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\authorrunninghead{VEIRS ET AL.}
\titlerunninghead{ENDEAVOUR HORIZONTAL HEAT FLUX} 
\journalid{} \articleid{}{} \paperid{}
\cpright{}{}
\received{} \revised{}
\accepted{} \published{}

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\authoraddr{S. R. Veirs
School of Oceanography, University of Washington, 
Box 357940, Seattle, WA  98195, USA.
(scottv@ocean.washington.edu)}
\authoraddr{R. E. McDuff
School of Oceanography, University of Washington,
Box 357940, Seattle, WA  98195, USA.
(mcduff@ocean.washington.edu)}
\authoraddr{F. R. Stahr 
School of Oceanography, University of Washington, 
Box 357940, Seattle, WA  98195, USA.
(stahr@ocean.washington.edu)}


\begin{document}

\title{Magnitude and variance of horizontal heat flux at the Main Endeavour
hydrothermal vent field}

\author{Scott R. Veirs, Russell E. McDuff, Frederick R. Stahr}
\affil{School of Oceanography, University of Washington, Seattle, WA, USA}


\begin{abstract} We characterize hydrothermal plume hydrography with
unprecedented resolution using data acquired within the axial valley of the
Endeavour segment, Juan de Fuca ridge, northeast Pacific, by an autonomous
underwater vehicle (the Autonomous Benthic Explorer), a lowered CTD, and 2
current meter moorings.  Our survey of the Main Endeavour hydrothermal vent
field (MEF) shows hydrographic variability on unexpectedly short scales of
$\sim$20~m and $\sim$10~min.  Northward mean flow of 2--5~cm/s within the
confines of the valley enables us to estimate a mean horizontal heat flux in
the bottom $\sim$100~m despite variability induced by tidal oscillations with
$\sim$5~cm/s amplitude.  The mean northward transport implies that fluid
entrained by plumes in the MEF is best characterized at the southern boundary
of the field where the observed mean temperature anomaly is
$\sim$0.05$^\circ$C, an important result for a companion study that quantifies
the vertical heat flux from the field.  Differences in temperature anomaly
north and south of the MEF, combined with the mean flow, lead to a net
along-axis horizontal heat flux with a mean magnitude of $\sim$65~MW.  An
advection/diffusion model forced by nearby current data explains the
variability in the observed temperature field and indicates that the variance
of the mean horizontal flux is high (standard deviation $\sim$100~MW).  A
steady state MEF heat budget, constrained by the observed horizontal flux and
measurements of vertical fluxes from other studies has 2 implications: the MEF
heat flux is partitioned about equally between diffuse and focused vents, and
about $4/5$ of diffuse plumes are entrained by focused plumes.  \end{abstract}

\begin{article}

% insert the table of contents 
%\tableofcontents 

\section{Introduction}

Within the axial valley of the Endeavour segment in the northeast Pacific
(Figure~\ref{location-map}), currents near the Main Endeavour field (MEF)
consistently exhibit a mean northward flow ($\sim$1-5~cm/s) superimposed on
tidal oscillations of comparable amplitude
\citep{franks92,veirs+99,thomson+02}.  Similar combinations of tidal and mean
flows have been observed near hydrothermal sites within the axial valleys of
other oceanic ridges \citep{keller+75,thurnherr00}.  

When such flows distribute tracer from a source enclosed by a control volume,
the net outward flux of tracer through the boundaries can vary significantly
over time.  In the case of a hydrothermal vent field, even if the source heat
flux is constant, nearby temperatures can change quickly as thermal energy
pools within the volume during slack flow periods and streams outward through the
perimeter during peak cross flow.  Attempts to measure the total flux through
the boundaries can result in a time series that has surprisingly high variance
and, depending on how temperature and velocity signals are averaged, a mean
magnitude dramatically different from the source magnitude \citep{wetzler+98}.  

Hydrothermal plumes from diverse types of vents are embedded in the flow at
MEF.  A key parameter that determines the fate of these plumes is their source
buoyancy flux,   

\begin{equation}
B = {\frac{g (\rho-\rho_o)}{\rho_o}} Q, 
\label{B}
\end{equation}

which depends on the density of the vented fluid ($\rho$) and the volume flux
at the vent ($Q$), as well as two constants:  the acceleration due to gravity
($g=9.8$~m/s$^2$) and a reference density ($\rho_o\sim10^3$~kg/m$^3$).  The
vent fluid temperature ($T$) and salinity ($S$) are the primary controls on
$\rho$, while $Q$ is simply the product of the source area ($A$) and the
venting velocity ($w$).

Plumes from low $B$ (``diffuse'') MEF sources are expected to equilibrate
relatively close to the valley floor ($\lesssim$100~m above source, hereafter
abbreviated ``mas'') (J.W. Lavelle, NOAA/PMEL, pers.\ comm.).  For comparison,
plumes from high $B$ (``focused'') sources, like MEF black smokers, typically
have rise heights of 100--300~mas \citep{speer+rona89,middleton+thomson86}.
Unlike high $B$ plumes that rise above the ridge crests to be advected
away, the low-lying plumes contain thermal and chemical energy with less 
certain fate.  Their distribution may be controlled by entrainment into
nearby plumes from high buoyancy flux sources, by lateral transport in ambient
currents, or by a combination of both.  Each possibility has distinct
implications for the design of flux measurements and the dispersal of vent
larvae and microbes. 

The Flow Mow experiment (August 3--21, 2000) was designed to measure the
advective heat flux through both the top and sides of a control volume
enclosing all known MEF hydrothermal sources (Figure~\ref{location-map}).  The
vertical flow of hydrothermal plumes rising through the top control surface was
surveyed in a back and forth pattern (mowed) by the autonomous underwater
vehicle Autonomous Benthic Explorer (ABE).  Estimates of the vertical heat flux
through this upper surface are presented in \citet{stahr+02}.  The side
surfaces were surveyed repetitively during the experiment with ABE or a
navigated CTD with the intent of calculating the net horizontal heat flux.
Motivated by the predominance of along-axis motions in a 1995 current record
acquired near the MEF and close to the sea floor, we focused on monitoring the
north and south sides.  Meanwhile, near-bottom currents were recorded at 2
moorings located $\sim$1.1~km north and south of the field
(Figure~\ref{location-map}).  

This paper begins with a description of the Flow Mow experiment, its setting,
and instrumentation.  We then highlight the differences between the regional
background and hydrothermally-influenced hydrography.  After summarizing
current records from within the axial valley, we present temperature anomaly
measurements made north and south of the MEF.  We combine the temperature and
current data sets to estimate the net horizontal heat flux through the sides of
the MEF control volume.  Subsequently, we use a simple advection-diffusion
model to interpret the observed flux magnitudes and gain insight into the flux
variance expected near the MEF.  Finally, we discuss the implications of the
horizontal heat flux estimates for the calculation of vertical flux and the
partitioning of heat flux between distinct types of hydrothermal sources within
the MEF.

