--- manual/s_ecco/text/ecco_costfunction.tex	2005/07/14 21:02:29	1.5
+++ manual/s_ecco/text/ecco_costfunction.tex	2010/08/30 23:09:19	1.8
@@ -4,6 +4,8 @@
 <!-- CMIREDIR:ecco_cost: -->
 \end{rawhtml}
 
+Author: Patrick Heimbach
+
 The current ECCO state estimation covers an $nYears = 11$ year
 model trajectory.
 A variety of data sets enter a least squares cost function,
@@ -35,7 +37,7 @@
 \subsubsection{Input fields}
 ~
 
-\begin{table}[h!]
+\begin{table}[!ht]
 \begin{center}
 \begin{tabular}{lllc}
 \hline \hline
@@ -74,12 +76,12 @@
 Compute global offset between $nYears$ model and T/P mean:
 %
 \begin{equation}
-\begin{split}
+\begin{aligned}
 offset & = \, \overline{tpmean} \, - \, \overline{psmean} \\
 ~ & = \, \frac{1}{normaliz.} \sum_{i,j}
 \left\{ tpmean(i,j) \, - \, psmean(i,j) \right\} 
 \cdot cosphi(i,j) \cdot tpmeanmask(i,j)
-\end{split}
+\end{aligned}
 \end{equation}
 %
 \item
@@ -88,14 +90,14 @@
 First spatial distribution:
 %
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_ssh\_mean(i,j) & = \,
 \frac{1}{wp^2} \left\{ \,
 \left[ \, psmean(i,j) - \overline{psmean} \, \right] \, - \,
 \left[ \, tpmean(i,j) - \overline{tpmean} \, \right] \, \right\}^2 \\ 
 ~ & = \, \frac{1}{wp^2} \left\{ \,
 psmean(i,j) \, - \, tpmean(i,j) \, + \, offset \, \right\}^2
-\end{split}
+\end{aligned}
 \end{equation}
 
 %
@@ -120,12 +122,12 @@
 Compute difference in anomalies:
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_ssh\_anom(i,j,t) & = \, \frac{1}{wtp^2} \left\{ \, 
 \left[ \, psbar(i,j,t) - psmean(i,j) \, \right] \, - \, 
 \left[ \, tpobs(i,j,t) \, \right] \,
 \right\}^2
-\end{split}
+\end{aligned}
 \end{equation}
 %
 where $t$ denotes time (day) index, and
@@ -136,10 +138,10 @@
 Sum over all spatial points and all times
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 \overline{cost\_ssh\_anom} & = \, \sum_{t} \sum_{i,j}
 cost\_ssh\_anom(i,j,t)
-\end{split}
+\end{aligned}
 \end{equation}
 
 \end{enumerate}
@@ -259,7 +261,7 @@
 \subsubsection{Input fields}
 ~
 
-\begin{table}[h!]
+\begin{table}[!ht]
 \begin{center}
 \begin{tabular}{lllc}
 \hline \hline
@@ -269,30 +271,30 @@
 \hline
 ~&~&~&~\\
 {\it tbar} & {\tt tbarfile} & monthly model mean pot. temperature & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it sbar} & {\tt sbarfile} & monthly model mean salinity & 
 [ppt] \\
 {\it tdat} & {\tt tdatfile} & monthly mean Levitus pot. temperature & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it sdat} & {\tt sdatfile} & monthly mean Levitus salinity & 
 [ppt] \\
 {\it ctdtobs}  & {\tt ctdtfile} & monthly WOCE CTD pot. temperature & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it ctdsobs}  & {\tt ctdsfile} & monthly WOCE CTD salinity & 
 [ppt] \\
 {\it xbtobs} & {\tt xbtfile} & monthly XBT in-situ(!) temperature & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it sstdat}  & {\tt sstdatfile} & monthly Reynolds pot. SST & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it sssdat}  & {\tt sssdatfile} & monthly Reynolds SSS & 
 [ppt] \\
 {\it argotobs}  & {\tt argotfile} & monthly ARGO in-situ(!) temperature & 
-[$^{\circ}$C] \\
+[$^{\circ}\mathrm{C}$] \\
 {\it argosobs}  & {\tt argosfile} & monthly ARGO salinity & 
 [ppt] \\
 {\it wti, wsi} & {\tt data\_errfile} & vert. stdev. profile for $T$, $S$ &
 ~ \\
-{\it wtvar} & {\tt temperrfile} & spatially varying stdev. & [$^{\circ}$C] \\
+{\it wtvar} & {\tt temperrfile} & spatially varying stdev. & [$^{\circ}\mathrm{C}$] \\
 {\it wsvar} & {\tt salterrfile} & spatially varying stdev. & [ppt] \\
 ~&~&~&~\\
 \hline \hline
@@ -303,18 +305,18 @@
 \subsubsection{XBT data}
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_xbt\_t(i,j,k) & = \,
 \left[ \, \frac{fac \cdot ratio}{wti^2 + wtvar^2} \sum_{\tau=1}^{nMonsRec}
 \left\{ Tbar(\tau) \, - \, T2\theta[xbtobs(\tau)] \right\}^2 \, \right](i,j,k)
  \\
-\end{split}
+\end{aligned}
 \end{equation}
 
