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Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery
Data Analysis Methods in Physical Oceanography 2nd
Edition W. J. Emery Digital Instant Download
Author(s): W. J. Emery, Richard E. Thomson
ISBN(s): 0444507574
Edition: 2
File Details: PDF, 36.04 MB
Year: 2001
Language: english
Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery
Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery
Preface
Numerous books have been written on data analysis methods in the physical sciences
over the past several decades. Most of these books lean heavily toward the theoretical
aspects of data processing and few have been updated to include more modern
techniques such as fractal analysis and rotary spectral decomposition. In writing this
book we saw a clear need for a practical reference volume for earth and ocean sciences
that brings established and modern techniques together under a single cover. The text
is intended for students and established scientists alike. For the most part, graduate
programs in oceanography have some form of methods course in which students learn
about the measurement, calibration, processing and interpretation of geophysical
data. The classes are intended to give the students needed experience in both the
logistics of data collection and the practical problems of data processing and analysis.
Because the class material generally is based on the experience of the faculty members
giving the course, each class emphasizes different aspects of data collection and
analysis. Formalism and presentation can differ widely. While it is valuable to learn
from the first-hand experiences of the class instructor, it seemed to us important to
have available a central reference text that could be used to provide some uniformity
in the material being covered within the oceanographic community.
Many of the data analysis techniques most useful to oceanographers can be found in
books and journals covering a wide variety of topics ranging from elementary statistics
to wavelet transforms. Much of the technical information on these techniques is
detailed in texts on numerical methods, time series analysis, and statistical tech-
niques. In this book, we attempt to bring together many of the key data processing
methods found in the literature, as well as add new information on data analysis
techniques not readily available in older texts. We also provide, in Chapter 1, a
description of most of the instruments used today in physical oceanography. Our hope
is that the book will provide instructional material for students in the oceanographic
sciences and serve as a general reference volume for those directly involved with
oceanographic research.
The broad scope and rapidly evolving nature of oceanographic sciences has meant
that it has not been possible for us to cover all existing or emerging data analysis
methods. However, we trust that many of the methods and procedures outlined in the
book will provide a basic understanding of the kinds of options available to the user
for interpretation of data sets. Our intention is to describe general statistical and
analytical methods that will be sufficiently fundamental to maintain a high level of
utility over the years.
xii Data Analysis Methods in Physical Oceanography
Finally, we believe that the analysis procedures discussed in this book apply to a
wide readership in the geophysical sciences. As with oceanographers, this wider
community of scientists would likely benefit from a central source of information that
encompasses not only a description of the mathematical methods but also considers
some of the practical aspects of data analyses. It is this synthesis between theoretical
insight and the logistical limitations of real data measurement that is a primarily goal
of this text.
WilliamJ. Emery and Richard E. Thomson
Boulder, Colorado and Sidney, BC
Acknowledgments
Many people have contributed to this book over the years that it has taken to write.
The support and encouragement we received from our colleagues while we were
drafting the manuscript is most gratefully acknowledged. Bill Emery began work on
the book during a sabbatical year at the Institut ft~rMeereskunde (IFM) in Kiel and is
grateful for the hospitality of Drs Gerold Siedler, Wolfgang Kraus, Walter Zenk, Rolf
Kas~, Juergen Willebrand, Juergen Kielman, and others. Additional progress was
made at the University of British Columbia where Mrs Hiltrud Heckel aided in typing
the handwritten text. Colleagues at the University of Colorado who helped with the
book include Dr Robert Leben, who reviewed the text, contributed advice, text and
figures, and Mr Dan Leatzow, who converted all of the initial text and figures to the
Macintosh. The author would like to thank Mr Tom Kelecy for serving as the teaching
assistant the first time that the material was presented in a course on "Engineering
Data Analysis". Bill Emery also thanks the students who helped improve the book
during the course on data analysis and the National Space and Aeronautics
Administration (NASA) whose grant funding provided the laptop computer used in
preparation of the manuscript. The author also thanks his family for tolerating the
ever growing number of files labelled "dampo" on the family computer.
Rick Thomson independently began work on the book through the frustration of too
much time spent looking for information on data analysis methods in the literature.
There was clearly a need for a reference-type book that covers the wide range of
analysis techniques commonly used by oceanographers and other geoscientists. Many
of the ideas for the book originated with the author's studies as a research scientist
within Fisheries and Oceans Canada, but work on the book was done strictly at home
during evenings and weekends. Numerous conversations with Drs Dudley Chelton
and Alexander Rabinovich helped maintain the author's enthusiasm for the project.
The author wishes to thank his wife and two daughters (Justine and Karen) for
enduring the constant tapping of the keyboard and hours of dark despair when it
looked as if the book would never come to an end, and his parents (John and Irene) for
encouraging an interest in science.
The authors would like to thank the colleagues and friends who took time from their
research to review sections of the text or provide figures. There were others, far too
numerous to mention, whose comments and words of advice added to the usefulness of
the text. We are most grateful to Dudley Chelton of Oregon State University and
Alexander Rabinovich of Moscow State University who spent considerable time
criticizing the more mathematical chapters of the book. Dudley proved to be a most
impressive reviewer and Sasha contributed several figures that significantly improved
xvi Data Analysis Methods in Physical Oceanography
the section on time series analysis. George Pickard, Professor Emeritus of the
University of British Columbia (UBC), and Susumu Tabata, Research Scientist
Emeritus of the Institute of Ocean Sciences (IOS), provided thorough, and much
appreciated, reviews of Chapters 1 and 2. We thank Andrew Bennett of Oregon State
University for his comments on inverse methods in Chapter 4, Brenda Burd of Ecostat
Research for reviewing the bootstrap method in Chapter 3, and Steve Mihaly for
reviewing Appendix A. Contributions to the text were provided by Libe Washburn
(University of California, Santa Barbara), Peter Schlussel (IFM), Patrick Cummins
(lOS), and Mike Woodward (lOS). Figures or data were generously provided by Mark
E. Geneau (Inter-Ocean Systems, Inc.), Gail Gabel (G.S. Gabel Associates), R. Lee
Gordon (RD Instruments, Inc.), Diane Masson, Humfrey Melling, George Chase, John
Love, and Tom Juhfisz (lOS), Jason Middleton and Greg Nippard (University of New
South Wales), Doug Bennett (Sea-Bird Electronics, Inc.), Dan Schaas and Marcia
Gracia (General Oceanics), Mayra Pazos (National Oceanic and Atmospheric Admini-
stration), Chris Garrett (University of Victoria), David Halpern (Jet Propulsion
Laboratory), Phillip Richardson (Woods Hole Oceanographic Institution), Daniel
Jamous (Massachusetts Institute of Technology), Paul Dragos (Battelle Ocean
Sciences), Thomas Rossby (University of Rhode Island), Lynne Talley (Scripps),
Adrian Dolling and Jane Eert (Channel Consulting), and Gary Hamilton (Intelex
Research).
The authors would also like to thank Anna Allen for continued interest in this
project from the time she took over until now. There were a great many delays and
postponements, but through it all she remained firm in her support of the project.
This continued support made it easier to work through these delays and gave us
courage to believe that the project would one day be completed.
