Changeset 9983
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 20180720T15:45:54+02:00 (6 years ago)
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 NEMO/trunk/doc/si3_doc
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NEMO/trunk/doc/si3_doc/tex_main/SI3_manual.bbl
r9974 r9983 1 \begin{thebibliography}{3 8}1 \begin{thebibliography}{39} 2 2 \providecommand{\natexlab}[1]{#1} 3 3 \providecommand{\url}[1]{\texttt{#1}} … … 111 111 Geophysical Research}, \textbf{112}, C03S9, \doi{doi:10.1029/2005JC003355}. 112 112 113 \bibitem[{Massonnet et~al.(2018)Massonnet, Barth\'el\'emy, Worou, Fichefet, 114 Vancoppenolle, and Rousset}]{Massonnetetal18b} 115 Massonnet, F., A.~Barth\'el\'emy, K.~Worou, T.~Fichefet, M.~Vancoppenolle, and 116 C.~Rousset, 2018: Insights on the discretization of the ice thickness 117 distribution in largescale sea ice models. \textit{submitted}. 118 113 119 \bibitem[{Maykut(1986)}]{Maykut86} 114 120 Maykut, G.~A., 1986: \textit{The Geophysics of Sea Ice}, NATO ASI Series. 
NEMO/trunk/doc/si3_doc/tex_main/SI3_manual.tex
r9974 r9983 84 84 85 85 \subfile{../tex_sub/chap_dynamics} 86 86 % 87 87 \subfile{../tex_sub/chap_transport} 88 88 % 89 89 \subfile{../tex_sub/chap_ridging_rafting} 90 90 % 91 91 \subfile{../tex_sub/chap_radiative_transfer} 92 92 % 93 93 \subfile{../tex_sub/chap_thermo} 94 94 % 95 95 \subfile{../tex_sub/chap_interfaces} 96 96 % 97 97 \subfile{../tex_sub/chap_output_diagnostics} 98 98 % 99 99 \subfile{../tex_sub/chap_single_category_use} 100 100 % 101 101 \subfile{../tex_sub/chap_bdy_agrif} 102 102 % 103 103 \subfile{../tex_sub/chap_miscellaneous} 104 104 
NEMO/trunk/doc/si3_doc/tex_sub/chap_domain.tex
r9974 r9983 14 14 \newpage 15 15 $\ $\newline % force a new line 16 Excel 16 17 Having defined the model equations in previous Chapter, we need now to choose the numerical discretization. In the present chapter, we provide a general description of the SI$^3$ discretization strategy, in terms of time, space and thickness, which is considered as an extra independent variable. 18 19 Sea ice state variables are typically expressed as: 20 \begin{equation} 21 X(ji,jj,\textcolor{gray}{jk},jl). 22 \end{equation} 23 $ji$ and $jj$ are xy spatial indices, as in the ocean. $jk=1, ..., nlay\_i$ corresponds to the vertical coordinate system in sea ice (ice layers), and only applies to verticallyresolved quantities (ice enthalpy and salinity). $jl=1, ..., jpl$ corresponds to the ice categories, discretizing thickness space. 24 17 25 \section{Time domain} 18 26 19 Time stepping. Dynamics then thermodynamics. nn\_fsbc. EVP subcycles. 27 % 28 % 29 % FIG x : Time Stepping 30 % 31 \begin{figure}[ht] 32 \begin{center} 33 \vspace{0cm} 34 \includegraphics[height=6cm,angle=00]{../Figures/time_stepping.png} 35 \caption{Schematic representation of time stepping in SI$^3$, assuming $nn\_fsbc=5$.} 36 \label{ice_scheme} 37 \end{center} 38 \end{figure} 39 % 40 % 41 42 The sea ice time stepping is synchronized with that of the ocean. Because of the potentially large numerical cost of sea ice physics, in particular rheology, SI$^3$ can be called every nn\_fsbc time steps (namsbc in \textit{namelist\_ref}). The sea ice time step is therefore $rdt\_ice = rdt * nn\_fsbc$. In terms of quality, the best value for \textit{nn\_fsbc} is 1, providing full consistency between sea ice and oceanic fields. Larger values (typically 2 to 5) can be used but numerical instabilities can appear because of the progressive decoupling between the state of sea ice and that of the ocean, hence changing $nn\_fsbc$ must be done carefully. 43 44 Ice dynamics (rheology, advection, ridging/rafting) and thermodynamics are called successively. To avoid pathological situations, thermodynamics were chosen to be applied on fields that have been updated by dynamics, in a somehow semiimplicit procedure. 45 46 There are a few iterative / subcycling procedures throughout the code, notably for rheology, advection, ridging/ rafting and the diffusion of heat. In some cases, the arrays at the beginning of the sea ice time step are required. Those are referred to as $X\_b$. 