\section{The Flow Mow experiment}

\subsection{Setting}

The topography and hydrography of the Endeavour segment present a distinct
opportunity to measure heat fluxes.  The vertical relief of the axial valley
($\sim$100~m) is greater than the rise height of diffuse plumes, but less than
the rise height of focused plumes.  The top of the axial valley also marks a
change in currents --- from strong and rotary flow above the ridge crests to
relatively weak and rectified flow within the axial valley.  Thus, the
topography and currents motivate different methodologies for measuring heat
flux within the axial valley versus above it.  Above the ridge crests, flux
measurements depend on interception of advected plumes
\citep[e.g.][]{baker+massoth87}.  This approach is required at fast spreading
centers where the axial caldera is typically too shallow to constrain
hydrothermal plumes.  In contrast, a typical slow spreading center has a deep
axial valley that can confine hydrothermal plumes \citep[e.g.][]{rudnicki+94}
and motivates a budgetary approach to quantifying fluxes \citep{murton+99} and
diapycnal diffusivities \citep{thurnherr+02}.  The Flow Mow experiment was
designed to intercept plumes within the Endeavour axial valley, accounting both
for equilibrated plumes moving horizontally near the bottom and for buoyant
plumes rising out of the valley, but not yet exposed to the overlying flow.

The Endeavour segment is essentially a short linear ridge with an elongate
summit depression, or axial valley, that is open at both ends, but shoals to a
sill near the north end (Figure~\ref{location-map}).  When defined by the
2170~m isobath (the depth of the sill) the east and west crests of the segment
are $\sim$10 and $\sim$12~km long, respectively.  At the latitude of the MEF,
the segment is $\sim$4~km wide when measured between the points where the outer
flanks rise abruptly from adjacent depressions that are 2350--2400~m deep.  The
rounded outer flanks rise about 250~m to crests near 2100~m depth.  

Tectonic spreading at a half rate of 29~mm/yr \citep{elvers+73} has created an
axial valley that has a uniform width of $\sim$1~km between the rims
\citep{kappel+ryan86}.  Near the MEF the valley floor is $\sim$500~m wide and
is bounded by basaltic talus slopes and/or fault scarps.  Analysis of segment
bathymetry shows that these valley walls have an average relief of $\sim$100~m
and slopes of 10-30$^\circ$.  Along-axis, the valley floor shoals to the north
at an average rate of $\sim$18~m/km.  Like the other known fields to the north
and south  (see Figure~\ref{location-map} for names), the MEF rests on the
relatively flat valley floor where basaltic sheet and pillow flows are
intermittently broken by along-strike fissures that are 10--100~cm wide and
normal faults with typical throws of 1-10~m.  

While the major fields are separated along-strike with spacing of $\sim$2~km
\citep{delaney+96}, a growing number of high and low $B$ sources have been
located or are suspected in-between (Figure~\ref{location-map})
\citep{veirs+99,johnson+02,kelley+02}.  Of particular importance to this study
is a low $B$ area $\sim$500~m south of MEF called Quebec.  This area is
roughly 40~m square, rich in tube worm beds venting $\sim$12$^\circ$C fluid,
and potentially close enough to the MEF to exert an influence on measurements
of horizontal heat flux through the south side of the MEF control volume.

The MEF is the most thoroughly mapped hydrothermal area on the Endeavour
segment, having been the subject of myriad Alvin dives (more than any other
site in the world) and numerous geophysical surveys.  The field consists of 2
clusters of sulfide structures separated by $\sim$150~m along-strike
(020$^\circ$ true).  Most structures are based on basalt near 2195~m depth and
are 3-21~m tall.  While some structures in the north rest as deep as 2205~m,
and a few in the south have bases as shallow as 2190~m, source depths are
similar throughout the field because the 7 major northern structures are
distinctly larger than the $\sim$11 southern structures.  Based on elevation
and dimensions in the map of \citet{delaney+92}, the active sulfide structures
in the north have larger diameters (20--40~m versus 10--20~m in the south) and
are taller on average ($\sim$12$\pm$4~m versus $\sim$7$\pm$2~m).  Consequently,
the average depth of MEF high $B$ sources is about the same in the north and
south clusters (2185$\pm$6~m versus 2188$\pm$5~m).

Within the MEF, the top and side surfaces of the active sulfide structures may
act as low $B$ vents with areas up to 20--30~m in diameter.  Tube worm patches,
typically 2--10~m in extent, constitute low $B$ fluid sources on the sea floor,
either abutting sulfide structures or distributed along faults near sulfide
structures.  The maximum vertical separation of MEF sources is 38~m --- between
a high $B$ source, the 21~m high chimney at 2174~m on Dante, and a low $B$
source, a tube worm bed at 2212~m just southwest of Crypto.  More typical
separations are $\lesssim$1~m between sulfide top surfaces and high $B$ vents,
and 10--15~m between tube worm beds and nearby black smokers.

The spatial distribution of distinct hydrothermal sources within the MEF is
important for measuring fluxes because it guides the sizing of a control volume
that encloses all sources in the field and intercepts all hydrothermal plumes
ideally.  The perimeter of the Flow Mow control volume (Figure
\ref{location-map}) is a rectangle aligned with the strike of the valley.  With
a width of $\sim$300~m and a length of $\sim$700~m, it encompasses all the
known MEF hydrothermal sources with a buffer of $\gtrsim$100~m.  The top
surface of the volume is a horizontal (constant pressure) plane $\sim$80~mas,
an altitude near which the signal strength of rising plumes and the likelihood
of intercepting them are simultaneously optimized \citep{stahr+02}.  The
vertical surfaces of the control volume were surveyed from the top surface
($\sim$2110~m) to within 5--10~m of the local sea floor (as deep as
$\sim$2210~m).  


\subsection{Instrumentation}

Hydrographic data were collected with pumped and ducted Sea Bird Electronics
conductivity and temperature (CT) sensors mounted either within a lowered cage
or in free flow on the front of ABE.  In addition to deriving potential
temperature ($\theta$) and $S$ from redundant CT sensor pairs, the lowered CTD
recorded pressure, transmissivity, optical backscatter, fluorescence, oxygen
concentration, redox potential, and cage altitude.  An acoustic altimeter
enabled ABE to monitor its elevation and avoid contact with the sea floor.

For the lowered hydrographic sensors, pre- and post-cruise calibrations did not
differ significantly.  Raw 24~Hz data were bin averaged to 0.5~Hz.  The 0.5~Hz
series were hand-edited for non-hydrothermal outliers and the resulting gaps
were filled through linear interpolation.  Processing of data from the
ABE-mounted CT sensors is detailed in \citep{stahr+02}.

The hydrographic observations were located through long-baseline acoustic
navigation whenever only one platform (CTD cage or ABE) was submerged.  Only at
stations $>$5~km from the MEF did the long baseline navigation degrade.  When
both platforms were submerged simultaneously, only ABE was navigated to
preclude  multiple interrogations of the transponders.  In these instances, the
CTD cage locations were estimated from the R/V Thompson GPS fixes, the ship
heading, and the geometric relation between the block on the CTD boom and the
ship GPS antenna.  Comparison of CTD long-baseline and ship GPS fixes during
similarly slow tows ($\lesssim$10~cm/s) indicates that the CTD rarely deviated
laterally more than 10~m from the tip of the boom that supported it.  All fixes
were edited for outliers and interpolated onto the 0.5~Hz hydrographic time
base.

