Changeset 11015 for NEMO/trunk/doc/latex/SI3/subfiles
- Timestamp:
- 2019-05-20T20:57:09+02:00 (5 years ago)
- Location:
- NEMO/trunk/doc/latex/SI3/subfiles
- Files:
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- 14 edited
- 1 moved
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NEMO/trunk/doc/latex/SI3/subfiles/abstract_foreword.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_bdy_agrif.tex
r9974 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_domain.tex
r9983 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} … … 32 32 \begin{center} 33 33 \vspace{0cm} 34 \includegraphics[height=6cm,angle=-00]{ ../Figures/time_stepping.png}34 \includegraphics[height=6cm,angle=-00]{time_stepping} 35 35 \caption{Schematic representation of time stepping in SI$^3$, assuming $nn\_fsbc=5$.} 36 36 \label{ice_scheme} … … 56 56 \begin{center} 57 57 \vspace{0cm} 58 \includegraphics[height=10cm,angle=-00]{ ../Figures/thermogrid.eps}58 \includegraphics[height=10cm,angle=-00]{thermogrid.eps} 59 59 \caption{\footnotesize{Vertical grid of the model, used to resolve vertical temperature and salinity profiles}}\label{fig_dom_icelayers} 60 60 \end{center} … … 69 69 To increase numerical efficiency of the code, the two horizontal dimensions of an array $X(ji,jj,jk,jl)$ are collapsed into one (array $X\_1d(ji,jk,jl)$) for thermodynamic computations, and re-expanded afterwards. 70 70 71 \ forfile{../namelists/nampar}71 \nlst{nampar} 72 72 73 73 \section{Thickness space domain} 74 74 75 \ forfile{../namelists/namitd}75 \nlst{namitd} 76 76 77 77 Thickness space is discretized using $jl=1, ..., jpl$ thickness categories, with prescribed boundaries $hi\_max(jl-1),hi\_max(jl)$. Following \cite{Lipscomb01}, ice thickness can freely evolve between these boundaries. The number of ice categories $jpl$ can be adjusted from the namelist ($nampar$). … … 91 91 \begin{center} 92 92 \vspace{0cm} 93 \includegraphics[height=6cm,angle=-00]{ ../Figures/ice_cats.eps}93 \includegraphics[height=6cm,angle=-00]{ice_cats.eps} 94 94 \caption{\footnotesize{Boundaries of the model ice thickness categories (m) for varying number of categories and prescribed mean thickness ($\overline h$). The formerly used $tanh$ formulation is also depicted.}}\label{fig_dom_icecats} 95 95 \end{center} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_dynamics.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_interfaces.tex
r9974 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_miscellaneous.tex
r9974 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_model_basics.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} … … 41 41 \begin{center} 42 42 \vspace{0cm} 43 \includegraphics[height=10cm,angle=-00]{ ../Figures/ice_scheme.png}44 \caption{Representation of the ice pack, using multiple categories with specific ice concentration ($a_l, l=1, 2, ..., L$), thickness ($h^i_l$), snow depth ($h^s_l$), vertical temperature and salinity profiles ($T^i_{kl}$, $S^{*}_{kl}$) and a single ice velocity vector ($\ bm{u}$).}43 \includegraphics[height=10cm,angle=-00]{ice_scheme} 44 \caption{Representation of the ice pack, using multiple categories with specific ice concentration ($a_l, l=1, 2, ..., L$), thickness ($h^i_l$), snow depth ($h^s_l$), vertical temperature and salinity profiles ($T^i_{kl}$, $S^{*}_{kl}$) and a single ice velocity vector ($\mathbf{u}$).