Evapotranspiration

interception_mm(P_24, vc, lai, int_max=0.2)

Computes the daily interception. The daily interception of a vegetated area is calculated according to Braden[1] and Hoyningen-Huene[2].

\[I^*=I_{max} \cdot I_{lai} \cdot \left(1-\frac{1}{1+\frac{c_{veg} \cdot P} {I_{max} \cdot I_{lai}}}\right)\]
Parameters:

  • P_24 (float) – daily rainfall, \(P\) [mm day \(^{-1}\)]

  • vc (float) – vegetation cover, \(c_{veg}\) [-]

  • lai (float) – leaf area index, \(I_{lai}\) [-]

  • int_max (float) – maximum interception per leaf, \(I_{max}\) [mm day \(^{-1}\)]

Returns:

int_mm – interception, \(I^*\) [mm day \(^{-1}\)]

Return type:

float

et_reference(rn_24_grass, ad_24, psy_24, vpd_24, ssvp_24, u_24)

Computes the reference evapotranspiration.

The reference evapotranspiration \(ET_{ref}\) is an important concept in irrigation science. The reference evapotranspiration can be inferred from routine meteorological measurements.

The reference evapotranspiration is the evapotranspiration of grass under well watered conditions. First the aerodynamical resistance for grass \(r_{a,grass}\) [sm \(^{-1}\)] is calculated:

\[r_{a,grass}=\frac{208}{u_{obs}}\]

Then the reference evapotranspiration \(ET_{ref}\) [W m \(^{-2}\)] can be calculated as follows, with taking the default value for the grass surface resistance \(r_{grass}\) = 70 sm \(^{-1}\)

\[ET_{ref}=\frac{\Delta \cdot Q_{grass}^{*}+ \rho c_{p}\frac{\Delta_{e}}{r_{a,grass}}} {\Delta+\gamma \cdot \left(1+\frac{r_{grass}}{r_{a,grass}}\right)}\]

The soil heat flux is assumed to be zero or close to zero on a daily basis.

Parameters:

  • rn_24_grass (float) – net radiation for reference grass surface, \(Q^{*}_{grass}\) [Wm-2]

  • u_24 (float) – daily wind speed at observation height, \(u_{obs}\) [m/s]

  • ad_24 (float) – daily air density, \(\rho_{24}\) [kg m-3]

  • psy_24 (float) – daily psychrometric constant, \(\gamma_{24}\) [mbar K-1]

  • vpd_24 (float) – daily vapour pressure deficit, \(\Delta_{e,24}\) [mbar]

  • ssvp_24 (float) – daily slope of saturated vapour pressure curve, \(\Delta_{24}\) [mbar K-1]

Returns:

et_ref_24 – reference evapotranspiration (well watered grass) energy equivalent, \(ET_{ref}\) [W m-2]

Return type:

float

et_reference_mm(et_ref_24, lh_24)

Computes the reference evapotranspiration.

\[ET_{ref}=ET_{ref} \cdot d_{sec} \cdot \lambda_{24}\]

where:

  • \(d_{sec}\) seconds in the day = 86400 [s]

Parameters:

  • et_ref_24 (float) – daily reference evapotranspiration energy equivalent, \(ET_{ref}\) [W m-2]

  • lh_24 (float) – daily latent heat of evaporation, \(\lambda_{24}\) [J/kg]

Returns:

et_ref_24_mm – reference evapotranspiration (well watered grass), \(ET_{ref}\) [mm d-1]

Return type:

float

eti_actual_mm(e_24_mm, t_24_mm, int_mm)

Computes the actual evapotranspiration based on the separate calculations of evaporation and transpiration.

\[ET = E + T\]
Parameters:

  • e_24_mm (float) – daily evaporation in mm, \(E\) [mm d-1]

  • t_24_mm (float) – daily transpiration in mm, \(T\) [mm d-1]

  • int_mm (float) – daily interception in mm \(I\) [mm d-1]

Returns:

aeti_24_mm – daily evapotranspiration and interception in mm, \(AETI\) [mm d-1]

Return type:

float