Currents were recorded during the experiment by Aanderaa RCM5 instruments
moored $\sim$1.1~km north and south of the MEF.  Each current meter generated
hourly mean speed and direction.  The north mooring consisted of 2 RCM5s, 14
and 15 meters above bottom (mab).  We use data exclusively from the shallower
meter (2161~m depth) because the deeper meter failed prior to the beginning of
the Flow Mow experiment.  The south mooring supported 5 current meters at 50~m
intervals (from 50--250~mab), but in this study we focus only on the lowest
meter (2142~m depth) because its depth was comparable to that of the north
meter and central to the Flow Mow control volume depth range (2100--2200~m).  

Additional current observations were made with Nobska Modular Acoustic Velocity
Sensors (MAVS).  One MAVS was mounted on ABE during the experiment.  Others
were placed within the MEF by collaborating scientific programs and recorded
near-bottom ($\lesssim$1~mab) velocity for short periods during the Flow Mow
experiment.  Data from the latter instruments have provided useful comparisons 
(courtesy of M. Tivey, S. Hautala, I. Garcia-Berdeal, and their associates).


\subsection{Hydrographic context and anomaly definition} 

Current meters deployed \emph{above} the ridge crests during the Flow Mow
experiment and previous Endeavour segment studies show that the regional mean
flow is $\sim$5~cm/s to the southwest.  Although tidal and inertial
oscillations are amplified in this depth range (1900--2100~m)
\citep{thomson+02}, neither is capable of displacing hydrothermal plumes more
than a few km from their axial sources.  Consequently, we assume that vertical
CTD casts acquired 10 and 15~km due east of the MEF prior to the experiment
define the regional hydrographic context, or "background" for the Flow Mow
experiment.  The more distant station was at 47$^\circ$57.01'N,
128$^\circ$54.02'W, while the closer station was at 47$^\circ$56.99'N,
128$^\circ$58.02'W.

In particular, we assume that these upstream stations define the condition of
the northeast Pacific deep water prior to topographic and hydrothermal
influences.  Like past casts taken at similar distances east of the axis, these
stations display a near-linear $\theta$--$S$ trend and constant (clear water)
transmissivity or backscatter signals over the depths where Endeavour
hydrothermal plumes typically equilibrate (1700--2300~m).  We calculate an
\emph{isohaline} potential temperature anomaly ($\Delta\theta$), using as a
reference a 2nd-order polynomial fit to the near-linear $\theta$--$S$
background data (10-m depth-binned average of both stations).  This is an
important and strategic choice because the plume temperature anomaly reference
(density, salinity, or depth) affects the relationship between source heat flux
and the vertical flux measured in the rising plume
\citep{mcdougall90,mcduff95,lavelle+98,mcdougall+speer99,thurnherr00}; the
relationship also depends on the $S$ and $\theta$ of the source and entrained
fluid, as well as whether the measurement is in zero or non-zero $B$ parts of
the plume.  Through examination of a 1-dimensional plume model
\citep{morton59,speer+rona89,mcduff95}, we find that isohaline $\Delta\theta$
requires the smallest correction ($\lesssim$5\% at 100~mas) for plumes
originating from sources with near-zero $S$ anomalies, like the diffuse sources
found in the MEF that have source $S\approx99\%$ seawater $S$ \citep{veirs03}.
This low correction factor motivates us to use isohaline $\Delta\theta$ to
define the plume temperature anomalies.

Approaching from the east, hydrothermal influence on the $\theta$--$S$ trend
first becomes evident on the outer ridge flank \citep{veirs+99}.  Above 2100~m
on the southeast flank (only about 1~km southeast of the MEF) water properties
are nearly indistinguishable from the background stations.  Below 2100~m, the
water is slightly above background in $\theta$--$S$ space, but less so than at
any more central axial station.  Similarly, a station taken on axis, but at the
extreme north end of the segment, $\sim$15~km north of MEF, reveals no
departure from the background trend over a wide range of depths (1700--2250~m).
In contrast, axial stations located over or between the vent fields always
sample fluid that has positive $\Delta\theta$ and high backscatter, indicating
hydrothermal plume influence \citep{veirs03}.  Above and near ridge crest
depth, background water is interspersed with layers of this plume water that
vary in depth and thickness between sequential casts that are typically 0.3~hr
apart or offset by $\sim$100~m.  In this upper layer (1850--2100~m), stations
taken $\lesssim$1~km southwest (downstream with respect to the regional mean
current) of known fields tend to be the most anomalous.  The intermittent
returns to the background in this depth range (as well as below plume depths in
distal downstream casts) assure that the near-linear background relationship
can be extended, rather than extrapolated, through equilibrated plumes, as well
as the axial valley depths.

Within the axial valley ($\gtrsim$2100~m) near MEF, water with background
$\theta$--$S$ character is extremely rare.  The $\Delta\theta$ of near-bottom
fluid is almost always positive and generally increases along-axis toward the
center of hydrothermal activity.  In $\theta$--$S$ space, a profile within the
valley typically plots parallel to, but above the background \cite{veirs03}.  


\subsection{Axial valley currents}

Northward mean flows were observed within the axial valley both north and south
of the MEF in 2000, and near the northeast corner of the MEF in 1995 (see
Figure~\ref{location-map} for mooring locations and mean vectors).  The
magnitudes of the mean flow increase from south to north (1.6, 2.3, 4.7~cm/s),
while the meter elevation decreases (50, 25, 15~mab).  Similar south-to-north
acceleration of mean flow was measured at the same locations during a 2001
deployment in which all meters were 15--17~mab; an additional 2001 record from
further north (just south of the 2170~m saddle) showed a mean flow that was to
the south at 1--2~cm/s \citep{thomson+02}.  Each of the records in 2000 and
2001 covered about 4 summer months, approximately from July through October.

The most prominent oscillation in the axial valley currents is at the M$_2$
semidiurnal frequency.  At all depths on all moorings deployed in 2000 and 2001
the semidiurnal frequency band, dominated by the M$_2$, but also including the
S$_2$ component, accounts for a greater proportion of the variance than any
other constituent (low- or high-, inertial, or diurnal frequencies); and within
100~m of the bottom it consistently accounts for more than $50\%$ of the total
variance \citep{thomson+02}.  The vertical array of meters on the southern
mooring reveals that the M$_2$ tidal ellipse has major axes that diminish from
$\sim$4~cm/s at and above the ridge crest to 2--3~cm/s within the valley
\citep{thomson+02}.  Consequently, along-axis flow reversals occur often at the
south meter, where the oscillatory amplitude commonly exceeds the mean flow,
and rarely at the north meter (Figure~\ref{quiver}).  At the 1995 meter, the
combination of mean and oscillatory flow is intermediate, as is the
intermittence of southward net fluid motion.

