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%\usepackage{textcomp}
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\title{Heat flux and hydrography at the Main Endeavour vent field}
\subtitle{MGG seminar and Final Examination \\ May 8, 2003}
\author{Scott Veirs}
\email{scottv@ocean.washington.edu}
\institution{University of Washington School of Oceanography}
\slideCaption{}

\begin{document}

\maketitle

\begin{slide}{My motivations}
%\begin{figure}
\begin{tabular}{rc}
\begin{minipage} {5cm}
Plume form and flux
\begin{itemize}
\item{In the atmosphere}
\item{In the ocean}
\end{itemize}

Flux and its evolution
\begin{itemize}
\item{Crustal formation}
\item{Ocean chemistry}
\item{Habitat \& dispersal}
\end{itemize}
\end{minipage}
&
\begin{minipage} {10cm}
\includegraphics*[width=.5\textwidth]{baghdad_plumes.eps}
%\caption[]{NASA Earth Observatory}
%\label{}
%\end{center}
%\end{figure}
%\onlySlide[2]{This is the puff model perspective...}
\end{minipage}
\end{tabular}
\end{slide}


\begin{slide}{Outline (minutes)}
\begin{itemize}
  \item{(05) The Flow Mow study}
  \item{(15) General results: flow and hydrography}
  \item{(15) Heat flux results}
  \item{(10) Conclusions and acknowledgements}
\end{itemize}
\end{slide}


\overlays{6}{
\begin{slide}{Endeavour study site}
\begin{tabular}{rc}
\begin{minipage}{4cm}

\begin{tiny}
\begin{itemstep}
\item $\sim$10\,km long 

\item $\sim$300\,m relief, crest at $\sim$2100\,m

\item Russ's home: 47$^\circ$54.5'N

\item Valley $\sim$1\,km wide, $\sim$100\,m deep

\item Saddle $\sim$2170\,m

\item Hydrothermal activity 
\end{itemstep}
\end{tiny}

\end{minipage}
&
\begin{minipage}{12cm}
\includegraphics*[width=0.5\textwidth]{../figs/maps/field_location_map.eps}
\end{minipage}
\end{tabular}

\end{slide}
}

\begin{slide}{Main Endeavour vent field (MEF)}
\includegraphics*[width=.5\textwidth]{../figs/maps/abebathy_ctdmap.eps}\hfill
\includegraphics*[width=.5\textwidth]{../figs/maps/mefnamemap.eps}
\end{slide}


\begin{slide}{Heat flux from a control volume}
\includegraphics*[width=.75\textwidth]{../figs/xfig/crustbox.eps} 
\begin{itemize}
\item Net heat flux via \emph{advection} through $A$:
\end{itemize}
\begin{tiny}
  \begin{equation*}
  \mathbf{H} = \int_A \rho c_p \theta \mathbf{ u \cdot \hat{n} } dA \simeq \rho {c_p} \sum_{i=1}^{N} \Delta_S\theta_i u_i \dif A_i
  \end{equation*}


We need to measure $\theta$ (and $S$) and $u$ over $A\ldots$...
\end{tiny}
\end{slide}


\begin{slide}{Instruments: CTD \& ABE}
\includegraphics*[width=.43\textwidth]{../figs/ctd_on_deck.eps}\hfill
\includegraphics*[width=.43\textwidth]{../figs/abe_front.eps}
\end{slide}


\begin{slide}{Instruments: Current meters}
\includegraphics*[width=.85\textwidth]{../figs/setting/alongaxisbathy.eps}
\end{slide}


\begin{slide}{Mean flow}
\begin{center}
\includegraphics*[width=.65\textwidth]{../figs/cms/5cmmultipvd.eps}
\end{center}

\tiny{Idea: measure heat flux in plume bent over by mean flow!}
\end{slide}

\begin{slide}{MEF control volumes and heat fluxes}
\begin{center}
\includegraphics*[width=.4\textwidth]{../figs/xfig/fmcv.eps}
\end{center}

\begin{tiny}
\begin{tabular}{lrrr}
Study             & Estimate [MW] & Heat flux\\
\hline
% use corrected $H_p$ values??!
Thomson et al., 1992   &  995$\pm$605   & $H_p$ \\
Baker \& Massoth, 1987 & 1700$\pm$1100  & $H_p$ \\
Rosenberg et al., 1988 & 3000$\pm$2000  & $H_p$ \\
%Ginster et al., 1994   &  364$\pm$73    & $H_f$ \\     
Ginster et al., 1994   &  615$\pm$120    & $H_f$ \\
%Stahr et al., 2003     &  550$\pm$100   & $H_v$ 
Stahr et al., 2003     &  640$\pm$115   & $H_v$

