 289.7 mm/dec, whereas dual crop coefficients are 266.1 and 264.5 mm/dec as given in Tables 10 and 11. For wheat, crop water requirement and irrigation requirement using single crop coefficients are 263.6 and 262 mm/dec, whereas dual crop coefficients are 256.6 and 255 mm/dec as shown in Tables 12 and 13. Also, various analyzed crops like barley, gram, mustard, potato, onion, lentil, millet, sunflower and tomato clearly indicates that the dual crop coefficient has a lower crop water requirement and lower irrigation requirement. Due to data limitations, the single crop coefficient is used for crop water requirement throughout the study area. The crop water requirement and irrigation requirement of crops grown in kharif, rabi, hot weather, and annual seasons in the study area are calculated by using CROPWAT 8.0 software and are given in Table 14 (Surendran et al. 2019).

Table 10

Crop water requirements for Maize-1 (Rabi) based on single crop coefficient (⁠⁠)

ETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decamm/deca
Nov 3 Inita 0.34 8.4 0 8.4 
Dec 1 Init 0.34 7.5 0 7.5 
Dec 2 Devea 0.49 9.7 0 9.7 
Dec 3 Deve 0.78 17.3 0.1 17.2 
Jan 1 Mida 1.07 21.9 0.4 21.5 
Jan 2 Mid 1.17 24.3 0.6 23.7 
Jan 3 Mid 1.17 30.7 0.4 30.3 
Feb 1 Mid 1.17 31.5 0.1 31.4 
Feb 2 Mid 1.17 35.1 0 35.1 
Feb 3 Late 1.12 31.4 0 31.4 
Mar 1 Late 0.88 35.5 0 35.5 
Mar 2 Late 0.61 27.6 0 27.6 
Mar 3 Late 0.4 10.5 0 10.5 
Total (in mm) 291.4 1.6 289.7 
ETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decamm/deca
Nov 3 Inita 0.34 8.4 0 8.4 
Dec 1 Init 0.34 7.5 0 7.5 
Dec 2 Devea 0.49 9.7 0 9.7 
Dec 3 Deve 0.78 17.3 0.1 17.2 
Jan 1 Mida 1.07 21.9 0.4 21.5 
Jan 2 Mid 1.17 24.3 0.6 23.7 
Jan 3 Mid 1.17 30.7 0.4 30.3 
Feb 1 Mid 1.17 31.5 0.1 31.4 
Feb 2 Mid 1.17 35.1 0 35.1 
Feb 3 Late 1.12 31.4 0 31.4 
Mar 1 Late 0.88 35.5 0 35.5 
Mar 2 Late 0.61 27.6 0 27.6 
Mar 3 Late 0.4 10.5 0 10.5 
Total (in mm) 291.4 1.6 289.7 

amm/dec, millimetres per 10 days; mm/day, millimetres per day; Init, Initial stage; Mid, Middle stage; Deve, Development stage; Coeff., Coefficient; Eff. rain, Effective rainfall; Irr. req., Irrigation requirement.

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Table 11

Crop water requirements for Maize-1 (Rabi) based on dual crop coefficient (i.e. Kc = Kcb + Ke)

KcETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 3 Inita 0.31 7.6 0 7.6 
Dec 1 Init 0.31 6.9 0 6.9 
Dec 2 Devea 0.44 8.6 0 8.6 
Dec 3 Deve 0.68 15.1 0.1 15 
Jan 1 Mida 0.93 18.9 0.4 18.5 
Jan 2 Mid 1.01 21 0.6 20.4 
Jan 3 Mid 1.01 26.5 0.4 26.1 
Feb 1 Mid 1.01 27.2 0.1 27.1 
Feb 2 Mid 1.01 30.3 0 30.3 
Feb 3 Late 0.98 27.4 0 27.4 
Mar 1 Late 0.83 33.3 0 33.3 
Mar 2 Late 0.66 29.6 0 29.6 
Mar 3 Late 0.52 13.6 0 13.6 
Total (in mm) 266.1 1.6 264.5 
KcETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 3 Inita 0.31 7.6 0 7.6 
Dec 1 Init 0.31 6.9 0 6.9 
Dec 2 Devea 0.44 8.6 0 8.6 
Dec 3 Deve 0.68 15.1 0.1 15 
Jan 1 Mida 0.93 18.9 0.4 18.5 
Jan 2 Mid 1.01 21 0.6 20.4 
Jan 3 Mid 1.01 26.5 0.4 26.1 
Feb 1 Mid 1.01 27.2 0.1 27.1 
Feb 2 Mid 1.01 30.3 0 30.3 
Feb 3 Late 0.98 27.4 0 27.4 
Mar 1 Late 0.83 33.3 0 33.3 
Mar 2 Late 0.66 29.6 0 29.6 
Mar 3 Late 0.52 13.6 0 13.6 
Total (in mm) 266.1 1.6 264.5 

amm/dec, millimetres per 10 days; mm/day, millimetres per day; Init, Initial stage; Mid, Middle stage; Deve, Development stage; Coeff., Coefficient; Eff. rain, Effective rainfall; Irr. req., Irrigation requirement.

