Engineering & Science
Priestley-Taylor Potential Evapotranspiration (PET) Radiation Formula
Calculate daily radiation-driven crop/watershed Potential Evapotranspiration PET = alpha_PT * (Delta / (Delta + gamma)) * ((R_n - G) / lambda_v) (mm/day) using the FAO-56 Tetens vapor-pressure slope Delta.
Estimate daily watershed & crop evapotranspiration when wind/humidity station data are unavailable!
Full Penman-Monteith evapotranspiration requires continuous anemometer wind-speed and relative-humidity sensors that remote agricultural basins and satellite land-surface grids often lack. C. H. B. Priestley and R. J. Taylor (1972) showed that over well-watered vegetated surfaces, aerodynamic advection adds ~26% on top of equilibrium radiative evaporation—yielding the classic Priestley-Taylor coefficient alpha_PT = 1.26: PET (mm/day) = alpha_PT * (Delta / (Delta + gamma)) * ((R_n - G) / lambda_v)!
Here Delta = 4098 * (0.6108 * EXP((17.27 * T) / (T + 237.3))) / (T + 237.3)^2 (kPa/°C) is the FAO-56 saturation vapor-pressure curve slope at mean air temperature T (°C), gamma (~0.0665 kPa/°C at sea level) is the psychrometric constant, R_n - G (MJ/(m^2*day)) is net available radiant energy minus soil heat flux, and lambda_v = 2.45 MJ/kg converts energy into mm/day of evaporated water! On a warm summer day (T = 25°C -> Delta = 0.1887 kPa/°C, R_n = 16.5 MJ/(m^2*day), G = 1.2 MJ/(m^2*day)), PET = 5.82 mm/day—dropping to 4.90 mm/day at a cooler 15°C under the exact same net solar radiation!
| Air Temperature Scenario (Rn = 16.5, G = 1.2 MJ/m^2/d, alpha = 1.26) | Vapor Slope Delta (kPa/°C) | Energy Share Delta / (Delta + gamma) | Daily PET (mm/day) |
|---|---|---|---|
| Warm Summer Canopy (T = 25°C) | 0.1887 kPa/°C | 73.94% | 5.82 mm/day |
| Cool Spring Canopy (T = 15°C) | 0.1098 kPa/°C | 62.28% | 4.90 mm/day |
| Invalid Psychrometric Constant <= 0 | Guarded Hydrology Error | N/A | "Invalid PET Inputs" |
FAO-56 Saturation Vapor-Pressure Curve Slope Delta (kPa/°C)
Computes Tetens derivative d(e_s)/dT at mean daily air temperature B2 (°C).
=IF(OR(B2 < -50, B5 <= 0, B6 <= 0), "Invalid PET Inputs", ROUND((4098 * (0.6108 * EXP((17.27 * B2) / (B2 + 237.3)))) / ((B2 + 237.3) ^ 2), 4))Priestley-Taylor Daily Potential Evapotranspiration PET (mm/day)
Multiplies alpha_PT (B6 = 1.26) by radiative partitioning Delta / (Delta + gamma) and net available water-equivalent energy (R_n - G) / 2.45.
=IF(OR(B2 < -50, B5 <= 0, B6 <= 0), "Invalid PET Inputs", ROUND(B6 * (((4098 * (0.6108 * EXP((17.27 * B2) / (B2 + 237.3)))) / ((B2 + 237.3) ^ 2)) / (((4098 * (0.6108 * EXP((17.27 * B2) / (B2 + 237.3)))) / ((B2 + 237.3) ^ 2)) + B5)) * ((B3 - B4) / 2.45), 2))Try the example
Use the original values or change them to test your understanding.