What ETc is, and why it is expressed in inches
Evapotranspiration is the water leaving a field as vapour: evaporation from the soil surface plus transpiration through the crop's stomata. It is measured as a depth — inches or millimetres — because that makes it directly comparable with rainfall and with the water a soil can hold. A field using 0.30 inches a day is losing the equivalent of a third of an inch of rain every day, whatever its area.
The reason for splitting it into a reference and a coefficient is that the atmospheric demand and the crop's response to it are different problems. Reference evapotranspiration, ETo, describes the weather: it is the ET of a hypothetical, uniform, well-watered grass surface 12 centimetres tall, computed from solar radiation, temperature, humidity and wind by the FAO Penman–Monteith equation. It is a property of the air, not of your crop, which is why a single weather station can serve every field within its area.
The crop coefficient, Kc, is the ratio of your crop's water use to that reference under the same weather. It moves through the season with the canopy: low at emergence when there is little leaf and only wet soil to evaporate from, rising to a plateau at full canopy, and falling again at senescence. Multiply the two and you have ETc, the water your crop is actually using.
Then two adjustments turn ETc into an irrigation decision. Subtract what rain and stored soil water supplied, because the crop does not care where the water came from. Divide by application efficiency, because some of what leaves the pump never reaches the root zone. What is left is the gross depth to apply.
Each term, and where it goes wrong
ETo should come from a network station running the FAO-56 Penman–Monteith equation over a properly maintained reference surface, not from a pan or a temperature-only estimate. Most states run one: CIMIS in California, the Kansas Mesonet, AZMET in Arizona, and equivalents elsewhere. Take the daily average across the period you are scheduling, and check whether the station reports grass reference ETo or alfalfa reference ETr, because the alfalfa reference runs roughly 15 to 30% higher and its coefficients are a different set entirely. Mixing an ETr value with a grass-referenced Kc overstates water use badly.
Kc is where most of the error lives, because it changes continuously through the season and the tabulated values assume a specific climate. FAO-56 tabulates Kc for a sub-humid climate with minimum relative humidity around 45% and wind around 2 m s−1, and gives an adjustment for climates outside that: drier and windier conditions raise Kc for tall crops, because a tall rough canopy couples to the air more effectively than short grass does. In an arid, windy site the mid-season Kc for maize is meaningfully above the tabulated 1.20.
Effective rainfall is not gauge rainfall. It is the part that entered the root zone and stayed there. A one-inch storm on dry soil may be almost fully effective; the same storm on a saturated profile or a slope may be mostly runoff and deep percolation. There are formal methods for estimating it, but the practical approach on a well-instrumented farm is to watch soil moisture sensors and let them tell you what arrived.
Application efficiency is the fraction of pumped water reaching the root zone, and it varies enormously by system. Subsurface drip is at the top, followed by low-pressure sprinkler packages on a pivot, then high-pressure impact sprinklers, then surface and furrow systems, which lose the most to deep percolation at the head of the run and to tailwater at the foot. Use your own measured figure if you have one from a system evaluation; otherwise use your extension service's figure for your specific system, and treat a manufacturer's headline number as optimistic.
Worked example: a week on 130 acres of maize
A quarter-section centre pivot covering 130 acres of maize at full canopy. The ET network reports ETo averaging 0.25 inches a day for the week, mid-season Kc is 1.20, and 0.40 inches of the rain that fell entered the root zone. The pivot's low-pressure package is 85% efficient.
- Daily crop use. 1.20 × 0.25 = 0.30 inches per day.
- Weekly crop use. 0.30 × 7 = 2.10 inches.
- Net requirement. 2.10 − 0.40 = 1.70 inches the crop still needs from irrigation.
- Gross depth. 1.70 ÷ 0.85 = 2.00 inches at the pivot. The 0.30-inch difference is the water that never reaches the root zone.
- Volume per acre. 2.00 × 27,154 = 54,308 gallons per acre.
- Volume for the field. 54,308 × 130 = 7,060,040 gallons, which is 2.00 ÷ 12 × 130 = 21.67 acre-feet.
- Pump flow. A week is 7 × 1,440 = 10,080 minutes, so 7,060,040 ÷ 10,080 = 700 GPM running continuously, or 700 ÷ 130 = 5.4 GPM per acre.
That per-acre flow figure is the one to check your well against. If the well delivers 800 GPM you have headroom; if it delivers 550 you cannot keep up with peak demand and the crop will draw on stored soil water, which is acceptable for a while and not indefinitely. Note also that no system runs 168 hours a week — allow for moving, maintenance and power restrictions, and the required instantaneous flow rises in proportion to the hours you are actually down.
