2.2 Radiation

Metphomod contains parameterizations for solar- and IR-radiation in clear sky conditions.

2.2.1 Solar radiation

  The parameterizations for solar radiation were taken from Paltridge and Platt (1976). The direct radiation is given by:

 

$$\tau_{R}^{} \tau_{D}^{} \cdot \cdot$$ (21)

The definitions of the symbols are listed in table 1.

Total indirect short-wave radiation is:

 

D_R = D_RI + D_RR (22)

where D_RI is the indirect irradiation from the sky:

$$\tau_{R}^{} \tau_{D}^{} \cdot \cdot \tau_{D}^{} \alpha_{R}^{}$$ (23)

D_RR is the indirect radiation coming from the albedo of the earth's surface:

$$\cdot$$ (24)

$\alpha_{R}^{}$(Z) is the fraction of radiation which is scattered back to space. The parameterizations for I₀,a_O3,$\tau_{R}^{}$(m),$\tau_{D}^{}$,m,a_H2O,CO2, and $\alpha_{R}^{}$(Z) are described in Perego (1996) in full detail.

2.2.2 Long-wave radiation

  The parameterization for IR-radiation was taken from Pielke (1984):

$$\uparrow \sigma \int_{0}^{u} \epsilon \hat{u} {\frac{d}{d \hat u}} \sigma \hat{u}$$ = (25)

$$\downarrow \sigma \int_{u_T}^{u} \epsilon \hat{u} {\frac{d}{d \hat u}} \sigma \hat{u}$$ = (26)

$$\int_{0}^{z} \rho$$ u = (27)

The definitions of the symbols are explained in table 1.

 

Figure 1: Metphomod uses a rectangular coordinate system. Most of the physical parameters are stored in the center of the according grid cells. Only turbulence parameters and fluxes are stored at the faces. Topography is considered, by having two categories of grid cells: normal grid cells, and underground grid cells. All fluxes at the boundaries of underground grid cells set to zero.

The change of air temperature due to the IR-radiation divergence can then be calculated with:

$${\frac{\partial T}{\partial t}} {\textstyle\frac{1}{\rho_0 C_p}} {\frac{\partial (R \downarrow - R \uparrow)}{\partial z}}$$ (28)