Lastly, we would like to thank our colleagues who found and reported errors and
omissions in the first printing of the book. Although the inevitable typos and mistakes
are discouraging for the authors (and frustrating for the reader), it is better that we
know about them so that they can be corrected in future printings and revisions. Our
thanks to Brian Blanton (University of North Carolina), Mike Foreman (Institute of
Ocean Sciences), Denis Gilbert (Institute Maurice-Lamontagne), Jack Harlan (NOTkA,
Boulder, Colorado), Clive Holden (Oceanographic Field Services, Pymbla, New South
Wales), Frank Janssen (University of Hamburg), Masahisa Kubota (Tokai University),
Robert Leben (University of Colorado), Rolf Lueck (University of Victoria), Andrew
Slater (University of Colorado), and Roy Hourston (WeatherWorks Consulting,
Victoria).
C HAPTER 1
Data Acquisition and Recording
1.1 INTRODUCTION
Physical oceanography is an evolving science in which the instruments, types of
observations and methods of analysis have undergone considerable change over the
last few decades. With most advances in oceanographic theory, instrumentation, and
software, there have been significant advances in marine science. The advent of digital
computers has revolutionized data collection procedures and the way that data are
reduced and analyzed. No longer is the individual scientist personally familiar with
each data point and its contribution to his or her study. Instrumentation and data
collection are moving out of direct application by the scientist and into the hands of
skilled technicians who are becoming increasingly more specialized in the operation
and maintenance of equipment. New electronic instruments operate at data rates not
possible with earlier mechanical devices and produce volumes of information that can
only be handled by high-speed computers. Most modern data collection systems
transmit sensor data directly to computer-based data acquisition systems where they
are stored in digital format on some type of electronic medium such as a tape, hard-
drive, or optical disk. High-speed analog-to-digital (AD) converters and digital-signal-
processors (DSPs) are now used to convert voltage or current signals from sensors to
digital values.
With the many technological advances taking place, it is important for oceano-
graphers to be aware of both the capabilities and limitations of their sampling
equipment. This requires a basic understanding of the sensors, the recording systems
and the data-processing tools. If these are known and the experiment carefully
planned, many problems commonly encountered during the processing stage can be
avoided. We cannot overemphasize the need for thoughtful experimental planning
and proper calibration of all oceanographic sensors. If instruments are not in near-
optimal locations or the researcher is unsure of the values coming out of the machines,
then it will be difficult to believe the results gathered in the field. To be truly reliable,
instruments should be calibrated on a regular basis at intervals determined by use and
the susceptibility of the sensor to drift. More specifically, the output from some
instruments such as the piezoelectric pressure sensors and fixed pathlength trans-
missometers drift with time and need to be calibrated before and after each field
deployment. For example, the zero point for the Paroscientific Digiquartz (0-
10,000 psi) pressure sensors used in the Hawaii Ocean Time-series (HOT) at station
"Aloha" 100 km north of Honolulu drifts about 4 dbar in three years. As a con-
sequef~ce, the sensors are calibrated about every six months against a Paroscientific
2 Data Analysis Methods in Physical Oceanography
laboratory standard, which is recalibrated periodically at special calibration facilities
in the United States (Lukas, 1994). Our experience also shows that over-the-side field
calibrations during oceanic surveys can be highly valuable. As we discuss in the
following chapters, there are a number of fundamental requirements to be considered
when planning the collection of field records, including such basic considerations as
the sampling interval, sampling duration and sampling location.
It is the purpose of this chapter to review many of the standard instruments and
measurement techniques used in physical oceanography in order to provide the reader
with a common understanding of both the utility and limitations of the resulting
measurements. The discussion is not intended to serve as a detailed "user's manual"
nor as an "observer's handbook". Rather, our purpose is to describe the fundamentals
of the instruments in order to give some insight into the data they collect. An under-
standing of the basic observational concepts, and their limitations, is a prerequisite for
the development of methods, techniques and procedures used to analyze and interpret
the data that are collected.
Rather than treat each measurement tool individually, we have attempted to group
them into generic classes and to limit our discussion to common features of the
particular instruments and associated techniques. Specific references to particular
company products and the quotation of manufacturer's engineering specifications
have been avoided whenever possible. Instead, we refer to published material
addressing the measurement systems or the data recorded by them. Those studies
which compare measurements made by similar instruments are particularly valuable.
The emphasis of the instrument review section is to give the reader a background in
the collection of data in physical oceanography. For those readers interested in more
complete information regarding a specific instrument or measurement technique, we
refer to the references at the end of the book where we list the sources of the material
quoted. We realize that, in terms of specific measurement systems, and their review,
this text will be quickly dated as new and better systems evolve. Still, we hope that the
general outline we present for accuracy, precision and data coverage will serve as a
useful guide to the employment of newer instruments and methods.
1.2 BASIC SAMPLING REQUIREMENTS
A primary concern in most observational work is the accuracy of the measurement
device, a common performance statistic for the instrument. Absolute accuracy
requires frequent instrument calibration to detect and correct for any shifts in
behavior. The inconvenience of frequent calibration often causes the scientist to
substitute instrument precision as the measurement capability of an instrument.
Unlike absolute accuracy, precision is a relative term and simply represents the ability
of the instrument to repeat the observation without deviation. Absolute accuracy
further requires that the observation be consistent in magnitude with some absolute
reference standard. In most cases, the user must be satisfied with having good
precision and repeatability of the measurement rather than having absolute
measurement accuracy. Any instrument that fails to maintain its precision, fails to
provide data that can be handled in any meaningful statistical fashion. The best
Data Acquisition and Recording 3
instruments are those that provide both high precision and defensible absolute
accuracy.
Digital instrument resolution is measured in bits, where a resolution of N bits
means that the full range of the sensor is partitioned into 2N equal segments (N = 1, 2,
...). For example, eight-bit resolution means that the specified full-scale range of the
sensor, say V = 10 volts, is divided into 28 = 256 increments, with a bit-resolution of
V/256 = 0.039 volts. Whether the instrument can actually measure to a resolution or
accuracy of V/2 N units is another matter. The sensor range can always be divided into
an increasing number of smaller increments but eventually one reaches a point where
the value of each bit is buried in the noise level of the sensor.
1.2.1 Sampling interval
Assuming the instrument selected can produce reliable and useful data, the next
highest priority sampling requirement is that the measurements be collected often
enough in space and time to resolve the phenomena of interest. For example, in the
days when oceanographers were only interested in the mean stratification of the world
ocean, water property profiles from discrete-level hydrographic (bottle) casts were
adequate to resolve the general vertical density structure. On the other hand, these
same discrete-level profiles failed to resolve the detailed structure associated with
interleaving and mixing processes that now are resolved by the rapid vertical sampling
of modern conductivity-temperature-depth (CTD) profilers. The need for higher
resolution assumes that the oceanographer has some prior knowledge of the process of
interest. Often this prior knowledge has been collected with instruments incapable of
resolving the true variability and may only be suggested by highly aliased (distorted)
data collected using earlier techniques. In addition, theoretical studies may provide
information on the scales that must be resolved by the measurement system.
For discrete digital data x(ti) measured at times ti, the choice of the sampling
increment At (or Zk~cin the case of spatial measurements) is the quantity of import-
ance. In essence, we want to sample often enough that we can pick out the highest
frequency component of interest in the time-series but not oversample so that we fill
up the data storage file, use up all the battery power, or become swamped with a lot of
unnecessary data. We might also want to sample at irregular intervals to avoid built-in
bias in our sampling scheme. If the sampling interval is too large to resolve higher
frequency components, it becomes necessary to suppress these components during
sampling using a sensor whose response is limited to frequencies equal to that of the
sampling frequency. As we discuss in our section on processing satellite-tracked
drifter data, these lessons are often learned too latemafter the buoys have been cast
adrift in the sea.
