Crop water requirement: ET₀, Kc and irrigation scheduling
How much water a crop uses and when to irrigate it: reference evapotranspiration, the crop coefficient curve, available soil water and worked calculations.
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A crop's water requirement is the depth of water it needs to replace what it loses by evapotranspiration: evaporation from the soil plus transpiration through its leaves. Almost all the water a crop takes up passes straight through it to the air; only about one per cent stays in the plant.
Irrigation uses around 70 per cent of the freshwater withdrawn worldwide, so estimating crop water needs accurately is one of the most valuable calculations in agriculture. The method set out by FAO in Irrigation and Drainage Paper 56 is used in almost every country and is the standard in agronomy and irrigation exams.
The two-step method
FAO-56 splits the problem into the weather's demand and the crop's response.
- ET0, reference evapotranspiration, is how much water a standard surface would use under the day's weather: a hypothetical, well-watered grass 0.12 m tall, fully covering the ground. It depends only on climate.
- Kc, the crop coefficient, scales ET0 to a particular crop at a particular stage. It depends on the crop's height, leaf area, ground cover and how wet the soil surface is.
Separating them means weather data from one station can be applied to any crop, and crop coefficients measured in one place can be used anywhere.
Reference evapotranspiration, ET₀
The standard method is the FAO Penman–Monteith equation. It combines an energy balance (how much radiant energy is available to evaporate water) with an aerodynamic term (how fast the air carries vapour away). It needs four kinds of daily weather data:
- solar radiation (or sunshine hours),
- air temperature (maximum and minimum),
- humidity, and
- wind speed at 2 m height.
Typical ET0 values range from about 1–2 mm/day in cool, cloudy weather to 6–8 mm/day or more in hot, dry, windy weather. ET0 rises with radiation, temperature and wind, and falls with humidity.
When data are limited, simpler methods are used, each with a known bias: the Hargreaves equation (temperature and extraterrestrial radiation only), and the evaporation pan, where ET0 = Kp × Epan, with a pan coefficient Kp usually between about 0.6 and 0.85 depending on humidity, wind and the pan's surroundings.
The crop coefficient curve
A crop's Kc changes through the season in a recognisable shape, which FAO-56 simplifies to four stages.
- Initial stage, from sowing to about 10 per cent ground cover. The crop is small and most water loss is evaporation from the soil surface. Kc,ini is low (often 0.3–0.5) but rises if the soil surface is wetted often by rain or irrigation.
- Crop development, from 10 per cent to effective full cover. Kc rises roughly in a straight line.
- Mid-season, from full cover to the start of maturity. Kc,mid is at its maximum, typically 1.0–1.2 for most field crops; taller crops in dry, windy climates have higher values.
- Late season, from the start of maturity to harvest. Kc falls as leaves senesce; Kc,end is low for crops harvested dry (grain), higher for those harvested fresh (vegetables, forage).
A Kc above 1 means the crop uses more water than the short reference grass, because it is taller and rougher and catches more wind and radiation.
From crop water use to irrigation
Not all of ETc needs irrigation.
- Effective rainfall is the part of rainfall that stays in the root zone and is used by the crop; runoff and deep percolation are excluded.
- Net irrigation requirement = ETc − effective rainfall (and minus any contribution from shallow groundwater).
- Gross irrigation requirement = net requirement ÷ application efficiency. Typical efficiencies are about 50–70 per cent for surface irrigation, 70–85 per cent for sprinklers and 85–95 per cent for drip.
- Where water is saline, a leaching fraction is added to carry salts below the roots.
Seasonal water requirement
A crop has the four stages shown in the figure. Average ET0 is 4 mm/day in the initial stage, 5 in development, 6 in mid-season and 5 in the late season.
| Stage | Days | Average Kc | ET0 (mm/day) | ETc (mm) |
|---|---|---|---|---|
| Initial | 20 | 0.30 | 4 | 20 × 0.30 × 4 = 24 |
| Development | 35 | 0.75 | 5 | 35 × 0.75 × 5 = 131 |
| Mid-season | 40 | 1.20 | 6 | 40 × 1.20 × 6 = 288 |
| Late season | 30 | 0.85 | 5 | 30 × 0.85 × 5 = 128 |
| Season | 125 | 571 mm |
The average Kc for a straight-line stage is the mean of its start and end values. If effective rainfall over the season is 180 mm, the net irrigation requirement is 571 − 180 = 391 mm. With surface irrigation at 60 per cent efficiency, the gross requirement is 391 ÷ 0.6 ≈ 652 mm, or about 6,500 m3 of water per hectare (1 mm over 1 ha = 10 m3). With drip at 90 per cent it is about 434 mm.