Turning the depth into a schedule
The net requirement tells you how much water the crop needs; the soil tells you when it must arrive. Divide the plant-available water your root zone holds by the daily ETc and you get the number of days from a full profile to complete depletion. Irrigate at a fraction of that — the management allowed depletion, commonly around half of available water for many field crops, less for shallow-rooted or high-value crops — and you have your interval.
Compare the gross depth with what the system can physically apply in one pass. A pivot's application depth per revolution is set by its speed; asking for two inches from a machine that applies 0.9 inches per pass means two revolutions, and a slow revolution may exceed the soil's infiltration rate and run off. Sandy soils take water quickly and hold little, so they want frequent light applications; heavy soils hold more and take it more slowly.
Watch the efficiency term rather than accepting it. The difference between 85% and 60% on this example is 1.70 ÷ 0.60 − 2.00 = 0.83 inches of extra pumped water a week, which at 27,154 gallons an acre-inch over 130 acres is 2.9 million gallons every week, or about 29 million across a ten-week season. That gap is the entire economic argument for system upgrades, and it is worth measuring your real efficiency with a catch-can test rather than assuming.
Finally, treat the whole calculation as a planning estimate that soil moisture sensors and crop observation should correct. ETc models the demand; they measure the result. Where the two disagree, the sensors are usually right, and the most common cause is an effective-rainfall assumption that did not hold.
Mid-season crop coefficients (Kc mid) from FAO-56
| Crop | Kc mid | Note |
|---|---|---|
| Maize (field corn) | 1.20 | Kc rises from about 0.30 at emergence and falls toward 0.35 at maturity |
| Alfalfa (individual cutting) | 1.20 | Resets after each cutting |
| Soybean | 1.15 | — |
| Wheat (spring) | 1.15 | — |
| Cotton | 1.15 | — |
| Potato | 1.15 | — |
| Tomato | 1.15 | — |
| Small vegetables | 1.05 | Group value for the short-season vegetable crops |
| Grapes (table or raisin) | 0.85 | Trellised, with the ground between rows kept bare |
| Citrus, 70% canopy, no ground cover | 0.60 | Rises substantially where a cover crop is grown between trees |
Values as tabulated in FAO Irrigation and Drainage Paper 56, Table 12. Use your local extension service's coefficients where they exist, because they will already carry the regional climate adjustment.
Grass reference or alfalfa reference — check which one you have
Two reference surfaces are in common use. FAO-56 standardises on the grass reference, ETo, and its crop coefficients are matched to it. Much of the western United States, and the ASCE standardised equation, also publishes an alfalfa reference, ETr, computed for a taller 0.5-metre crop; ETr runs materially higher than ETo for the same weather, and it has its own coefficient set, usually written Kcr.
Multiplying an alfalfa-reference ET by a grass-reference Kc overstates crop water use every single day of the season. Check the units and the reference on the station page before you enter a number here, which assumes a grass-referenced ETo.
Assumptions and limits of this method
- It assumes a well-watered crop. The single-coefficient ETc is potential water use. A crop already under stress uses less, so applying the full ETc to a stressed field over-estimates its demand.
- It assumes standard conditions. FAO-56 Kc values presume a healthy, uniform, disease-free stand at normal density. A thin or damaged stand transpires less.
- Gauge rain is not effective rain. Runoff, interception and deep percolation all remove part of what the gauge caught, and the fraction varies with intensity, slope and antecedent moisture.
- Salinity is not accounted for. Saline water or saline soil requires a leaching fraction on top of the crop requirement, which raises the gross depth beyond what efficiency alone explains.
- The single coefficient blurs soil evaporation. For wide-row crops before canopy closure, and for drip systems that wet only part of the surface, the dual coefficient method separates evaporation from transpiration and is materially more accurate.
- Constant weather is assumed within the period. A week with one 100-degree day and six mild ones has the same average ETo as a uniform week but a very different peak demand.
- System capacity is not checked. The continuous flow figure assumes the system runs every minute of the period. Real downtime raises the instantaneous flow you need.
Where ETc fits with the rest of the irrigation decision
ETc sizes the demand. The next questions are supply and delivery. If your water comes from a farm pond, check that the volume is there before planning a season on it — the pond volume and acre-feet calculator converts surface area and depth into acre-feet, which is the same unit this page reports. A 21.67 acre-foot weekly demand against a 40 acre-foot pond is a two-week supply, not a season.
For delivery, the depth has to become run time on real hardware. On a drip or micro system, the drip irrigation flow rate and run time calculator takes the gallons this page produces and converts them to hours at your emitter flow, and checks the zone against the supply GPM. That pairing is the whole schedule: this page says how much, that one says how long.
Crop stage drives Kc, and stage is driven by heat rather than by the calendar, so the growing degree days calculator is the right tool for deciding when to move from the initial to the mid-season coefficient. And when a fungicide or insecticide pass has to fit around an irrigation event, size the spray day with the acres per spray tank calculator so the two do not collide.