Reference Evapotranspiration Calculator
Estimate how much water a crop uses each day from latitude, day of year, temperatures and a crop coefficient.
What it does
Evapotranspiration is the water that leaves a field as evaporation from the soil and transpiration from the plants. Reference evapotranspiration, written ET0 in the FAO method, is the same idea for a standard reference surface, so it measures the weather rather than the crop. Crop evapotranspiration, ETc, is that reference multiplied by a crop coefficient.
The FAO Irrigation and Drainage Paper 56 sets out the method in detail, and chapter 3 gives the equation used here. The Hargreaves and Samani form needs only the maximum and minimum temperature for the day, the latitude and the day of the year, which makes it the practical choice when there is no weather station nearby. FAO also recommends checking it against the full Penman-Monteith method when you can, and warns that it can underpredict in windy places and overpredict where the humidity is high.
The sunshine part of the calculation comes from the geometry of the orbit. Equation 21 of the paper works out the extraterrestrial radiation from the solar constant, the distance of the earth from the sun through the year, the declination of the sun and the sunset hour angle for the latitude. That value is converted to an equivalent evaporation depth, and it is what sets the ceiling on how much water the day can possibly move.
The crop coefficient is where the crop enters, and it is not a fixed property of the plant. FAO table 12 lists values by crop and growth stage: a tomato crop at mid season uses 1.15, lettuce 1.00, cool season turf 0.95 and warm season turf 0.85, and the end of season values are lower. A young crop with little leaf area uses less water than a full grown one.
What the tool produces is crop water use, not an irrigation schedule. Rainfall has to be subtracted, and on top of that you need an efficiency factor for whatever applies the water, since sprinkler and drip systems lose a good share of what they deliver to evaporation and to the wind.
How to use
- Pick metric or imperial units.
- Enter the latitude of the site, negative in the southern hemisphere.
- Enter the day of the year, which sets the solar geometry.
- Enter the daily maximum and minimum temperature.
- Enter the crop coefficient for your crop and its growth stage.
- Read the daily and weekly water use, then subtract rainfall and add the losses of your irrigation system.
Formula
- ET0
- Reference evapotranspiration in mm per day.
- ETc
- Crop evapotranspiration in mm per day.
- Kc
- Crop coefficient, which scales the reference figure for the crop and its stage.
- Ra
- Extraterrestrial radiation converted to an equivalent evaporation depth, in mm per day.
- Tmax, Tmin
- Daily maximum and minimum temperature in °C.
The solar constant in equation 21 is 0.0820 MJ per square metre per minute, and the value it produces in MJ per square metre per day is divided by 2.45 MJ per kilogram to turn it into millimetres of water equivalent. FAO prints the conversion as 0.408, which is the same thing rounded. The Hargreaves form assumes a standard day length behaviour for the latitude and does not use cloud cover, wind or humidity at all.
Worked example
Example: 40 degrees north on day 120 with 25 and 12 °C
Defaults: metric units, latitude 40, day 120, a maximum of 25 °C, a minimum of 12 °C and a crop coefficient of 1.15.
- Mean temperature: (25 + 12) / 2 = 18.5 °C, and the temperature range is 13 °C.
- Solar declination and the sunset hour angle follow from the latitude and day of year.
- Extraterrestrial radiation: 37.53 MJ per square metre per day, which is 15.32 mm per day.
- Reference evapotranspiration: 0.0023 x (18.5 + 17.8) x sqrt(13) x 15.32 = 4.61 mm/day.
- Crop evapotranspiration: 1.15 x 4.61 = 5.30 mm/day.
- Over a week that is 37.12 mm, which is 37.12 liters per square meter.
- The tool shows 15.32 mm/day, 4.61 mm/day, 5.30 mm/day, 37.12 mm/week and 37.12 L per m2.
Reference table
| Crop | Mid season Kc | End of season Kc |
|---|---|---|
| Tomato | 1.15 | 0.70 to 0.90 |
| Lettuce | 1.00 | 0.95 |
| Cool season turf grass | 0.95 | 0.95 |
| Warm season turf grass | 0.85 | 0.85 |
Limits
- Uses the Hargreaves form, which ignores wind, humidity and cloud cover, so it is a screening figure rather than a measurement.
- Gives crop water use, not an irrigation depth, so rainfall and system losses still have to be added in.
- Takes a single crop coefficient for the whole period, while the coefficient changes through the season.
- Assumes a healthy, unstressed crop, which is how FAO sets the reference conditions.
Common mistakes
- Using the ET0 figure as the water the crop needs and forgetting the crop coefficient.
- Mixing up a daily average temperature with the daily maximum, which changes the temperature range in the formula.
- Forgetting that the day of the year changes the geometry, so the same temperatures give different answers in May and July.
- Using a mid season crop coefficient for a young crop, which overestimates the water needed.
- Treating the result as a watering schedule without allowing for rainfall or for the efficiency of the system.
Try it yourself
Quick checks. Answers sit tucked under each question.
On the same day and site, what does a crop coefficient of 0.95 give?
ETc = 0.95 x 4.61 = 4.38 mm/day, which is 30.67 mm a week instead of 37.12 mm.
What happens at 40 degrees north on day 166 instead of day 120?
The extraterrestrial radiation rises to 17.08 mm/day, the reference evapotranspiration to 5.14 mm/day and the crop figure to 5.91 mm/day, so 41.38 mm a week.
How much more water does a tomato crop use than lettuce at the same site?
The difference in the coefficient is 0.15, so 0.15 x 4.61 = 0.69 mm a day, or 4.85 mm a week.
Questions
What is reference evapotranspiration?
The amount of water a standard reference grass surface would use at that site, on that day, with the weather as it was. It measures the weather, not any particular crop.
What is a crop coefficient?
A number that scales the reference figure for a specific crop at a specific growth stage. It reflects the leaf area and the physiology of the crop, and it changes through the season.
How much water does a tomato crop use in midsummer?
With a coefficient of 1.15 and a reference figure of 4.61 mm a day, the crop uses 5.30 mm a day, which is 37.12 mm a week.
Is this the same as a watering schedule?
No. This is the water the crop uses. To turn it into a watering plan you subtract the rainfall, divide by the efficiency of your system and spread the result over the days you water.
Why does latitude matter?
It sets the length of the day and the height of the sun, which together decide how much solar energy arrives. A site at 40 degrees north in April gets far less than the same site in June.
Which method should a serious grower use?
The FAO Penman-Monteith method, which uses radiation, wind, humidity and temperature together. It needs a weather station or a local estimate, and FAO recommends checking a Hargreaves estimate against it.
Sources
- FAO Irrigation and Drainage Paper 56, chapter 3: meteorological data and reference evapotranspiration
- FAO Irrigation and Drainage Paper 56, chapter 6: crop evapotranspiration and crop coefficients
- University of Florida IFAS Extension: step by step evapotranspiration calculations