Evapotranspiration Simulator: FAO Penman-Monteith Water Loss Calculator

simulator intermediate ~10 min
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ET₀ = 4.8 mm/day — reference crop evapotranspiration

At 25°C, 15 MJ/m²/day radiation, 2 m/s wind, and 50% RH, the FAO Penman-Monteith reference ET is approximately 4.8 mm/day — typical for a temperate summer day.

Formula

ET₀ = [0.408Δ(Rn - G) + γ(900/(T+273))u₂(es - ea)] / [Δ + γ(1 + 0.34u₂)]
es = 0.6108 × exp(17.27T / (T + 237.3)) (saturation vapor pressure, kPa)
VPD = es × (1 - RH/100)

The Invisible Water Loss

Evapotranspiration silently returns most terrestrial rainfall to the atmosphere. Plants draw soil water through roots and release it as vapor through stomatal pores, while bare soil and water surfaces lose moisture directly to the air. In many regions, ET exceeds 60% of annual precipitation — making it the dominant term in the water budget and the key to understanding drought, irrigation needs, and ecosystem health.

The Penman-Monteith Framework

John Monteith combined Penman's energy balance approach with a canopy resistance term to create the most physically complete ET equation. The FAO-56 version standardizes this for a reference grass crop, producing ET₀ values from four readily available weather variables. The radiation term drives ET in humid conditions; the aerodynamic (wind and VPD) term dominates in arid climates.

Temperature, Humidity, and VPD

The saturation vapor pressure increases exponentially with temperature — following the Clausius-Clapeyron relation. A 10°C warming roughly doubles the atmosphere's moisture capacity. When actual humidity does not keep pace, the vapor pressure deficit widens, pulling more water from surfaces. This simulation visualizes how each climate variable contributes to the total ET rate and how changing conditions shift the energy-aerodynamic balance.

Global Water Stress

As temperatures rise under climate change, potential ET increases even where precipitation remains stable, tightening water budgets. Agriculture accounts for 70% of global freshwater withdrawals, most of it replacing ET losses. Accurate ET estimation — whether by Penman-Monteith, remote sensing, or eddy covariance — is essential for irrigation efficiency, drought monitoring, and sustaining river flows for ecosystems and communities downstream.

FAQ

What is evapotranspiration?

Evapotranspiration (ET) is the combined process of water evaporation from soil and plant surfaces plus transpiration through plant stomata. It returns approximately 60% of terrestrial precipitation to the atmosphere and is the largest water loss term in most catchment water budgets.

What is the Penman-Monteith equation?

The FAO Penman-Monteith equation combines energy balance and aerodynamic approaches to estimate reference evapotranspiration (ET₀) from a hypothetical grass surface. It requires net radiation, air temperature, wind speed, and humidity as inputs. It is the international standard method recommended by FAO since 1998.

What is vapor pressure deficit (VPD)?

VPD is the difference between saturated and actual vapor pressure at a given temperature. It represents the atmosphere's drying power — the larger the deficit, the more water the air can absorb. VPD is the primary atmospheric driver of ET and increases exponentially with temperature.

How does ET relate to irrigation scheduling?

Crop water requirements are estimated as ETc = Kc × ET₀, where Kc is a crop-specific coefficient. By computing daily ET₀ and applying appropriate Kc values, farmers can schedule irrigation to replace exactly the water lost by ET, minimizing waste while preventing crop stress.

Sources

Embed

<iframe src="https://homo-deus.com/lab/hydrology/evapotranspiration/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub