9 PET, AET and Penman's method

Potential and Actual Evapotranspiration

Evapotranspiration is the total water loss from a vegetated surface to the atmosphere. It encompasses two primary processes:  

• Evaporation: The loss of water vapor from the soil surface and surrounding water bodies.  
• Transpiration: The release of water vapor from plant leaves through stomata.  

Therefore, evapotranspiration is the sum of evaporation and transpiration.  

Potential Evapotranspiration (PET):

• PET represents the maximum possible evapotranspiration rate under ideal conditions.
• These conditions assume an unlimited water supply, ensuring that plants' water needs are fully met.
• Essentially, PET reflects the atmospheric demand for water.

Actual Evapotranspiration (AET):

• AET is the real evapotranspiration occurring in a specific environment.
• It accounts for the actual water availability, which may be limited by factors like soil moisture.  
• Therefore, AET reflects the actual water loss under existing conditions.  

Relationship between PET and AET:

• When soil moisture is at field capacity (F.C.), plants have adequate water, and AET equals PET (AET/PET = 1).  
• As soil moisture decreases, AET becomes less than PET, and the AET/PET ratio declines.  
• At the permanent wilting point, where plants can no longer extract water, AET reaches zero.  
• The relationship between AET/PET and available soil moisture is impacted by soil type. Sandy soils show a faster reduction of the AET/PET ratio with reduced soil moisture when compared to clay soils.
  

Penman's Method for Potential Evapotranspiration (PET)

Penman's method is a widely used and physically based approach to estimate potential evapotranspiration (PET). It combines energy balance and aerodynamic (wind) principles to provide a more accurate estimate compared to empirical methods that rely solely on temperature.  

Key Concepts:

• Energy Balance:
  • It considers the net radiation received by the surface, which is the difference between incoming and outgoing radiation.  
  • This net radiation is used for heating the air, evaporating water, and other processes.  
• Aerodynamic Approach:
  • It accounts for the transport of water vapor away from the surface by wind.
  • Wind speed, humidity gradients, and surface roughness play crucial roles.
• Combination Equation:
  • Penman's method combines these energy balance and aerodynamic components into a single equation.  
  • This combination makes it more robust and applicable to a wider range of climatic conditions.

Penman's Equation:

The general form of Penman's equation is:

PET = (A * Hn + γ * Ea) / (A + γ)

Where:

• PET = Potential evapotranspiration
• A = Slope of the saturation vapor pressure-temperature curve
• Hn = Net radiation
• γ = Psychrometric constant
• Ea = Aerodynamic term (wind function)  

Components of the Equation:

• Net Radiation (Hn):
  • Calculated considering incoming solar radiation, albedo (surface reflectivity), and outgoing longwave radiation.
• Aerodynamic Term (Ea):
  • Represents the water vapor transport due to wind and humidity differences.
  • It depends on wind speed and the difference between saturation vapor pressure and actual vapor pressure.
• Slope of Saturation Vapor Pressure Curve (A):
  • Relates changes in saturation vapor pressure to changes in temperature.  
• Psychrometric Constant (γ):
  • Relates the partial pressure of water in air to the air temperature.

Example Calculation:

Now, let's apply Penman's method using the provided example:

Given Data:

• Latitude (φ) = 28°4'
• Saturation vapor pressure (es) = 17.54 mm Hg
• Mean solar radiation (Hc) = 9.506 mm/day
• Average temperature (T) = 20°C
• Average relative humidity (RH) = 75%
• Δ = 1.05 mm/°C
• Average sunshine hours (n) = 9 hours/day
• Maximum sunshine hours (N) = 10.7 hours/day
• Average wind velocity (v2) = 85 km/day
• Surface cover: close grained crops.

Solution:

1. Calculate Actual Vapor Pressure (ea):

   • ea = RH * es = 0.75 * 17.54 = 13.16 mm Hg

2. Calculate Parameters a and b:

   • a = 0.29 * cos(φ) = 0.29 * cos(28°4') = 0.2559
   • b = 0.52 (assumed average value)

3. Convert Temperature to Kelvin (Ta):

   • Ta = 273 + 20 = 293 K

4. Calculate Net Radiation (Hn):

   • Hn = Hc (1 - r) (a + b (n/N)) - σTa^4 (0.56 - 0.092 √ea) (0.10 + 0.90 (n/N))
   • r = 0.25 (reflection coefficient for close-grained crops)
   • σ = 2.01 x 10^-9 mm/day (Stefan-Boltzmann constant)
   • Hn = 9.506 (1 - 0.25) (0.2559 + 0.52 (9/10.7)) - 2.01 x 10^-9 (293)^4 (0.56 - 0.092 √13.16) (0.10 + 0.90 (9/10.7))
   • Hn = 2.07 mm/day

5. Calculate Aerodynamic Term (Ea):

   • Ea = 0.35 (1 + v2 / 160) (es - ea)
   • Ea = 0.35 (1 + 85 / 160) (17.54 - 13.16)
   • Ea = 2.347 mm/day

6. Calculate PET:

   • PET = (Δ * Hn + γ * Ea) / (Δ + γ)
   • γ = 0.49 (psychrometric constant)
   • PET = (1.05 * 2.07 + 0.49 * 2.347) / (1.05 + 0.49)
   • PET = 2.158 mm/day

Therefore, the potential evapotranspiration (PET) for the given location is approximately 2.158 mm/day.