Changeset 11543 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex
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- 2019-09-13T15:57:52+02:00 (5 years ago)
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NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex
r11537 r11543 53 53 additional tendency terms to the prognostic equations: 54 54 \begin{align*} 55 % \label{eq: wa_traj_iau}55 % \label{eq:ASM_wa_traj_iau} 56 56 {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a} 57 57 \end{align*} … … 66 66 The first function (namelist option \np{niaufn}=0) employs constant weights, 67 67 \begin{align} 68 \label{eq: F1_i}68 \label{eq:ASM_F1_i} 69 69 F^{(1)}_{i} 70 70 =\left\{ … … 80 80 with the weighting reduced linearly to a small value at the window end-points: 81 81 \begin{align} 82 \label{eq: F2_i}82 \label{eq:ASM_F2_i} 83 83 F^{(2)}_{i} 84 84 =\left\{ … … 92 92 \end{align} 93 93 where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 94 The weights described by \autoref{eq: F2_i} provide a smoother transition of the analysis trajectory from95 one assimilation cycle to the next than that described by \autoref{eq: F1_i}.94 The weights described by \autoref{eq:ASM_F2_i} provide a smoother transition of the analysis trajectory from 95 one assimilation cycle to the next than that described by \autoref{eq:ASM_F1_i}. 96 96 97 97 %========================================================================== … … 106 106 107 107 \begin{equation} 108 \label{eq: asm_dmp}108 \label{eq:ASM_dmp} 109 109 \left\{ 110 110 \begin{aligned} … … 120 120 121 121 \[ 122 % \label{eq: asm_div}122 % \label{eq:ASM_div} 123 123 \chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 124 124 \left( {\delta_i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right] … … 126 126 \] 127 127 128 By the application of \autoref{eq: asm_dmp} the divergence is filtered in each iteration,128 By the application of \autoref{eq:ASM_dmp} the divergence is filtered in each iteration, 129 129 and the vorticity is left unchanged. 130 130 In the presence of coastal boundaries with zero velocity increments perpendicular to the coast
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