The important aspect to keep in mind is that, for a given sampling interval At, the
highest frequency we can hope to resolve is the Nyquist (or folding)frequency, fx,
defined as
fN = 1/(2At) (1.2.1)
We cannot resolve any higher frequencies than this. For example, if we sample every
10 h, the highest frequency we can hope to see in the data isfN = 0.05 cph (cycles per
hour). Equation (1.2.1) states the obvious--that it takes at least two sampling intervals
(or three data points) to resolve a sinusoidal-type oscillation with period 1/fN (Figure
4 Data Analysis Methods in Physical Oceanography
1.2.1). In practice, we need to contend with noise and sampling errors so that it takes
something like three or more sampling increments (i.e. _>four data points) to
accurately determine the highest observable frequency. Thus,fx is an upper limit. The
highest frequency we can resolve for a sampling of At - 10 h in Figure 1.2.1 is closer
to 1~3At ~ 0.033 cph.
An important consequence of (1.2.1) is the problem ofaliasing. In particular, if there
is considerable energy at frequencies f > fN--Which we obviously cannot resolve
because of the At we pickedmthis energy gets folded back into the range of frequen-
cies, f < fN, which we are attempting to resolve. This unresolved energy doesn't
disappear but gets redistributed within the frequency range of interest. What is worse
is that the folded-back energy is disguised (or aliased) within frequency components
different from those of its origin. We cannot distinguish this folded-back energy from
that which actually belongs to the lower frequencies. Thus, we end up with erroneous
(aliased) estimates of the spectral energy variance over the resolvable range of fre-
quencies. An example of highly aliased data would be 13-h sampling of currents in a
region having strong semidiurnal tidal currents. More will be said on this topic in
Chapter 5.
As a general rule, one should plan a measurement program based on the frequencies
and wavenumbers (estimated from the corresponding periods and wavelengths) of the
parameters of interest over the study domain. This requirement then dictates the
selection of the measurement tool or technique. If the instrument cannot sample
rapidly enough to resolve the frequencies of concern it should not be used. It should be
emphasized that the Nyquist frequency concept applies to both time and space and
the Nyquist wavenumber is a valid means of determining the fundamental wavelength
that must be sampled.
1.2.2 Sampling duration
The next concern is that one samples long-enough to establish a statistically
significant picture of the process being studied. For time-series measurements, this
amounts to a requirement that the data be collected over a period sufficiently long that
1.0
0.4
~" 0.2
= 0.0
o
.m
ca -0.2
= -0.4
[.l.,
-0.6
-- ~ 9 True value
0.8 -- .If "~"~, o Measured value
*i
0.6 -- t
- j
-0.8
-l.o j
0 0 4 8 12 16 20 24
Time (n)
Figure 1.2.1. Plot of the function F(n) = sin (27m/20 + 4~)where time is given by the integer n - -1,
O, .... 24. The period 2At =l/fN is 20 units and ~ is a random phase with a small magnitude in the
range +0.1. Open circles denote measured points and solid points the curve F(n). Noise makes it
necessary to use more than three data values to accurately define the oscillation period.
Data Acquisition and Recording 5
repeated cycles of the phenomenon are observed. This also applies to spatial sampling
where statistical considerations require a large enough sample to define multiple
cycles of the process being studied. Again, the requirement places basic limitations on
the instrument selected for use. If the equipment cannot continuously collect the data
needed for the length of time required to resolve repeated cycles of the process, it is
not well suited to the measurement required.
Consider the duration of the sampling at time step At. The longer we make the
record the better we are to resolve different frequency components in the data. In the
case of spatially separated data, AJc, resolution increases with increased spatial
coverage of the data. It is the total record length T = NAt obtained for N data samples
that: (1) determines the lowest frequency (the fundamental frequency)
fo = 1/(NAt) = 1/T (1.2.2)
that can be extracted from the time-series record; (2) determines the frequency
resolution or minimum difference in frequency Af = If2-fll = 1~NAt that can be
resolved between adjoining frequency components, fl and f2 (Figure 1.2.2); and (3)
determines the amount of band averaging (averaging of adjacent frequency bands)
that can be applied to enhance the statistical significance of individual spectral esti-
mates. In Figure 1.2.2, the two separate waveforms of equal amplitude but different
frequency produce a single spectrum. The two frequencies are well resolved for
Af = 2~NAt and 3~2NAt, just resolved for Af--1~NAt, and not resolved for
Af = 1~2NAt.
In theory, we should be able to resolve all frequency components,f, in the frequency
rangefo <_f <_fN, wherefx andfo are defined by (1.2.1) and (1.2.2), respectively. Herein
lies a classic sampling problem. In order to resolve the frequencies of interest in a
time-series, we need to sample for a long time (T large) so that fo covers the low end of
the frequency spectrum and Af is small (frequency resolution is high). At the same
time, we would like to sample sufficiently rapidly (At small) so thatfN extends beyond
all frequency components with significant spectral energy. Unfortunately, the longer
and more rapidly we want to sample the more data we need to collect and store, the
more time, effort and money we need to put into the sampling and the better
resolution we require from our sensors.
Our ability to resolve frequency components follows from Rayleigh's criterion for
the resolution of adjacent spectral peaks in light shone onto a diffraction grating. It
states that two adjacent frequency components are just resolved when the peaks of the
spectra are separated by frequency difference Af =fo = 1~NAt (Figure 1.2.2). For
example, to separate the spectral peak associated with the lunar-solar semidiurnal
tidal component M2 (frequency - 0.08051 cph) from that of the solar semidiurnal
tidal component $2 (0.08333 cph), for which Af - 0.00282 cph, requires N - 355 data
points at a sampling interval At - 1 h or N = 71 data points at At = 5 h. Similarly, a
total of 328 data values at 1-h sampling are needed to separate the two main diurnal
constituents Kl and O1 (Af - 0.00305 cph). Note that iffN is the highest frequency we
can measure and fo is the limit of frequency resolution, then
fX/fo = (1/2At)/(1/NAt) = N/2 (1.2.3)
is the maximum number of Fourier components we can hope to estimate in any
analysis.
6 Data Analysis Methods in Physical Oceanography
(a) ~ -- Af ----q (b)
wb
0
ra~
(c)
Frequency
(d)
t
~ Combined
spectra
Figure 1.2.2. Spectral peaks of two separate waveforms of equal amplitude and frequencies f z and f2
(dashed and thin line) together with the calculated spectrum (solid line). (a) and (b) are well-resolved
spectra; (c) just resolved spectra; and (d) not resolved. Thick solid line is total spectrum for two
underlying signals with slightly different peak frequencies.
1.2.3 Sampling accuracy
According to the two previous sections, we need to sample long and often if we hope to
resolve the range of scales of interest in the variables we are measuring. It is
intuitively obvious that we also need tolsample as accurately as possible--with the
degree of recording accuracy determined by the response characteristics of the
sensors, the number of bits per data record (or parameter value) needed to raise
measurement values above background noise, and the volume of data we can live ~ith.
There is no use attempting to sample the high or low ends of the spectrum if the
instrument cannot respond rapidly or accurately enough to resolve changes in the
parameter being measured. In addition, there are several approaches to this aspect of
data sampling including the brute-force approach in which we measure as often as we
can at the degree of accuracy available and then improve the statistical reliability of
each data record through post-survey averaging, smoothing, and other manipulation.
