Albedo and emissivity
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Overview
Albedo is the fraction of incident shortwave radiation reflected back to space:
\[\begin{equation} \alpha = \frac{\text{SW}_{\uparrow}}{\text{SW}_{\downarrow}} \end{equation}\]
where $S_{\uparrow}$ is the reflected (upwelling) shortwave and $\text{SW}_{\downarrow}$ is the incident (downwelling) shortwave. Albedo ranges from 0 (perfectly absorbing) to 1 (perfectly reflecting).
Variability of albedo and emissivity
Albedo can depend on multiple factors:
- Surface type: Snow (0.7–0.9, highly reflective), vegetation (0.1–0.3), bare soil (0.2–0.4), water (0.05–0.15)
- Soil moisture: Darker, wetter soils have lower albedo
- Vegetation density: Denser vegetation lowers albedo
- Snow age: Fresh snow is bright; aging snow darkens with deposition of impurities and increases in grain size
Emissivity is the efficiency with which the surface emits thermal (longwave) radiation:
\[\begin{equation} \epsilon = \frac{L_{\uparrow}}{\sigma T_0^4} \end{equation}\]
where $L_{\uparrow}$ is the total upwelling longwave radiation (including both surface emission and reflection of incident longwave), and $\sigma T_0^4$ is the blackbody emission at skin temperature $T_0$.
Most natural surfaces behave fairly similarly to black bodies with emissivity ~0.9. However, snow and water covered surfaces tend to have higher emissivity (>0.95) while certain types of rock and manmade surfaces are known to have lower emissivities.
The total upwelling longwave includes both surface emission and reflection: $L_{\uparrow} = \epsilon \sigma T_0^4 + (1-\epsilon) L_{\downarrow}$
Implementations
Terrarium currently provides only two very simple formulations of albedo and emissivity. The simplest scheme is ConstantAlbedo which treats both albedo and emissivity as spatially and temporally constants parameters:
Terrarium.ConstantAlbedo — Type
struct ConstantAlbedo{NF} <: Terrarium.AbstractAlbedo{NF}Properties:
albedo::Any: Surface albedo, i.e. ratio of outgoing to incoming shortwave radiation [-]emissivity::Any: Surface emissivity, i.e. fraction of thermal radiation emitted from the surface [-]
Alternative, they can be prescribed as user-specified input fields via PrescribedAlbedo:
Terrarium.PrescribedAlbedo — Type
struct PrescribedAlbedo{NF} <: Terrarium.AbstractAlbedo{NF}Properties:
In the case where they are prescribed, they are permitted to vary in time and/or space at the discretion of the user and/or the corresponding InputSource. However, their values will not be derived from the model state and thus could lead to inconsistencies.
Dynamic (state-dependent) albedo and emissivity are not yet implemented but will be added soon!
Methods
Terrarium.albedo — Function
albedo(i, j, grid, fields, ::AbstractAlbedo)Return the current albedo at the given indices.
albedo(i, j, grid, fields, albedo::ConstantAlbedo) -> Any
Return the surface albedo at grid point i, j.
Terrarium.emissivity — Function
emissivity(i, j, grid, fields, ::AbstractAlbedo)Return the current emissivity at the given indices.
emissivity(
i,
j,
grid,
fields,
albedo::ConstantAlbedo
) -> Any
Return the surface emissivity at grid point i, j.