Radiation

Longwave radiation implementations

Currently implemented is

using SpeedyWeather
subtypes(SpeedyWeather.AbstractLongwave)

4-element Vector{Any}:
 JeevanjeeRadiation
 NoLongwave
 OneBandRadiation
 UniformCooling

Uniform cooling

Following Paulius and Garner^[PG06], the uniform cooling of the atmosphere is defined as

\[\frac{\partial T}{\partial t} = \begin{cases} - \tau^{-1}\quad&\text{for}\quad T > T_{min} \\ \frac{T_{strat} - T}{\tau_{strat}} \quad &\text{else.} \end{cases}\]

with $\tau = 16~h$ resulting in a cooling of -1.5K/day for most of the atmosphere, except below temperatures of $T_{min} = 207.5~K$ in the stratosphere where a relaxation towards $T_{strat} = 200~K$ with a time scale of $\tau_{strat} = 5~days$ is present.

Jeevanjee radiation

Jeevanjee and Zhou ^[JZ22] (eq. 2) define a longwave radiative flux $F$ for atmospheric cooling as (following Seeley and Wordsworth ^[SW23], eq. 1)

\[\frac{dF}{dT} = α*(T_t - T)\]

The flux $F$ (in $W/m^2/K$) is a vertical upward flux between two layers (vertically adjacent) of temperature difference $dT$. The change of this flux across layers depends on the temperature $T$ and is a relaxation term towards a prescribed stratospheric temperature $T_t = 200~K$ with a radiative forcing constant $\alpha = 0.025 W/m^2/K^2$. Two layers of identical temperatures $T_1 = T_2$ would have no net flux between them, but a layer below at higher temperature would flux into colder layers above as long as its temperature $T > T_t$. This flux is applied above the lowermost layer and above, leaving the surface fluxes unchanged. The uppermost layer is tied to $T_t$ through a relaxation at time scale $\tau = 6~h$

\[\frac{\partial T}{\partial t} = \frac{T_t - T}{\tau}\]

The flux $F$ is converted to temperature tendencies at layer $k$ via

\[\frac{\partial T_k}{\partial t} = (F_{k+1/2} - F_{k-1/2})\frac{g}{\Delta p c_p}\]

The term in parentheses is the absorbed flux in layer $k$ of the upward flux from below at interface $k+1/2$ ($k$ increases downwards, see Vertical coordinates and resolution and Sigma coordinates). $\Delta p = p_{k+1/2} - p_{k-1/2}$ is the pressure thickness of layer $k$, gravity $g$ and heat capacity $c_p$.

Shortwave radiation

Currently implemented is

subtypes(SpeedyWeather.AbstractShortwave)

2-element Vector{Any}:
 NoShortwave
 TransparentShortwave

References