1.2.4 Burst sampling versus continuous sampling
Regularly-spaced, digital time-series can be obtained in two different ways. The most
common approach is to use a continuous sampling mode, in which the data are sampled
at equally spaced intervals tk -- to + kAt from the start time to. Here, k is a positive
integer. Regardless of whether the equally spaced data have undergone internal
averaging or decimation using algorithms built into the machine, the output to the
data storage file is a series of individual samples at times tk. (Here, "decimation" is
used in the loose sense of removing every nth data point, where n is any positive
integer, and not in the sense of the ancient Roman technique of putting to death one
in ten soldiers in a legion guilty of mutiny or other crime.) Alternatively, we can use a
Data Acquisition and Recording 7
burst sampling mode, in which rapid sampling is undertaken over a relatively short time
interval AtB or "burst" embedded within each regularly spaced time interval, At. That
is, the data are sampled at high frequency for a short duration starting (or ending) at
times tk for which the burst duration Atn << At. The instrument "rests" between bursts.
There are advantages to the burst sampling scheme, especially in noisy (high fre-
quency) environments where it may be necessary to average-out the noise to get at the
frequencies of interest. Burst sampling works especially well when there is a "spectral
gap" between fluctuations at the high and low ends of the spectrum. As an example,
there is typically a spectral gap between surface gravity waves in the open ocean
(periods of 1-20 s) and the 12-hourly motions that characterize semidiurnal tidal cur-
rents. Thus, if we wanted to measure surface tidal currents using the burst-mode option
for our current meter, we could set the sampling to a 2-min burst every hour; this option
would smooth out the high-frequency wave effects but provide sufficient numbers of
velocity measurements to resolve the tidal motions. Burst sampling enables us to filter
out the high-frequency noise and obtain an improved estimate of the variability hidden
underneath the high-frequency fluctuations. In addition, we can examine the high-
frequency variability by scrutinizing the burst sampled data. If we were to sample
rapidly enough, we could estimate the surface gravity wave energy spectrum. Many
oceanographic instruments use (or have provision for) a burst-sampling data collection
mode. The "duty cycle" often used to collect positional data from satellite-tracked
drifters is a cost-saving form of burst sampling in which all positional data within a 24-h
period (about 10 satellite fixes) are collected only every third day. Tracking costs paid to
Service Argos are reduced by a factor of three using the duty cycle. Problems arise when
the length of each burst is too short to resolve energetic motions with periods
comparable to the burst sample length. In the case of satellite-tracked drifters poleward
of tropical latitudes, these problems are associated with highly energetic inertial
motions whose periods T = 1/(2f~ sin 0) are comparable to the 24-h duration of the
burst sample (here, f~ = 0.1161 • 10-4 cycles per second is the earth's rate of rotation
and 0 =_ latitude). Since 1992, it has been possible to improve resolution of high-
frequency motions using a 1/3 duty cycle of 8 h "on" followed by 16 h "off". According
to Bograd et al. (1999), even better resolution of high-frequency mid-latitude motions
could be obtained using a duty cycle of 16 h "on" followed by 32 h "off".
1.2.5 Regularly versus irregularly sampled data
In certain respects, an irregular sampling in time or nonequidistant placement of
instruments can be more effective than a more esthetically appealing uniform samp-
ling. For example, unequal spacing permits a more statistically reliable resolution of
oceanic spatial variability by increasing the number of quasi-independent estimates of
the dominant wavelengths (wavenumbers). Since oceanographers are almost always
faced with having fewer instruments than they require to resolve oceanic features,
irregular spacing can also be used to increase the overall spatial coverage (funda-
mental wavenumber) while maintaining the small-scale instrument separation for
Nyquist wavenumber estimates. The main concern is the lack of redundancy should
certain key instruments fail, as often seems to happen. In this case, a quasi-regular
spacing between locations is better. Prior knowledge of the scales of variability to
expect is a definite plus in any experimental array design.
In a sense, the quasi-logarithmic vertical spacing adopted by oceanographers for
bottle cast (hydrographic) sampling of 0, 10, 20, 30, 50, 75, 100, 125, 150 m, etc.
represents a "spectral window" adaptation to the known physical-chemical structure
8 Data Analysis Methods in Physical Oceanography
of the ocean. Highest resolution is required near the surface where vertical changes
are most rapid. Similarly, an uneven spatial arrangement of observations increases the
number of quasi-independent estimates of the wavenumber spectrum. Digital data are
most often sampled (or subsampled) at regularly-spaced time increments. Aside from
the usual human propensity for order, the need for regularly-spaced data derives from
the fact that most analysis methods have been developed for regular-spaced data.
However, digital data do not necessarily need to be sampled at regularly-spaced time
increments to give meaningful results, although some form of interpolation between
values may eventually be required.
1.2.6 Independent realizations
As we review the different instruments and methods, the reader should keep in mind
the three basic concerns of accuracy/precision, resolution (spatial and temporal), and
statistical significance (statistical sampling theory). A fundamental consideration in
ensuring the statistical significance of a set of measurements is the need for inde-
pendent realizations. If repeat measurements of a process are strongly correlated, they
provide no new information and do not contribute to the statistical significance of the
measurements. Often a subjective decision must be made on the question of statistical
independence. While this concept has a formal definition, in practice it is often
difficult to judge. A simple guide suggested here is that any suite of measurements
that is highly correlated (in time or space) cannot be independent. At the same time, a
group of measurements that is totally uncorrelated, must be independent. In the case
of no correlation, the number of "degrees of freedom" is defined by the total number
of measurements; for the case of perfect correlation, the redundancy of the data values
reduces the degrees of freedom to one for scalar quantity and to two for a vector
quantity. The degree of correlation in the data set provides a way of roughly
estimating the number of degrees of freedom within a given suite of observations.
While more precise methods will be presented later in this text, a simple linear
relation between degrees of freedom and correlation often gives the practitioner a way
to proceed without developing complex mathematical constructs.
As will be discussed in detail later, all of these sampling recommendations have
statistical foundations and the guiding rules of probability and estimation can be
carefully applied to determine the sampling requirements and dictate the appropriate
measurement system. At the same time, these same statistical methods can be applied
to existing data in order to better evaluate their ability to measure phenomena of
interest. These comments are made to assist the reader in evaluating the potential of a
particular instrument (or method) for the measurement of some desired variable.
1.3 TEMPERATURE
The measurement of temperature in the ocean uses conventional techniques except
for deep observations where hydrostatic pressures are high and there is a need to
protect the sensing system from ambient depth/temperature changes higher in the
water column as the sensor is returned to the ship. Temperature is the ocean property
that is easiest to measure accurately. Some of the ways in which ocean temperature
can be measured are:
Data Acquisition and Recording 9
(a) Expansion of a liquid or a metal.
(b) Differential expansion of two metals (bimetallic strip).
(c) Vapor pressure of a liquid.
(d) Thermocouples.
(e) Change in electrical resistance.
(f) Infrared radiation from the sea surface.
In most of these sensing techniques, the temperature effect is very small and some form
of amplification is necessary to make the temperature measurement detectable. Usually,
the response is nearly linear with temperature so that only the first-order term is needed
when converting the sensor measurement to temperature. However, in order to achieve
high precision over large temperature ranges, second, third and even fourth order terms
must sometimes be used to convert the measured variable to temperature.
1.3.1 Mercury thermometers
Of the above methods, (a), (e), and (f) have been the most widely used in physical
oceanography. The most common type of the liquid expansion sensor is the mercury-
in-glass thermometer. In their earliest oceanographic application, simple mercury
thermometers were lowered into the ocean with hopes of measuring the temperature at
great depths in the ocean. Two effects were soon noticed. First, thermometer housings
with insufficient strength succumbed to the greater pressure in the ocean and were
crushed. Second, the process of bringing an active thermometer through the oceanic
vertical temperature gradient sufficiently altered the deeper readings that it was not
possible to accurately measure the deeper temperatures. An early solution to this
problem was the development of min-max thermometers that were capable of
retaining the minimum and maximum temperatures encountered over the descent
and ascent of the thermometer. This type of thermometer was widely used on the
Challenger expedition of 1873-1876.
