Evapotranspiration Calculator (Hargreaves)

How it works

ET₀ = 0.0023 × (T_mean + 17.8) × (T_max − T_min)^0.5 × 0.408 R_a (mm/day) · R_a = (24·60/π) G_sc d_r [ω_s sin φ sin δ + cos φ cos δ sin ω_s] · G_sc = 0.0820 MJ m⁻² min⁻¹, d_r = 1 + 0.033 cos(2πJ/365), δ = 0.409 sin(2πJ/365 − 1.39), ω_s = arccos(−tan φ tan δ) · ETc = Kc × ET₀

Evapotranspiration is the water lost from soil and plants to the air. FAO Irrigation and Drainage Paper 56 recommends the Penman–Monteith equation, but when only air temperatures are available it gives the Hargreaves equation (eq. 52), which estimates the reference crop (well-watered grass) evapotranspiration from the temperature range and the extraterrestrial radiation for the latitude and date. Multiply by a crop coefficient Kc for other crops. Hargreaves can over-estimate in humid places and under-estimate in very windy ones; weekly or monthly averages are more reliable than single days.

Worked example

At latitude 40° N on 15 July (day 196), with a maximum of 30 °C and a minimum of 18 °C: R_a = 40.8 MJ/m² per day, T_mean = 24 °C, so ET₀ = 0.0023 × (24 + 17.8) × √12 × 0.408 × 40.8 = 5.54 mm/day. With Kc = 1 a 100 m² lawn loses about 554 L of water a day. (Check: FAO-56 example 8 gives R_a = 32.2 MJ/m² for 20° S on 3 September, as does this calculator.)

Sources: FAO Irrigation and Drainage Paper 56 — Crop evapotranspiration, chapter 3 (eqs. 21–25, 52) · Hargreaves & Samani (1985) Reference crop evapotranspiration from temperature, Applied Engineering in Agriculture 1(2)

Frequently asked questions