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: References : Two dimensional anelastic model : 5 Radiation


6 Ground surface

The grand temperature is calculated by the 1D thermal conduction equation.

\begin{displaymath}
\rho _{g}c_{p,g}\DP{T_{g}}{t} = k_{g}\DP[2]{T_{g}}{z}.
\end{displaymath} (55)

where $T_{g}$ is the grand temperature (K), $\rho _{g}$ is the soil density (kgm${}^{-3}$), $c_{p,g}$ is the specific heat of soil (Jkg${}^{-1}$K${}^{-1}$), and $k_{g}$ is the thermal conductivity (Wm${}^{-1}$K${}^{-1}$). The surface temperature $T_{sfc}$ is given by $T_{sfc} = T_{g}\vert _{z=0}$.

The boundary condition at the surface is given as follows.

\begin{displaymath}
- k\left.\DP{T}{z}\right\vert _{z=0} = - F_{SR}(1-A) + F_{IR,net} + H ,
\end{displaymath} (56)

where $F_{SR}$ is the solar radiative flux at the surface (the sign of downward flux is positive), $A$ is the surface albedo, $F_{IR,net}$ is the net infrared radiative flux emitted from the surface and $H$ is the sensible heat flux (the sign of upward flux is positive). The lower boundary of the grand surface is given as a insulation boundary.

Parameters

The values of soil density, thermal conductivity and specific heat are same as those of standard model of Kieffer et al. (1977).


表 11: Parameters of ground surface model
Parameters Standard values Note
$A$ 0.25 Kieffer et al. (1977)
$\rho _{g}$ 1650 kgm${}^{-3}$
$c_{p,g}$ 588 JK${}^{-1}$kg${}^{-1}$
$k_{g}$ 7.63 $\times 10^{-2}$JK${}^{-1}$m${}^{-1}$sec${}^{-1}$

By using these values, the thermal inertia $I\equiv \sqrt{\rho
_{g}c_{p,g}k_{g}}$ is 272 Wm${}^{-2}$sec${}^{1/2}$K${}^{-1}$ and the diurnal skin depth of $\delta
_{d}\equiv\sqrt{k_{g}t_{d}/(\rho_{g}c_{p,g})}$ is about 8.2 cm.


next up previous
: References : Two dimensional anelastic model : 5 Radiation
Odaka Masatsugu 平成19年4月25日