Changeset 9983

2018-07-20T15:45:54+02:00 (2 years ago)

SI3 doc update

4 edited


  • NEMO/trunk/doc/si3_doc/tex_main/SI3_manual.bbl

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    1 \begin{thebibliography}{38} 
    111111  Geophysical Research}, \textbf{112}, C03S9, \doi{doi:10.1029/2005JC003355}. 
     113\bibitem[{Massonnet et~al.(2018)Massonnet, Barth\'el\'emy, Worou, Fichefet, 
     114  Vancoppenolle, and Rousset}]{Massonnetetal18b} 
     115Massonnet, 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 large-scale sea ice models. \textit{submitted}. 
    114120Maykut, G.~A., 1986: \textit{The Geophysics of Sea Ice}, NATO ASI Series. 
  • NEMO/trunk/doc/si3_doc/tex_main/SI3_manual.tex

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  • NEMO/trunk/doc/si3_doc/tex_sub/chap_domain.tex

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    1515$\ $\newline    % force a new line 
    16 Excel 
     17Having defined the model equations in previous Chapter, we need now to choose the numerical discretization.  In the present chapter, we provide a general description of the SI$^3$ discretization strategy, in terms of time, space and thickness, which is considered as an extra independent variable.  
     19Sea ice state variables are typically expressed as: 
     23$ji$ and $jj$ are x-y 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 vertically-resolved quantities (ice enthalpy and salinity). $jl=1, ..., jpl$ corresponds to the ice categories, discretizing thickness space. 
    1725\section{Time domain} 
    19 Time stepping. Dynamics then thermodynamics. nn\_fsbc. EVP subcycles.  
     29% FIG x : Time Stepping 
     35\caption{Schematic representation of time stepping in SI$^3$, assuming $nn\_fsbc=5$.} 
     42The 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. 
     44Ice 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 semi-implicit procedure. 
     46There 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 $X\_b$. 
    2148\section{Spatial domain} 
    23 Not much to say about domain. Handled by NEMO. C-grid. Scale factors. 
     52% FIGx : Vertical grid 
     59\caption{\footnotesize{Vertical grid of the model, used to resolve vertical temperature and salinity profiles}}\label{fig_dom_icelayers} 
    25 Vertical layers (nlay\_i, nlay\_s) 
     65The horizontal indices $ji$ and $jj$ are handled as for the ocean in NEMO, assuming C-grid discretization and in most cases a finite difference expression for scale factors. 
    27 \section{Thickness category boundaries} 
     67The 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 $nlay\_i$ equally-spaced layers. The number of snow layers can currently only be set to $nlay\_s=1$ (Fig. \ref{fig_dom_icelayers}). 
    29 [ jpl, nn\_virtual\_itd ] 
     69To 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. 
    31 2 formulations to describe 
    33 [ ln\_cat\_hfn (function), rn\_himean ] 
     73\section{Thickness space domain} 
    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. 
    39 Recall recommendations from Francois's, Antoine et al's paper. 
     77Thickness 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 ($nampar$). 
    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 %%-------------------------------------------------------------------------------------------------------------------- 
     79There 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 $jl=1, ..., jpl-1$ are: 
     81hi\_max(jl) = \biggr ( \frac{jl \cdot (3\overline h + 1 )^{\alpha}}{ (jpl-jl)(3 \overline h + 1)^{\alpha} + jl }\biggr )^{\alpha^{-1}} - 1, 
     83with $hi\_max(0)$=0 m and $\alpha = 0.05$. The last category has no upper boundary, so that it can contain arbitrarily thick ice. 
    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 
    58 %Each thickness category has a mean thickness $h^i_l$ ranging over $[H^*_{l-1}$, $H^*_{l}$]. $H^*_{0}=0$, while the other boundaries are typically chosen with greater resolution for thin ice. 
    60 %There are two options for discretization in $h$-space, illustrated in Fig. \ref{ice_cats}.  
     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} 
    62 %\textbf{1.} The tanh hyperbolic formulation from CICE. 
    63 %\begin{linenomath} 
    64 %\begin{align} 
    65 %H^*_l &= H^*_{l-1} + \frac{3}{L} + \frac{30}{L} \biggr [ 1 + tanh \biggr ( \frac{3l - 3 - 3L}{L} \biggr ) \biggr] \quad (l=1, ..., L-1). 
    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 home-made $1/h^\alpha$ 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, ..., L-1), 
    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}{(L-l)( 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 
     100The 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). 
     102The 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. 
     104With 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. 
  • NEMO/trunk/doc/si3_doc/tex_sub/todolist.tex

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    14 \item Documentation infrastructure ready by Jul 19, 2018. 
     14\item \textcolor{gray}{Documentation infrastructure ready by Jul 19, 2018.} 
    16 \item Abstract: v1 written. 
     16\item \textcolor{gray}{Abstract: v1 written.} 
    18 \item Disclaimer: v1 written. 
     18\item \textcolor{gray}{Disclaimer: v1 written.} 
    2020\item Introduction: list of chapters and change between realeases to be written (1h) 
    22 \item 1. Model basics: v1 written. 
     22\item \textcolor{gray}{1. Model basics: v1 written.} 
    24 \item Add namelist infrastructure as in NEMO doc 
     24\item \textcolor{gray}{Add namelist infrastructure as in NEMO doc (done)} 
    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} 
    2828\item 3. Ice dynamics: to be written (Clem \& Martin, 3h) 
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