Changeset 10406 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_OBS.tex

Timestamp:

2018-12-18T11:25:09+01:00 (5 years ago)

Author:

nicolasmartin

Message:

Edition of math environments

• Use LaTeX shortanted syntax for unnumbered equations (\[ ... \])
• Replace deprecated eqnarray with align environment (reference ​http://en.wikibooks.org/w/index.php?title=LaTeX/Advanced_Mathematics&#Other_environments)
• Remove some space before indices

Location:

NEMO/trunk/doc/latex

Files:

• . (modified) (1 prop)
• NEMO (modified) (1 prop)
• NEMO/subfiles (modified) (1 prop)
• NEMO/subfiles/chap_OBS.tex (modified) (8 diffs)

NEMO/trunk/doc/latex

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NEMO/trunk/doc/latex/NEMO

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NEMO/trunk/doc/latex/NEMO/subfiles

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

@@ -578 +578 @@
 All horizontal interpolation methods implemented in NEMO estimate the value of a model variable $x$ at point $P$ as
 a weighted linear combination of the values of the model variables at the grid points ${\rm A}$, ${\rm B}$ etc.:
-\begin{eqnarray}
+\begin{align}
 {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & 
 \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} + 
@@ -584 +584 @@
                    {w_{}}_{\rm C} {x_{}}_{\rm C} + 
                    {w_{}}_{\rm D} {x_{}}_{\rm D} \right)
-\end{eqnarray}
+\end{align}
 where ${w_{}}_{\rm A}$, ${w_{}}_{\rm B}$ etc. are the respective weights for the model field at
 points ${\rm A}$, ${\rm B}$ etc., and $w = {w_{}}_{\rm A} + {w_{}}_{\rm B} + {w_{}}_{\rm C} + {w_{}}_{\rm D}$.
@@ -597 +597 @@
   For example, the weight given to the field ${x_{}}_{\rm A}$ is specified as the product of the distances
   from ${\rm P}$ to the other points:
-  \begin{eqnarray}
+  \begin{align}
   {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D})
   \nonumber
-  \end{eqnarray}
+  \end{align}
   where 
-  \begin{eqnarray}
+  \begin{align}
    s\left ({\rm P}, {\rm M} \right ) 
      & \hspace{-2mm} = \hspace{-2mm} & 
@@ -610 +610 @@
                \cos ({\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P}) 
                    \right\}
-   \end{eqnarray}
+   \end{align}
    and $M$ corresponds to $B$, $C$ or $D$.
    A more stable form of the great-circle distance formula for small distances ($x$ near 1)
    involves the arcsine function ($e.g.$ see p.~101 of \citet{Daley_Barker_Bk01}:
-   \begin{eqnarray}
+   \begin{align}
    s\left( {\rm P}, {\rm M} \right) 
      & \hspace{-2mm} = \hspace{-2mm} & 
       \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
    \nonumber
-   \end{eqnarray}
+   \end{align}
    where
-   \begin{eqnarray}
+   \begin{align}
     x & \hspace{-2mm} = \hspace{-2mm} & 
       {a_{}}_{\rm M} {a_{}}_{\rm P} + {b_{}}_{\rm M} {b_{}}_{\rm P} + {c_{}}_{\rm M} {c_{}}_{\rm P}
    \nonumber
-   \end{eqnarray}
+   \end{align}
    and 
-   \begin{eqnarray}
+   \begin{align}
       {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, 
       \nonumber \\
@@ -641 +641 @@
       \nonumber
    \nonumber
-  \end{eqnarray}
+  \end{align}
 
 \item[2.] {\bf Great-Circle distance-weighted interpolation with small angle approximation.}
   Similar to the previous interpolation but with the distance $s$ computed as
-  \begin{eqnarray}
+  \begin{align}
     s\left( {\rm P}, {\rm M} \right) 
      & \hspace{-2mm} = \hspace{-2mm} & 
@@ -651 +651 @@
       + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2}
         \cos^{2} {\phi_{}}_{\rm M} }
-  \end{eqnarray}
+  \end{align}
   where $M$ corresponds to $A$, $B$, $C$ or $D$.
 
@@ -719 +719 @@
 denote the bottom left, bottom right, top left and top right corner points of the cell, respectively. 
 To determine if P is inside the cell, we verify that the cross-products 
-\begin{eqnarray}
+\begin{align}
 \begin{array}{lllll}
 {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC}
@@ -743 +743 @@
 \end{array}
 \label{eq:cross}
-\end{eqnarray}
+\end{align}
 point in the opposite direction to the unit normal $\widehat{\bf k}$
 (i.e., that the coefficients of $\widehat{\bf k}$ are negative),

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