20 47 21 48 \section{Spatial domain} 22 49 23 Not much to say about domain. Handled by NEMO. Cgrid. Scale factors. 50 % 51 % 52 % FIGx : Vertical grid 53 % 54 % 55 \begin{figure}[!ht] 56 \begin{center} 57 \vspace{0cm} 58 \includegraphics[height=10cm,angle=00]{../Figures/thermogrid.eps} 59 \caption{\footnotesize{Vertical grid of the model, used to resolve vertical temperature and salinity profiles}}\label{fig_dom_icelayers} 60 \end{center} 61 \end{figure} 62 % 63 % 24 64 25 Vertical layers (nlay\_i, nlay\_s) 65 The horizontal indices $ji$ and $jj$ are handled as for the ocean in NEMO, assuming Cgrid discretization and in most cases a finite difference expression for scale factors. 26 66 27 \section{Thickness category boundaries} 67 The vertical index $jk=1, ..., nlay\_i$ is used for enthalpy (temperature) and salinity. In each ice category, the temperature and salinity profiles are vertically resolved over $nlay\_i$ equallyspaced layers. The number of snow layers can currently only be set to $nlay\_s=1$ (Fig. \ref{fig_dom_icelayers}). 28 68 29 [ jpl, nn\_virtual\_itd ] 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 reexpanded afterwards. 30 70 31 2 formulations to describe 71 \forfile{../namelists/nampar} 32 72 33 [ ln\_cat\_hfn (function), rn\_himean ] 73 \section{Thickness space domain} 34 74 35 ln\_cat\_usr (user defined), rn\_catbnd, rn\_himin 36 Categories: boundary definitions. 37 See doc 2.0, there are commented bits of text in the tex file. 75 \forfile{../namelists/namitd} 38 76 39 Recall recommendations from Francois's, Antoine et al's paper.77 Thickness space is discretized using $jl=1, ..., jpl$ thickness categories, with prescribed boundaries $hi\_max(jl1),hi\_max(jl)$. Following \cite{Lipscomb01}, ice thickness can freely evolve between these boundaries. The number of ice categories $jpl$ can be adjusted from the namelist ($nampar$). 40 78 41 %% 42 %% 43 %% FIGx : Ice categories 44 %% 45 %% 46 %\begin{figure}[ht] 47 %\begin{center} 48 %\vspace{0cm} 49 %\includegraphics[height=6cm,angle=00]{./Figures/ice_cats_new.eps} 50 %\caption{\footnotesize{Boundaries of the model ice thickness categories (m) for varying number of categories, prescribed mean thickness ($\overline h$ and formulation}}\label{ice_cats} 51 %\end{center} 52 %\end{figure} 53 %% 54 %% 79 There are two means to specify the position of the thickness boundaries of ice categories. The first option (ln\_cat\_hfn) is to use a fitting function that places the category boundaries between 0 and 3$\overline h$, with $\overline h$ the expected mean ice thickness over the domain (namelist parameter rn\_himean), and with a greater resolution for thin ice (Fig. \ref{fig_dom_icecats}). More specifically, the upper limits for ice in category $jl=1, ..., jpl1$ are: 80 \begin{eqnarray} 81 hi\_max(jl) = \biggr ( \frac{jl \cdot (3\overline h + 1 )^{\alpha}}{ (jpljl)(3 \overline h + 1)^{\alpha} + jl }\biggr )^{\alpha^{1}}  1, 82 \end{eqnarray} 83 with $hi\_max(0)$=0 m and $\alpha = 0.05$. The last category has no upper boundary, so that it can contain arbitrarily thick ice. 84 85 % 55 86 % 56 % The thickness distribution function $g(h)$ is numerically discretized into several ice thickness categories. The numerical formulation of the thickness categories follows Bitz et al. (2001) and Lipscomb (2001). A fixed number $L$ of thickness categories with a typical value of $L=5$ is imposed. For some variables, sea ice in each category is further divided into N vertical layers of ice and one layer of snow. In the remainder of the text, the $l=1, ..., L$ index runs for ice thickness categories and $k=1, ..., N$ for the vertical ice layers.87 % FIGx : Ice categories 57 88 % 58 %Each thickness category has a mean thickness $h^i_l$ ranging over $[H^*_{l1}$, $H^*_{l}$]. $H^*_{0}=0$, while the other boundaries are typically chosen with greater resolution for thin ice.59 89 % 60 %There are two options for discretization in $h$space, illustrated in Fig. \ref{ice_cats}. 