Environmental Science, Ecology & Hydrology
Oudin (2005) Potential Evapotranspiration (PET) Formula: Extraterrestrial R_a & Temperature
Calculate daily watershed Potential Evapotranspiration PET (mm/day) for lumped and distributed rainfall-runoff models (GR4J, HBV, SWAT) using Ludovic Oudin et al.’s (2005) parsimonious 308-catchment radiation-temperature law.
Why Oudin’s 2-input PET formula matched or beat complex 27-equation Penman-Monteith across 308 watersheds!
Full FAO-56 Penman-Monteith evapotranspiration requires wind speed, relative humidity / dewpoint, and surface solar radiation sensors that are missing or noisy in > 80% of upland river gauges and historical climate reconstructions! Testing 27 different PET formulations inside four rainfall-runoff models across 308 watersheds in France, Australia, and the United States, Ludovic Oudin, Vazken Andreassian, Charles Perrin et al. (2005, Journal of Hydrology) discovered a stunning result: a parsimonious Jensen-Haise-style formula driven ONLY by Mean Daily Air Temperature T_mean (°C) and latitude/day-of-year Extraterrestrial Solar Radiation R_a (MJ/(m^2·day)) outperformed data-hungry aerodynamic formulas in streamflow simulation!
With Latent Heat of Vaporization lambda = 2.45 MJ/kg and Water Density rho_w = 1,000 kg/m^3 (so lambda * rho_w converts 1 MJ/m^2 of radiation into 1 / 2.45 = 0.4082 mm of evaporated water!), Oudin’s Daily PET Equation is: PET (mm/day) = MAX(0, (R_a / 2.45) * ((T_mean + 5) / 100)) whenever T_mean > -5.0°C (and 0 mm/day in deep frost <= -5.0°C)!
| Seasonal Watershed Day (Mid-Latitude Catchment) | Extraterrestrial R_a (MJ/m^2/day) | Mean Air Temp T_mean (°C) | Oudin Daily PET (mm/day) |
|---|---|---|---|
| Deep Winter Frost (Jan 15) | 13.5 MJ/m^2/d | -6.5 °C (<= -5°C) | 0.00 mm/day (Dormant / Frozen) |
| Cool Spring Snowmelt (Apr 10) | 31.8 MJ/m^2/d | 9.5 °C | 1.88 mm/day |
| Peak Midsummer Solstice (Jun 25) | 41.4 MJ/m^2/d | 23.5 °C | 4.82 mm/day |
Oudin et al. (2005) Daily Potential Evapotranspiration PET (mm/day)
Evaluates MAX(0, (R_a / 2.45) * ((T_mean + 5) / 100)) across daily top-of-atmosphere Extraterrestrial Radiation R_a (B2 MJ/(m^2·day) in 0..46) and daily mean air temperature T_mean (B3 °C).
=IF(OR(B2 < 0, B2 > 46, B3 < -60, B3 > 60), "Requires Extraterrestrial R_a in [0, 46] MJ/m^2/d and Valid Air Temp (°C)", ROUND(MAX(0, (B2 / 2.45) * ((B3 + 5) / 100)), 2))Monthly Watershed Volumetric PET Demand (m^3 / km^2) over N Days
Multiplies Daily PET (mm/day = 1,000 m^3/km^2 per mm) by Month_Days B4 (28..31) to return catchment evaporative water demand per km^2.
=IF(OR(B2 < 0, B2 > 46, B3 < -60, B3 > 60, B4 < 1, B4 > 31), "Invalid Oudin Monthly Inputs", ROUND(1000 * B4 * MAX(0, (B2 / 2.45) * ((B3 + 5) / 100)), 0))Try the example
Use the original values or change them to test your understanding.