Evapotranspiration calculation - AWS810

AWS810 System Description
Document code
M212417EN
Revision
H
ft:locale
en-US
Product
AWS810
Document type
Technical description

Evapotranspiration is calculated using the Penman–Monteith equation. The evapotranspiration calculation estimates the loss of water from a vegetative surface through the combined process of plant transpiration and soil evaporation.

Evapotranspiration is calculated with the following formula:

E t o = 0.408 Δ ( R n − G ) + γ 900 T + 273 U 2 ( e a − e d ) Δ + γ ( 1 + 0.34 U 2 )
Explanation of evapotranspiration calculation formula
Item Explanation
Eto Reference crop evapotranspiration [mm/d]
Δ Slope of vapor pressure curve [kPa(°C)] (see Slope of vapor pressure curve (Δ) calculation)
Rn Net radiation at crop surface [MJ/m2/d]
G Soil heat flux [MJ/m2/d]
γ Psychrometric constant [kPa(°C)]
T Average air temperature [°C]
U2 Wind speed measured at 2‑meter height [m/s]
(ea−ed) Vapor pressure deficit [kPa]

Slope of vapor pressure curve (Δ) calculation

Δ = 4098 e a ( T + 237.3 ) 2

Net radiation (Rn) calculation

This is the average radiation from the sensor or sensors. The net radiation is calculated with one of the following methods:
  • Using 1 net radiation sensor (SR1)
  • Using 2 net radiation sensors (SR1 and SR2). Net radiation = SR1−SR2.
  • Using a net radiation sensor (SR1) and surface albedo (station parameter).

    Net radiation = (1−albedo) × SR1.

The radiation value [W/m2] from measurements is converted to [MJ/m2/d] by multiplying the radiation value with 0.0864.

Soil heat flux (G) calculation

G = c s d s ( T n − T n − 1 Δ t )
Explanation of soil heat flux (G) calculation formula
Item Explanation
G Soil heat flux [MJ/m2/d]
cs Volumetric heat capacity [MJ m−3°C−1] (~2.1 for average moist soil)
ds Estimated effective soil depth [m] (typically used as ~0.2 m)
Tn Temperature on day n [°C]
Tn−1 Temperature on the preceding day n−1 [°C]
Δt Time period [days]

Psychrometric constant (γ) calculation

γ = C p P ε γ ⋅ 10 − 4 = 0.000163 P λ
Explanation of psychrometric constant (γ) calculation formula
Item Explanation
γ Psychrometric constant [kPa °C−1]
Cp Specific heat of moist air = 1.013 kJ kg−1 °C−1
P Atmospheric pressure [hPa]
ε Ratio molecular weight water vapor / dry air = 0.622
λ Latent heat of vaporization [ML kg−1]

λ is given by the following formula:

λ = 2.501 − ( 2.361 ⋅ 10 − 3 ) T

Average air temperature (T) calculation

Where hourly data is available:

T = ∑ i = 0 24 T i 24

Wind speed (U2) calculation

U 2 = U z [ 4 , 87 ln ⁡ ( ( 67.8 z ) − 5.42 ) ]
Explanation of wind speed (U2) calculation formula
Item Explanation
Uz Wind speed measured at height z [ms−1]
z Height of wind speed measurement [m]

Vapor pressure deficit (ea−ed) calculation

V P D = ( e a − e d ) = [ ( e a ( T max ⁡ ) + e a ( T min ⁡ ) 2 ) − e d ]
e a ( T max ⁡ ) = 0.611 exp ⁡ ( 17.27 T max ⁡ T max ⁡ + 237.3 )
e a ( T min ⁡ ) = 0.611 exp ⁡ ( 17.27 T min ⁡ T min ⁡ + 237.3 )
e d = ⁡ ( 1 2 e a ( T min ⁡ ) R H max ⁡ 100 ) + ( 1 2 e a ( T max ⁡ ) R H min ⁡ 100 )
Explanation of vapor pressure deficit (ea−ed) calculation formula
Item Explanation
ea Saturation vapor pressure [kPa]
ed Actual vapor pressure [kPa]
Tmax Maximum daily temperature [°C]
Tmin Minimum daily temperature [°C]
ea(Tmax) Saturation vapor pressure at Tmax
ea(Tmin) Saturation vapor pressure at Tmin
ed(Tmax) Actual vapor pressure at Tmax
ed(Tmin) Actual vapor pressure at Tmin
RHmax Maximum daily relative humidity [%]
RHmin Minimum daily relative humidity [%]
Inputs for evapotranspiration calculation
Input Variable
Net radiation Rn SRAVG1D (24‑hour average solar radiation) of SR1 and SR2. Station parameters stype and, in some cases, albedo.
Temperature values T, Tn, Tn−1, Tmax, Tmin Daily statistical values derived from TAAVG1M (1‑minute average temperature)
Relative humidity values RHmax, RHmin Daily statistical values derived from RHAVG1M
Wind speed Uz Daily average of WSAVG2M (2‑minute average wind speed). Wind speed reduction height z is 10 meters.
Atmospheric pressure P Daily average of the measured atmospheric pressure (hPa).