Ignore:
Timestamp:
2019-07-19T19:20:02+02:00 (14 months ago)
Author:
djlea
Message:

#2297 Updates to OBS and ASM documentation

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1 edited

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

    r11151 r11316  
    88\label{chap:ASM} 
    99 
    10 Authors: D. Lea,  M. Martin, K. Mogensen, A. Weaver, ...   % do we keep 
     10\minitoc 
    1111 
    12 \minitoc 
     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} 
    1321 
    1422\newpage 
    1523 
    1624The ASM code adds the functionality to apply increments to the model variables: temperature, salinity, 
    17 sea surface height, velocity and sea ice concentration.  
     25sea surface height, velocity and sea ice concentration. 
    1826These are read into the model from a NetCDF file which may be produced by separate data assimilation code. 
    1927The code can also output model background fields which are used as an input to data assimilation code. 
     
    5664Typically the increments are spread evenly over the full window. 
    5765In addition, two different weighting functions have been implemented. 
    58 The first function employs constant weights,  
     66The first function (namelist option \np{niaufn} = 0) employs constant weights, 
    5967\begin{align} 
    6068  \label{eq:F1_i} 
     
    6674    0     &    {\mathrm if} \; \; \; t_{i} > t_{n} 
    6775  \end{array} 
    68             \right.  
     76            \right. 
    6977\end{align} 
    7078where $M = m-n$. 
    71 The second function employs peaked hat-like weights in order to give maximum weight in the centre of the sub-window, 
     79The 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, 
    7280with the weighting reduced linearly to a small value at the window end-points: 
    7381\begin{align} 
     
    8391                                   \right. 
    8492\end{align} 
    85 where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even.  
     93where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 
    8694The weights described by \autoref{eq:F2_i} provide a smoother transition of the analysis trajectory from 
    8795one assimilation cycle to the next than that described by \autoref{eq:F1_i}. 
     
    92100\label{sec:ASM_div_dmp} 
    93101 
    94 The velocity increments may be initialized by the iterative application of a divergence damping operator. 
    95 In iteration step $n$ new estimates of velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by: 
     102It is quite challenging for data assimilation systems to provide non-divergent velocity increments. 
     103Applying divergent velocity increments will likely cause spurious vertical velocities in the model. This section describes a method to take velocity increments provided to \NEMO ($u^0_I$ and $v^0_I$) and adjust them by the iterative application of a divergence damping operator. The method is also described in \citet{dobricic.pinardi.ea_OS07}. 
     104 
     105In iteration step $n$ (starting at $n=1$) new estimates of velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by: 
     106 
    96107\begin{equation} 
    97108  \label{eq:asm_dmp} 
     
    105116  \right., 
    106117\end{equation} 
    107 where 
     118 
     119where the divergence is defined as 
     120 
    108121\[ 
    109122  % \label{eq:asm_div} 
     
    112125      +\delta_j \left[ {e_{1v}\,e_{3v}\,v^{n-1}_I} \right]} \right). 
    113126\] 
    114 By the application of \autoref{eq:asm_dmp} and \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 
     127 
     128By the application of \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 
    115129and the vorticity is left unchanged. 
    116130In the presence of coastal boundaries with zero velocity increments perpendicular to the coast 
     
    122136The divergence damping is activated by assigning to \np{nn\_divdmp} in the \textit{nam\_asminc} namelist 
    123137a value greater than zero. 
    124 By choosing this value to be of the order of 100 the increments in 
    125 the vertical velocity will be significantly reduced. 
     138This 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. 
    126139 
    127140 
     
    131144\label{sec:ASM_details} 
    132145 
    133 Here we show an example \ngn{namasm} namelist and the header of an example assimilation increments file on 
     146Here we show an example \ngn{nam\_asminc} namelist and the header of an example assimilation increments file on 
    134147the ORCA2 grid. 
    135148 
    136 %------------------------------------------namasm----------------------------------------------------- 
     149%------------------------------------------nam_asminc----------------------------------------------------- 
    137150% 
    138151\nlst{nam_asminc} 
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