 \subsubsection{WOCE CTD data}
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_ctd\_t(i,j,k) & = \,
 \left[ \, \frac{fac \cdot ratio}{wti^2 + wtvar^2} \sum_{\tau=1}^{nMonsRec}
 \left\{ Tbar(\tau) \, - \, ctdTobs(\tau) \right\}^2 \, \right](i,j,k)
@@ -323,13 +325,13 @@
 \left[ \, \frac{fac \cdot ratio}{wsi^2 + wsvar^2} \sum_{\tau=1}^{nMonsRec}
 \left\{ Sbar(\tau) \, - \, ctdSobs(\tau) \right\}^2 \, \right](i,j,k)
  \\
-\end{split}
+\end{aligned}
 \end{equation}
 
 \subsubsection{ARGO float data}
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_argo\_t(i,j,k) & = \,
 \left[ \, \frac{fac \cdot ratio}{wti^2 + wtvar^2} \sum_{\tau=1}^{nMonsRec}
 \left\{ Tbar(\tau) \, - \, T2\theta[argoTobs(\tau)] \right\}^2 \, \right](i,j,k)
@@ -338,13 +340,13 @@
 \left[ \, \frac{fac \cdot ratio}{wsi^2 + wsvar^2} \sum_{\tau=1}^{nMonsRec}
 \left\{ Sbar(\tau) \, - \, argoSobs(\tau) \right\}^2 \, \right](i,j,k)
  \\
-\end{split}
+\end{aligned}
 \end{equation}
 
 \subsubsection{Reynolds sea surface T, S data}
 
 \begin{equation}
-\begin{split}
+\begin{aligned}
 cost\_sst(i,j) & = \,
 \left[ \, wsst \sum_{\tau=1}^{nMonsRec}
 \left\{ Tbar(\tau) \, - \, sstDat(\tau) \right\}^2 \, \right](i,j)
@@ -353,7 +355,7 @@
 \left[ \, wsss \sum_{\tau=1}^{nMonsRec}
 \left\{ Sbar(\tau) \, - \, sssDat(\tau) \right\}^2 \, \right](i,j)
  \\
-\end{split}
+\end{aligned}
 \end{equation}
 
 \subsubsection{Levitus montly T, S climatological data}
@@ -415,10 +417,10 @@
 \item
 Take inverse squares:
 \[
-\begin{split}
+\begin{aligned}
 wtheta(k) & = \, \frac{ratio}{wti(k)^2} \\
 wsalt(k) & = \, \frac{ratio}{wsi(k)^2} \\
-\end{split}
+\end{aligned}
 \]
 %
 \end{enumerate}
@@ -436,13 +438,13 @@
 \item
 Weights are combination of spatially constant and varying parts:
 \[
-\begin{split}
+\begin{aligned}
 wtheta2(i,j,k) & = \, \frac{ratio}
 {wti(k)^2 \, + \,wtvar(i,j,k)^2 } \\
 wsalt2(i,j,k) & = \, 
 \frac{ratio}
 {wsi(k)^2 \, + \,wsvar(i,j,k)^2 } \\
-\end{split}
+\end{aligned}
 \]
 %
 \end{enumerate}