Changeset 11316 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex
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 20190719T19:20:02+02:00 (14 months ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex
r11151 r11316 8 8 \label{chap:ASM} 9 9 10 Authors: D. Lea, M. Martin, K. Mogensen, A. Weaver, ... % do we keep 10 \minitoc 11 11 12 \minitoc 12 \vfill 13 \begin{figure}[b] 14 \subsubsection*{Changes record} 15 \begin{tabular}{llm{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} 13 21 14 22 \newpage 15 23 16 24 The ASM code adds the functionality to apply increments to the model variables: temperature, salinity, 17 sea surface height, velocity and sea ice concentration. 25 sea surface height, velocity and sea ice concentration. 18 26 These are read into the model from a NetCDF file which may be produced by separate data assimilation code. 19 27 The code can also output model background fields which are used as an input to data assimilation code. … … 56 64 Typically the increments are spread evenly over the full window. 57 65 In addition, two different weighting functions have been implemented. 58 The first function employs constant weights,66 The first function (namelist option \np{niaufn} = 0) employs constant weights, 59 67 \begin{align} 60 68 \label{eq:F1_i} … … 66 74 0 & {\mathrm if} \; \; \; t_{i} > t_{n} 67 75 \end{array} 68 \right. 76 \right. 69 77 \end{align} 70 78 where $M = mn$. 71 The second function employs peaked hatlike weights in order to give maximum weight in the centre of the subwindow,79 The second function (namelist option \np{niaufn} = 1) employs peaked hatlike weights in order to give maximum weight in the centre of the subwindow, 72 80 with the weighting reduced linearly to a small value at the window endpoints: 73 81 \begin{align} … … 83 91 \right. 84 92 \end{align} 85 where $\alpha^{1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 93 where $\alpha^{1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 86 94 The weights described by \autoref{eq:F2_i} provide a smoother transition of the analysis trajectory from 87 95 one assimilation cycle to the next than that described by \autoref{eq:F1_i}. … … 92 100 \label{sec:ASM_div_dmp} 93 101 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: 102 It is quite challenging for data assimilation systems to provide nondivergent velocity increments. 103 Applying 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}. 104 105 In iteration step $n$ (starting at $n=1$) new estimates of velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by: 106 96 107 \begin{equation} 97 108 \label{eq:asm_dmp} … … 105 116 \right., 106 117 \end{equation} 107 where 118 119 where the divergence is defined as 120 108 121 \[ 109 122 % \label{eq:asm_div} … … 112 125 +\delta_j \left[ {e_{1v}\,e_{3v}\,v^{n1}_I} \right]} \right). 113 126 \] 114 By the application of \autoref{eq:asm_dmp} and \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 127 128 By the application of \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 115 129 and the vorticity is left unchanged. 116 130 In the presence of coastal boundaries with zero velocity increments perpendicular to the coast … … 122 136 The divergence damping is activated by assigning to \np{nn\_divdmp} in the \textit{nam\_asminc} namelist 123 137 a 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. 138 This 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. 126 139 127 140 … … 131 144 \label{sec:ASM_details} 132 145 133 Here we show an example \ngn{nam asm} namelist and the header of an example assimilation increments file on146 Here we show an example \ngn{nam\_asminc} namelist and the header of an example assimilation increments file on 134 147 the ORCA2 grid. 135 148 136 %nam asm149 %nam_asminc 137 150 % 138 151 \nlst{nam_asminc}
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