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Changeset 11799 for NEMO/branches/2019/dev_r11470_HPC_12_mpi3/doc/latex/NEMO/subfiles/chap_ASM.tex – NEMO

Ignore:
Timestamp:
2019-10-25T16:27:34+02:00 (5 years ago)
Author:
mocavero
Message:

Update the branch to v4.0.1 of the trunk

Location:
NEMO/branches/2019/dev_r11470_HPC_12_mpi3/doc
Files:
5 edited

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  • NEMO/branches/2019/dev_r11470_HPC_12_mpi3/doc/latex/NEMO/subfiles/chap_ASM.tex

    r11435 r11799  
    22 
    33\begin{document} 
    4 % ================================================================ 
    5 % Chapter Assimilation increments (ASM) 
    6 % ================================================================ 
     4 
    75\chapter{Apply Assimilation Increments (ASM)} 
    86\label{chap:ASM} 
    97 
     8%    {\em 4.0} & {\em D. J. Lea} & {\em \NEMO\ 4.0 updates}  \\ 
     9%    {\em 3.4} & {\em D. J. Lea, M. Martin, K. Mogensen, A. Weaver} & {\em Initial version}  \\ 
     10 
     11\thispagestyle{plain} 
     12 
    1013\chaptertoc 
    1114 
    12 \vfill 
    13 \begin{figure}[b] 
    14 \subsubsection*{Changes record} 
    15 \begin{tabular}{l||l|m{0.65\linewidth}} 
    16     Release   & Author        & Modifications \\ 
    17     {\em 4.0} & {\em D. J. Lea} & {\em \NEMO\ 4.0 updates}  \\ 
    18     {\em 3.4} & {\em D. J. Lea, M. Martin, K. Mogensen, A. Weaver} & {\em Initial version}  \\ 
    19 \end{tabular} 
    20 \end{figure} 
     15\paragraph{Changes record} ~\\ 
    2116 
    22 \newpage 
     17{\footnotesize 
     18  \begin{tabularx}{\textwidth}{l||X|X} 
     19    Release & Author(s) & Modifications \\ 
     20    \hline 
     21    {\em   4.0} & {\em ...} & {\em ...} \\ 
     22    {\em   3.6} & {\em ...} & {\em ...} \\ 
     23    {\em   3.4} & {\em ...} & {\em ...} \\ 
     24    {\em <=3.4} & {\em ...} & {\em ...} 
     25  \end{tabularx} 
     26} 
     27 
     28\clearpage 
    2329 
    2430The ASM code adds the functionality to apply increments to the model variables: temperature, salinity, 
    … …  
    2632These are read into the model from a NetCDF file which may be produced by separate data assimilation code. 
    2733The code can also output model background fields which are used as an input to data assimilation code. 
    28 This is all controlled by the namelist \nam{\_asminc}. 
     34This is all controlled by the namelist \nam{_asminc}{\_asminc}. 
    2935There is a brief description of all the namelist options provided. 
    3036To build the ASM code \key{asminc} must be set. 
    3137 
    32 %=============================================================== 
    33  
     38%% ================================================================================================= 
    3439\section{Direct initialization} 
    3540\label{sec:ASM_DI} 
    … …  
    3742Direct initialization (DI) refers to the instantaneous correction of the model background state using 
    3843the analysis increment. 
    39 DI is used when \np{ln\_asmdin} is set to true. 
     44DI is used when \np{ln_asmdin}{ln\_asmdin} is set to true. 
    4045 
     46%% ================================================================================================= 
    4147\section{Incremental analysis updates} 
    4248\label{sec:ASM_IAU} 
    … …  
    4753This technique is referred to as Incremental Analysis Updates (IAU) \citep{bloom.takacs.ea_MWR96}. 
    4854IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI. 
    49 IAU is used when \np{ln\_asmiau} is set to true. 
     55IAU is used when \np{ln_asmiau}{ln\_asmiau} is set to true. 
    5056 
    5157With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$) 
    … …  
    5359additional tendency terms to the prognostic equations: 
    5460\begin{align*} 
    55   % \label{eq:wa_traj_iau} 
     61  % \label{eq:ASM_wa_traj_iau} 
    5662  {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a} 
    5763\end{align*} 
    … …  
    6470Typically the increments are spread evenly over the full window. 
    6571In addition, two different weighting functions have been implemented. 
    66 The first function (namelist option \np{niaufn} = 0) employs constant weights, 
     72The first function (namelist option \np{niaufn}{niaufn}=0) employs constant weights, 
