Changeset 11151 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex

Timestamp:

2019-06-20T14:59:58+02:00 (5 years ago)

Author:

nicolasmartin

Message:

New version of NEMO_manual.tex
New class scrreport for the document (KOMA-script version of default report)
Foreword is now placed before ToC.
All figures are configured with 1.0\textwidth as default.
For compatibilty, \frontmatter, \mainmatter and \backmatter cmds have been removed and old fonts in LaTeX subfiles have been replaced

• \bf -> \mathbf or \bfseries
• \it -> \itshape
• \rm -> \mathrm or \rmfamily
• \tt -> \ttfamily

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/chap_ASM.tex (modified) (3 diffs)

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

@@ -41 +41 @@
 IAU is used when \np{ln\_asmiau} is set to true.
 
-With IAU, the model state trajectory ${\bf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$)
+With IAU, the model state trajectory ${\mathbf x}$ in the assimilation window ($t_{0} \leq t_{i} \leq t_{N}$)
 is corrected by adding the analysis increments for temperature, salinity, horizontal velocity and SSH as
 additional tendency terms to the prognostic equations:
 \begin{align*}
   % \label{eq:wa_traj_iau}
-  {\bf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\bf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\bf x}^{a}
+  {\mathbf x}^{a}(t_{i}) = M(t_{i}, t_{0})[{\mathbf x}^{b}(t_{0})] \; + \; F_{i} \delta \tilde{\mathbf x}^{a}
 \end{align*}
-where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\bf x}^{a}$ defined such that
+where $F_{i}$ is a weighting function for applying the increments $\delta\tilde{\mathbf x}^{a}$ defined such that
 $\sum_{i=1}^{N} F_{i}=1$.
-${\bf x}^b$ denotes the model initial state and ${\bf x}^a$ is the model state after the increments are applied.
+${\mathbf x}^b$ denotes the model initial state and ${\mathbf x}^a$ is the model state after the increments are applied.
 To control the adjustment time of the model to the increment,
 the increment can be applied over an arbitrary sub-window, $t_{m} \leq t_{i} \leq t_{n}$,
@@ -62 +62 @@
   =\left\{
   \begin{array}{ll}
-    0     &    {\rm if} \; \; \; t_{i} < t_{m}                \\
-    1/M &    {\rm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\
-    0     &    {\rm if} \; \; \; t_{i} > t_{n}
+    0     &    {\mathrm if} \; \; \; t_{i} < t_{m}                \\
+    1/M &    {\mathrm if} \; \; \; t_{m} < t_{i} \leq t_{n} \\
+    0     &    {\mathrm if} \; \; \; t_{i} > t_{n}
   \end{array}
             \right. 
@@ -76 +76 @@
   =\left\{
   \begin{array}{ll}
-    0                           &    {\rm if} \; \; \; t_{i}       <     t_{m}                        \\
-    \alpha \, i               &    {\rm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\
-    \alpha \, (M - i +1) &    {\rm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\
-    0                            &   {\rm if} \; \; \; t_{i}        >    t_{n}
+    0                           &    {\mathrm if} \; \; \; t_{i}       <     t_{m}                        \\
+    \alpha \, i               &    {\mathrm if} \; \; \; t_{m}    \leq t_{i}    \leq   t_{M/2}   \\
+    \alpha \, (M - i +1) &    {\mathrm if} \; \; \; t_{M/2}  <    t_{i}    \leq   t_{n}       \\
+    0                            &   {\mathrm if} \; \; \; t_{i}        >    t_{n}
   \end{array}
                                    \right.