Hargreaves-Samani Reference Evapotranspiration and Crop ET in Excel

A limited-data estimate, not the default for every climate

FAO-56 presents Hargreaves as an alternative when weather data are missing. It recommends checking it against FAO Penman-Monteith estimates in each new region and calibrating when needed. It can underestimate in high winds and overestimate under high humidity. Estimating missing inputs for Penman-Monteith can be more accurate.

This example calculates Hargreaves reference ET0. It does not implement Thornthwaite, despite the legacy page address. Do not interchange results from different evapotranspiration methods without checking their assumptions and time scales.

Keep extraterrestrial radiation and surface radiation separate

Enter daily extraterrestrial radiation Ra in B2 in MJ/m2/day, and the same day’s maximum and minimum air temperatures in Celsius in B3 and B4. Ra depends on latitude and date; it is not reduced just because that day is cloudy. Surface solar radiation is a different quantity.

The formula uses 0.408 to convert Ra from energy units to equivalent water depth. If an Ra source already supplies mm/day, do not apply that conversion twice: convert it back to MJ/m2/day before using this workbook. E3 shows the mean temperature and E4 the converted Ra.

Use the raw ET0 output before applying Kc

E5 evaluates 0.0023*0.408*Ra*(Tmean+17.8)*SQRT(Tmax-Tmin). At Ra=36, Tmax=32 and Tmin=18, ET0 is about 5.41 mm/day. E6 multiplies the unrounded E5 by B5: with illustrative Kc=1.2, ETc is about 6.49 mm/day. Format results to two decimals for display.

E2 rejects missing or nonnumeric weather data, negative Ra and Tmax below Tmin. This demonstration also rejects Tmean at or below -17.8 C rather than reporting zero or negative ET from the empirical expression. That guard is not a validated climate range. Equal Tmax and Tmin or Ra=0 gives a mathematical zero, which is not proof of zero actual water loss.

=IF(E2="OK",0.0023*E4*(E3+17.8)*SQRT(B3-B4),E2)

Crop ET is not the irrigation depth to apply

Under standard, non-water-stressed conditions ETc=Kc*ET0. Kc depends on crop, growth stage and conditions; 1.2 is an illustration, not a universal crop coefficient. E6 rejects missing, text or negative Kc. Kc=0 gives zero crop ET mathematically.

=IF(E2<>"OK",E2,IF(OR(COUNT(B5)<>1,N(B5)<0),"Invalid Kc",B5*E5))

Work through a second case and plan the water balance

Try Ra=22, Tmax=24 and Tmin=19. E5 is about 1.81 mm/day and E6 about 2.17 mm/day when Kc=1.2. This is a separate latitude/date and temperature scenario, not a claim that clouds change Ra from 36 to 22. Restore the original values, then double Kc: ETc doubles while ET0 stays unchanged.

Irrigation scheduling also needs effective rainfall and soil-water accounting. Actual water applied can differ further because of application losses and special requirements. Do not treat E6 alone as a watering instruction. Use a crop and site-specific water balance and verify the weather method first.

Further reading

• FAO-56 Chapter 3 — Meteorological data and Hargreaves equation 52
• FAO-56 Chapter 6 — Single crop coefficient
• FAO — Irrigation water needs