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%                    N E S P I / B R A C K E T . T E X 
%                    doc: Sun Aug 29 18:08:55 1999
%                    dlm: Wed Jun  7 23:30:47 2000
%                    (c) 1999 A.M. Thurnherr
%                    uE-Info: 50 31 NIL 0 0 72 3 2 4 ofnI
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% STD METHOD IS NOT CLEARLY DEFINED

In the Pacific ocean geothermal temperature anomalies are often
calculated as deviations from background $T/\rho$ or $T/S$ trends. A
number of different methods are used to estimate the background trends,
effectively resulting in different anomaly definitions.
\citeN{EPSL/lupton+80}, for example, use a visual method based on the
observation of abrupt changes in the $T/S$ trend at the top and bottom
of a layer characterized by hydrothermal helium anomalies;
\citeN{Nature/lupton+85} use a similar method in $T/\rho$ space with
the additional assumption of a linear background relationship. In other
studies the backgrounds are defined by extrapolating the hydrographic
trends observed above bottom layers characterized by hydrothermal
particle and chemical anomalies to the sea floor
\citeEG{JGR/baker+90,Nature/baker+lupton90}. This method will be called
the \emph{extrapolation method.} Following \citeN{JGR/thomson+95}, the
geothermally modified bottom layer will be called the \emph{geothermal
boundary layer (GBL).}

% PROBLEMS OF STD METHOD => NEED INFO => USE NEPHELS

There are two potential problems associated with hydrographic anomalies
defined as deviations from $T/\rho$ or $T/S$ trends extrapolated into
the GBL, namely the lack of separation of the hydrographic effects
caused by different geothermal processes \citeEG{EPSL/thomson+92} and
the anomalies caused by non-geothermal hydrographic variability
\citeEG{JGR/baker+hammond92}. To solve these problems additional
information is required to separate the geothermal signals from
``hydrographic noise''. Light-scattering and transmissometry anomalies
are often used in conjunction with hydrographic measurements to detect
and map hydrothermal plumes and to limit the volume integrals from
which the geothermal heat content of the water column is calculated
\citeEG{JGR/baker+hammond92,GRL/helfrich+98}.

% METHOD ILLUSTRATION

\begin{figure}[t]

\placeFig{NESPI/PBM}

\caption[Methods for estimating isopycnal hydrographic
anomalies]{Illustration of two methods for estimating isopycnal
hydrographic anomalies; thick lines represent nephelometry and
temperature profiles in density space. The straight line connecting the
temperature profile between the top (\sfT) and the bottom (\sfB) of the
particle peak shows the linear approximation to the background $T/\rho$
relationship relative to which the temperature (spice) anomalies of the
plume-bracketing method {\sffamily (a)} are defined. The dashed line
shows the extrapolation of the $T/\rho$ trend of the water column
overlying the plume into the GBL, defining the temperature anomalies of
the extrapolation method {\sffamily (a+b)}.}

\labelFig{PBM}

\end{figure}

% METHOD DESCRIPTION

\callout{\rFigNP{PBM}} shows a sketch illustrating a new anomaly
definition and method (related to that of \citeN{Nature/lupton+85})
which incorporates nephelometry or transmissometry data to constrain
the hydrographic anomalies associated with the hydrothermal particle
plume. The background $T/\rho$ relationship within the particle layer
of a single profile is approximated by linearly interpolating the
measured $T/\rho$ properties between the top \sfTP and the bottom
\sfBP of the particle layer. Above \sfT and below \sfB, the anomalies
are set to zero. This method will be called the \emph{plume-bracketing
method.} For comparison, the extrapolation method is shown as well.

% FLAME CTD DATA SET

\begin{figure}[t]

\placeTwoFigs[.6]{NESPI/pbm29}{NESPI/pbm30u}

\caption[Plume-bracketing method]{Application of the plume-bracketing
method to two profiles of the 1997 CTD data set.}

\labelFig{Fmethod}

\end{figure}

\begin{figure}[t]

\placeFig{NESPI/bfit}

\caption[Spice vs.\ nephel regressions]{Spice vs.\ nephel scatter plots
and linear regressions derived from the particle peaks of the profiles
shown in \protect\rfigNP{Fmethod}; the origin of profile \pb is
horizontally offset by \V{0.8}; correlation coefficients are $r=-0.97$
and $r=-0.69$, regression slopes \degCpV*{-2.3}{-2} and
\degCpV*{-1.9}{-2}, and RMS errors \RMS{2.9} and \RMS{2.7},
respectively.}

\labelFig{Ffit}

\end{figure}

To test the plume-bracketing method it was applied to the CTD data set
from the 1997 survey \rsec{F-methods}. Because of the small vertical
separation between the observed interleaving structures
\rsec{F-waterorigin} and the particle plume the extrapolation method
cannot be used. \callout{\rFigNP{Fmethod}} illustrates the
plume-bracketing method applied to the two profiles with the largest
(\V{1.3}) and the smallest (\V{0.4}) nephelometry peak values where the
corresponding thermal anomalies are distinguishable from temperature
scatter (see below). The deviations from the near-linear $T/\rho$
trends at the top of the temperature profiles are signatures of the
interleaving structures. The bands bracketing the nephelometry peaks
were positioned visually and span $10^{-3}$ $\sigma_2$ units each.
\callout{\rFigNP{Ffit}} shows the scatter plots and linear regressions
of the resulting spice vs.\ nephel anomalies. The respective
correlation coefficients are $r=-0.97$ and $r=-0.69$, and both RMS
errors are \RMS{<\!3}.

Out of the 31 \F CTD profiles containing particle-plume signatures, 16
do not extend below the plume (they are \emph{truncated),} implying
that the plume-bracketing method cannot be applied. It was found that
the method failed to establish correlations in 4 of the remaining
profiles, all of which have nephelometry peak values \V{<\!0.3}. (Using
a regression slope estimate of \degCpV*{-2}{-2}, this corresponds to
peak temperature anomalies of less than twice the RMS error.) The
weighted mean ($\pm1\sigma$) correlation coefficient of the remaining
11 profiles is $r=-0.84(\pm0.03)$.\REM{and the RMS errors of the
individual regressions are \RMS{2.6$--$5.9}.}

