--- manual/s_ecco/text/ecco_costfunction.tex 2006/04/08 01:50:50 1.7 +++ manual/s_ecco/text/ecco_costfunction.tex 2010/08/30 23:09:19 1.8 @@ -37,7 +37,7 @@ \subsubsection{Input fields} ~ -\begin{table}[h!] +\begin{table}[!ht] \begin{center} \begin{tabular}{lllc} \hline \hline @@ -76,12 +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 @@ -90,14 +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} % @@ -122,12 +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 @@ -138,10 +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} @@ -261,7 +261,7 @@ \subsubsection{Input fields} ~ -\begin{table}[h!] +\begin{table}[!ht] \begin{center} \begin{tabular}{lllc} \hline \hline @@ -305,18 +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) @@ -325,13 +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) @@ -340,13 +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) @@ -355,7 +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} @@ -417,10 +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} @@ -438,13 +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}