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Table 12

Crop water requirements for wheat based on single crop coefficient Kc

ETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 2 Inita 0.39 10.6 0 10.6 
Nov 3 Init 0.39 9.6 0 9.6 
Dec 1 Devea 0.5 11 0 11 
Dec 2 Deve 0.69 13.7 0 13.7 
Dec 3 Deve 0.9 19.8 0.1 19.7 
Jan 1 Mida 1.06 21.7 0.4 21.3 
Jan 2 Mid 1.08 22.3 0.6 21.7 
Jan 3 Mid 1.08 28.1 0.4 27.7 
Feb 1 Mid 1.08 28.9 0.1 28.8 
Feb 2 Late 1.07 31.9 0 31.9 
Feb 3 Late 0.89 24.9 0 24.9 
Mar 1 Late 0.63 25.4 0 25.4 
Mar 2 Late 0.35 15.8 0 15.8 
Total (in mm) 263.6 1.6 262 
ETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 2 Inita 0.39 10.6 0 10.6 
Nov 3 Init 0.39 9.6 0 9.6 
Dec 1 Devea 0.5 11 0 11 
Dec 2 Deve 0.69 13.7 0 13.7 
Dec 3 Deve 0.9 19.8 0.1 19.7 
Jan 1 Mida 1.06 21.7 0.4 21.3 
Jan 2 Mid 1.08 22.3 0.6 21.7 
Jan 3 Mid 1.08 28.1 0.4 27.7 
Feb 1 Mid 1.08 28.9 0.1 28.8 
Feb 2 Late 1.07 31.9 0 31.9 
Feb 3 Late 0.89 24.9 0 24.9 
Mar 1 Late 0.63 25.4 0 25.4 
Mar 2 Late 0.35 15.8 0 15.8 
Total (in mm) 263.6 1.6 262 

amm/dec, millimetres per 10 days; mm/day, millimetres per day; Init, Initial stage; Mid, Middle stage; Deve, Development stage; Coeff., Coefficient; Eff. rain, Effective rainfall; Irr. req., Irrigation requirement.

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Table 13

Crop water requirements for wheat based on dual crop coefficient (Kcb + Ke)

KcETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 2 Inita 0.32 8.7 0 8.7 
Nov 3 Init 0.32 7.9 0 7.9 
Dec 1 Devea 0.43 9.5 0 9.5 
Dec 2 Deve 0.62 12.3 0 12.3 
Dec 3 Deve 0.83 18.3 0.1 18.2 
Jan 1 Mida 0.99 20.3 0.4 19.9 
Jan 2 Mid 1.01 20.8 0.6 20.2 
Jan 3 Mid 1.01 26.3 0.4 25.9 
Feb 1 Mid 1.01 27 0.1 26.9 
Feb 2 Late 1 29.9 0 29.9 
Feb 3 Late 0.88 24.6 0 24.6 
Mar 1 Late 0.7 28.2 0 28.2 
Mar 2 Late 0.51 23 0 23 
Total (in mm) 256.6 1.6 255 
KcETcEff. rainaIrr. req.a
MonthDecadeStageCoeff.amm/decamm/decmm/dec
Nov 2 Inita 0.32 8.7 0 8.7 
Nov 3 Init 0.32 7.9 0 7.9 
Dec 1 Devea 0.43 9.5 0 9.5 
Dec 2 Deve 0.62 12.3 0 12.3 
Dec 3 Deve 0.83 18.3 0.1 18.2 
Jan 1 Mida 0.99 20.3 0.4 19.9 
Jan 2 Mid 1.01 20.8 0.6 20.2 
Jan 3 Mid 1.01 26.3 0.4 25.9 
Feb 1 Mid 1.01 27 0.1 26.9 
Feb 2 Late 1 29.9 0 29.9 
Feb 3 Late 0.88 24.6 0 24.6 
Mar 1 Late 0.7 28.2 0 28.2 
Mar 2 Late 0.51 23 0 23 
Total (in mm) 256.6 1.6 255 

amm/dec, millimetres per 10 days; mm/day, millimetres per day; Init, Initial stage; Mid, Middle stage; Deve, Development stage; Coeff., Coefficient; Eff. rain, Effective rainfall; Irr. req., Irrigation requirement.

