ET₀ is the evapotranspiration rate from a hypothetical, well‑watered reference surface, grown under the given weather conditions. It isolates the effect of climate from crop‑specific effects, so that the water use of any particular crop can be found as ETc = Kc × ET₀, where Kc is a crop coefficient.
FAO‑56 defines the reference surface as a hypothetical clipped grass with a canopy height of 0.12 m, a fixed bulk surface resistance of about 70 s/m, and an albedo of 0.23 — this is exactly the default "FAO‑56 reference grass" preset on the Location & Surface tab.
The Penman‑Monteith combination equation
Penman‑Monteith combines two physical drivers of evaporation into one equation:
Energy balance term — driven by net radiation (Rn) minus soil heat flux (G), weighted by Δ (the slope of the saturation vapor pressure curve) relative to Δ+γ.
Aerodynamic (mass transfer) term — driven by the vapor pressure deficit (VPD = es − ea) and wind speed, weighted by γ relative to Δ+γ.
Two resistances control how fast heat and water vapor actually move:
ra, aerodynamic resistance — resistance to transport through the air above the canopy; falls as wind speed rises.
rc, (bulk) surface resistance — resistance to water loss through the canopy/stomata; fixed for the reference surface, but can differ for day vs. night in this tool.
This tool computes every term explicitly (Rn, Rs, Rso, Ra, es, ea, Δ, γ, ra, rc) rather than using the simplified "FAO‑56 grass" shortcut constants, and validates against the FAO‑56 Example 17 worked problem.
Why timestep matters
Hourly, daily, and monthly calculations differ in some details: hourly runs track a changing cloudiness ratio and let rc switch between day and night values; daily and monthly runs use Tmax/Tmin‑based humidity and radiation estimates and generally assume soil heat flux G ≈ 0 (daily) or a small month‑to‑month correction (monthly).
Why use a simpler (empirical) formula?
Penman‑Monteith needs temperature, humidity, wind speed, and solar radiation. When one of those is missing or unreliable — a common situation at many weather stations — a simpler formula calibrated on fewer inputs can still give a usable ET₀ estimate. This tool can compute three classic methods alongside PM, for daily and monthly timesteps, so you can see directly how well they agree with PM at your own site.
Needs only Tmax, Tmin, and extraterrestrial radiation (which depends on latitude and date). Designed as a last‑resort substitute for PM when solar radiation, humidity, and wind data aren't available.
Priestley‑Taylor (1972)
ET₀ = α × [Δ/(Δ+γ)] × (Rn − G) / λ, with α ≈ 1.26
Radiation‑driven: it scales up the energy‑only "equilibrium" evaporation rate by a constant factor and drops the aerodynamic (wind/VPD) term entirely. Works best in humid, well‑watered climates where that term is small; tends to under‑predict on windy, dry days.
Turc (1961)
ET₀ = 0.013 × [Tmean/(Tmean+15)] × (Rs + 50), with a correction factor applied when relative humidity is below 50%
A simple temperature + radiation method, widely used in European agronomy and hydrology; includes a built‑in correction for arid conditions.
Using the comparison responsibly
These formulas were each calibrated and validated on particular climates and are not universally accurate. Treat them as approximations, and use the "Compare with empirical formulas" option on the Results tab — with its bias, RMSE and R² statistics against PM — to judge how well each one performs for your specific site and season before relying on it operationally.
Walking through the four tabs
1. Location & Surface
Set the site's location by searching a place name, clicking the map, dragging the pin, or typing latitude/longitude/elevation directly. Choose a surface preset (reference grass is the FAO‑56 default) or enter custom albedo, canopy height, surface resistance, and measurement heights.
2. Weather Data
Pick a timestep — hourly, daily, or monthly — then load weather data from NASA POWER (daily/monthly) or Open‑Meteo (hourly), import an Excel/CSV file, or type values in by hand. Rainfall can be loaded alongside the other variables when the source provides it.
3. Results
Click Compute ET₀ to run the calculation. The Summary card shows totals and a chart with ET₀ and rainfall on a shared axis; the table below lists every record and can be exported to CSV or Excel. Tick "Compare with empirical formulas" (daily/monthly only) to add Hargreaves‑Samani, Priestley‑Taylor and Turc columns, a time‑series overlay chart, and a scatter plot against the 1:1 line with bias/RMSE/R² statistics.
4. Sensitivity Analysis
Pick a baseline record (or the whole series), then drag sliders for temperature, humidity, wind, radiation, ra, or rc to see how much ET₀ responds. The tornado chart ranks each input by its normalized sensitivity (elasticity), showing which inputs matter most for your conditions.
Quick quiz
Covers both the Penman‑Monteith theory and how to use this tool. Pick an answer for each question, then check your score.