When to irrigate: soil water and scheduling
The soil is the crop's reservoir. Two soil water constants bound it:
- Field capacity (FC): the water held after free drainage stops, a day or two after a soaking.
- Permanent wilting point (PWP): the water content at which plants can no longer extract water and wilt without recovering.
Total available water (TAW) is the water between field capacity and wilting point over the rooting depth Zr. The crop cannot use all of it without stress: as the soil dries, water is held more tightly. Readily available water (RAW) is the fraction p that can be used before stress begins; p is about 0.5 for many crops, lower for shallow-rooted, sensitive crops such as vegetables, higher for tolerant ones, and lower when ET is high.
Irrigation is applied when the root zone has used its readily available water, and the depth applied refills it to field capacity.
Irrigation interval and depth
A loam holds volumetric water contents of 0.30 at field capacity and 0.15 at wilting point. The crop's roots reach 0.8 m, p is 0.5, and in mid-season ETc is 1.2 × 5 mm = 6 mm/day.
- TAW = (0.30 − 0.15) × 800 mm = 120 mm.
- RAW = 0.5 × 120 = 60 mm.
- Interval = RAW ÷ ETc = 60 ÷ 6 = 10 days.
- Net depth per irrigation = 60 mm (600 m3 per hectare).
- Gross depth: 60 ÷ 0.6 = 100 mm with furrows; 60 ÷ 0.9 ≈ 67 mm with drip, which is in practice applied in many small, frequent doses instead.
On a sandy soil with TAW of only 50 mm, the same crop would need irrigating every four days.
Scheduling in practice combines this soil water balance with measurements: tensiometers and capacitance probes for soil water, plant indicators, and, increasingly, satellite estimates of crop ET and weather-driven scheduling apps.
Deficit irrigation
Where water, not land, is scarce, it often pays to supply less than full ETc deliberately, concentrating water at the most sensitive stages (usually flowering and early grain or fruit set) and accepting a small yield loss for a large water saving. FAO Paper 33 and its successor Paper 66 describe crop yield response to water with a yield response factor, Ky: the relative yield loss for each unit of relative evapotranspiration deficit.
Key points
- ETc = Kc × ET0. ET0 is the weather's demand on a standard grass surface; Kc adjusts for the crop and stage.
- The FAO Penman–Monteith equation is the standard for ET0; it uses radiation, temperature, humidity and wind.
- Kc follows four stages: initial (low), development (rising), mid-season (peak, often 1.0–1.2) and late season (falling).
- Net irrigation = ETc − effective rainfall; gross = net ÷ application efficiency.
- TAW = (θFC − θPWP) × root depth; irrigate when the readily available water (p × TAW) is used.
- 1 mm of water over 1 hectare is 10 m3.
What the exams ask
- School-leaving and entrance papers: definitions of evapotranspiration, field capacity, wilting point and available water; factors affecting crop water need.
- Degree and research-fellowship entrances: the ET0–Kc approach, the four growth stages, effective rainfall, irrigation efficiencies, and critical stages for irrigation.
- Licensing and professional examinations for agricultural engineers: computing seasonal requirements, irrigation interval and depth, gross depth for a method, pump and canal capacity, and leaching requirements.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why is Kc low at the start if the young crop still needs water?
Because a small crop transpires little; most loss is from the soil surface, which dries quickly. Frequent light wetting raises Kc,ini because the surface stays wet and evaporates more.
Is pan evaporation the same as crop water use?
No. A pan of open water loses more than a grass surface; its reading must be multiplied by a pan coefficient to estimate ET0, then by Kc for the crop.
Which growth stage is most sensitive to water shortage?
For most grain crops, flowering and early grain filling; for many fruit and vegetable crops, flowering and fruit set. Stress at these stages costs the most yield per millimetre of deficit.
Sources
- Allen, R. G., Pereira, L. S., Raes, D. and Smith, M. Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, 1998.
- Steduto, P., Hsiao, T. C., Fereres, E. and Raes, D. Crop Yield Response to Water. FAO Irrigation and Drainage Paper 66, 2012.
- Doorenbos, J. and Kassam, A. H. Yield Response to Water. FAO Irrigation and Drainage Paper 33, 1979.
- FAO AQUASTAT. Water uses. Food and Agriculture Organization of the United Nations, online database.
- Hillel, D. Introduction to Environmental Soil Physics. Academic Press, 2004.
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