The real breakthrough in thermometry was the development of reversing thermo-
meters, first introduced in London by Negretti and Zambra in 1874 (Sverdrup et al.,
1942, p. 349). The reversing thermometer contains a mechanism such that, when the
thermometer is inverted, the mercury in the thermometer stem separates from the
bulb reservoir and captures the temperature at the time of inversion. Subsequent
temperature changes experienced by the thermometer have limited effects on the
amount of mercury in the thermometer stem and can be accounted for when the
temperature is read on board the observing ship. This "break-off' mechanism is based
on the fact that more energy is required to create a gas-mercury interface (i.e. to break
the mercury) than is needed to expand an interface that already exists. Thus, within
the "pigtail" section of the reversing thermometer is a narrow region called the
"break-off point", located near appendix C in Figure 1.3.1, where the mercury will
break when the thermometer is inverted.
The accuracy of the reversing thermometer depends on the precision with which
this break occurs. In good reversing thermometers this precision is better than 0.01 ~
In standard mercury-in-glass thermometers, as well as in reversing thermometers,
there are concerns other than the break point which affect the precision of the temp-
erature measurement. These are:
(a) Linearity in the expansion coefficient of the liquid.
(b) The constancy of the bulb volume.
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'If you come to that, I'll invite the whole company!' cried the
spoiled child of fortune.
The curtain came down at this moment, and Mr. Elgood returned
to the green-room, unbuckling his sword-belt as he came along.
'I waited to remind you of your promise to sup with us to-night,
Mr. Elgood,' said James.
'My dear sir, it is not an engagement to be forgotten. I shall be
there.'
'Will half-past eleven be too early?'
'No; "The Stranger" has played quick to-night, and the afterpiece
is short. I shall be there.'
'Miss Elgood will accompany you, I hope?'
'Thanks, no. The proprieties would be outraged by her
appearance at a bachelor's table. The only lady present.'
'We could easily remedy that, if any other lady of the company
would honour us.'
'Upon my word you are very kind; and I know the child would
consider it a treat. If you put the question in such a friendly manner
I feel sure that Mr. and Mrs. Dempson would be delighted to join us.'
'Pray bring them. Is Mrs. Dempson also dramatic?'
'You have seen her to-night in one of her greatest parts—Mrs.
Haller.'
'I thought the lady was a Miss Villeroy.'
'Her professional name, merely. Joe Dempson and Miss Villeroy
have been united in the sacred bonds of matrimony for some years.'
'I shall be charmed to make the lady's acquaintance. You know
your way to the "Waterfowl?"
'It is familiar to me as the path of my infancy.'
'And you'll be sure to bring Miss Elgood?'
'Judy shall come without fail.'
'Judy?'
'The pet name chosen by affection. She was christened Justina.
Pardon me if I leave you hastily, I play in the next piece.'
Mr. Elgood hurried away. James Penwyn glanced at his friend
with the glance of triumph.
'Out of leading-strings, you see, Maurice,' he said.
Maurice Clissold shrugged his shoulders and turned away with a
sigh. James, more touched by silence than reproof, put his arm
through his friend's with a gay laugh, and they went out of the
green-room and out of the theatre together, arm-in-arm, like
brothers who loved each other.
CHAPTER III.
'ÉVEILLONS LE PLAISIR, SON AURORE EST LA
NUIT.'
The supper at the 'Waterfowl' was a success. Every one, except
perhaps Clissold, was in the humour to be pleased with everything,
and even Clissold could not find it in his heart to make himself
vehemently disagreeable amidst mirth so harmless, gaiety so
childishly simple. To an actor, supper after the play is just the one
crowning delight of life—that glimpse of paradise upon earth which
we all get in some shape or other. A supper at a comfortable
hostelry like the 'Waterfowl,' where the landlord knew how to do
things in good style for a customer who could pay the piper, was
certainly not to be despised. In this northern district there was a
liberal plenty, a bounteous wealth of provision hardly known
elsewhere. Tea at Eborsham meant dinner and breakfast rolled into
one. Supper at Eborsham meant aldermanic barn-door fowls, and a
mighty home-cured ham, weighing five-and-twenty pounds, or so—
lobsters nestling among crisp green lettuces—pigeon pie—cheese-
cakes—tarts—and, lest these lighter trifles should fail to satisfy
appetite, a lordly cold sirloin by way of corps de reserve, to come in
at a critical juncture, like Blucher at Waterloo.
Mr. Dempson made himself the life of the party. The small
melancholy man who had bewailed the decline of the drama,
vanished altogether at sight of that plenteously-furnished table, and
in his place appeared a jester of the first water. So James Penwyn
thought at any rate, as he laughed—with youth's gay silver-clear
laughter—at the low comedian's jokes. Even Miss Villeroy was
sprightly, though she had a worn look about the eyes, as if she had
aged herself prematurely with the woes of Mrs. Haller, and other
heroines of tragedy. Justina sat next to James Penwyn, and was
supremely happy, though only an hour ago she had shed tears of
girlish shame at the idea of coming to a supper party in her
threadbare brown merino gown—last winter's gown—which she was
obliged to wear in the warm glad spring for want of fitter raiment.
No one thought of her shabby gown, however, when the pale young
face brightened and flushed with unwonted pleasure, and the large
thoughtful eyes took a new light, and darkened to a deeper grey.
James Penwyn did his uttermost to make her happy and at ease,
and succeeded only too well. There is no impression so swift and so
vivid as that which the first admirer makes upon a girl of seventeen.
The tender words, the subdued tones, the smiles, the praises, have
such a freshness. The adulation of a Cæsar in after years would
hardly seem so sweet as these first flatteries of commonplace youth
to the girl on the threshold of womanhood.
Mr. Elgood saw what was going on, but was by no means
alarmed by the aspect of affairs. He felt himself quite able to take
care of Justina, even if Mr. Penwyn had been a hardened libertine
instead of a kind-hearted youth fresh from the university. He had no
desire to stifle admiration which might mean very little, but which
would most likely result in liberal patronage for his own benefit, and
a trifling present or two for Justina, a ring, or a bracelet, or a box of
gloves.
'I don't want to stand in Justina's light,' mused Mr. Elgood, as he
leaned back in his chair and sipped his last glass of champagne,
when the pleasures of the table had given way to an agreeable
sense of repletion.
'What did that gipsy woman mean by the line of life, and the
planets?' asked Justina. She had lost all sense of shyness by this
time, and she and James were talking to each other in lowered
voices, as much alone as if the rest of the party had been pictures
on the wall. Maurice marked them as he sat a little way apart from
the others, smoking his black-muzzled pipe.
'Pshaw, only the professional jargon. What does she know of the
planets?'
'But she stared at your hand in such a curious way, and looked
so awful that she frightened me. Do tell me what she meant.'
James laughed, and laid his left hand in Justina's, palm upwards.
'Look there,' he said; 'you see that line, a curved channel that goes
from below the first finger to the base of the thumb—that is to say,
it should go to the base of the thumb, but in my hand it doesn't. See
where the line disappears, midway, just by that seam left by my
pocket-knife. You can see no line beyond that scar, ergo the line
never travelled further than that point.'
Justina closely scrutinized the strong unwrinkled palm.
'What does that mean?' she asked; 'I don't understand even
now.'
