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NEMO/trunk/doc/latex/SI3/subfiles/chap_radiative_transfer.tex
r11015 r11031 36 36 %-------------------------------------------------------------------------------------------------------------------- 37 37 38 Solar radiation in the snow-ice system is represented following the principles of \cite{ MaykutUntersteiner71}, see Fig.\ref{fig_radiative_transfer}, using a unique band of solar radiation. Incident solar radiation (W/m$^2$, counted per unit ice area - not per grid cell area) is specified in the SBC routines and is a priori category dependent, because multiple atmosphere-surface reflexions are frequent in polar regions imply that incident radiation depends on the surface albedo and therefore surface state.38 Solar radiation in the snow-ice system is represented following the principles of \cite{maykut_1971}, see Fig.\ref{fig_radiative_transfer}, using a unique band of solar radiation. Incident solar radiation (W/m$^2$, counted per unit ice area - not per grid cell area) is specified in the SBC routines and is a priori category dependent, because multiple atmosphere-surface reflexions are frequent in polar regions imply that incident radiation depends on the surface albedo and therefore surface state. 39 39 40 40 Net solar radiation qsr\_ice(i,j,l) is obtained by substracting the reflected part of the incident radiation using the surface albedo $\alpha(i,j,l)$, parameterized as a function of environmental conditions. … … 50 50 The surface albedo determines the amount of solar radiation that is reflected by the ice surface, hence also net solar radiation. The philosophy of the parameterization of surface albedo is the following: each ice category has its own albedo value $\alpha(i,j,l)$, determined as a function of cloud fraction, ice thickness, snow depth, melt pond fraction and depth, using observation-based empirical fits. 51 51 52 The original \cite{ ShineHenderson85} parameterization had a few inconsistencies and flaws that the revisited parameterization described hereafter fixes. In particular, the dependencies of albedos on ice thickness, snow depth and cloud fraction have been revised in the light of recent observational constraints \citep{Brandtetal05,GrenfellPerovich04}. In addition, the asymptotic properties of albedo are better specified and now fully consistent with oceanic values. Finally, the effect of melt ponds has been included \citep{Lecomteetal15}.53 54 The user has control on 5 reference namelist values, which describe the asymptotic values of albedo of snow and ice for dry and wet conditions, as well as the deep ponded-ice albedo. Observational surveys, in particular during SHEBA in the Arctic \citep{ Perovichetal02alb} and further additional experiments \citep{GrenfellPerovich04}, as well as by \cite{Brandtetal05} in the Antarctic, have provided relatively strong constraints on the surface albedo. In this context, the albedo can hardly be used as the main model tuning parameter, at least outside of these observation-based bounds (see namalb for reference values).52 The original \cite{shine_1985} parameterization had a few inconsistencies and flaws that the revisited parameterization described hereafter fixes. In particular, the dependencies of albedos on ice thickness, snow depth and cloud fraction have been revised in the light of recent observational constraints \citep{brandt_2005,grenfell_2004}. In addition, the asymptotic properties of albedo are better specified and now fully consistent with oceanic values. Finally, the effect of melt ponds has been included \citep{lecomte_2015}. 53 54 The user has control on 5 reference namelist values, which describe the asymptotic values of albedo of snow and ice for dry and wet conditions, as well as the deep ponded-ice albedo. Observational surveys, in particular during SHEBA in the Arctic \citep{perovich_2002} and further additional experiments \citep{grenfell_2004}, as well as by \cite{brandt_2005} in the Antarctic, have provided relatively strong constraints on the surface albedo. In this context, the albedo can hardly be used as the main model tuning parameter, at least outside of these observation-based bounds (see namalb for reference values). 55 55 56 56 \nlst{namalb} … … 64 64 \vspace{0cm} 65 65 \includegraphics[height=10cm,angle=-00]{albedo_cloud_correction} 66 \caption{Albedo correction $\Delta \alpha$ as a function of overcast sky (diffuse light) albedo $\alpha_os$, from field observations \cite[][their Table 3]{ GrenfellPerovich04} (squares) and 2nd-order fit (Eq. \ref{eq_albedo_cloud_correction}). Red squares represent the irrelevant data points excluded from the fit. For indication, the amplitude of the correction used in the ocean component is also depicted (blue circle).}66 \caption{Albedo correction $\Delta \alpha$ as a function of overcast sky (diffuse light) albedo $\alpha_os$, from field observations \cite[][their Table 3]{grenfell_2004} (squares) and 2nd-order fit (Eq. \ref{eq_albedo_cloud_correction}). Red squares represent the irrelevant data points excluded from the fit. For indication, the amplitude of the correction used in the ocean component is also depicted (blue circle).