ET₀ Calculator
Estimate daily reference evapotranspiration ET₀ (mm/day) with the Hargreaves method from daily max/min air temperature and extraterrestrial radiation Ra. Used for irrigation scheduling and crop water demand.
Input Data
Results
At a glance:Reference evapotranspiration (ET₀) is the rate at which water is lost by soil evaporation and plant transpiration from a well-watered, uniform reference grass surface. It is the baseline for estimating actual crop water demand and planning irrigation. The full FAO Penman-Monteith method needs air temperature, humidity, sunshine and wind; when those are missing, the Hargreaves method uses only Tmax, Tmin and the table-based extraterrestrial radiation Ra: ET₀ = 0.0023 × (0.408 × Ra) × (Tmean + 17.8) × √(Tmax − Tmin), where Tmean = (Tmax + Tmin) ÷ 2, 0.408 converts energy (MJ·m⁻²·day⁻¹) to equivalent water depth (mm), and √(Tmax − Tmin) proxies clear-sky radiation. Actual crop evapotranspiration ETc = Kc × ET₀, where Kc is the crop coefficient.
Formula
Daily mean temperature: Tmean = (Tmax + Tmin) ÷ 2.
Hargreaves method: ET₀ = 0.0023 × (0.408 × Ra) × (Tmean + 17.8) × √(Tmax − Tmin).
Crop water demand: ETc = Kc × ET₀ (Kc = crop coefficient).
$$T_{mean} = \frac{T_{max} + T_{min}}{2}$$$$ET_0 = 0.0023 \times (0.408\,R_a) \times (T_{mean} + 17.8) \times \sqrt{T_{max} - T_{min}}$$$$ET_c = K_c \times ET_0$$How to Use
- Enter the daily maximum temperature Tmax and minimum temperature Tmin (°C).
- Enter the extraterrestrial radiation Ra (from latitude/date tables; ~38 in Hong Kong summer, ~25 in winter).
- The tool returns ET₀ (mm/day); multiply by the crop coefficient Kc to get crop water demand.
Approximate monthly extraterrestrial radiation Ra near Hong Kong (~22°N)
| Month | Ra (MJ·m⁻²·day⁻¹) | Note |
|---|---|---|
| Jun–Jul (midsummer) | ≈ 38 | Longest daylight, strongest radiation |
| Mar, Sep (spring/autumn) | ≈ 34 | Transition seasons |
| Apr–May | ≈ 37 | Close to summer |
| Oct–Nov | ≈ 30 | Cool autumn |
| Dec–Jan (midwinter) | ≈ 25 | Shortest daylight, weakest radiation |
Ra depends only on latitude and date (see FAO tables); values above are rough for 22°N. Use precise tabulated values in practice.
Case Studies
Reference ET₀ on a summer day in Hong Kong
Midsummer day: Tmax = 32°C, Tmin = 24°C, Ra = 38 MJ·m⁻²·day⁻¹.
Tmean = 28°C; ET₀ = 0.0023 × (0.408 × 38) × (28 + 17.8) × √(32 − 24) ≈ 4.62 mm/day.
For a vigorous vegetable crop with Kc = 1.1, crop demand ETc ≈ 1.1 × 4.62 ≈ 5.08 mm/day, used to plan daily irrigation.
Lower ET₀ on a cool, cloudy day
Cool day: Tmax = 25°C, Tmin = 15°C, Ra = 30 MJ·m⁻²·day⁻¹.
Tmean = 20°C; ET₀ = 0.0023 × (0.408 × 30) × (20 + 17.8) × √(25 − 15) ≈ 3.37 mm/day.
Cooler air and weaker radiation lower evapotranspiration, so irrigation can be reduced to avoid waterlogging.
FAQ
Where do I look up extraterrestrial radiation Ra?
Ra (solar radiation at the top of the atmosphere) depends only on latitude and day of year, not local weather. Look it up in the FAO Irrigation and Drainage Paper 56 tables, or compute it from latitude and day number. Hong Kong (~22°N) is about 38 in summer and 25 MJ·m⁻²·day⁻¹ in winter; use the value for the corresponding month or date.
How does Hargreaves differ from Penman-Monteith?
FAO Penman-Monteith is the international standard with the highest accuracy, but needs air temperature, relative humidity, sunshine hours and wind speed. The Hargreaves method is a simplified formula using only Tmax, Tmin and tabulated Ra, suited to sites lacking full weather data; its error is usually acceptable, especially for longer-period (dekad, monthly) averages.
Is ET₀ the same as actual crop water demand ETc?
No. ET₀ is the evapotranspiration of a 'reference grass' surface, reflecting the climate's evaporative power. Actual crop demand ETc = Kc × ET₀, multiplied by the crop coefficient Kc for the crop and growth stage. Kc varies by crop and stage (lower at seedling, higher at peak), so look up the crop Kc table to convert ET₀ into the real irrigation demand.
Why is there a square root of the temperature difference?
√(Tmax − Tmin) is the Hargreaves trick to estimate solar radiation and clear-sky conditions from the temperature swing: clear skies mean fast daytime warming and strong nighttime cooling (large gap), while cloudy days have a small gap. A larger gap implies stronger radiation and more evapotranspiration, so the square-root term approximates radiation effects when sunshine data are missing.
Is ET₀ suitable for irrigation planning in Hong Kong?
Yes, as a reference. Hong Kong is hot and humid with strong summer evapotranspiration; pairing ET₀ with Kc estimates daily or weekly water need and avoids under- or over-irrigation. But rainfall is concentrated and humidity is high, so in practice subtract effective rainfall and consider soil water holding and drainage. The Hargreaves method may slightly overestimate in humid areas, so calibrate with local observations.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.