Before calculating and modeling horizontal heat fluxes through the MEF control
surfaces, it is important to justify the local application of near-bottom
currents measured at moorings up to 1.1~km away.  Each mooring supported a
meter near 2150~m, the central depth of the Flow Mow control volume.  Auto- and
cross-spectral analysis of the north and south meters reveals that there is
statistically significant coherence and at most a +20{$^\circ$} phase
difference at the dominant (semidiurnal) frequency; the south meter (50~mab)
leads the north meter (15~mab) by $\sim$45~min.  

There is also evidence of general coherence in Figure~\ref{quiver} in which
similar tidal oscillations combine with different northward mean flows at the
north and south meters.  In these 65~hr records, the magnitude of the mean flow
relative to the amplitude of the tidal oscillations determines whether flow
reversals occur.  This short time series characterizes how rarely fluid is
advected southward in the axial valley.  Review of progressive vector diagrams
(PVDs) generated with the longer records confirms that northward transport
predominates at both meters throughout the Flow Mow experiment.  On the other
hand, the PVDs reveal a discrepancy between the 2 meters.  North of the MEF, an
eastward component of flow generates a mean direction parallel to the strike of
the valley, while at the south meter a westward component results in a mean
flow headed due north (Figure~\ref{location-map}).  A likely explanation for
these opposite cross-axis components is that the moorings landed in distinct
topography.  The north meter was next to the western wall of the valley and
likely experienced currents aligned with the 020$^\circ$ strike.  The south
mooring was centered in the valley and may have been influenced by westward
flow over $\sim$2160~m saddle in the adjacent eastern ridge crest.  The 1995
mooring was also centered in the valley and recorded a westward, albeit less
persistent and strong, component of flow.

That near-bottom currents are approximately in phase is reinforced by a few
short records of the flow that were acquired \emph{within} the MEF during the
Flow Mow experiment.  Figure~\ref{v-series} juxtaposes the zero-mean,
along-axis component of near-bottom flow from the north and south moorings with
3 different time series: the flow predicted through harmonic analysis of the
1995 data (H. Mofjeld, pers.\ comm.); the record from a MAVS deployed by M.
Tivey in the center of MEF; and the ambient current measured with the MAVS
mounted on ABE during 2 of the longest dives.  We note that the 3rd series was
calculated by subtracting ABE velocity, derived from navigational fixes of
$\sim$1~m accuracy, from the ABE-mounted MAVS readings.  That this method
resolved the ambient current at all is a tribute to both the MAVS, the
stability of the ABE platform, and the long baseline navigation system.  During
this characteristic 65~hr period (the same as in Figure~\ref{quiver}), the
$\sim$12~hr semidiurnal oscillations are approximately in phase.  Most
zero-crossings of the de-meaned records fall within $\pm$1~hr of the predicted
flow reversals.  

The consistency of the mean flow and the spatial coherence of tidal
oscillations within the axial valley flow justifies 2 strategies in this paper.
First, the northward mean velocities that we combine with temperature data to
calculate a range of observed fluxes will be bounded by the observed means
($\sim$1--5~cm/s) from the north and south meters.  Second, we elect to use a
spring--neap cycle of the 1995 harmonic analysis to model MEF heat fluxes.


\section{Observed flux magnitude}

A fundamental assumption in the Flow Mow experimental design was that
hydrographic conditions near the MEF control surfaces would be uniform.  In a
steady flow field, thermal homogeneity on the scale of the MEF would guarantee
that advection of heat in one side of the field would be balanced by advection
out the opposite side.  Additionally, any heat entrained by plumes rising
within the control volume could be accounted for by subtracting the mean
$\Delta\theta$ observed on the perimeter from that observed on the top.

Contrary to our expectations, hydrographic surveys in the MEF and within
$\pm$500~m along-axis show that near-bottom variability is high.  Upon spatial
and temporal averaging, however, an overall pattern emerges: near the bottom it
is warmer north of the MEF than south of it.

\subsection{MEF $\Delta\theta$ fields}

The $\Delta\theta$ fields on the north and south sides of the MEF control
volume were observed during 3 separate ABE dives (45, 46, and 50) and are
presented in Figure~\ref{ns_abe_walls}.  Each panel overlays the ABE track line
on $\Delta\theta$ data collected over a period of 2-3 hours.  The data were
subsequently projected orthogonally onto the north or south control surface for
spatial averaging.  The averaging bins ($\Delta x=$10~m, $\Delta z=$25~m) were 
designed to capture at least 2 ABE passes, obtaining $\gtrsim$100 points/bin.
Dives 45 and 50 have north sides that are warmer on average than south sides,
as expected, while dive 46 has a warmer south side, even when only the upper
50~m of the 2 sides are compared (means of 0.077$^\circ$C versus
0.074$^\circ$C).  

Figure~\ref{ns_abe_walls} also shows a higher spatial variability than
anticipated.  On any given pass along the 300~m wide side, plumes or thermal
patches as narrow as 20~m were traversed.  Sequential passes along the same
side, sometimes separated only 10~m vertically and $\sim$10-20~min temporally,
commonly encountered $\Delta\theta$ that varied by a factor of 2.  

An additional perspective on the north and south side $\Delta\theta$ fields is
gained through 3 vertically oscillating tows (VOTs), depicted in
Figure~\ref{allctd_NSwalls}.  These data were projected in the same way, and
averaged in bins ($\Delta x=$100~m, $\Delta z=$5~m) that encompassed at least
2 adjacent casts, or $\gtrsim$40 data points.  During station 10, the CTD
traversed the north side 3 times; the south side was surveyed $\sim$5.5 times
during stations 12 and 13.  While the south sides are uniformly warm in their
upper 25~m, their lowest 25-50~m are variable and generally cooler than the
same depth range on the north side.  In the sequential panels of
Figure~\ref{allctd_NSwalls}, the first north side has the highest mean
$\Delta\theta$, but many of the south sides are warmer than the second and
third north sides.  When sides are sorted into north and south groups and
averaged, however, the mean south side (0.0677$^\circ$C) is slightly cooler
than the mean north side (0.0690$^\circ$C).

The mean northward flow indicated by the 1995 current meter motivated us to
place special emphasis during the Flow Mow experiment on comparing 2 CTD survey
areas (dubbed ``NoMEF'' and ``SoMEF'') that extended $\sim$500~m along-axis
north and south of the MEF boundary (Figure~\ref{location-map}).  Both areas
were monitored intermittently during distinct tidal phases, and toward the end
of the experiment were reoccupied for longer, near-tidal periods.  NoMEF was
monitored for about 10 hours during a vertically oscillating cast (VOC) between
1800 and 2200~m (station 28).  A few days later, SoMEF was assessed
($\sim$200~m west of previous SOMEF stations) for 14 hr during a VOC between
1800 and 2150~m (station 33).  Figure~\ref{nosomef_waterfall} portrays the
evolution of the $\Delta\theta$ field in the NoMEF and SoMEF areas, with
averaging bins again designed to capture at least 2 adjacent casts ($\Delta
t=$30~min, $\Delta z=$5~m).  Averaging all data in the time series from each
area indicates that NoMEF (0.050$^\circ$C) is slightly warmer than SoMEF
(0.043$^\circ$C).  The extremes of mean $\Delta\theta$ in any bin are similar
in both areas, with values as low as $\sim$0.034$^\circ$C and as high as
$\sim$0.060$^\circ$C.

