Reference Evapotranspiration ET0 (Hargreaves / FAO-56)
Reference evapotranspiration (ET0) from air temperature alone.
Example
You enter
- Latitude (deg, + north / - south) 45
- Month jul
- Daily high Tmax (°F) 86
- Daily low Tmin (°F) 59
You get
- Et0 (mm/day) 5.9334
- Ra mj m2 (day) 40.494
Details, formula, and sources
by the Hargreaves method FAO-56 recommends when only temperature is reliable: ET0 = 0.0023 (Tmean + 17.8) sqrt(Tmax - Tmin) Ra. Enter latitude, month, and the daily high/low (F); the extraterrestrial radiation Ra comes from the FAO-56 astronomical equations by latitude and mid-month day, so no radiation table is needed. A 45 deg N site in July at 86/59 F reads ET0 = 0.234 in/day (5.93 mm). ET0 is the baseline every crop's demand scales from (crop ET = Kc x ET0), feeding acre-foot and irrigation-scheduling math. The daily temperature range stands in for cloudiness/humidity, so a clear dry site reads higher than a humid one at the same mean. A planning aid; a local station ET0 (CIMIS, Mesonet) and the full Penman-Monteith method govern when full climate data exist.
Hargreaves: ET0 = 0.0023 (Tmean + 17.8) sqrt(Tmax - Tmin) Ra (Ra as equivalent evaporation, mm/day = Ra_MJ/2.45). Ra (FAO-56 Annex 2): dr = 1 + 0.033 cos(2pi J/365); dec = 0.409 sin(2pi J/365 - 1.39); ws = arccos(-tan(phi) tan(dec)); Ra = (24*60/pi) 0.0820 dr (ws sin(phi) sin(dec) + cos(phi) cos(dec) sin(ws)). J = mid-month day; temperatures converted from F to C.
Hargreaves & Samani (1985) reference-ET equation as presented in FAO Irrigation & Drainage Paper 56 (Allen, Pereira, Raes, Smith 1998), Annex 2 for the extraterrestrial-radiation equations, by name.
FAO-56 is a free public PDF at fao.org; the Hargreaves equation and the FAO-56 astronomical Ra equations are public.
Estimate. AHJ and licensed professional govern.
Field names used by the API: latitude_deg, month, tmax_f, tmin_f, et0_mm_day, ra_mj_m2_day
- Hargreaves ET0 ET0 = 0.0023 (Tmean+17.8) sqrt(Tmax-Tmin) Ra; Ra as mm/day = Ra_MJ/2.45Hargreaves & Samani 1985 / FAO-56
- Extraterrestrial radiation Ra FAO-56 Annex 2 astronomical equations from latitude and day of year (mid-month J)FAO-56 Annex 2
- Scope temperature-only estimate; |lat| <= 66.5; a local station ET0 and Penman-Monteith govern with full datascope of this tile