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2 | \documentclass[../../tex_main/NEMO_manual]{subfiles} |
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3 | |
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4 | \begin{document} |
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5 | |
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6 | % ================================================================ |
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7 | % Chapter 2 Ñ Domain |
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8 | % ================================================================ |
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9 | |
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10 | \chapter{Time, space and thickness space domain} |
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11 | \label{chap:DOM} |
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12 | \minitoc |
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13 | |
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14 | \newpage |
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15 | $\ $\newline % force a new line |
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16 | Excel |
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17 | \section{Time domain} |
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18 | |
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19 | Time stepping. Dynamics then thermodynamics. nn\_fsbc. EVP subcycles. |
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20 | |
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21 | \section{Spatial domain} |
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22 | |
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23 | Not much to say about domain. Handled by NEMO. C-grid. Scale factors. |
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24 | |
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25 | Vertical layers (nlay\_i, nlay\_s) |
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26 | |
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27 | \section{Thickness category boundaries} |
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28 | |
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29 | [ jpl, nn\_virtual\_itd ] |
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30 | |
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31 | 2 formulations to describe |
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32 | |
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33 | [ ln\_cat\_hfn (function), rn\_himean ] |
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34 | |
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35 | ln\_cat\_usr (user defined), rn\_catbnd, rn\_himin |
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36 | Categories: boundary definitions. |
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37 | See doc 2.0, there are commented bits of text in the tex file. |
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38 | |
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39 | Recall recommendations from Francois's, Antoine et al's paper. |
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40 | |
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41 | %%-------------------------------------------------------------------------------------------------------------------- |
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42 | %% |
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43 | %% FIGx : Ice categories |
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44 | %% |
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45 | %% |
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46 | %\begin{figure}[ht] |
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47 | %\begin{center} |
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48 | %\vspace{0cm} |
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49 | %\includegraphics[height=6cm,angle=-00]{./Figures/ice_cats_new.eps} |
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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} |
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51 | %\end{center} |
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52 | %\end{figure} |
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53 | %% |
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54 | %%-------------------------------------------------------------------------------------------------------------------- |
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55 | % |
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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. |
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57 | % |
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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. |
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59 | % |
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60 | %There are two options for discretization in $h$-space, illustrated in Fig. \ref{ice_cats}. |
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61 | % |
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62 | %\textbf{1.} The tanh hyperbolic formulation from CICE. |
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63 | %\begin{linenomath} |
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64 | %\begin{align} |
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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). |
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66 | %\end{align} |
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67 | %\label{eq_301} |
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68 | %\end{linenomath} |
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69 | %The upper boundary $H^*_L$ is set to a very high value (99.). |
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70 | % |
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71 | %\textbf{2.} An adjustable home-made $1/h^\alpha$ formulation. |
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72 | % |
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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: |
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74 | %\begin{eqnarray} |
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75 | %f_l & = & f_0 - l \Delta f \qquad (l = 2, ..., L-1), |
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76 | %\label{eq_fl} |
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77 | %\end{eqnarray} |
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78 | %where $\Delta f = \frac{f_0 - f_L}{L}$. |
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79 | % |
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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: |
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81 | %\begin{eqnarray} |
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82 | %H^*_l = \left ( \frac{ L ( H^*_L + 1 ) ^\alpha}{(L-l)( H^*_L + 1 ) ^\alpha + l} \right ) ^{1/\alpha} - 1 |
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83 | %\end{eqnarray} |
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84 | %\label{intro} |
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85 | %There are two parameters to tune: $\overline h$ and $\alpha$ (typically 0.05, used for Fig. \ref{ice_cats}). |
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86 | % |
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87 | %Each ice category has its own set of global state variables |
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88 | |
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89 | \end{document} |
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