'It means a short life and a merry one.'
The rare bloom faded from Justina's cheek.
'You don't believe in that?' she said, anxiously.
'No more than I believe in gipsies, or spirit-rappers, or the cave
of Trophonius,' answered James, gaily. 'What a silly child you are to
look so scared!'
Justina gave a little sigh, and then tried to smile. Even this first
dawn of a girlish fancy, airy as a butterfly's passion for a rose,
brought new anxieties along with it. The gipsy's cant was an evil
omen that disturbed her like a shapeless fear. Women resemble
those mediæval roysterers of whom the old chronicler wrote. They
take their pleasure sadly.
The moon was at the full. There she sailed, a silver targe, above
the distant hill-tops. James looked up at her, looked into that
profound world above, which draws the fancies of youth with
irresistible power. The room opened on the garden by two long
windows, and the one nearest to Mr. Penwyn's end of the table
stood open.
'Let us get away from the smoke,' he said, vexed to see
Clissold's eye upon him, fixed and gloomy. The room was tolerably
full of tobacco-smoke by this time, and Mr. Elgood was urging Mr.
Dempson to favour the company with his famous song, 'The Ship's
Carpenteer.'
'Come into the garden, Maud,' said James, gaily, flinging a look
of defiance at his monitor.
Justina blushed, hesitated, and obeyed him. They went out into
the moonlit night together, and strolled side by side across the rustic
garden, a slope of grass on which the most ancient of apple-trees,
and pear-trees, big enough to have been mistaken for small elms,
cast their crooked shadows. It was more orchard than garden, a
homely, useful place altogether. Potherbs grew among the rose-
bushes on the border by the boundary hedge, and on one side of
the inn there was a patch of ground that grew cabbages and broad-
beans; but all the rest was grass and apple-trees.
At the end of that grassy slope ran the river, silver-shining under
the moon. Eborsham, seen across the level landscape, looked a
glorified city in that calm and mellow light. The boy and girl walked
silently down to the river's brim and looked at the distant hills and
woods, scattered cottages with lowly thatched roofs and antique
chimney-stacks, here and there the white walls of a mansion silvered
by the moon, and, dominating all in sublime and gloomy grandeur,
the mighty towers of the cathedral, God's temple, rising, like fortalice
and sanctuary, above all human habitations, as of old the Acropolis.
Justina gazed and was silent. It was one of those rare moments
of exaltation which poets tell us are worth a lifetime of sluggish
feeling. The girl felt as if she had never lived till now.
'Pretty, isn't it?' remarked James, very much in the tone of
Brummel, who after watching a splendid sunset was pleased to
observe, 'How well he does it!'
'It is too beautiful,' said Justina.
'Why too beautiful?'
'I don't know. It hurts me somehow, like actual pain!'
'You are like Byron's Lara,—
"But a night like this,
A night of beauty, mocked such breast as his."
I hope it is not a case of bad conscience with you, as it was with
him?'
'No, it is not my conscience. The worst I have ever done has
been to grumble at the profession; and though father says it is
wicked, the thought of my wickedness has never troubled me. But to
me there's something awful in the beauty of night and stillness, a
solemnity that chills me. I feel as if there were some trouble hanging
over me, some great sorrow. Don't you?'
'Not the least in the world. I think moonlight awfully jolly. Would
you much mind my lighting a cigar? You'll hardly feel the effects of
the smoke out here.'
'I never feel it anywhere,' answered Justina, frankly. 'Father
hardly ever leaves off smoking.'
There was a weeping willow at the edge of the garden, a willow
whose lower branches dipped into the river, and just beside the
willow a bench where these two seated themselves, in the full glory
of the moon. A much better place than the dusky summerhouse,
which might peradventure be a harbour for frogs, snails, or spiders.
They sat by the river's brim, and talked—talked as easily as if they
had a thousand ideas in common, these two, who had never met
until to-day, and whose lives lay so far apart.
They had youth and hope in common, and that bond was
enough to unite them.
James asked Justina a good many questions about stage life,
and was surprised to find the illusions of his boyhood vanish before
stern truth.
'I thought it was such a jolly life, and the easiest in the world,'
he said. 'I've often fancied I should like to be an actor. I think I could
do it pretty well. I can imitate Buckstone, and Charles Mathews.'
'Pray don't think of it,' exclaimed Justina. 'You'd be tired to death
in a year.'
'I dare say I should. I'm not much of a fellow for sticking to
anything. I got "ploughed" a year ago at Oxford, and now I've been
trying to read with Clissold walking through England and Wales, and
putting up at all the quietest places we can find. Clissold is a first-
rate coach, and it won't be his fault if I don't get my degree next
time. How do you like him?'
'I don't know. I haven't thought about him, answered the girl,
simply. This younger and fairer stranger had made her oblivious of
Maurice Clissold, with his tall, strong frame, dark, penetrating eyes,
and broad brow. Too manly a man altogether to be admired by a girl
of seventeen.
'He is as good a fellow as ever breathed; a little bitter, perhaps;
but most wholesome things are bitter,' said James. 'He has his
crotchets. One is that I am to be a model master of Penwyn by and
by, go into Parliament, marry an heiress, set up as a fine old English
gentleman, in fact. Rather a wearisome métier, I should think. The
worst of it is, he keeps it continually before my mind's eye, is always
reminding me of how much I owe to Penwyn Manor and my race,
and won't let me get much enjoyment out of youth's brief holiday.
He's a good fellow, but I might love him better if I didn't respect him
so much. He was a great favourite of my poor mother's. A romantic
story, by the way. She was engaged to Maurice's father some years
before she married mine. He was a captain in the East India
Company's service, and fell fighting the niggers at Goojerat. Years
afterwards, when my father was dead and gone, Clissold and I met
at Eton. My mother burst into tears when she heard my
schoolfellow's name, and asked me to bring him to see her. Of
course I obeyed, and from that time to the day of her death my
mother had a second son in Maurice. I think she loved him as well
as she loved me.'
'And you were never jealous?'
'No, I was too fond of both of them for that. And then my dear
mother was all love, all tenderness. I could afford to share her
affection with my adopted brother. And now tell me something about
your own life.'
'There is so little to tell,' answered the girl, drearily. 'Ever since I
can remember we have lived the same kind of life—sometimes in
one town, sometimes in another. When father could afford the
money he used to send me to a day school, so I've been a little
educated somehow, only I dare say I'm very ignorant, because my
education used to stop sometimes, and by the time it began again I
had forgotten a good deal.'
'Poor child,' murmured James, compassionately. 'Is your mother
still living?'
'She died seven years ago. She had had so much trouble, it wore
her out at last.' And Justina paid her dead mother the tribute of a
hidden tear.
'I say, Jim, do you know that it is half-past two o'clock, and that
Mr. Elgood is waiting for his daughter?' asked the voice of common
sense in the tones of Maurice Clissold.
The two children started up from the bench by the willow,
scared by the sudden question. There stood Mr. Clissold, tall and
straight, and severe-looking.
'I heard the cathedral clock a few minutes ago, and I am quite
aware of the time. If Mr. Elgood wants his daughter he can come for
her himself,' replied James.
Mr. Penwyn was resolved to make a stand against his mentor,
and he felt that now was the time for action.
Mr. Elgood and Mr. Dempson came strolling out into the garden,
cigars in their mouths. Penwyn's choicest brand had been largely
sacrificed at the altar of hospitality.
'Judy, have you forgotten the time?' asked the heavy father, with
accents that had a legato sound—one syllable gliding gently into
another,—a tone that was all sweetness and affection, though
indistinct.
