Changeset 10419 for NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex/NEMO/subfiles/chap_OBS.tex

Timestamp:

2018-12-19T20:46:30+01:00 (5 years ago)

Author:

smasson

Message:

dev_r10164_HPC09_ESIWACE_PREP_MERGE: merge with trunk@10418, see #2133

Location:

NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex

Files:

• . (modified) (1 prop)
• NEMO (modified) (1 prop)
• NEMO/subfiles (modified) (1 prop)
• NEMO/subfiles/chap_OBS.tex (modified) (13 diffs)

NEMO/branches/2018/dev_r10164_HPC09_ESIWACE_PREP_MERGE/doc/latex/NEMO/subfiles/chap_OBS.tex

@@ -1 @@
-\documentclass[../tex_main/NEMO_manual]{subfiles}
+\documentclass[../main/NEMO_manual]{subfiles}
+
 \begin{document}
 % ================================================================
@@ -11 +12 @@
 \minitoc
 
-
 \newpage
-$\ $\newline    % force a new line
 
 The observation and model comparison code (OBS) reads in observation files
@@ -573 +572 @@
 
 \subsubsection{Horizontal interpolation}
+
 Consider an observation point ${\rm P}$ with with longitude and latitude $({\lambda_{}}_{\rm P}, \phi_{\rm P})$ and
 the four nearest neighbouring model grid points ${\rm A}$, ${\rm B}$, ${\rm C}$ and ${\rm D}$ with
@@ -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}
-{x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & 
-\frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} + 
-                   {w_{}}_{\rm B} {x_{}}_{\rm B} + 
-                   {w_{}}_{\rm C} {x_{}}_{\rm C} + 
-                   {w_{}}_{\rm D} {x_{}}_{\rm D} \right)
-\end{eqnarray}
+\begin{align*}
+  {x_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} &
+                                                   \frac{1}{w} \left( {w_{}}_{\rm A} {x_{}}_{\rm A} +
+                                                   {w_{}}_{\rm B} {x_{}}_{\rm B} +
+                                                   {w_{}}_{\rm C} {x_{}}_{\rm C} +
+                                                   {w_{}}_{\rm D} {x_{}}_{\rm D} \right)
+\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}
-  {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D})
-  \nonumber
-  \end{eqnarray}
+  \begin{align*}
+    {w_{}}_{\rm A} = s({\rm P}, {\rm B}) \, s({\rm P}, {\rm C}) \, s({\rm P}, {\rm D})
+  \end{align*}
   where 
-  \begin{eqnarray}
-   s\left ({\rm P}, {\rm M} \right ) 
+  \begin{align*}
+    s\left ({\rm P}, {\rm M} \right ) 
      & \hspace{-2mm} = \hspace{-2mm} & 
       \cos^{-1} \! \left\{ 
@@ -610 +609 @@
                \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}
-   s\left( {\rm P}, {\rm M} \right) 
-     & \hspace{-2mm} = \hspace{-2mm} & 
-      \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
-   \nonumber
-   \end{eqnarray}
+   \begin{align*}
+     s\left( {\rm P}, {\rm M} \right) & \hspace{-2mm} = \hspace{-2mm} & \sin^{-1} \! \left\{ \sqrt{ 1 - x^2 } \right\}
+   \end{align*}
    where
-   \begin{eqnarray}
-    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}
+   \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}
+   \end{align*}
    and 
-   \begin{eqnarray}
-      {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, 
-      \nonumber \\
-      {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, 
-      \nonumber \\
-      {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, 
-      \nonumber \\
-      {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, 
-      \nonumber \\
-      {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, 
-      \nonumber \\
+   \begin{align*}
+      {a_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm M}, \\
+      {a_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \sin {\phi_{}}_{\rm P}, \\
+      {b_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \cos {\phi_{}}_{\rm M}, \\
+      {b_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \cos {\phi_{}}_{\rm P}, \\
+      {c_{}}_{\rm M} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm M} \sin {\phi_{}}_{\rm M}, \\
       {c_{}}_{\rm P} & \hspace{-2mm} = \hspace{-2mm} & \cos {\phi_{}}_{\rm P} \sin {\phi_{}}_{\rm P}.
-      \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}
-    s\left( {\rm P}, {\rm M} \right) 
-     & \hspace{-2mm} = \hspace{-2mm} & 
-      \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2} 
-      + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2}
-        \cos^{2} {\phi_{}}_{\rm M} }
-  \end{eqnarray}
+  \begin{align*}
+    s\left( {\rm P}, {\rm M} \right)
+    & \hspace{-2mm} = \hspace{-2mm} &
+                                      \sqrt{ \left( {\phi_{}}_{\rm M} - {\phi_{}}_{\rm P} \right)^{2}
+                                      + \left( {\lambda_{}}_{\rm M} - {\lambda_{}}_{\rm P} \right)^{2}
+                                      \cos^{2} {\phi_{}}_{\rm M} }
+  \end{align*}
   where $M$ corresponds to $A$, $B$, $C$ or $D$.
 