    6773\begin{align} 
    68   \label{eq:F1_i} 
     74  \label{eq:ASM_F1_i} 
    6975  F^{(1)}_{i} 
    7076  =\left\{ 
    … …  
    7783\end{align} 
    7884where $M = m-n$. 
    79 The second function (namelist option \np{niaufn} = 1) employs peaked hat-like weights in order to give maximum weight in the centre of the sub-window, 
     85The second function (namelist option \np{niaufn}{niaufn}=1) employs peaked hat-like weights in order to give maximum weight in the centre of the sub-window, 
    8086with the weighting reduced linearly to a small value at the window end-points: 
    8187\begin{align} 
    82   \label{eq:F2_i} 
     88  \label{eq:ASM_F2_i} 
    8389  F^{(2)}_{i} 
    8490  =\left\{ 
    … …  
    9298\end{align} 
    9399where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 
    94 The weights described by \autoref{eq:F2_i} provide a smoother transition of the analysis trajectory from 
    95 one assimilation cycle to the next than that described by \autoref{eq:F1_i}. 
     100The weights described by \autoref{eq:ASM_F2_i} provide a smoother transition of the analysis trajectory from 
     101one assimilation cycle to the next than that described by \autoref{eq:ASM_F1_i}. 
    96102 
    97 %========================================================================== 
    98 % Divergence damping description %%% 
     103%% ================================================================================================= 
    99104\section{Divergence damping initialisation} 
    100105\label{sec:ASM_div_dmp} 
    … …  
    106111 
    107112\begin{equation} 
    108   \label{eq:asm_dmp} 
     113  \label{eq:ASM_dmp} 
    109114  \left\{ 
    110115    \begin{aligned} 
    … …  
    120125 
    121126\[ 
    122   % \label{eq:asm_div} 
     127  % \label{eq:ASM_div} 
    123128  \chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 
    124129  \left( {\delta_i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right] 
    … …  
    126131\] 
    127132 
    128 By the application of \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 
     133By the application of \autoref{eq:ASM_dmp} the divergence is filtered in each iteration, 
    129134and the vorticity is left unchanged. 
    130135In the presence of coastal boundaries with zero velocity increments perpendicular to the coast 
    … …  
    134139\citep{talagrand_JAS72, dobricic.pinardi.ea_OS07}. 
    135140Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. 
    136 The divergence damping is activated by assigning to \np{nn\_divdmp} in the \nam{\_asminc} namelist 
     141The divergence damping is activated by assigning to \np{nn_divdmp}{nn\_divdmp} in the \nam{_asminc}{\_asminc} namelist 
    137142a value greater than zero. 
    138143This specifies the number of iterations of the divergence damping. Setting a value of the order of 100 will result in a significant reduction in the vertical velocity induced by the increments. 
    139144 
    140  
    141 %========================================================================== 
    142  
     145%% ================================================================================================= 
    143146\section{Implementation details} 
    144147\label{sec:ASM_details} 
    145148 
    146 Here we show an example \nam{\_asminc} namelist and the header of an example assimilation increments file on 
     149Here we show an example \nam{_asminc}{\_asminc} namelist and the header of an example assimilation increments file on 
    147150the ORCA2 grid. 
    148151 
    149 %------------------------------------------nam_asminc----------------------------------------------------- 
    150 % 
    151 \nlst{nam_asminc} 
    152 %------------------------------------------------------------------------------------------------------------- 
     152\begin{listing} 
     153  \nlst{nam_asminc} 
     154  \caption{\forcode{&nam_asminc}} 
     155  \label{lst:nam_asminc} 
     156\end{listing} 
    153157 
    154158The header of an assimilation increments file produced using the NetCDF tool 
    … …  
    190194\end{clines} 
    191195 
    192 \biblio 
    193  
    194 \pindex 
     196\onlyinsubfile{\input{../../global/epilogue}} 
    195197 
    196198\end{document} 
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