'Yes, father,' answered the girl, innocently. 'It's so beautiful out
here.'
'Beautiful,' echoed the father, thickly. '"Look how the floor of
heaven is thick inlaid with—what's its names—of bright gold." Come,
Jessica—Judy—put on your bonnet and shawl. Mrs. Dempson has
been fast asleep for the last half-hour. "But look! The morn, in russet
mantle clad, walks o'er the dew of yon high eastern hill," which
reminds me that we have nearly a mile to walk before we get home.'
'I'll go with you,' said James. 'I want to arrange about to-
morrow. We must make up a jolly party for the races. I'll get a
roomy carriage that will hold all of us.'
'I haven't seen a race in anything like comfort for the last fifteen
years,' responded Mr. Elgood.
'We'll make a day of it. Clissold and I will come to the theatre in
the evening.'
'Make your own engagements if you please, James, and allow
me to make mine,' said Mr. Clissold. 'I shall not go to the races to-
morrow—or if I do, it will be by myself, and on foot; and I shall not
go to the theatre in the evening.'
'Please yourself,' answered James, offended.
They were all ready by this time. Mrs. Dempson had been
awakened, and shaken out of the delusion that she had fallen asleep
on the sofa in her own lodgings, and somewhat harshly reminded
that she had a mile or so to walk before she could obtain complete
repose. Mr. Dempson had finished his cigar, and accepted another as
solace during the homeward walk. Justina had put on her shabby
little bonnet and mantle. Every one was ready.
The players took their leave of Maurice Clissold, who was but
coldly civil. James Penwyn went out with them, and gave his arm to
Justina, as if it were the most natural thing in the world. These two
walked on in front, the other three straggling after them—walked
arm in arm along the lonely footpath. The low murmur of the river
sounded near—the stream showed silvery now and again between a
break in the screen of alders.
They talked as they had talked in the garden—about each other
—their thoughts—and fancies—hopes—dreams—imaginings.
Oh youth! oh glamour! Strange world in which for the first bright
years we live as in a dream! Sweet dawn of life, when nothing in this
world seems so real as the hopes that are never to know fruition!
CHAPTER IV.
'LOVE'S A MIGHTY LORD.'
Sir Nugent Bellingham was one of those men who are born and
reared amidst pecuniary difficulties, and whose existence is spent
upon the verge of ruin. Yet it seems a tolerably comfortable kind of
life notwithstanding, and men of Sir Nugent's type hardly realize the
meaning of the word deprivation. Sir Nugent had never known what
it was to be out of debt. The Bellingham estate was mortgaged up
to the hilt when he inherited it. Indeed, to be thus encumbered was
the normal condition of all Bellingham property.
Of course Sir Nugent had from time to time possessed money.
He hardly could have drifted on so long without some amount of
specie, even in such an easy-going world as that patrician sphere in
which he revolved. He had inherited a modest fortune from his
mother, with which he had paid his creditors something handsome
on account all round, and made them his bondslaves for all time to
come, since they cherished the hope of something more in the
future. Sir Nugent had received legacies from an aunt and uncle or
two, and these afforded further sops for his Cerberus, and enabled
the baronet's dainty little household to sail gaily down the stream of
time for some years.
When the amelioration of manners brought bankruptcy within
the reach of any gentleman, Sir Nugent Bellingham availed himself
of the new code, and became insolvent in an easy, gentleman-like
fashion. And what with one little help and another, the bijou house in
May Fair, where Sir Nugent lived with his two motherless girls, was
always kept up in the same good style. The same dinners—small and
soigné—the same lively receptions after the little dinners. The best
music, the newest books, the choicest hothouse flowers, were
always to be found at No. 12, Cavendish Bow, May Fair. There were
only a dozen houses in Cavendish Bow, and Sir Nugent Bellingham's
was at the corner, squeezed into an angle made by the lofty wall of
Lord Loamshire's garden—one of those dismal, awe-inspiring London
gardens, grey and dull and blossomless, which look like a burial-
ground without any graves. Seen from the street, No. 12 looked a
mere doll's house, but the larger rooms were behind, abutting upon
Lord Loamshire's garden. It was an irregular old house, full of
corners, but, furnished after the peculiar tastes of Miss Bellingham,
was one of the most charming houses in London. No upholsterer
had been allowed to work his will—Madge Bellingham had chosen
every item. The chairs and tables, and sofas and cabinets, were the
cheapest that could be had, for they were all of unstained light
woods, made after designs from Miss Bellingham's own pencil. The
cabinets were mere frames for glass doors, behind which appeared
the Bellingham collection of bric-a-brac, upon numerous shelves
covered with dark-green silk. Madge's own clever hands had covered
the deal shelves; and the bronzes, the Venetian glass, the Sèvres,
Copenhagen, Berlin, Vienna, and Dresden porcelains looked all the
better for so simple a setting.
There were no draperies but chintz, the cheapest that could be
bought, but always fresh. The looking-glasses had no frame save a
natural garland of ivy. The floors were beeswaxed only, a Persian
carpet here and there offering accommodation for the luxurious. The
one costly object in the two drawing-rooms, after that bric-a-brac
upon which the Bellingham race had squandered a small fortune,
was the piano, a Broadwood grand, in a case made by a modern
workman out of veritable Louis Seize marqueterie. The old ormolu
mountings, goat's head, festoons, and masques, had been religiously
preserved, and the piano was a triumph of art. It occupied the
centre of the back drawing-room, the largest room in the house, and
when Madge Bellingham sat before it, girl and piano made a cabinet
picture of the highest school.
'People know we are out at elbows,' Madge said to her father
when they began housekeeping in Cavendish Row. 'If we have
expensive furniture every one will be sure we haven't paid for it; but
if you let me carry out my ideas, the bills will be so light that you
can pay them at once.'
'I can give the fellows something on account, at any rate,'
replied Sir Nugent.
Lady Bellingham's death, which occurred soon after the birth of
Viola, the second daughter, had left Sir Nugent free to lead the life of
a bachelor, for the most part in other people's houses, while his girls
were in his sister's nursery or at school. When they grew to
womanhood—and a very lovely womanhood, for good looks were
hereditary in the Bellingham family—Sir Nugent found it incumbent
upon him to provide them with a home; so he took the house in
Cavendish Bow, and brought home the Bellingham bric-a-bric, which
had been left him by the aforesaid aunts and uncles, and lodged at
the Pantechnicon pending his settlement in life. He began
housekeeping at five-and-forty years of age, and gave his little
dinners at home henceforward, instead of at one or other of his
clubs, and cherished high hopes of seeing his daughters splendidly
established by and by.
'I think you have seen enough of what it is to be tormented by a
set of harpies to teach you the value of money, Madge,' said Sir
Nugent one morning, pointing to a small heap of letters which he
had just now opened and dismissed with a glance. The harpies in
question were his creditors, who expressed an unwarrantable
eagerness for something more 'on account.'
'With your knowledge of life you are not likely to marry a
pauper,' pursued Sir Nugent, dipping into a Strasburg pie.
'No, papa, not with my knowledge of life,' answered Madge, with
ever so slight and upward curl of the firm lip. Miss Bellingham fondly
loved her father, but it is possible that respect may have been
somewhat lessened by her experience of that financial scramble in
which his life was spent.
