Radiant Heat Fluxes
Radiant Heat Fluxes
<wikitex>As was seen in Sea-Ice_Model#Thermodynamics, the model thermodynamics requires fluxes of latent and sensible heat and longwave and shortwave radiation. We follow the lead of Parkinson and Washington in computing these terms.</wikitex>
Shortwave Radiation
<wikitex> The Zillman equation for radiation under cloudless skies is: \begin{equation}
Q_o = {S \cos^2 Z \over (\cos Z + 2.7) e \times 10^{-5} + 1.085
\cos Z + 0.10}
\end{equation} where the variables are as in Table \ref{radvars}. The cosine of the zenith angle is computed using the formula: \begin{equation}
\cos Z = \sin \phi \sin \delta + \cos \phi \cos \delta \cos H\!A .
\end{equation} The declination is \begin{equation}
\delta = 23.44^{\circ} \times \cos \left[ (172 - {\rm day \, of \, year})
\times 2 \pi / 365 \right]
\end{equation} and the hour angle is \begin{equation}
H\!A = (12 \, {\rm hours - solar \, time}) \times \pi / 12 .
\end{equation} The correction for cloudiness is given by \begin{equation}
SW\!\!\downarrow = Q_o ( 1 - 0.6 c^3) .
\end{equation} An estimate of the cloud fraction $c$ will be provided by Jennifer Francis (\cite{Francis00}).
| Variable | Value | Description |
|---|---|---|
| $(a,b)$ | (9.5, 7.66) | vapor pressure constants over ice |
| $(a,b)$ | (7.5, 35.86) | vapor pressure constants over water |
| $c$ | cloud cover fraction | |
| $C_E$ | $1.75 \times 10^{-3}$ | transfer coefficient for latent heat |
| $C_H$ | $1.75 \times 10^{-3}$ | transfer coefficient for sensible heat |
| $c_p$ | 1004 J kg$^{-1}$ K$^{-1}$ | specific heat of dry air |
| $\delta$ | declination | |
| $e$ | vapor pressure in pascals | |
| $e_s$ | saturation vapor pressure | |
| $\epsilon$ | 0.622 | ratio of molecular weight of water to dry air |
| $H\!A$ | hour angle | |
| $L$ | $2.5 \times 10^6$ J kg$^{-1}$ | latent heat of vaporization |
| $L$ | $2.834 \times 10^6$ J kg$^{-1}$ | latent heat of sublimation |
| $\phi$ | latitude | |
| $Q_o$ | incoming radiation for cloudless skies | |
| $q_s$ | surface specific humidity | |
| $q_{10 \rm m}$ | 10 meter specific humidity | |
| $\rho_a$ | air density | |
| $S$ | 1353 W m$^{-2}$ | solar constant |
| $\sigma$ | $5.67 \times 10^{-8}$ W m$^{-2}$ K$^{-4}$ | Stefan-Boltzmann constant |
| $T_a$ | air temperature | |
| $T_d$ | dew point temperature | |
| $T_{s\!f\!c}$ | surface temperature of the water/ice/snow | |
| $V_{wg}$ | geostrophic wind speed | |
| $Z$ | solar zenith angle |
</wikitex>
