%======================================================================
%                    N E S P I / P A C I F I C . T E X 
%                    doc: Tue Aug 31 11:51:15 1999
%                    dlm: Wed Jun  7 23:46:58 2000
%                    (c) 1999 A.M. Thurnherr
%                    uE-Info: 6 21 NIL 0 0 72 3 2 4 ofnI
%======================================================================

% VISUAL COMPARISON

\begin{figure}[t]

\placeTwoFigs[.6]{NESPI/P16comp}{NESPI/P04comp}
\placeFig[.6]{NESPI/P25comp}

\caption[Pacific particle and temperature anomaly profiles]{Particle
and temperature anomaly profiles of Pacific hydrothermal plumes; \pa \&
\pc from \degS{17} on the East-Pacific Rise, and \pb from the Juan de
Fuca Ridge; the ``extrapolated'' anomalies were calculated as
deviations from extrapolated $T/\rho$ relationships of the water
overlying the plumes; the ``bilinear'' profiles were derived from the
particle peaks (shaded); horizontal lines show the upper limits of the
GBLs; vertical lines indicate the origins of the temperature and the
(arbitrarily scaled) particle anomaly axes; data courtesy of Ed Baker.}

\labelFig{NESPI-Pacific}

\end{figure}

% PACIFIC PROFILES

\rFigNP{PBM} indicates that the temperature anomalies calculated with
the new methods are related to the ones derived using the extrapolation
method. (In the following, ``bilinear'' and ``extrapolated'' will be
used to distinguish results from the two methods.) To compare the
different anomaly definitions, the bilinear method was applied to three
profiles (generously provided by Ed Baker) from Pacific hydrothermal
sites \callout{\rfig{NESPI-Pacific}} where the ``extrapolated''
anomalies were calculated as deviations from quadratic (\sfa and \sfc)
and linear (\sfb) trends \perscomm{E.T.\ Baker}. Interpretation of
individual profiles without knowledge of their associated contexts is
tenuous, but the Pacific profiles have some features in common with
each other (and with the \R data) which are worth pointing out.

% EPR PROFILE (a)

The particle anomalies of profile \pa from the East-Pacific Rise
are restricted to a well defined peak, similar to the \R data. The
``bilinear'' temperature anomalies vanish at the top and at the bottom
of the particle layer, and the profile shows the familiar bias towards
the hydrographic properties below the plume. Correlation between the
particle and the temperature anomalies within the shaded area is higher
for the ``bilinear'' anomalies ($r=0.95$, RMS error \RMS{1.6}) than for
the ``extrapolated'' anomalies ($r=0.85$, RMS error \RMS{2.7}). The
vertically integrated ``extrapolated'' temperature anomalies of the GBL
(i.e.\ below the horizontal line\REM{\m{2340}}, determined by the depth
where the ``extrapolated'' anomalies depart from
zero)\REM{\degCm{4.14}} are $4.4$ times larger than the corresponding
integrated ``bilinear'' anomalies\REM{\degCm{0.94}} (noting that the
latter are zero outside the particle plume by definition).

% JdFR PROFILE (b)

Profile \pb from the Juan de Fuca Ridge is characterized by a
qualitatively similar ``extrapolated'' temperature anomaly profile, 
while the particle distribution is different from that of profile \pa.
Compared to the water column above the GBL, there are significant
particle anomalies extending to the bottom of the cast. Below the main
particle peak they remain approximately uniform, consistent with an
elevated background particle concentration below the equilibrium plume.
There are therefore two reasonable choices for the origin of the
particle anomalies, namely the level in the water column above the GBL
and the level near the bottom of the profile. The ``bilinear''
temperature anomalies shown in \rfigNP{NESPI-Pacific} were derived by
choosing the latter. Physically, this is motivated by considering the
equilibrium plume to be a mixture of hydrothermal effluents and
background fluid entrained during plume rise, consistent with the
hydrographic bias of the new methods. (Applying the bilinear method to
the same profile with the particle anomalies referenced to the water
column above the GBL results in a temperature anomaly profile offset by
\degC{0.02} but otherwise identical to the one shown.) Compared to the
``extrapolated'' anomalies, the ``bilinear'' ones reduce the RMS error
of the temperature vs.\ particle anomaly correlation within the shaded
area by more than 50\% (from \RMS{4.5} to \RMS{1.9}) while the
corresponding correlation coefficient increases from $r=0.71$ to
$r=0.92$. The vertically integrated ``extrapolated'' temperature
anomalies of the GBL are\REM{\degCm{6.48}} $6.1$ times larger than the
corresponding integrated\REM{\degCm{1.06}} ``bilinear'' anomalies.

% EPR PROFILE (c)

In profile \pc from the East-Pacific Rise the particle plume occupies
nearly the entire GBL. The ``bilinear'' temperature anomalies
associated with the particle plume are virtually identical to the
``extrapolated'' anomalies offset by \degC{-0.01}. Statistically, the
temperature vs.\ particle anomaly correlations are indistinguishable
(``extrapolated'': $r=0.95$, RMS error \RMS{2.8}\REM{/\degCm{9.93}};
``bilinear'': $r=0.95$, RMS error \RMS{2.7}\REM{/\degCm{5.94}}).
Without additional information it is not clear which of the two anomaly
definitions is more appropriate in this case.

% RESIDUAL ANOMALIES

\begin{figure}[t]

\placeTwoFigs[.6]{NESPI/P16res}{NESPI/P04res}

\caption[Pacific residual particle and temperature anomaly
profiles]{Residual particle and temperature anomalies of Pacific
profiles \pa and \pb; the shaded regions and the horizontal and
vertical lines are the same as in \protect\rfigNP{NESPI-Pacific}.}

\labelFig{residual}

\end{figure}

% CONFIRM SUPERPOSITION

Combining the results from the bilinear and the extrapolation methods
allows the plume particle and the corresponding temperature anomalies
to be removed from the respective profiles. The residual temperature
anomalies shown in \callout{\rfigNP{residual}} were derived by
subtracting the ``bilinear'' from the ``extrapolated'' profiles, while
the corresponding residual particle anomalies $\Delta_r n(z)$\ls{Drn}
were calculated using
 %
\begin{equation}
\Delta_r n(z) = \Delta n(z) - \Delta_\rho T(z) / C.	\label{eqn:residual}
\end{equation}
 %
The residual particle anomalies within the shaded plume layers
fluctuate around zero, as expected from \rexpr{bilin}. The large
scatter in profile \pa is caused by the small magnitude of the
temperature vs.\ particle-anomaly regression slope $C$ which is
approximately 25 times smaller than the corresponding value of profile
\pb. The residual temperature anomalies increase towards the sea bed,
similar to geothermally modified profiles without hydrothermal particle
plume signatures \citeEG{JGR/thomson+95}.