We further visualize the variability of $\Delta\theta$ near MEF by aggregating
all data incorporated in Figures~\ref{ns_abe_walls}, \ref{allctd_NSwalls}, and
\ref{nosomef_waterfall} with all data acquired \emph{above} the ridge crests
during the same set of stations, sorting into 25~m depth bins, and generating
histograms of $\Delta\theta$ for each bin.  The resulting distributions of
$\Delta\theta$ (Figure~\ref{depth-hist}) characterize the full range of depths
(1800--2200~m) influenced by plumes in the vicinities north and south of MEF,
and therefore provide some context for Figures~\ref{ns_abe_walls},
\ref{allctd_NSwalls}, and \ref{nosomef_waterfall} which portray data from only
the deepest 4 bins (2100--2200).  While the spatial and temporal variability of
near-bottom $\Delta\theta$ around the MEF was higher than we expected, the
$\Delta\theta$ variance is low in the bottom 100~m relative to the depths
above 2100~m, where cross-axis flow increases the variability of plume
distributions.  

Since Figure~\ref{depth-hist} combines all of the observations made north or
south of the MEF, it can also be used to quantify north--south differences in
mean $\Delta\theta$ (hereafter $\overline{\Delta\theta}$).  Comparing the
bottom 100~m in the north and south, each 25~m bin has a
$\overline{\Delta\theta}$ that is greater in the north.  The average
$\overline{\Delta\theta}$ taken over these 4 deepest bins is 0.063$^\circ$C in
the north, versus 0.056$^\circ$C in the south.   


\subsection{Horizontal heat flux estimation}

The patchiness of hydrothermal plumes in the axial valley invalidates our
initial assumption of thermal heterogeneity, and suggests that unequal lateral
fluxes through the different control volume sides are probably commonplace.  In
the face of this variability, we generate a range of estimates of \emph{mean}
heat fluxes by combining the north--south difference in
$\overline{\Delta\theta}$ with measurements of $v$ (the along-axis component of
flow).  

Based on progressive vector diagrams which show that $v$ consistently dominates
the across-axis component, heat fluxes through the east and west control
surfaces are negligible.  With this simplification and the convention that
outward fluxes are positive, the net horizontal heat flux ($H_h$) is the sum of
the fluxes through the north and south control surfaces, each of which is
normal to $v$.  Thus, $H_h$ represents that fraction of the heat generated by
the MEF that leaves the control volume by horizontal advection within 100~m of
the sea floor.  The remaining fraction of MEF heat passes vertically through
the top control surface.  

We estimate $H_h$ by multiplying the difference in $\overline{\Delta\theta}$
observed north and south of the MEF by the range of observed along-axis mean
velocity ($\overline{v}$), the area of the north or south control surface
($A_h=3\times10^4$~m$^2$), the reference density ($\rho_o$), and a heat capacity
($C_p=4.2$~kJ/kg/$^\circ$C): 

\begin{equation}
H_h = A_h \rho {C}_p \overline{v} (\overline{\Delta\theta}_N-\overline{\Delta\theta}_S).
\label{hh}
\end{equation}

Using the north-south difference in $\overline{\Delta\theta}$ values from the
bottom 100~m of Figure~\ref{depth-hist} ($0.063-0.056=0.007^\circ$C) and a
range of observed $\overline{v}$ (+1--5~cm/s), we obtain a range of estimates
of $H_h$: +10--50~MW.  Changing the difference
$\overline{\Delta\theta}_N-\overline{\Delta\theta}_S$ by 0.001$^\circ$C changes
the value of $H_h$ by 1.25~MW, while increasing the magnitude of $\overline{v}$
by 1~cm/s increases $H_h$ by 10~MW.

The Flow Mow hydrographic survey resolved the MEF temperature field at temporal
and spatial scales that are unprecedented.  Despite the thermal variability,
the north and south control surfaces were sampled frequently enough, and at a
wide enough range of tidal phases, to enable estimation of the \emph{mean} net
flux, $H_h$.  However, the observations are too sparse and non-synoptic to
capture the variations of \emph{instantaneous} net flux out of the control
volume.  Indeed, given the limitations of the acoustic navigation network and
our instruments, it was a grand achievement to assess a single side and a top
simultaneously.  It was impossible to monitor all 4 sides and the top at once,
though that ability is critical if instantaneous fluxes are sought in such
variable hydrography.  Consequently, we use synthetic data to understand the
high variability and interpret our sparse observations.


\section{Modeled flux}

\subsection{Modeled variance and mean magnitudes}

To understand the observed hydrographic variability near the MEF and the affect
of variable currents on heat flux, we construct a 2-dimensional model of tracer
distribution by a point source subjected to a combination of advection and
diffusion (Figure~\ref{puff-model}).  Similar ``puff'' models have been used to
understand atmospheric plume distributions \citep[e.g.][]{rao+89} and more
recently to interpret temperature and current records from moorings near a
hydrothermal field \citep{wetzler+98,lavelle+01}.  The model allows the
calculation of a $\Delta\theta$ at any point and time in the control volume or
on its surfaces.

We force the model with a characteristic oscillation derived through harmonic
analysis of the 1995 near-bottom current record.  At each time step ($1/2$~hr),
a constant amount of heat (a puff) is added to the $4\times4$~km model domain
from a single source in the middle of the MEF.   The puff is thereafter
advected by the current, which in this case is purely along-axis and therefore
surface-normal.  It is also diffused according to a horizontal diffusivity
typical of the interior ocean, 0.4~m$^2$/s \citep{okubo71}.  These processes
modify the temperature anomalies measured on the surfaces of a
($300\times700\times100$~m) control volume, generating a time series that can
be used to calculate net heat flux through the sides.  We then add a range of
mean flows to the oscillation to investigate how flux magnitude and variance
evolve as the mean flow balances and then exceeds the amplitude of the
oscillation.  

The model also allows different averaging schemes to be compared.  For example,
once the temperature field has been recorded at both ends of the control volume
for every time step, a feat not yet attainable in the field, the time series
can be multiplied by the corresponding current velocities to obtain a series of
\emph{instantaneous} net flux across the control surfaces.  This flux series
may have extraordinarily high variance at low mean flows, but its long-term
mean flux must equal the source flux.  Alternatively, the temperature series
can be averaged before multiplying by the velocity series, or visa versa; this
results in \emph{temperature-averaged} or \emph{velocity-averaged} flux series
that have variances and means that are different from the instantaneous series.

