Radiation and Evapotranspiration#
This module contains a function (compute_radiation), which computes radiation components based on section 4.2.3 of Müller Schmied et al., 2016b [1] and another function (priestley_taylor), which computes Priestley-Taylor potential evapotranspiration based on H. Müller Schmied et al. 2021 [2].
Radiation#
The calculation of net radiation, is based on Müller Schmied et al., 2016b [1]. Net radiation \(R\) \([\frac{W}{m^-2}]\) is calculated as:
Net shortwave radiation \({S}_{net}\) \([Wm^-2]\) is calculated as:
where \(S↓\) describes the shortwave downward radiation \([Wm^-2]\), \({\alpha}_{LC}\) is the albedo \([-]\) based on land cover type (Müller, Schmied et al. Table C2 [2]). Albedo values for WaterGAP are taken from assumptions of the IMAGE model [3]. In the case of a reasonable snow cover, the albedo value is varying dynamically in WaterGAP to represent the influence of snow cover dynamics on radiation balance [2].
Net longwave radiation \({L}_{net}\) \([\frac{W}{m^-2}]\) is calculated as:
where L↓(L↑) describes the longwave downward(upward) radiation \([Wm^-2]\).
Upward longwave radiation \(L↑\) \([Wm^-2]\) is calculated as:
where \({ε}_{LC}\) is the emissivity \([-]\) based on land cover type Table C2) [2], \(σ\) is the Stefan–Boltzmann constant \((5.67 × 10−8 [Wm^-2·K^−4])\) and \(T\) is the temperature in \([K]\).
We also calculate the upward shortwave radiation \(S↑ [Wm−2]\) as:
Potential Evapotranspiration#
The potential evapotranspiration \({E}_{pot}\) \([mm/d]\) is calculated with the Priestley–Taylor equation according to Shuttleworth (1993) [4], as:
\(\alpha\) is set to 1.26 in humid and to 1.74 in (semi)arid cells (see Appendix B in Müller et al. [2]). \(R\) is the net radiation \([mm/d]\) that depends on land cover (Table C2, Müller et al. [2]). \({S_a}\) is the slope of the saturation vapor pressure–temperature relationship, and \(g\) is the psychrometric constant \([{\frac{kPa}{°C}}]\).
Note
All grid cells with an aridity index AI < 0.75 are defined as semiarid/arid grid cells. Furthermore, all grid cells north of 55° N are defined as humid grid cells. For further information on this see Müller et al. [2] Appendix B.
Slope of the saturation and psychrometric constant#
\(s_a\) is the slope of the saturation vapor pressure-temperature relationship \([\frac{kPa}{°C}]\) defined as:
where \(T\) \([°C]\) is the daily air temperature.
The the psychrometric constant \(g\) \([{\frac{kPa}{°C}}]\) is defined as:
where \(p_a\) is the atmospheric pressure of the standard atmosphere \((101.3 kPa)\), and \(l_h\) is latent heat \([{\frac{MJ}{kg}}]\). Latent heat is calculated as: