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- 2010-11-01T15:21:01+01:00 (13 years ago)
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branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_ASM.tex
r2298 r2349 16 16 temperature, salinity, sea surface height, velocity and sea ice concentration. 17 17 These are read into the model from a file which may be produced by data assimilation. 18 This code is controlled by the namelist \ np{nam\_asminc}.18 This code is controlled by the namelist \textit{nam\_asminc}. 19 19 There is a brief description of all the namelist options provided. 20 To build the ASM code \ np{key\_asminc} must be set.20 To build the ASM code \key{asminc} must be set. 21 21 22 22 %=============================================================== 23 23 24 \subsection{Direct initialization} 24 \section{Direct initialization} 25 \label{ASM_DI} 25 26 26 Direct initialization refers to the instantaneous correction27 Direct initialization (DI) refers to the instantaneous correction 27 28 of the model background state using the analysis increment. 29 DI is used when \np{ln\_asmdin} is set to true. 28 30 29 \subsection{Incremental Analysis Updates} 31 \section{Incremental Analysis Updates} 32 \label{ASM_IAU} 30 33 31 34 Rather than updating the model state directly with the analysis increment, … … 34 37 is referred to as Incremental Analysis Updates (IAU) \citep{Bloom_al_MWR96}. 35 38 IAU is a common technique used with 3D assimilation methods such as 3D-Var or OI. 39 IAU is used when \np{ln\_asmiau} is set to true. 36 40 37 41 With IAU, the model state trajectory in the assimilation window … … 40 44 for temperature, salinity, horizontal velocity and SSH 41 45 as additional tendency terms to the prognostic equations: 42 \begin{eqnarray} 46 \begin{eqnarray} \label{eq:wa_traj_iau} 43 47 {\bf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\bf x}^{b}(t_{0})] 44 48 \; + \; F_{i} \delta \tilde{\bf x}^{a} 45 \label{eq:wa_traj_iau}46 49 \end{eqnarray} 47 50 where $F_{i}$ is a weighting function defined such that $\sum_{i=1}^{N} F_{i}=1$. … … 53 56 In addition, two different weighting functions have been implemented. 54 57 The first function employs constant weights, 55 \begin{eqnarray} 58 \begin{eqnarray} \label{eq:F1_i} 56 59 F^{(1)}_{i} 57 60 =\left\{ \begin{array}{ll} 58 0 & 59 {\rm if} \; \; \; t_{i} < t_{m} \\ 60 1/M & 61 {\rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\ 62 0 & 63 {\rm if} \; \; \; t_{i} > t_{n} 61 0 & {\rm if} \; \; \; t_{i} < t_{m} \\ 62 1/M & {\rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\ 63 0 & {\rm if} \; \; \; t_{i} > t_{n} 64 64 \end{array} \right. 65 \label{eq:F1_i}66 65 \end{eqnarray} 67 66 where $M = m-n$. … … 69 68 weight in the centre of the sub-window, with the weighting reduced 70 69 linearly to a small value at the window end-points. 71 \begin{eqnarray} 70 \begin{eqnarray} \label{eq:F2_i} 72 71 F^{(2)}_{i} 73 72 =\left\{ \begin{array}{ll} 74 0 & 75 {\rm if} \; \; \; t_{i} < t_{m} \\ 76 \alpha \, i & 77 {\rm if} \; \; \; t_{m} \leq t_{i} \leq t_{M/2} \\ 78 \alpha \, (M - i +1) & 79 {\rm if} \; \; \; t_{M/2} < t_{i} \leq t_{n} \\ 80 0 & 81 {\rm if} \; \; \; t_{i} > t_{n} 73 0 & {\rm if} \; \; \; t_{i} < t_{m} \\ 74 \alpha \, i & {\rm if} \; \; \; t_{m} \leq t_{i} \leq t_{M/2} \\ 75 \alpha \, (M - i +1) & {\rm if} \; \; \; t_{M/2} < t_{i} \leq t_{n} \\ 76 0 & {\rm if} \; \; \; t_{i} > t_{n} 82 77 \end{array} \right. 83 \label{eq:F2_i}84 78 \end{eqnarray} 85 79 where $\alpha^{-1} = \sum_{i=1}^{M/2} 2i$ and $M$ is assumed to be even. 86 The weights described by Eq.~(\ref{eq:F2_i})provide a80 The weights described by \eqref{eq:F2_i} provide a 87 81 smoother transition of the analysis trajectory from one assimilation cycle 88 to the next than that described by Eq.~(\ref{eq:F1_i}).82 to the next than that described by \eqref{eq:F1_i}. 89 83 90 84 %========================================================================== … … 100 94 %------------------------------------------------------------------------------------------------------------- 101 95 102 \subsection{Assimilation increments file} 103 104 The header of an assimilation increments file produced using \np{ncdump -h} is shown below 96 The header of an assimilation increments file produced using \textit{ncdump~-h} is shown below 105 97 106 98 \begin{alltt}
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