} 67 67 % ocean uses 0.06 for overcast sky (Payne 74) and Briegleb and Ramanathan parameterization 68 68 \label{fig_albedo_cloud_correction} … … 72 72 %-------------------------------------------------------------------------------------------------------------------- 73 73 74 Because the albedo is not an intrinsic optical property, it depends on the type of light (diffuse of direct), which is practically handled by weighting the clear (cs) and overcast (os) skies values by cloud fraction $c(i,j)$ \citep{ FichefetMaqueda97}:74 Because the albedo is not an intrinsic optical property, it depends on the type of light (diffuse of direct), which is practically handled by weighting the clear (cs) and overcast (os) skies values by cloud fraction $c(i,j)$ \citep{fichefet_1997}: 75 75 \begin{equation} 76 76 \alpha(i,j,l) = [ 1 - c(i,j) ] \cdot \alpha_{cs} (i,j,l) + c (i,j) \cdot \alpha_{os}(i,j,l). 77 77 \end{equation} 78 For concision, we drop the spatial and category indices hereafter. \cite{ GrenfellPerovich04} observations at Point Barrow, on the Alaskan Coast, suggest that clear and overcast sky albedos are directly related through78 For concision, we drop the spatial and category indices hereafter. \cite{grenfell_2004} observations at Point Barrow, on the Alaskan Coast, suggest that clear and overcast sky albedos are directly related through 79 79 \begin{equation} 80 80 \alpha_{cs} = \alpha_{os} - \Delta \alpha(\alpha_{os}). … … 110 110 The surface fractions $f_{ice}$, $f_{snw}$ and $f_{pnd}$ are currently crudely parameterized: if snow is present ($h_s>0$), then $f_{snw}=1$ and $f_{ice}=f_{pnd}=0$. In the absence of snow, $f_{pnd}$ is either specified or calculated (depending on melt pond options in nampnd), and $f_{ice}=1.-f_{pnd}$. Admittedly, more refined parameterizations of $f_{snw}$ could improve the realism of the model. Note finally that the dependence of surface albedo on the presence of melt ponds can be included or not (namelist parameter ln\_pnd\_alb). If the latter is set to false, $f_{pnd}$ is always assumed zero in the albedo computations. 111 111 112 Works by \cite{ Brandtetal05} and references therein, indicate that the dependence of the albedo of bare ice on ice thickness depends is linear/logarithmic/constant from thin to thick ice. Hence, the following expressions capture the essence of their works:112 Works by \cite{brandt_2005} and references therein, indicate that the dependence of the albedo of bare ice on ice thickness depends is linear/logarithmic/constant from thin to thick ice. Hence, the following expressions capture the essence of their works: 113 113 \begin{eqnarray} 114 114 \alpha_{ice} = … … 129 129 values that are to be specified from the namelist. 130 130 131 \cite{ GrenfellPerovich04} suggest that the dependence of surface albedo on snow depth is exponential,131 \cite{grenfell_2004} suggest that the dependence of surface albedo on snow depth is exponential, 132 132 \begin{eqnarray} 133 133 \alpha_{snw} = \alpha_{snw}^{\infty} - ( \alpha_{snw}^{\infty} - \alpha_{ice} ) * exp( -h_s / h_s^{ref} ), … … 143 143 values that are to be specified from the namelist. 144 144 145 Based on ideas developed from melt ponds on continental ice \citep{ ZuoOerlemans96}, the albedo of ponded ice was proposed to follow \citep{Lecomteetal11}:145 Based on ideas developed from melt ponds on continental ice \citep{zuo_1996}, the albedo of ponded ice was proposed to follow \citep{lecomte_2011}: 146 146 \begin{eqnarray} 147 147 \alpha_{pnd} = \alpha_{dpnd} - ( \alpha_{dpnd} -\alpha_{ice} ) \cdot exp( -h_{pnd} / 0.05 ) 148 148 \end{eqnarray} 149 $\alpha_{dpnd}$ is a namelist parameter. \cite{ EbertCurry93} also use such dependency for their multi-spectral albedo.149 $\alpha_{dpnd}$ is a namelist parameter. \cite{ebert_1993} also use such dependency for their multi-spectral albedo. 150 150 151 151 The dependencies of surface albedo on ice thickness, snow depth and pond depth are illustrated in Fig. \ref{fig_albedo_dependencies}. … … 153 153 \subsection{Transmission below the snow/ice surface} 154 154 155 The transmitted solar radiation below the surface is represented following \cite{ FichefetMaqueda97} and \cite{MaykutUntersteiner71}:155 The transmitted solar radiation below the surface is represented following \cite{fichefet_1997} and \cite{maykut_1971}: 156 156 \begin{eqnarray} 157 157 qtr\_ice\_top(i,j,l) = i_o(i,j) qsr\_ice(i,j,l), 158 158 \end{eqnarray} 159 where $i_o=0$ in presence of snow, and depends on cloud fraction otherwise, based on works of \cite{ GrenfellMaykut77}. This parameterization needs to be re-evaluated and likely updated.159 where $i_o=0$ in presence of snow, and depends on cloud fraction otherwise, based on works of \cite{grenfell_1977}. This parameterization needs to be re-evaluated and likely updated. 160 160 161 161 \subsection{Attenuation and transmission below the ice/ocean interface}
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