90 \begin{figure}[!ht] 91 \begin{center} 92 \vspace{0cm} 93 \includegraphics[height=6cm,angle=00]{../Figures/ice_cats.eps} 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 \end{center} 96 \end{figure} 61 97 % 62 %\textbf{1.} The tanh hyperbolic formulation from CICE. 63 %\begin{linenomath} 64 %\begin{align} 65 %H^*_l &= H^*_{l1} + \frac{3}{L} + \frac{30}{L} \biggr [ 1 + tanh \biggr ( \frac{3l  3  3L}{L} \biggr ) \biggr] \quad (l=1, ..., L1). 66 %\end{align} 67 %\label{eq_301} 68 %\end{linenomath} 69 %The upper boundary $H^*_L$ is set to a very high value (99.). 70 % 71 %\textbf{2.} An adjustable homemade $1/h^\alpha$ formulation. 72 % 73 %To construct the discretization in $h$space, we first prescribe $H^*_0$ and $H^*_L=H_{max}$. We then introduce a fitting function $f$, defined over $[0,\infty]$, stricly positive and decreasing. We impose that the $H^*_l$'s must be such that their images in the $f$space ($f_l = f(H^*_l)$) are equally spaced. In mathematical terms: 74 %\begin{eqnarray} 75 %f_l & = & f_0  l \Delta f \qquad (l = 2, ..., L1), 76 %\label{eq_fl} 77 %\end{eqnarray} 78 %where $\Delta f = \frac{f_0  f_L}{L}$. 79 % 80 %Let us now construct a discretization in $h$space. We use the function $f(h)=1/(h+1)^\alpha$, where $\alpha$ is strictly positive; and impose that $H^*_{max}=3\overline h$, where $\overline h$ is the mean thickness in the domain $\overline h$. Replacing in $\ref{eq_fl}$, we get: 81 %\begin{eqnarray} 82 %H^*_l = \left ( \frac{ L ( H^*_L + 1 ) ^\alpha}{(Ll)( H^*_L + 1 ) ^\alpha + l} \right ) ^{1/\alpha}  1 83 %\end{eqnarray} 84 %\label{intro} 85 %There are two parameters to tune: $\overline h$ and $\alpha$ (typically 0.05, used for Fig. \ref{ice_cats}). 86 % 87 %Each ice category has its own set of global state variables 98 % 99 100 The other option (ln\_cat\_usr) is to specify category boundaries by hand using rn\_catbnd. The first category must always be thickner than rn\_himin (0.1 m by default). 101 102 The choice of ice categories is important, because it constraints the ability of the model to resolve the ice thickness distribution. The latest study \citep{Massonnetetal18b} recommends to use at least 5 categories, which should include one thick ice with lower bounds at $\sim$4 m and $\sim$2 m for the Arctic and Antarctic, respectively, for allowing the storage of deformed ice. 103 104 With a fixed number of cores, the cost of the model linearly increases with the number of ice categories. Using $jpl=1$ single ice category is also much cheaper than with 5 categories, but seriously deteriorates the ability of the model to grow and melt ice. Indeed, thin ice thicknes faster than thick ice, and shrinks more rapidly as well. When nn\_virtual\_itd=1 ($jpl$ = 1 only), two parameterizations are activated to compensate for these shortcomings. Heat conduction and areal decay of melting ice are adjusted to closely approach the 5 categories case. 88 105 89 106 \end{document} 
NEMO/trunk/doc/si3_doc/tex_sub/todolist.tex
r9974 r9983 12 12 \begin{itemize} 13 13 14 \item Documentation infrastructure ready by Jul 19, 2018.14 \item \textcolor{gray}{Documentation infrastructure ready by Jul 19, 2018.} 15 15 16 \item Abstract: v1 written.16 \item \textcolor{gray}{Abstract: v1 written.} 17 17 18 \item Disclaimer: v1 written.18 \item \textcolor{gray}{Disclaimer: v1 written.} 19 19 20 20 \item Introduction: list of chapters and change between realeases to be written (1h) 21 21 22 \item 1. Model basics: v1 written.22 \item \textcolor{gray}{1. Model basics: v1 written.} 23 23 24 \item Add namelist infrastructure as in NEMO doc24 \item \textcolor{gray}{Add namelist infrastructure as in NEMO doc (done)} 25 25 26 \item 2. Time, space and thickness space domain: to be written (Martin \& Clem, 2h)26 \item \textcolor{gray}{2. Time, space and thickness space domain} 27 27 28 28 \item 3. Ice dynamics: to be written (Clem \& Martin, 3h)
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