Figure~\ref{flux-comp} shows how the means and standard deviations ($s$) of
these 3 types of flux series evolve as the mean flow is incremented in the puff
model.  The instantaneous mean equals the source flux at mean flows
$>$1~cm/s; at 0~cm/s the mean of the flux series, a product of the zero-mean
velocity series, must also be zero, while at $\leqq$1~cm/s the $T$ gradients
are so steep that $\sim$5\% of the heat diffuses through the control surfaces
and is not accounted for.  The averaged flux series in the 1--5~cm/s range have
mean magnitudes of $\sim$75\% of the source flux.  This underestimation is due
to averaging one of the time series prior to multiplication, and motivates us
to adjust our estimates of observed $H_h$ in the next section.  The $s$ of the
instantaneous flux series is greater than the $s$ of either averaged flux at
all flows.  In the 1--5~cm/s range of mean flow, the instantaneous $s$ is
1--2$\times$ the source flux magnitude.  Expressed as a percentage of the
source flux magnitude, the velocity- and temperature-averaged $s$ converge from
low-flow values of 150\% and 30\%, respectively, to $\sim$60\% above 2~cm/s.
Over the range of typical flows, the model leads to the general expectation
that fluxes measured near the MEF will yield averaged flux series with
$s\sim1\times$ the source flux magnitude.

\subsection{Model implications for observed flux} 

Since our estimates of observed $H_h$ are essentially velocity- and
temperature-averaged fluxes made in an environment where mean flow is
1--5~cm/s, the model indicates that they should be adjusted upward by a factor
of $\sim$1.3~($=1/0.75$).  This increases the range of observed $H_h$ from
10--50~MW to $\sim$15--65~MW.  Within the same mean flow range, the standard
deviation of the modeled averaged flux is $\lesssim$100\% of the source flux.
Taking the high end of our $H_h$ magnitudes (65~MW) as the source flux that
warms the north control surface, the model results suggest that if the Flow Mow
experiment were redesigned to monitor both north and south control surfaces
simultaneously, then the time series of observed averaged horizontal heat flux
would have a maximum $s$ of $\sim$150\% of 65~MW, or $\sim$100~MW.


\section{Discussion}

\subsection{Sources of variability in MEF hydrography}

The hydrographic patterns observed within the Endeavour axial valley, and
particularly the thermal distribution near the MEF, are most likely generated
by hydrothermal plumes in a mean northward flow.  The puff model shows that
tidal pooling and streaming can generate surprisingly heterogeneous plume
distributions, especially when forced by a 2-dimensional record
(Figure~\ref{puff-model}), rather than the idealized along-axis oscillation and
mean flow.  Diffusion and bottom boundary layers will reduce variability over
time.  These 2 processes appear to balance such that thermal anomalies are
present throughout the valley, but are reduced in intensity away from sources.
Even midway between known vent fields, plume induced thermal variability rivals
that expected from the vertical displacement of isotherms by internal waves
\citep{veirs03}.  On the periphery of fields the signals are stronger and the
heterogeneity increases.  

Overall, these competing processes complicate the task of measuring the net
flux from a vent field.  If mixing rates were greater or there were no mean
flow, then the valley would eventually acquire a uniform hydrothermal anomaly
that could be more easily inventoried.  The observed complexity of the
hydrography in the valley suggests that the most successful efforts to measure
field-scale fluxes will be those that correctly establish and simultaneously
monitor up- and downstream positions over many tidal cycles, or otherwise
integrate the variability induced by the tides.

We used both ABE and CTD to monitor the hydrography near the MEF, and
endeavored to survey all sides of the control volume at all phases of the tide.
Our simple puff model can explain some of the observations, but cannot include
many of the possible sources of thermal variability.  Even without invoking the
possibility of variable source flux (or even fluxes that exhibit tidal
variability), multiple constant-flux sources with distinct effluent
characteristics (as opposed to the single model source) could enhance
variability.  Although we have documented that there is significant coherence
in the axial currents, small amounts of shear in the velocity field can greatly
affect the plume distribution and its variability, with profound ramifications
for the potential undersampling of narrow plumes.  Finally, a major reason the
puff model sometimes fails to explain why one side of the MEF is warmer than
the other is the proximity of other heat sources, beyond the perimeter of the
control volume.  Not only is the diffusely venting Quebec area located nearby,
but a major vent field, Mothra, lies upstream of the MEF.  The puff model
indicates that plumes from either source are likely to be advected
intermittently through the MEF.

Despite these numerous complications, plume theory suggests that our survey
strategy was optimal for characterizing the average plume distributions near
MEF.  Plumes from diffuse and focused MEF sources are expected to bend over in
the axial cross flows and equilibrate within the depth range we monitored.
To prevent equipment damage, we avoided the bottom 5--10~m of each side, but
based on knowledge of the source fluids within the MEF, we expect that the
lateral flux of heat through this gap is small compared to that through the
5--100~mab range.  

While it is possible that a low $B$ vent could produce a plume that hugs the
sea floor \citep[e.g.][]{trivett+williams94} and is advected beyond the field
through the gap, during the summer of 2000, all MEF sources had negative
salinity anomalies ($\Delta S$): -9 to -14\permil\ for high $B$ sources in the
south part of MEF; -4 to -8\permil\ in northern high $B$ vents; and about
-0.5\permil for low $B$ vents in general (D. Butterfield, pers.\ comm.).
Numerical models of diffuse plume rise (J.W. Lavelle, pers.\ comm., see caption
of Figure \ref{puff-model}) indicate that in typical stratifications, vents with
negative $\Delta S$, no matter the magnitude of their positive source
$\Delta\theta$, will produce plumes that separate from the sea floor downstream
of the source.  When the source properties (measured $S$ and $T$, and estimated
$w$ and $A$) are used to quantify a range of $B$ for MEF low $T$ vents, and the
results are used to initialize the plume rise models (along with a reasonable
range of environmental conditions, namely the buoyancy frequency, $N$, and
cross flow velocity, $U$), the range of expected rise heights and plume
thicknesses creates significant temperature anomalies at elevations of 15--35~m
for $\Delta S=+0.5$\permil\ and 20--90~m for $\Delta S=-0.5$\permil.  In cross
flow of 5~cm/s the modeled plumes equilibrate $\lesssim$250~m downstream of
their source.  These predictions suggest that low $B$, negative $\Delta S$ MEF
plumes may actually rise up through the top surface of the control volume on
their own accord unless they are first carried through a side surface by cross
flow or entrained by high $B$ plumes.  

If currents of $\sim$5~cm/s orthogonal to the sides are assumed to generate
variability on time scales of $\sim$1000~s (the time it took ABE or the CTD to
complete a lap horizontally or vertically), then the characteristic dimension
of thermal patches would be about 50~m, an estimate that is in rough agreement
with the smallest scale of variation observed on any individual pass.  This is
also the approximate scale of the smallest features generated by a numerical
model of a typical MEF diffuse plume (J.W.  Lavelle, pers.\ comm.).

