Evapotranspiration

Transpiration and Surface Evaporation are calculated based off a modified penomon monteith equation.

Transpiration

\[Tr_{ly1} + Tr_{ly2} = \frac{\Delta \cdot (R_{nl}) + \rho_a \cdot c_p \cdot VPD \cdot g_a}{\Delta + \gamma \cdot \left(1 + g_a \cdot \left(\frac{1}{g_a} + \frac{1}{g_s}\right)\right)} \cdot \frac{24}{\lambda \cdot 60 \cdot 60}\]
  • \(\Delta\) is the rate of change of saturated vapor pressure with air temperature:
    \(\Delta = 0.04145 \cdot e^{0.06088 \cdot T_C}\)

    • \(T_C\) is the air temperature (°C)

  • \(R_{nl}\) is the net fraction of radiation absorbed by leaves
    \(R_{nl} = SRAD \cdot (1 - 0.5 \cdot (\rho_{PAR} + \rho_{NIR})) \cdot \left(1 - e^{-K \cdot LAI \cdot \Omega}\right)\)

    • \(SRAD\) is the incident shortwave radiation (W m⁻²)

    • \(\rho_{PAR}\) parameter describing reflectance for photosynthetically active radiation

    • \(\rho_{NIR}\) parameter describing reflectance for near infrared radiation

    • \(K\) is the vegetation extinction coefficient

    • \(LAI\) is the leaf area index

    • \(\Omega\) is the clumping index

  • \(g_s\) is the stomatal conductance calculated using the Medlyn stomatal conducatance model
    \(g_s = 1.6\cdot 0.02405 \cdot LAI \cdot \frac{A_n}{c_a-c_i}\)

    • \(LAI\) is the leaf area index (\(m^2/m^2\))

    • \(c_{a}\) is the atmospheric CO2 concentration

    • \(c_i\) is the intercellular CO2 concentration
      \(c_i = c_{a} \cdot \left(1 - \frac{1}{1 + \frac{g_1}{\sqrt{VPD}}}\right)\)

      • \(g_1\) is the stomatal slope parameter

      • \(VPD\) is the vapor pressure deficit

  • \(g_a\) parameter describing aerodynamic conductance (m s-1)

  • \(VPD\) is the vapor pressure deficit

  • \(\rho_a\) is the air density: 1.225 (\(kg/m^3\))

  • \(c_p\) is the specific heat capacity of air: 1000 (J/kg/K)

  • \(\lambda\) is the latent heat of vaporization: \(2.26 \cdot 10^6\) (J/kg)

  • \(\gamma\) is the psychrometric constant \(\frac{100*1005}{\lambda*0.622}\)

Evaporation

\[Ev = \min\left(\frac{P_{tot}}{Ev_{max}}, 1.\right) \cdot \frac{1.26 \cdot \left(1 - 0.5 \cdot (\rho_{PAR} + \rho_{NIR})\right) \cdot SRAD \cdot e^{-K \cdot LAI \cdot \Omega}}{\lambda + \gamma} \cdot \frac{24}{\lambda \cdot 60 \cdot 60}\]

  • \(P_{tot}\) is the total precipitation

  • \(Ev_{max}\) parmater for maximum pan evaporation

  • \(SRAD\) is the incident shortwave radiation (W m⁻²)

  • \(\rho_{PAR}\) parameter describing reflectance for photosynthetically active radiation

  • \(\rho_{NIR}\) parameter describing reflectance for near infrared radiation

  • \(K\) is the vegetation extinction coefficient

  • \(LAI\) is the leaf area index

  • \(\Omega\) is the clumping index

  • \(\lambda\) is the latent heat of vaporization: \(2.26 \cdot 10^6\) (J/kg)

  • \(\gamma\) is the psychrometric constant \(\frac{100*1005}{\lambda*0.622}\)