} 45 45 \label{ice_scheme} 46 46 \end{center} … … 162 162 %------------------------------------------------------------------------------------------------------------------------- 163 163 164 We first present the essentials of the thickness distribution framework \citep{Thorndikeetal75}. Consider a given region of area $R$ centered at spatial coordinates $(\ bm{x})$ at a given time $t$. $R$ could be e.g. a model grid cell. The ice thickness distribution $g(\mathbf{x},t, h)$ is introduced as follows:164 We first present the essentials of the thickness distribution framework \citep{Thorndikeetal75}. Consider a given region of area $R$ centered at spatial coordinates $(\mathbf{x})$ at a given time $t$. $R$ could be e.g. a model grid cell. The ice thickness distribution $g(\mathbf{x},t, h)$ is introduced as follows: 165 165 \begin{linenomath} 166 166 \begin{align} … … 184 184 \begin{center} 185 185 \vspace{0cm} 186 \includegraphics[height=6cm,angle=-00]{ ../Figures/g_h.png}186 \includegraphics[height=6cm,angle=-00]{g_h} 187 187 \caption{Representation of the relation between real thickness profiles and the ice thickness distribution function $g(h)$} 188 188 \label{fig_g_h} … … 202 202 \begin{linenomath} 203 203 \begin{align} 204 \frac{\partial a_l}{\partial t} = - \ bm{\nabla} \cdot (a_l \mathbf{u}) + \Theta^a_l + \int_{H^*_{l-1}}^{H^*_l} dh \psi.204 \frac{\partial a_l}{\partial t} = - \mathbf{\nabla} \cdot (a_l \mathbf{u}) + \Theta^a_l + \int_{H^*_{l-1}}^{H^*_l} dh \psi. 205 205 \label{eq:gt} 206 206 \end{align} … … 211 211 \begin{linenomath} 212 212 \begin{align} 213 A(\ bm{x},t) &=\int_{0^+}^{\infty} dh \cdot g(h,\bm{x},t) \sim A_{ij} = \sum_{l=1}^L a_{ijl}, & \\214 V_i(\ bm{x},t)&=\int_{0}^{\infty} dh \cdot g(h,\bm{x},t) \cdot h \sim V^i_{ij} = \sum_{l=1}^L v^i_{ijl}. & \\213 A(\mathbf{x},t) &=\int_{0^+}^{\infty} dh \cdot g(h,\mathbf{x},t) \sim A_{ij} = \sum_{l=1}^L a_{ijl}, & \\ 214 V_i(\mathbf{x},t)&=\int_{0}^{\infty} dh \cdot g(h,\mathbf{x},t) \cdot h \sim V^i_{ij} = \sum_{l=1}^L v^i_{ijl}. & \\ 215 215 \end{align} 216 216 \end{linenomath} … … 228 228 \begin{linenomath} 229 229 \begin{align} 230 m \frac{\partial \ bm{u}} {\partial t} & = \bm{\nabla}\cdot\bm{\sigma} +A \left(\bm{\tau}_{a}+\bm{\tau}_{w}\right) - m f \bm{k} \times \bm{u} - m g \bm{\nabla}{\eta},230 m \frac{\partial \mathbf{u}} {\partial t} & = \mathbf{\nabla}\cdot\mathbf{\sigma} +A \left(\mathbf{\tau}_{a}+\mathbf{\tau}_{w}\right) - m f \mathbf{k} \times \mathbf{u} - m g \mathbf{\nabla}{\eta}, 231 231 \label{a} 232 232 \end{align} 233 233 \end{linenomath} 234 where $m=\rho_i V_i + \rho_s V_s $ is the ice and snow mass per unit area, $\ bm{u}$ is the ice velocity, $\bm{\sigma}$ is the internal stress tensor, $\bm{\tau}_a$ and $\bm{\tau}_w$ are the air and ocean stresses, respectively, $f$ is the Coriolis parameter, $\bm{k}$ is a unit vector pointing upwards, $g$ is the gravity acceleration and $\eta$ is the ocean surface elevation. The EVP approach used in LIM \citep{Bouillonetal13} gives the stress tensor as a function of the strain rate tensor $\dot{\bm{\epsilon}}$ and some of the sea ice state variables:235 \begin{linenomath} 236 \begin{align} 237 \ bm{\sigma} & = \bm{\sigma} (\dot{ \bm{\epsilon}}, \text{ice state}).234 where $m=\rho_i V_i + \rho_s V_s $ is the ice and snow mass per unit area, $\mathbf{u}$ is the ice velocity, $\mathbf{\sigma}$ is the internal stress tensor, $\mathbf{\tau}_a$ and $\mathbf{\tau}_w$ are the air and ocean stresses, respectively, $f$ is the Coriolis parameter, $\mathbf{k}$ is a unit vector pointing upwards, $g$ is the gravity acceleration and $\eta$ is the ocean surface elevation. The EVP approach used in LIM \citep{Bouillonetal13} gives the stress tensor as a function of the strain rate tensor $\dot{\mathbf{\epsilon}}$ and some of the sea ice state variables: 235 \begin{linenomath} 236 \begin{align} 237 \mathbf{\sigma} & = \mathbf{\sigma} (\dot{ \mathbf{\epsilon}}, \text{ice state}). 238 238 \end{align} 239 239 \end{linenomath} … … 245 245 \end{align} 246 246 \end{linenomath} 247 including the effets of transport, thermodynamics ($\Theta^X$) and mechanical redistribution ($\Psi^X$). Solving these $jpl.(4+2.jpk)$ equations gives the temporal evolution of $\ bm{u}$, $\bm{\sigma}$ and the rest of the global (extensive) variables listed in Table \ref{GVariables_table}.247 including the effets of transport, thermodynamics ($\Theta^X$) and mechanical redistribution ($\Psi^X$). Solving these $jpl.