About Evapotranspiration (ET0) Calculator
The evapotranspiration calculator estimates reference crop evapotranspiration ET0 using the Hargreaves equation, ET0 = 0.0023 * Ra * (Tmean + 17.8) * sqrt(Tmax - Tmin). The Hargreaves method is the FAO-56 recommended alternative for situations where the humidity, wind, and solar-radiation data needed for the full Penman-Monteith equation are not available; it requires only air-temperature data and the extraterrestrial radiation Ra.
You can supply Ra directly (MJ/m^2/day) or let the tool compute it from latitude and the day of year using the FAO-56 solar-geometry equations. Multiplying ET0 by a crop coefficient Kc gives the crop evapotranspiration ETc, and subtracting effective rainfall gives the net irrigation requirement. The tool also reports monthly totals and plots a seasonal ET0 curve so you can size irrigation schemes and schedule irrigation.
How It Works
- Choose how to supply the extraterrestrial radiation Ra: enter it directly in MJ/m^2/day, or provide the site latitude (negative in the southern hemisphere) and the day of year so the tool computes Ra from solar geometry.
- Enter the maximum, minimum, and (optionally) mean daily air temperatures. When Tmean is omitted the calculator uses (Tmax + Tmin)/2.
- Ra is converted to an equivalent depth of evaporation (mm/day) by multiplying by 0.408, then the Hargreaves equation gives ET0 = 0.0023 * Ra_mm * (Tmean + 17.8) * sqrt(Tmax - Tmin).
- Crop evapotranspiration is ETc = ET0 * Kc, and the net irrigation requirement is ETc minus the effective rainfall (clamped at zero). Daily values are multiplied by 30 to give monthly totals, and the seasonal curve plots ET0 month by month.
Worked Example
A site at latitude -20 degrees on day of year 246 (3 September) has Tmax = 30 C, Tmin = 18 C, Tmean = 24 C, a crop coefficient Kc = 1.0, and 1 mm/day of effective rainfall. The FAO-56 solar-geometry equations give an extraterrestrial radiation Ra = 32.2 MJ/m^2/day, which as an equivalent evaporation depth is Ra_mm = 32.2 * 0.408 = 13.14 mm/day. The Hargreaves equation then gives ET0 = 0.0023 * 13.14 * (24 + 17.8) * sqrt(30 - 18) = 0.0023 * 13.14 * 41.8 * 3.464 = 4.38 mm/day. With Kc = 1.0 the crop ET is ETc = 4.38 mm/day, so the net irrigation requirement is ETc - rainfall = 4.38 - 1 = 3.38 mm/day, or about 4.38 * 30 = 131 mm over a 30-day month.
Formulas
- Hargreaves reference ET0
ET0 = 0.0023 * Ra_mm * (Tmean + 17.8) * sqrt(Tmax - Tmin)- Radiation conversion
Ra_mm = 0.408 * Ra[MJ/m^2/day]- Extraterrestrial radiation (FAO-56)
Ra = (24*60/pi)*Gsc*dr*[ws*sin(phi)*sin(d) + cos(phi)*cos(d)*sin(ws)]- Crop ET and irrigation requirement
ETc = ET0 * Kc; Net irrigation = max(0, ETc - Peff)
Standards & References
- FAO Irrigation and Drainage Paper 56 (Allen et al., 1998)
- Hargreaves & Samani (1985) temperature-based ET0 method
- ASCE Standardized Reference Evapotranspiration Equation (context)
Frequently Asked Questions
When should I use the Hargreaves method instead of Penman-Monteith?
FAO-56 recommends the Penman-Monteith equation as the standard, but it requires temperature, humidity, wind speed, and solar radiation. When only air-temperature data are reliable, FAO-56 endorses the Hargreaves equation as the best temperature-based alternative. It needs only Tmax, Tmin, and the extraterrestrial radiation Ra, which is a deterministic function of latitude and date.
What is extraterrestrial radiation Ra and how is it found?
Ra is the solar radiation that would reach a horizontal surface at the top of the atmosphere. It depends only on latitude and day of year, not on weather, so it can be computed exactly from solar geometry using the FAO-56 equations. This tool either accepts Ra directly in MJ/m^2/day or computes it from the latitude and day of year you enter.
What is the crop coefficient Kc?
The crop coefficient Kc scales the reference ET0 (for a hypothetical grass surface) up or down to the actual crop and growth stage, giving crop evapotranspiration ETc = ET0 * Kc. Values typically range from about 0.3 at initial stages to 1.15 or more at mid-season for many field crops. FAO-56 tabulates Kc values by crop and growth stage.
How is the net irrigation requirement calculated?
The net irrigation requirement is the crop water demand not met by rainfall: ETc minus the effective rainfall, clamped at zero so it is never negative. It represents the depth of water that must be applied by irrigation each day. Dividing by the irrigation system efficiency gives the gross application depth.