source: NEMO/trunk/doc/latex/SI3/subfiles/chap_domain.tex @ 11015

Last change on this file since 11015 was 11015, checked in by nicolasmartin, 17 months ago

Modification of the content to be in line with the NEMO manual
SI3 manual can now be build like the NEMO manual with ./manual_build.sh SI3

  • Mimick the directory organisation with main and subfiles folders.
  • Regarding the particular case of namelists
    • Remove the duplicates already contained in the global namelists folder at 1st level of ./doc
    • Keep the namelists sub-folder only for namdyn_adv & namsbc which already exist in ocean namelists
  • Rewriting of SI3_manual.tex with NEMO_manual.tex as template to easily highlight differences
  • Updating of several paths for figures/namelists inclusion or LaTeX files referencing
  • LaTeX source:
    • Replacement of \forfile command for namelists with pre-configured \nlst alias
    • " "" \bm with \mathbf (save installation of an extra package)
File size: 6.8 KB
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1
2\documentclass[../main/SI3_manual]{subfiles}
3
4\begin{document}
5
6% ================================================================
7% Chapter 2 Ñ Domain
8% ================================================================
9
10\chapter{Time, space and thickness space domain}
11\label{chap:DOM}
12\minitoc
13
14\newpage
15$\ $\newline    % force a new line
16
17Having defined the model equations in previous Chapter, we need now to choose the numerical discretization.  In the present chapter, we provide a general description of the SI$^3$ discretization strategy, in terms of time, space and thickness, which is considered as an extra independent variable.
18
19Sea ice state variables are typically expressed as:
20\begin{equation}
21X(ji,jj,\textcolor{gray}{jk},jl).
22\end{equation}
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.
24
25\section{Time domain}
26
27%--------------------------------------------------------------------------------------------------------------------
28%
29% FIG x : Time Stepping
30%
31\begin{figure}[ht]
32\begin{center}
33\vspace{0cm}
34\includegraphics[height=6cm,angle=-00]{time_stepping}
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
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.
43
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.
45
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 $X\_b$.
47
48\section{Spatial domain}
49
50%--------------------------------------------------------------------------------------------------------------------
51%
52% FIGx : Vertical grid
53%
54%
55\begin{figure}[!ht]
56\begin{center}
57\vspace{0cm}
58\includegraphics[height=10cm,angle=-00]{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%--------------------------------------------------------------------------------------------------------------------
64
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.
66
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}).
68
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.
70
71\nlst{nampar}
72
73\section{Thickness space domain}
74
75\nlst{namitd}
76
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 ($nampar$).
78
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:
80\begin{eqnarray} 
81hi\_max(jl) = \biggr ( \frac{jl \cdot (3\overline h + 1 )^{\alpha}}{ (jpl-jl)(3 \overline h + 1)^{\alpha} + jl }\biggr )^{\alpha^{-1}} - 1,
82\end{eqnarray}
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.
84
85%--------------------------------------------------------------------------------------------------------------------
86%
87% FIGx : Ice categories
88%
89%
90\begin{figure}[!ht]
91\begin{center}
92\vspace{0cm}
93\includegraphics[height=6cm,angle=-00]{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}
97%
98%--------------------------------------------------------------------------------------------------------------------
99
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).
101
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.
103
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.
105
106\end{document}
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