The behavior of focused hydrothermal plumes in uniform cross flow has been
modeled both analytically \citep{middleton+thomson86} and numerically
\citep{lavelle97}.  With some approximation of the typical in-valley
stratification, plumes from MEF focused sources (with the observed range of
source $S$ and $T$) are expected to rise anywhere from 200~m in nearly
quiescent conditions (1~cm/s cross flow) to 100~m in typical peak MEF cross
flows of 10~cm/s.   Although measurements of 20~cm/s peak cross flows are rare
in the 1995 and 2000 records ($\sim$1 event in 20~days), plume rise during such
flow could be reduced to $\sim$50~m.  

The surprisingly small-scale heterogeneities observed on the sides of the MEF
likely originate when diffuse sources with different $B$ and depth (10--15~m
vertical separation) vent into a mean cross flow, generating plumes with
distinct rise heights.  When tidal oscillations also influence the dynamics and
distribution of plumes, high temporal variability becomes the norm, especially
when observations are made close to the hydrothermal sources.  During peak
cross flows, even plumes from high $B$ sources may transit the upper $1/2$ of
the sides of the control volume.


\subsection{Implications for vertical heat flux calculation}

The heterogeneous hydrography observed within the axial valley implies that the
fluid entrained by rising MEF plumes can have variable heat content.  This
complicates the interpretation of the heat flux measurements made on the top
surface of the Flow Mow control volume because relating measured anomalies to
source heat flux through 1-dimensional plume theory requires an assumption of a
linear background $\theta$--$S$ relationship in the entrained fluid.  

However, the consistent northward flow within the axial valley means that fluid
entrained by MEF plumes enters the field predominantly through the south side
of the control volume.   As detailed in \citep{stahr+02}, a viable approach is
to average all $\Delta\theta$ estimates from the area south of the MEF and
subtract the result (${\overline{\Delta\theta}}_S\simeq0.05^\circ$C) from each
of $N$ observations of $\Delta\theta$ made on the top surface (with area,
$A_v$) by ABE to calculate the vertical heat flux ($H_v$) as

\begin{equation}
H_{v} = A_v \rho C_p \sum_{i=1}^{N}{ w_i (\Delta\theta_i - {\overline{\Delta\theta}}_S) },
\label{hv}
\end{equation}

where $w$ is vertical velocity.  This is equivalent to assuming that fluid
entrained at any depth within 100~mas has the same average $T$ and $S$, which
is partially justified by the observation of intermittent well-mixed layers
$<50$~mab.  Additionally, during horizontal CTD tows through the MEF at depths
of 30--60~mas, the $\Delta\theta$ between buoyant plumes is typically
$0.05\pm0.01^\circ$C.  Altering the value of ${\overline{\Delta\theta}_S}$ by
0.01$^\circ{C}$ changes the vertical flux estimate by $\sim$10 MW.

\subsection{Partitioning heat flux between MEF sources}

The Flow Mow experimental results can be combined with past measurements in a
heat budget to infer how MEF heat flux is partitioned between focused and
diffuse vents.  We first assume that the total flux through the sea floor into
the control volume is the sum of the flux through focused sources ($H_f$) and
the flux through diffuse sources ($H_d$).  Similarly, we take the total flux
out of the MEF control volume to be the sum of the vertical flux through the
top ($H_v$) and the horizontal flux through the sides ($H_h$).  This leads to
an expression for the steady state heat budget:

\begin{equation}
H_d + H_f + H_v + H_h = 0.
\label{hcons}
\end{equation}

As indicated previously for $H_h$ (Equation~\ref{hh}) and $H_v$
(Equation~\ref{hv}), we treat ${\overline{\Delta\theta}_S}$ as a reference
temperature anomaly, subtracting it from the measured $\Delta\theta$ in each of
the $H$ terms in Equation~\ref{hcons}.  Making this adjustment, and following
the outward flux sign convention, estimates of $H_f$ range from about $-$350~MW
\citep{ginster+94} to roughly $-$200~MW \citep{bemis+93}.  With attention to
the uncertainties involved in the 2 studies, a reasonable estimate of $H_f$ is
$-300$~MW.  The mean value of $H_v$ is about +550~MW \citep{stahr+02} while
$H_h$ is approximately +65~MW.  Solving Equation~\ref{hcons} for $H_d$ and
dividing both sides by $H_f$, the ratio of diffuse to focused flux becomes 

\begin{equation}
{\frac{H_d}{H_f}} = {\frac{-(H_f+H_v+H_h)}{H_f} } = {\frac{-(-300+550+65)}{-300} } 
= {\frac{-315}{-300} }.
\label{hdhf}
\end{equation}

Thus, MEF heat flux is partitioned about equally between diffuse and focused
sources, that is $H_d \simeq H_f \simeq$300~MW.  This constitutes a revision of
the idea that diffuse flux dominates focused flux in a ratio of about 10:1
\citep{schultz+92}.  If we assume that only diffuse sources are responsible for
the observed horizontal flux, then an additional implication of $H_h$ having a
magnitude of $\lesssim$65~MW is that roughly $4/5$ of $H_d$ is entrained into
rising plumes within the MEF perimeter, while only $\sim1/5$ escapes the field
laterally.

\subsection{Future directions}

The Flow Mow experiment, through both its vertical and horizontal components,
improved the precision of heat flux measurements made at the field scale.  The
same methodology could be applied at other fields along the Endeavour segment
and the results summed to obtain a segment-scale flux.  Such an effort could
take advantage of the mean northward flow within the axial valley to quantify
horizontal fluxes between fields.  Instrumenting a segment would help to
discern whether near-bottom heat is exported laterally below the equilibrium
depths, vertically through entrainment in higher-rising plumes, or both.  An
outstanding question is whether all heat within the axial valley is ultimately
entrained, and thereby integrated, by high $B$ plumes.  Effluent with a
positive $\Delta S$ is least likely to be entrained \citep{turner+campbell87};
near the sources of such fluid it will be particularly critical to monitor the
near-bottom environment for lateral fluxes.

At segments where the topography of the axial valley does not rectify deep sea
oscillations, synoptic and precise measurement of the horizontal flux from a
field may be very difficult.  In unconstrained and often rotary flow, long time
series will be required to achieve accurate mean fluxes \citep{thomson+92},
while meaningful instantaneous fluxes will only be obtained if all sides of a
control volume are monitored, ideally through a strategy guided by
advection/diffusion models that predict the evolution of the $T$ field.


\section{Acknowledgments}

This work was supported through NSF grant OCE-9872090.  Special thanks to
Christian Sarason Parker and the
\href{http://www.ocean.washington.edu/outreach/revel00/}{REVEL 2000}
participants, who acquired 179~hr of CTD data in just over 2~weeks.  This
exceptional resolution of the MEF hydrography was also made possible by the
(ABE) engineering genius of Dana Yoeger, Al Bradley, and their WHOI
collaborators, as well as the captain, marine technicians, and crew of the
R/V~Thompson who patiently cycled the ship and CTD around the MEF control
volume.  Rick Thomson and his team at the Institute for Ocean Science, Canada
deployed, recovered, and processed all current meter moorings and generously
provided the northern meter record.  Meg Tivey graciously made her MAVS data
available for comparison.  We greatly appreciate many helpful discussions and
reviews with Bill Lavelle, who also provided numerical simulations of MEF
diffuse plumes.  Figure generation, modeling, and typesetting were accomplished
with GMT \citep{wessel+smith91}, Matlab, and \LaTeX.  