(4+2.jpk)$ equations gives the temporal evolution of $\mathbf{u}$, $\mathbf{\sigma}$ and the rest of the global (extensive) variables listed in Table \ref{GVariables_table}. 248 248 249 249 \section{Ice Dynamics} … … 272 272 \begin{center} 273 273 \vspace{0cm} 274 \includegraphics[height=6cm,angle=-00]{ ../Figures/yield_curve.png}274 \includegraphics[height=6cm,angle=-00]{yield_curve} 275 275 \caption{Elliptical yield curve used in the VP rheologies, drawn in the space of the principal components of the stress tensor ($\sigma_1$ and $\sigma_2$).} 276 276 \label{fig_yield} … … 383 383 \begin{center} 384 384 \vspace{0cm} 385 \includegraphics[height=8cm,angle=-00]{ ../Figures/Thermal_properties.png}385 \includegraphics[height=8cm,angle=-00]{Thermal_properties} 386 386 \caption{Thermal properties of sea ice vs temperature for different bulk salinities: brine fraction, specific enthalpy, thermal conductivity, and effective specific heat.} 387 387 \label{fig_thermal_properties} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_output_diagnostics.tex
r9974 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_radiative_transfer.tex
r9995 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} … … 28 28 \begin{center} 29 29 \vspace{0cm} 30 \includegraphics[height=6cm,angle=-00]{ ../Figures/radiative_transfer.png}30 \includegraphics[height=6cm,angle=-00]{radiative_transfer} 31 31 \caption{Partitionning of solar radiation in the snow-ice system, as represented in SI$^3$.} 32 32 \label{fig_radiative_transfer} … … 54 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). 55 55 56 \ forfile{../namelists/namalb}56 \nlst{namalb} 57 57 58 58 %-------------------------------------------------------------------------------------------------------------------- … … 63 63 \begin{center} 64 64 \vspace{0cm} 65 \includegraphics[height=10cm,angle=-00]{ ../Figures/albedo_cloud_correction.png}65 \includegraphics[height=10cm,angle=-00]{albedo_cloud_correction} 66 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).} 67 67 % ocean uses 0.06 for overcast sky (Payne 74) and Briegleb and Ramanathan parameterization … … 94 94 \begin{center} 95 95 \vspace{0cm} 96 \includegraphics[height=4cm,angle=-00]{ ../Figures/albedo_dependencies.png}96 \includegraphics[height=4cm,angle=-00]{albedo_dependencies} 97 97 \caption{Example albedo dependencies on ice thickness, snow depth and pond depth, as parameterized in SI$^3$.} 98 98 \label{fig_albedo_dependencies} … … 183 183 \begin{center} 184 184 \vspace{0cm} 185 \includegraphics[height=8cm,angle=-00]{ ../Figures/radiation_atm_ice_oce.png}185 \includegraphics[height=8cm,angle=-00]{radiation_atm_ice_oce} 186 186 \caption{Framing solar radiation transfer through sea ice into the atmosphere-ice-ocean context.} 187 187 % ocean uses 0.06 for overcast sky (Payne 74) and Briegleb and Ramanathan parameterization -
NEMO/trunk/doc/latex/SI3/subfiles/chap_ridging_rafting.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_single_category_use.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_thermo.tex
r9974 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document} … … 34 34 \begin{center} 35 35 \vspace{0cm} 36 \includegraphics[height=10cm,angle=-00]{ ../Figures/Openwater_eb.png}36 \includegraphics[height=10cm,angle=-00]{Openwater_eb} 37 37 \caption{Scheme of the estimate of the heat budget of the first ocean level.} 38 38 \label{fig_yield} -
NEMO/trunk/doc/latex/SI3/subfiles/chap_transport.tex
r9974 r11015 1 1 2 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}2 \documentclass[../main/SI3_manual]{subfiles} 3 3 4 4 \begin{document} -
NEMO/trunk/doc/latex/SI3/subfiles/todolist.tex
r9995 r11015 1 \documentclass[../ ../tex_main/NEMO_manual]{subfiles}1 \documentclass[../main/SI3_manual]{subfiles} 2 2 3 3 \begin{document}
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