@@ -688 +676 @@
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}      \begin{center}
-\includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rec}
-\caption{      \protect\label{fig:obsavgrec}
-  Weights associated with each model grid box (blue lines and numbers)
-  for an observation at -170.5E, 56.0N with a rectangular footprint of 1\deg x 1\deg.}
-\end{center}      \end{figure}
+\begin{figure}
+  \begin{center}
+    \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rec}
+    \caption{
+      \protect\label{fig:obsavgrec}
+      Weights associated with each model grid box (blue lines and numbers)
+      for an observation at -170.5E, 56.0N with a rectangular footprint of 1\deg x 1\deg.
+    }
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}      \begin{center}
-\includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rad}
-\caption{      \protect\label{fig:obsavgrad}
-  Weights associated with each model grid box (blue lines and numbers)
-  for an observation at -170.5E, 56.0N with a radial footprint with diameter 1\deg.} 
-\end{center}      \end{figure}
+\begin{figure}
+  \begin{center}
+    \includegraphics[width=0.90\textwidth]{Fig_OBS_avg_rad}
+    \caption{
+      \protect\label{fig:obsavgrad}
+      Weights associated with each model grid box (blue lines and numbers)
+      for an observation at -170.5E, 56.0N with a radial footprint with diameter 1\deg.
+    } 
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
@@ -719 +715 @@
 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{array}{lllll}
-{{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC}
-& = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )
-    - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
-{{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA}
-& = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )
-    - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
-{{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD}
-& = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm D}   \; -\; {\phi_{}}_{\rm P} )
-    - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
-{{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB}
-& = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )
-    - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
-      ({\phi_{}}_{\rm D}  \;  - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
-\end{array}
-\label{eq:cross}
-\end{eqnarray}
+\begin{align*}
+  \begin{array}{lllll}
+    {{\bf r}_{}}_{\rm PA} \times {{\bf r}_{}}_{\rm PC}
+    & = & [({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )
+          - ({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
+    {{\bf r}_{}}_{\rm PB} \times {{\bf r}_{}}_{\rm PA}
+    & = & [({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm A}   \; -\; {\phi_{}}_{\rm P} )
+          - ({\lambda_{}}_{\rm A}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
+    {{\bf r}_{}}_{\rm PC} \times {{\bf r}_{}}_{\rm PD}
+    & = & [({\lambda_{}}_{\rm C}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm D}   \; -\; {\phi_{}}_{\rm P} )
+          - ({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm C}   \; -\; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
+    {{\bf r}_{}}_{\rm PD} \times {{\bf r}_{}}_{\rm PB}
+    & = & [({\lambda_{}}_{\rm D}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm B}   \; -\; {\phi_{}}_{\rm P} )
+          - ({\lambda_{}}_{\rm B}\; -\; {\lambda_{}}_{\rm P} )
+          ({\phi_{}}_{\rm D}  \;  - \; {\phi_{}}_{\rm P} )] \; \widehat{\bf k} \\
+  \end{array}
+  % \label{eq:cross}
+\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),
@@ -774 +770 @@
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}      \begin{center}
-\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local}
-\caption{      \protect\label{fig:obslocal}
-  Example of the distribution of observations with the geographical distribution of observational data.} 
-\end{center}      \end{figure}
+\begin{figure}
+  \begin{center}
+    \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_local}
+    \caption{
+      \protect\label{fig:obslocal}
+      Example of the distribution of observations with the geographical distribution of observational data.
+    }
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
@@ -799 +799 @@
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}     \begin{center}
-\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global}
-\caption{      \protect\label{fig:obsglobal}
-  Example of the distribution of observations with the round-robin distribution of observational data.}
-\end{center}     \end{figure}
+\begin{figure}
+  \begin{center}
+    \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_ASM_obsdist_global}
+    \caption{
+      \protect\label{fig:obsglobal}
+      Example of the distribution of observations with the round-robin distribution of observational data.
+    }
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
@@ -1153 +1157 @@
 This technique has not been used before so experimentation is needed before results can be trusted.
 
-
-
-
 \newpage
 
@@ -1367 +1368 @@
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}     \begin{center}
-%\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main}
-\includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main}
-\caption{      \protect\label{fig:obsdataplotmain}
-  Main window of dataplot.}
-\end{center}     \end{figure}
+\begin{figure}
+  \begin{center}
+    % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_main}
+    \includegraphics[width=9cm,angle=-90.]{Fig_OBS_dataplot_main}
+    \caption{
+      \protect\label{fig:obsdataplotmain}
+      Main window of dataplot.
+    }
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
@@ -1379 +1384 @@
 
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
-\begin{figure}     \begin{center}
-%\includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof}
-\includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof}
-\caption{      \protect\label{fig:obsdataplotprofile}
-  Profile plot from dataplot produced by right clicking on a point in the main window.}
-\end{center}     \end{figure}
+\begin{figure}
+  \begin{center}
+    % \includegraphics[width=10cm,height=12cm,angle=-90.]{Fig_OBS_dataplot_prof}
+    \includegraphics[width=7cm,angle=-90.]{Fig_OBS_dataplot_prof}
+    \caption{
+      \protect\label{fig:obsdataplotprofile}
+      Profile plot from dataplot produced by right clicking on a point in the main window.
+    }
+  \end{center}
+\end{figure}
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 
-
-
+\biblio
 
 \end{document}