\end{tabular}
\end{tiny}

\tiny{So, what might explain the difference?  $H_d$?  Change?  Errors?}
\end{slide}


\begin{slide}{Oscillatory flow over ridge}
\begin{minipage}{4cm}
\begin{tiny}
$\Delta x_c$ 
\begin{itemize}
\item{$\sim$2.2\,km above ridge}
\item{$\sim$1.3\,km in valley}
\end{itemize}

$\Delta x_{\overline{u}}$ in 12\,hr:
\begin{itemize}
\item{$\sim$2.2\,km at 5\,cm/s}
\item{$\sim$0.5\,km at 1\,cm/s}
\end{itemize}

\href{http://notes.html}{\blue notes}

\href{run:../animations/cm200.fli}{Animation of plume in multidirectional flow}
\end{tiny}
\end{minipage}

\begin{minipage}{13cm}
\includegraphics*[width=.5\textwidth]{../figs/cms/thomson/ellipses.eps}
\tiny{Figure courtesy Rick Thomson, IOS Canada}
\end{minipage}
\end{slide}


\begin{slide}{Oscillatory flow in valley}
\begin{center}
\includegraphics*[width=0.7\textwidth]{../figs/cms/fm1_quiver.eps2} 
\end{center}

\begin{tiny}
\href{run:../animations/3cms.fli}{Animation of plume in rectilinear flow}
\end{tiny}
\end{slide}



\begin{slide}{ABE survey of lower control surfaces}
\begin{center}
\includegraphics*[width=0.8\textwidth]{../figs/fm1/allabe_NSwalls.eps2}
\end{center}
\end{slide}

\begin{slide}{CTD survey of north and south surfaces}
\begin{center}
\includegraphics*[width=.75\textwidth]{../figs/upper/allctd_NSwalls_fullz.eps2}
\end{center}
\end{slide}

\begin{slide}{CTD time series north and south of MEF}
\begin{center}
\includegraphics*[width=.75\textwidth]{../figs/upper/Dth.nosomef.image.all2.eps}
\end{center}
\end{slide}

\begin{slide}{Hydrography and heat flux above the ridge}
\begin{center}
\includegraphics*[width=.85\textwidth]{../figs/upper/Dth35-39_annot.eps}
\end{center}

%${H_{qs}}_j = \sum_{i=j}^{j+3} {H_h}_i$ for $j=$1..16 observed surfaces yields
$\overline{H_{qs}}=378\pm182$\,MW. 
% Use corrected value!!
\end{slide}


\begin{slide}{Hydrography and heat flux in the valley}
\begin{center}
\includegraphics*[width=.75\textwidth]{../figs/setting/NoSoMEF_5m_meanDTh2.allstns.eps2}
\end{center}

\begin{tiny}
$H_h=\overline{H}_N+\overline{H}_S = \rho c_p \overline{v} A (\overline{\Delta\theta}_N - \overline{\Delta\theta}_S)=75\pm115$\,MW
\end{tiny}

% Changing dTh or v by 0.01 units alters heat flux by 10MW
\end{slide}


\begin{slide}{MEF heat flux budget}

\begin{center}
$H_d + H_f = H_v + H_h$
\end{center}

\begin{itemize}
\item $H_h=75\pm115$\,MW, $H_v=640\pm115$\,MW, $H_f=615\pm120$\,MW

\item $H_d \simeq 100$\,MW versus $9000\pm760$\,MW (Schultz et al., 1992) and $H_d\sim$150\,MW (Johnson et al., 2002)

\item Partitioning of heat flux between sources: \\
$H_d$:$H_f\simeq$100:615$\simeq$1:6$=$0.17 ($<$1)

\item Rather than $\sim$10:1...
\end{itemize}

\end{slide}

\begin{slide}{Conclusions}

\begin{itemize}
\item{Net heat flux at MEF is $\sim$715\,MW, about 10$\times$ geologic mean.}
\item{Partitioning $\sim$1:6, with $\sim$1/4 $H_d$ entrained.}
\item{Currents disperse MEF plumes, warranting use of control volumes.}
\item{Mean inflows and rectilinear tidal flow in valley (Sea Breeze?).}
%($\Delta x\simeq$1\,km).}
\item{Multidirectional flow above ridge ($\Delta x_c=2.2$\,km).}
\end{itemize}
\end{slide}

\begin{slide}{Acknowledgements}

\end{slide}

\end{document}