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- 2019-12-10T15:03:24+01:00 (4 years ago)
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old new 1 *.aux 2 *.bbl 3 *.blg 4 *.dvi 5 *.fdb* 6 *.fls 7 *.idx 1 *.ind 8 2 *.ilg 9 *.ind10 *.log11 *.maf12 *.mtc*13 *.out14 *.pdf15 *.toc16 _minted-*
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NEMO/branches/2019/ENHANCE-03_closea/doc/latex/NEMO/subfiles/chap_ASM.tex
r11151 r12149 2 2 3 3 \begin{document} 4 % ================================================================ 5 % Chapter Assimilation increments (ASM) 6 % ================================================================ 4 7 5 \chapter{Apply Assimilation Increments (ASM)} 8 6 \label{chap:ASM} 9 7 10 Authors: D. Lea, M. Martin, K. Mogensen, A. Weaver, ... % do we keep 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} \\ 11 10 12 \ minitoc11 \thispagestyle{plain} 13 12 14 \newpage 13 \chaptertoc 14 15 \paragraph{Changes record} ~\\ 16 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 15 29 16 30 The ASM code adds the functionality to apply increments to the model variables: temperature, salinity, 17 sea surface height, velocity and sea ice concentration. 31 sea surface height, velocity and sea ice concentration. 18 32 These are read into the model from a NetCDF file which may be produced by separate data assimilation code. 19 33 The code can also output model background fields which are used as an input to data assimilation code. 20 This is all controlled by the namelist \ textit{\ngn{nam\_asminc}}.34 This is all controlled by the namelist \nam{_asminc}{\_asminc}. 21 35 There is a brief description of all the namelist options provided. 22 36 To build the ASM code \key{asminc} must be set. 23 37 24 %=============================================================== 25 38 %% ================================================================================================= 26 39 \section{Direct initialization} 27 40 \label{sec:ASM_DI} … … 29 42 Direct initialization (DI) refers to the instantaneous correction of the model background state using 30 43 the analysis increment. 31 DI is used when \np{ln \_asmdin} is set to true.44 DI is used when \np{ln_asmdin}{ln\_asmdin} is set to true. 32 45 46 %% ================================================================================================= 33 47 \section{Incremental analysis updates} 34 48 \label{sec:ASM_IAU} … … 39 53 This technique is referred to as Incremental Analysis Updates (IAU) \citep{bloom.takacs.ea_MWR96}. 40 54 IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI. 41 IAU is used when \np{ln \_asmiau} is set to true.55 IAU is used when \np{ln_asmiau}{ln\_asmiau} is set to true. 42 56 43 57 With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$) … … 45 59 additional tendency terms to the prognostic equations: 46 60 \begin{align*} 47 % \label{eq: wa_traj_iau}61 % \label{eq:ASM_wa_traj_iau} 48 62 {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a} 49 63 \end{align*} … … 56 70 Typically the increments are spread evenly over the full window. 57 71 In addition, two different weighting functions have been implemented. 58 The first function employs constant weights,72 The first function (namelist option \np{niaufn}{niaufn}=0) employs constant weights, 59 73 \begin{align} 60 \label{eq: F1_i}74 \label{eq:ASM_F1_i} 61 75 F^{(1)}_{i} 62 76 =\left\{ … … 66 80 0 & {\mathrm if} \; \; \; t_{i} > t_{n} 67 81 \end{array} 68 \right. 82 \right. 69 83 \end{align} 70 84 where $M = m-n$. 71 The second function employs peaked hat-like weights in order to give maximum weight in the centre of the sub-window,85 The 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, 72 86 with the weighting reduced linearly to a small value at the window end-points: 73 87 \begin{align} 74 \label{eq: F2_i}88 \label{eq:ASM_F2_i} 75 89 F^{(2)}_{i} 76 90 =\left\{ … … 83 97 \right. 84 98 \end{align} 85 where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 86 The weights described by \autoref{eq: F2_i} provide a smoother transition of the analysis trajectory from87 one assimilation cycle to the next than that described by \autoref{eq: F1_i}.99 where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 100 The weights described by \autoref{eq:ASM_F2_i} provide a smoother transition of the analysis trajectory from 101 one assimilation cycle to the next than that described by \autoref{eq:ASM_F1_i}. 88 102 89 %========================================================================== 90 % Divergence damping description %%% 103 %% ================================================================================================= 91 104 \section{Divergence damping initialisation} 92 105 \label{sec:ASM_div_dmp} 93 106 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: 107 It is quite challenging for data assimilation systems to provide non-divergent velocity increments. 108 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}. 109 110 In iteration step $n$ (starting at $n=1$) new estimates of velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by: 111 96 112 \begin{equation} 97 \label{eq: asm_dmp}113 \label{eq:ASM_dmp} 98 114 \left\{ 99 115 \begin{aligned} … … 105 121 \right., 106 122 \end{equation} 107 where 123 124 where the divergence is defined as 125 108 126 \[ 109 % \label{eq: asm_div}127 % \label{eq:ASM_div} 110 128 \chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 111 129 \left( {\delta_i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right] 112 130 +\delta_j \left[ {e_{1v}\,e_{3v}\,v^{n-1}_I} \right]} \right). 113 131 \] 114 By the application of \autoref{eq:asm_dmp} and \autoref{eq:asm_dmp} the divergence is filtered in each iteration, 132 133 By the application of \autoref{eq:ASM_dmp} the divergence is filtered in each iteration, 115 134 and the vorticity is left unchanged. 116 135 In the presence of coastal boundaries with zero velocity increments perpendicular to the coast … … 120 139 \citep{talagrand_JAS72, dobricic.pinardi.ea_OS07}. 121 140 Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. 122 The divergence damping is activated by assigning to \np{nn \_divdmp} in the \textit{nam\_asminc} namelist141 The divergence damping is activated by assigning to \np{nn_divdmp}{nn\_divdmp} in the \nam{_asminc}{\_asminc} namelist 123 142 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. 143 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. 126 144 127 128 %========================================================================== 129 145 %% ================================================================================================= 130 146 \section{Implementation details} 131 147 \label{sec:ASM_details} 132 148 133 Here we show an example \n gn{namasm} namelist and the header of an example assimilation increments file on149 Here we show an example \nam{_asminc}{\_asminc} namelist and the header of an example assimilation increments file on 134 150 the ORCA2 grid. 135 151 136 %------------------------------------------namasm----------------------------------------------------- 137 % 138 \nlst{nam_asminc} 139 %------------------------------------------------------------------------------------------------------------- 152 \begin{listing} 153 \nlst{nam_asminc} 154 \caption{\forcode{&nam_asminc}} 155 \label{lst:nam_asminc} 156 \end{listing} 140 157 141 158 The header of an assimilation increments file produced using the NetCDF tool … … 177 194 \end{clines} 178 195 179 \biblio 180 181 \pindex 196 \subinc{\input{../../global/epilogue}} 182 197 183 198 \end{document}
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