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Table 14

Crop water requirement and irrigation requirement of crops grown in the study area

Sl. No.CropCrop water requirement (mm/dec)Irrigation requirement (mm/dec)
1. Rice 524.9 473.6 
2. Maize-I 291.4 289.7 
3. Wheat 263.6 262 
4. Barley 248.2 246.5 
5. Gram 174.7 172.9 
6. Mustard 225.9 224.1 
7. Potato 175.1 173.4 
8. Onion 208.5 206.8 
9. Maize-II 573.1 401.9 
10. Lentil 262.7 262.6 
11. Millet 474.7 453.4 
12. Sunflower 590.6 372 
13. Egg Plant 629.3 386.8 
14. Tomato 680.9 415.9 
Sl. No.CropCrop water requirement (mm/dec)Irrigation requirement (mm/dec)
1. Rice 524.9 473.6 
2. Maize-I 291.4 289.7 
3. Wheat 263.6 262 
4. Barley 248.2 246.5 
5. Gram 174.7 172.9 
6. Mustard 225.9 224.1 
7. Potato 175.1 173.4 
8. Onion 208.5 206.8 
9. Maize-II 573.1 401.9 
10. Lentil 262.7 262.6 
11. Millet 474.7 453.4 
12. Sunflower 590.6 372 
13. Egg Plant 629.3 386.8 
14. Tomato 680.9 415.9 
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By analyzing the results of crop water requirements using single and dual crop coefficients (Table 15), the dual crop coefficient yields lower values compared to the single crop coefficient. The irrigation scheduling of all crops grown in the study are calculated using the CROPWAT 8.0. The irrigation scheduling patterns of wheat and maize crops are shown in Figures 5 and 6. RAM and total available moisture(TAM) increase with root growth during the initial and development stages (25 + 30 days = 55 days, as shown in Figures 5 and 6 for wheat and maize crops), and then become constant in the later growth stages. Additionally, RAM increases further during the maturity stage.
Table 15

Crop water requirement using single and dual crop coefficients for all crops grown in the study area

Sl. No.CropCrop water requirement (mm/dec) single crop coefficientCrop water requirement (mm/dec) dual crop coefficient
1. Rice 524.9 476.5 
2. Maize-I 291.4 266.1 
3. Wheat 263.6 256 
4. Barley 248.2 230.1 
5. Gram 174.7 152.9 
6. Mustard 225.9 204.6 
7. Potato 175.1 153.4 
8. Onion 208.5 196.8 
9. Maize-II 573.1 531.9 
10. Lentil 262.7 242.5 
11. Millet 474.7 453.4 
12. Sunflower 590.6 472 
13. Egg Plant 629.3 586.8 
14. Tomato 680.9 515.7 
Sl. No.CropCrop water requirement (mm/dec) single crop coefficientCrop water requirement (mm/dec) dual crop coefficient
1. Rice 524.9 476.5 
2. Maize-I 291.4 266.1 
3. Wheat 263.6 256 
4. Barley 248.2 230.1 
5. Gram 174.7 152.9 
6. Mustard 225.9 204.6 
7. Potato 175.1 153.4 
8. Onion 208.5 196.8 
9. Maize-II 573.1 531.9 
10. Lentil 262.7 242.5 
11. Millet 474.7 453.4 
12. Sunflower 590.6 472 
13. Egg Plant 629.3 586.8 
14. Tomato 680.9 515.7 
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Figure 5
Irrigation scheduling of wheat crop. RAM, readily available moisture; TAM, total available moisture.
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Irrigation scheduling of wheat crop. RAM, readily available moisture; TAM, total available moisture.

Figure 5
Irrigation scheduling of wheat crop. RAM, readily available moisture; TAM, total available moisture.
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Irrigation scheduling of wheat crop. RAM, readily available moisture; TAM, total available moisture.

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Figure 6
Irrigation scheduling of maize crop. RAM, readily available moisture; TAM, total available moisture.
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Irrigation scheduling of maize crop. RAM, readily available moisture; TAM, total available moisture.

Figure 6
Irrigation scheduling of maize crop. RAM, readily available moisture; TAM, total available moisture.
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Irrigation scheduling of maize crop. RAM, readily available moisture; TAM, total available moisture.

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The current study is based on climate data collected from the study area for 31 years. The reference evapotranspiration is calculated by using the Allen et al. 1998 Modified Penman–Monteith equation, and the maximum, minimum, and average values of ET0 were found to be 7.65, 1.31, and 3.86 mm/day, respectively. The FAO-CROPWAT 8 model was used to calculate the net irrigation water requirements, gross irrigation water requirements, and irrigation intervals for the three major crops grown in the Palignaj Distributary, namely paddy, wheat, and maize. The single and dual crop coefficients of the study area are calculated by using the methodology of both Doorenbos & Pruitt 1977 FAO-24 and Allen et al. 1998. The results show that the estimation of crop water requirement by using dual crop coefficient gives a lower irrigation requirements compared with a single crop coefficient. The current research will contribute to the enhancement of water resource and production monitoring. Additionally, it would assist local farmers, legislators in making effective use of nation's incredibly limited resources with correct estimation of crop water requirements. The study may also be used by engineers and planners in devising proper irrigation water distribution systems.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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© 2025 The Authors
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