1.3. Longwave Radiation

Incoming atmospheric longwave radiation \(R_{\mathrm{lw}}^\downarrow =\) lwdown_Wm2 [W m-2; Driver: downward longwave (infrared) radiation at the surface] interacts with vegetation and ground through emission, absorption, and transmission. ADELM treats longwave radiation as broadband thermal exchange in an atmosphere-canopy-ground column (Fig. 1.2.1). Each layer transmits a fraction \((1-\varepsilon)\) of the incident flux and emits \(\varepsilon\sigma T^4\) upward and downward. The main outputs are the net absorbed longwave radiation by vegetation and by ground, which satisfy the conservation relation:

(1.3.1)\[R_{\mathrm{lw}}^\downarrow = R_{\mathrm{lw,vg}}^\uparrow + R^{\mathrm{n}}_{\mathrm{lw},\mathrm{v}} + R^{\mathrm{n}}_{\mathrm{lw},\mathrm{g}}\]

Fig. 1.3.1 Schematic diagram of shortwave (red; direct beam shown as solid lines and diffuse radiation as dashed lines) and longwave (blue) radiation absorbed, transmitted, and reflected by vegetation and the ground.

See also

model.processes.radiative_transfer.calculate_longwave_balance()

Notation

• subscript \(\mathrm{v}\) denotes the vegetation layer

• subscript \(\mathrm{g}\) denotes the ground surface

• subscript \(\mathrm{vg}\) denotes the top of the vegetation–ground system

• superscript \(\mathrm{n}\) denotes net (absorbed) radiation

• superscripts \(\downarrow\) and \(\uparrow\) denote downward and upward directions

Coupling to other components

• Potential Evapotranspiration uses canopy_net_lwrad_Wm2 and soil_net_lwrad_Wm2.

1. Thermal emission

Vegetation and ground emit longwave radiation according to the Stefan-Boltzmann law. The upward-and-downward emission from the vegetation layer is

(1.3.2)\[E_{\mathrm{v}} = \varepsilon_{\mathrm{v}}\,\sigma T_{\mathrm{v}}^4\]

and ground thermal emission is

(1.3.3)\[E_{\mathrm{g}} = \varepsilon_{\mathrm{g}}\,\sigma T_{\mathrm{g}}^4\]

where \(\varepsilon_{\mathrm{v}}\) is the canopy emissivity diagnosed from vegetation area index in the longwave routine, and \(\varepsilon_{\mathrm{g}}\) (surface_emissivity [default: 0.96; Fixed parameter: broadband thermal infrared emissivity of the soil or snow surface]) is the ground emissivity. Here \(\sigma\) is stefan_boltzmann_constant [default: 5.67037e-08 W m-2 K-4; Constant: stefan–Boltzmann constant], and \(T_{\mathrm{v}}\), \(T_{\mathrm{g}}\) are vegetation and ground temperatures in Kelvin.

Attention

In the current ADELM version, canopy and ground thermal emission are evaluated with a common air temperature, \(T_{\mathrm{a}} =\) ta_degC [degC; Driver: near-surface air temperature] + absolute_zero_offset [default: 273.15 K; Constant: zero degrees Celsius expressed in Kelvin], so that \(T_{\mathrm{v}} = T_{\mathrm{g}} = T_{\mathrm{a}}\).

2. Longwave fluxes at each interface

The column is solved top-down then bottom-up, applying the same transmission-plus-emission rule at each layer.

Downward flux below the canopy (lwdown_below_canopy_Wm2 [W m-2; Flux: downward longwave radiation below the vegetation canopy]):

(1.3.4)\[R_{\mathrm{lw,v}}^\downarrow = (1-\varepsilon_{\mathrm{v}})\,R_{\mathrm{lw}}^\downarrow + E_{\mathrm{v}}\]

Upward flux below the canopy (lwup_below_canopy_Wm2 [W m-2; Flux: upward longwave radiation below the vegetation canopy]):

(1.3.5)\[R_{\mathrm{lw,g}}^\uparrow = (1-\varepsilon_{\mathrm{g}})\,R_{\mathrm{lw,v}}^\downarrow + E_{\mathrm{g}}\]

Upward flux above the canopy (lwup_above_canopy_Wm2 [W m-2; Flux: upward longwave radiation above the vegetation canopy]):

(1.3.6)\[R_{\mathrm{lw,vg}}^\uparrow = (1-\varepsilon_{\mathrm{v}})\,R_{\mathrm{lw,g}}^\uparrow + E_{\mathrm{v}}\]

Each downward step transmits the fraction \((1-\varepsilon)\) of the incident flux and adds the layer’s own thermal emission; the same rule applies on the upward pass.

3. Net longwave radiation

Net longwave for vegetation (canopy_net_lwrad_Wm2 [W m-2; Flux: longwave radiative flux absorbed by the canopy]) is the total flux intercepted by the canopy layer on both passes:

(1.3.7)\[R^{\mathrm{n}}_{\mathrm{lw},\mathrm{v}} = \left(R_{\mathrm{lw}}^\downarrow - R_{\mathrm{lw,v}}^\downarrow\right) + \left(R_{\mathrm{lw,g}}^\uparrow - R_{\mathrm{lw,vg}}^\uparrow\right)\]

Net longwave for the ground (soil_net_lwrad_Wm2 [W m-2; Flux: longwave radiative flux absorbed by the soil surface]) is the difference between the downward and upward fluxes at the soil surface:

(1.3.8)\[R^{\mathrm{n}}_{\mathrm{lw},\mathrm{g}} = R_{\mathrm{lw,v}}^\downarrow - R_{\mathrm{lw,g}}^\uparrow\]

The total land-surface net longwave net_lwrad_Wm2 [W m-2; Flux: net longwave radiative flux absorbed by the land surface] is:

(1.3.9)\[R^{\mathrm{n}}_{\mathrm{lw}} = R^{\mathrm{n}}_{\mathrm{lw},\mathrm{v}} + R^{\mathrm{n}}_{\mathrm{lw},\mathrm{g}}\]