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#
- radiation_evapotranspiration.calculate_net_radiation(temperature, down_shortwave_radiation, down_longwave_radiation, snow_water_storage, snow_albedo_thresh, openwater_albedo, snow_albedo, albedo, emissivity, x, y)[source]#
Compute Radition according to Müller Schmied et al., 2016.
(doi:10.3390/w8100450)
- Parameters:
- temperaturefloat
Daily air tempeature, Units : [K]
- down_shortwave_radiationfloat
Downward shortwave radiation Units: [Wm−2]
- down_longwave_radiationfloat
Downward longwave radiation Units: [Wm−2]
- snow_water_storagefloat
Daily snow water storage (for shortwave radiation), Units: [mm]
- snow_albedo_threshfloat
Threshold to use snow albedo (3mm), Units: [mm]
- openwater_albedofloat
Open water albedo, Units: [-]
- snow_albedofloat
Snow albedo, Units: [-]
- albedofloat
Albedo per landcover (Müller Schmied et al 2014, Table A2), Units: [-]
- emissivityfloat
Emisivity per landcover (Müller Schmied et al 2014, Table A2), Units: [-]
- xint
Latitude index of cell
- yint
Longitude index of cell
- Returns:
- net_radiationfloat
Net radiation according to Müller Schmied et al., 2016., Units: [Wm−2]
- openwater_net_radiationfloat
Open water radiation according to Müller Schmied et al., 2016., Units: [Wm−2]
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#
- radiation_evapotranspiration.priestley_taylor_pet(temperature, pt_coeff_humid_arid, net_radiation, openwater_net_radiation, x, y)[source]#
Potential evapotranspiration based on Priestly-Taylor algorithm
- Parameters:
- temperaturefloat
Daily air tempeature, Units : [K]
- pt_coeff_humid_aridflaot
Priestley-Taylor coefficient for humid and arid cells (alpha), Units: [-]
- net_radiationfloat
Net radiation according to Müller Schmied et al., 2016., Units: [Wm−2]
- openwater_net_radiationfloat
Open water radiation according to Müller Schmied et al., 2016., Units: [Wm−2]
- xint
Latitude index of cell
- yint
Longitude index of cell
- Returns:
- potential_evapfloat
Potential evapotranspiration, Units: [mm/day]
- openwater_pot_evapfloat
Open water potential evapotranspiration, Units: [mm/day]
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: