Penman-Monteith Equation
Also known as: PM Equation, FAO-56 PM, Evapotranspiration Model
The Penman-Monteith equation is a mechanistic model for estimating evapotranspiration (ET), the combined loss of water from soil and plant canopies to the atmosphere. First proposed by Penman (1948) for bare soil and water surfaces, then extended by Monteith (1965) to incorporate plant resistance to water vapor diffusion, it has become the international standard for water balance studies, crop water requirement calculation, and hydrological modeling.
Key highlights
- Mechanistic: explicitly represents energy and mass transfer physics, not purely empirical
- Widely applicable: validated for crops, grass, water, and diverse climates from wet to arid
- Weather-driven: requires only standard meteorological inputs, suitable for remote locations and future climate scenarios
- Standardized: FAO-56 reference ET and crop coefficients are internationally recognized and shared
- Integrates plant physiology: stomatal resistance accounts for drought stress and cultivar/species differences
Intuition
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How it works
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When to use it
Use Penman-Monteith when: (1) you need daily or sub-daily ET estimates for irrigation scheduling or hydrological modeling; (2) you have reliable weather data but limited soil moisture measurements; (3) you evaluate crop water stress across diverse climates (works well in arid and humid regions); (4) you integrate with crop growth or land-surface models. Strongly preferred in FAO guidelines and operational weather-based irrigation advisory systems. Less suitable when wind speed is poorly measured or vegetation structure is very heterogeneous.
Strengths & limitations
- Mechanistic: explicitly represents energy and mass transfer physics, not purely empirical
- Widely applicable: validated for crops, grass, water, and diverse climates from wet to arid
- Weather-driven: requires only standard meteorological inputs, suitable for remote locations and future climate scenarios
- Standardized: FAO-56 reference ET and crop coefficients are internationally recognized and shared
- Integrates plant physiology: stomatal resistance accounts for drought stress and cultivar/species differences
- Sensitive to wind speed measurements, which are often poorly instrumented at small scales
- Requires specification of crop resistance and height; these vary with phenology and management, introducing uncertainty
- Assumes atmospheric stability and uniform canopy; fails over very rough terrain, forest edges, or heterogeneous landscapes
- Soil heat flux (G) is often assumed as a fraction of Rn, introducing bias in early morning or late afternoon when G is large
- Does not account for soil salinity stress, flooding, or shallow water tables, which alter actual transpiration
Common pitfalls
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Applications
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Frequently asked
What is the difference between ET₀ and ETc?
ET₀ (reference ET) is the evapotranspiration from a hypothetical reference crop (short, healthy grass, well-watered, uniform, 0.12 m tall) under standard conditions. ETc (crop ET) is the actual ET from your specific crop, computed as ETc = Kc × ET₀, where Kc is a crop coefficient (dimensionless, typically 0.3-1.2). ET₀ depends only on weather; Kc depends on crop type, growth stage, and management.
What happens if I don't have radiation data?
You can estimate daily solar radiation from sunshine hours (Angstrom method) or temperature range (Hargreaves-Samani). If you have neither, use a simplified method like Priestley-Taylor (requires only temperature and humidity) or Hargreaves (temperature-based). FAO-56 provides equations for all these. Accuracy decreases as you simplify, so collect radiation data if possible.
How do I account for dry seasons or drought stress?
Under water scarcity, actual transpiration (TA) is less than potential (Tp) because stomata close and Kc decreases. You can model this using soil water-limited Kc functions (Kc,adj = Kc × (θ - θwp)/(θfc - θwp), where θ is soil water content). Alternatively, embed the equation in a soil water balance model that computes available water and drought stress feedback.
Why does Penman-Monteith give very high ET on windy days?
Wind increases the aerodynamic resistance term (ra), which reduces the denominator and increases ET. This is physically correct: wind removes boundary-layer air saturated with water vapor, enhancing diffusion. However, if wind speed is measured at the wrong height or is a poor point sample, errors propagate. Always standardize wind speed to reference height and validate against field lysimeters.
Can I use Penman-Monteith over a lake or reservoir?
Yes, by setting crop resistance rs = 0 (open water has no stomatal control) and adjusting surface roughness. This gives the Penman equation. However, over lakes, boundary conditions (air-water interface temperature, fetch effects, stratification) are complex. Use simple Penman for open-water evaporation and check against energy balance measurements (eddy covariance) for closure.
Sources
- 1.Penman, H. L. (1948). Natural evaporation from open water, bare soil and grass. Proceedings of the Royal Society A, 193(1032), 120-145.
- 2.Monteith, J. L. (1965). Evaporation and environment. Symposia of the Society for Experimental Biology, 19, 205-234.
- 3.Allen, R. G., Pereira, L. S., Raes, D., Smith, M., & Hargreaves, G. H. (1998). Crop evapotranspiration-Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56, Rome: FAO.
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Cite this page
ScholarGate. (2026, June 3). Penman-Monteith Equation. ScholarGate. https://scholargate.app/agronomy/penman-monteith-equation