%\section{Bibliography}
\bibliography{/home/scott/thesis/bib/mgg,/home/scott/thesis/bib/po,/home/scott/thesis/bib/atmo}
\bibliographystyle{agu}

\end{article}

\newpage

\begin{figure}[htbp] \begin{center} \begin{center}
\includegraphics[width=0.75\textwidth]{figs/fm1_location_map.eps} \end{center}
\end{center} \caption{Endeavour segment bathymetric map showing known
hydrothermal sources: open boxes are major fields (MF=Mothra, MEF=Main,
HRF=High Rise, SDF=Salty Dawg, SF=Sasquatch) and small solid squares are
diffuse or isolated focused vents (Q=Quebec, R=Raven/ReddFox, CB=Clam Bed,
D=Dune, C=Cirque).  Contours are every 100~m and 2170~m.  Inset map locates
segment on Juan de Fuca ridge.  Mean current vectors superimposed on mooring
locations ($+$) labeled (year,depth,elevation); 5~cm/s vector scale at lower
right.  Open black box aligned with ridge axis is perimeter of MEF and Flow Mow
control volume.  Solid circles ($\bullet$) are CTD monitoring stations (NoMEF
and SoMEF).} \label{location-map} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.9\textwidth]{figs/fm1_quiver.eps2} \end{center}
\caption{A 65~hr time series of hourly-mean currents within the axial valley north 
(top) and south (bottom) of the MEF.  True north is up.} \label{quiver} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.9\textwidth]{figs/fm1_v-tseries.pred_n_s_tivey_50_51.eps2}
\end{center} \caption{The zero-mean, along-axis component of flow measured at
the north and south moorings (top) and at the MEF (bottom), recorded during the
same period as in Figure \ref{quiver}.  Each is referenced to the flow
extrapolated to the year 2000 through harmonic analysis (H. Mofjeld, pers.\
comm.) using 60 days of 10~min mean data acquired 25~mab at the northeast
corner of the MEF in 1995.  Time series in the lower panel are from: a MAVS
deployed by M.  Tivey $\sim$0.5~mab near the center of the MEF, about 40~m
north of the S\&M sulfide structure; a MAVS mounted on ABE during the 2 longest
dives (ABE50 and ABE51).  All MAVS data were smoothed with Butterworth low pass
filters.} \label{v-series} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.8\textwidth]{figs/allabe_NSwalls.eps2} \end{center}
\caption{Spatially averaged $\Delta\theta$ from ABE dives 45, 46, and 50
projected orthogonally onto south and north control surfaces.  Black line is
ABE track.  Different maximum survey depths are due to tuning of ABE's
bottom-avoidance algorithm.  Averaging bins are 10~m wide and 25~m high.  White
areas have no data.  The title begins with a number indicating the order in
which the surfaces were surveyed and ends with the mean of all bins (noted
parenthetically).  Annotations in lower left corner of each panel are duration
of that surface, followed by time since the end of the previous surface, both
in hours.} \label{ns_abe_walls} \end{figure}
 
\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.8\textwidth]{figs/allctd_NSwalls.eps2} \end{center}
\caption{Spatially averaged $\Delta\theta$ from CTD stations 10, 12, and 13
projected orthogonally onto south (S) and north (N) control surfaces.  Black
line is CTD track.  Averaging bins are 100~m wide and 5~m high.  Mean of all
bins is noted parenthetically for each surface.  White areas have no data.
Bottoms of successive vertical oscillations are spaced $\sim$20~min apart; most
surfaces were surveyed in 80--100~min.  Station 12 began $\sim$3.8~hr after
station 10 ended, and station 13 began $\sim$14.2~hr after the end of station
12.} \label{allctd_NSwalls} \end{figure}

\newpage

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.8\textwidth]{figs/Dth.nosomef.image.alldeep.eps}
\end{center}
\caption{Time series of spatially and temporally averaged $\Delta\theta$ 
from CTD and ABE surveys of the
NoMEF and SoMEF areas.  Dotted black line is CTD track.  Averaging bins are
$1/2$~hr wide and 5~m high.  Vertical black lines mark temporal breaks
($\sim$1-5~days) between stations, each of which is numbered in lower left
corner.  White areas have no data.  Station 33 does not extend below 2155~m
because it was located west of stations 4, 6, and 7, where the western scarp
shoals to $\sim$2160~m (see dual SoMEF locations, Figure~\ref{location-map}).} 
\label{nosomef_waterfall} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.6\textwidth]{figs/all_zbin_dth_hist_nomef.eps2}
\includegraphics[width=0.6\textwidth]{figs/all_zbin_dth_hist_somef.eps2}
\end{center} \caption{Stacked histograms of depth-binned $\Delta\theta$
observed north (upper) and south (lower) of the MEF.  Depth range of each bin
is 25~m and upper extent of each bin is noted on the left axis.  For reference,
the nearby ridge crests have a mean depth of $\sim$2100--2125~m.
$\Delta\theta$ for each distribution is tabulated at right.  North data is from
CTD stations 3, 5, 10, 14, and 28, and ABE dives 45, 46, and 50; south data is
from CTD stations 4, 6, 7, 12, 13, and 33, and ABE dives 45, 46, 50.}
\label{depth-hist} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.8\textwidth]{figs/puffframe.eps} \end{center}
\caption{A single frame from a puff model animation showing a plan view of the
distribution of temperature around the MEF (black box).  In this snapshot, the
model is forced by the idealized flow (harmonic analysis + 1 cm/s mean) and the
source flux is constant (300~MW).  Smaller panels show the instantaneous net
flux through the MEF perimeter, the half-hourly current vector, and a colorbar
with temperature anomaly units in $^\circ$C.  Animations of the puff model and
Bill Lavelle's diffuse plume model have been submitted as supplementary
material, and may be presented through a web page akin to the temporary 
prototype that can be accessed via the authors' 
\href{http://econscience.org/scott/g3/}{website}: econscience.org/scott/g3/}
\label{puff-model} \end{figure}

\newpage

\begin{figure}[htbp] \begin{center}
\includegraphics[width=0.8\textwidth]{figs/mof_fluxcomp2.eps2} \end{center}
\caption{Means and standard deviations of horizontal flux ($H_h$) series
modeled over a range of mean flows, expressed as percentage of source heat flux
($H_{source}$).  Upper panel shows the means for instantaneous ($<$Tivi$>$) and
averaged ($<$Ti$><$vi$>$) flux series.  Lower panel shows standard deviations
of instantaneous (Tivi), velocity-averaged (Ti$<$vi$>$), and
temperature-averaged ($<$Ti$>$vi) flux series.} \label{flux-comp} \end{figure}

\end{document}