Two or three evenings before the night which made James
Penwyn acquainted with life behind the scenes of a small provincial
theatre, Sir Nugent Bellingham gave one of his snug little dinners—a
dinner of eight—the guests of choicest brands, like the wines. Lady
Cheshunt, one of the most exalted matrons in the great world, kept
the Miss Bellinghams in countenance. Madge was her pet protegée
whose praises she was never tired of sounding among the chosen
ones of the earth. Mr. Albert Noyce, a distinguished wit and
littérateur, supplied the salt of the banquet. He was a small, mild-
looking man, with a pretty, unoffending wife, and dined out
perpetually during the London season. Mr. Shinebar, the famous
barrister, made a fourth. Lord George Bulrose, a West of England
man, a gourmet, and, in so far as after-dinner talk went, a mighty
hunter, was the fifth; and Sir Nugent and his two daughters
completed the circle.
After dinner there was to be an evening party, and before the
small hours of the morning a great many famous people would have
dropped in at the corner house in Cavendish Row.
The ladies had retired, leaving Sir Nugent and his chosen friends
to talk about law, and horses, and the last new burlesque actress, as
they drew closer in to the dainty round table, where the glass
sparkled and the deep-hued blossoms brightened under the cluster
of wax lights in the central chandelier.
Viola and Lady Cheshunt went upstairs arm-in-arm, the girl
nestling affectionately against the substantial shoulder of the portly
matron. Mrs. Noyce tripped lightly after these two, and Madge
followed, alone, with a grave brow, and that lofty air which so well
became Sir Nugent Bellingham's elder daughter.
Barely were sisters less alike than these two. Viola was a blonde,
complexion alabaster, hair the colour of raw silk—plenteous flaxen
hair, which the girl wound into a crown of pale gold upon the top of
her small head; eyes of turquoise blue; figure a thought too slim,
but the perfection of grace in every movement and attitude; foot
and hand absolutely faultless: altogether a girl to be put under a
glass case.
'I should admire the younger Miss Bellingham more if she were a
little less like Sèvres china,' one of the magnates of society had
observed.
Madge was a brunette—hair almost black, and with a natural
ripple—complexion a rich olive, eyes darkest hazel—features the true
Bellingham type, clearly cut as a profile on an old Roman medal—
figure tall and commanding, a woman born to rule, one would say,
judging by externals—a woman with the stuff in her to make a
general, Sir Nugent was wont to boast. But although she was of a
loftier mould than the generality of women, there was no hardness
about Madge Bellingham. In love or in anger she was alike strong.
For hate she was too noble.
The rooms were deliciously cool, the light somewhat subdued,
the windows open to the warm spring night. There were flowers
enough in the small front drawing-room to make it an indoor garden.
The dowager seated herself upon the most comfortable sofa in
this room, a capacious, square-backed sofa, in a dusky corner,
fenced off and sheltered by a well-filled jardinière.
'Come here, Madge,' she cried, with good-natured
imperiousness, 'I want to talk to you.—Viola, child, go and amuse
yourself with Mrs. Noyce. Show her your photograph album, or
parlez chiffons. I want Madge all to myself.'
Madge obeyed without a word, and squeezed herself into the
corner of the sofa, which Lady Cheshunt and Lady Cheshunt's dress
almost filled.
'How big you are growing, child! there's hardly room enough for
you!' remarked the matron. 'And now tell me the truth, Madge; what
is the matter with you to-night?'
'I don't think there is anything the matter more than usual, Lady
Cheshunt.'
'I know better than that. You were dull and distrait all dinner-
time. True, there was no one to talk to but two married men, and
that old twaddler, Bulrose; but a young lady should be always
equally agreeable—that is one of the fundamental principles of good
breeding.'
'If I seemed a little out of spirits you can hardly wonder. Papa's
sadly involved state is enough to make me uneasy.'
'My dear, your papa has been involved ever since my first season
—when my waist was only eighteen inches, and Madame Devy made
my gowns. He is no worse off now than he was then, and he will go
on being hopelessly involved till the end of the chapter. I don't see
why you should be unhappy about it. He will be able to give you and
Viola a tolerable home till you marry and make better homes for
yourselves, which it is actually incumbent upon you to do.'
This was said with a touch of severity. Madge sighed, and the
slender foot in the satin shoe tapped the ground with a nervous,
impatient movement.
'Madge, I hope there is no truth in what I hear about you and
Mr. Penwyn.'
A deep tell-tale glow burned in Miss Bellingham's cheek. She
fanned herself vehemently.
'I cannot imagine what you have heard, Lady Cheshunt.'
'I have heard your name coupled with Mr. Penwyn's—the poor
Mr. Penwyn.'
'I only know one Mr. Penwyn.'
'So much the worse for you, my dear. You know the wrong one.
There is a cousin of that young man's who has a fine estate in
Cornwall—the Penwyn estate. You must have heard of that.'
'Yes, I have heard Mr. Penwyn speak of his cousin's property.'
'Of course. Poor penniless young man; very natural that he
should talk of it. Don't suppose that I have no feeling for him. He is
next heir to the property, but no doubt the other young man, James
Penwyn's son, will marry and have a herd of children. I knew James
Penwyn, this young man's father, years ago. There were three
brothers—George, the eldest, who was in the army, and was killed in
a skirmish with some wild Indians in Canada—very sad story; James,
who was in the church, and had a living somewhere near London;
and Balfour, in the law, I believe, whose son you know.'
'Yes,' sighed Madge.
She had heard the family history from Churchill Penwyn, but the
dowager liked to hear herself talk, and did not like to be interrupted.
'Now, if by any chance the present James Penwyn, who is little
more than a lad, were to die unmarried, Churchill Penwyn could
come into the property under his grandfather's will, which left the
estate to the eldest surviving son and his children after him. George
died unmarried. James left an only son. Churchill is therefore heir
presumptive. But it's a very remote contingency, my love, and it
would be madness for you to give it a thought—with your chances.'
Madge shrugged her shoulders despondently.
'I don't think my chances are particularly brilliant, Lady
Cheshunt.'
'Nonsense, Madge! Everybody talks of the beautiful Bellinghams.
And you refused a splendid offer only the other day—that Mr.
Cardingham, the great manufacturer.'
'Who had only seen me four times when he had the impudence
to ask me to marry him! He was old and ugly, too.'
'When the end is a good establishment one must not look at the
means too closely. Poor dear Cheshunt was many years my senior,
and no beauty, even in his wig. You must take a more serious view
of things, my dear Madge. It will not do for you and your sister to
hang fire. The handsomer girls are, the more vital it is for them to
go off quickly. A plain little unobtrusive thing may creep through half
a dozen seasons and surprise everybody by making a good match at
last. But a beauty who doesn't marry soon is apt to get talked about.
Malicious people put it down to too much flirtation. And then, my
love, consider your milliner's bills; what will they be at the end of a
few seasons?'
'Not very much, Lady Cheshunt. I cut out all my own dresses
and Viola's too, and our maid runs them together. Viola and I help
sometimes, when we can steal an hour from society. I couldn't bear
to wear anything that wasn't paid for.'
'Upon my word you are an exemplary girl, Madge,' exclaimed
Lady Cheshunt, astounded by such Roman virtue. 'What a wife you
will make!'
'Yes, I think I might make a tolerable wife, for a poor man.'
'Don't speak of such a thing. You were born for wealth and
power. You are bound to make a great marriage—if not for your own
sake, for Viola's. See what a poor helpless child she is—sadly
wanting in moral stamina. If you had a good establishment she
would have a haven of refuge. But if you were to marry badly what
will become of her? She would never be able to manage your papa.'
Madge sighed again, and this time deeply. Love for her sister
was Madge Bellingham's weakest point. She positively adored the
fair fragile girl who had been given into her childish arms eighteen
years ago, on that bitter day which made her an orphan. There was
only four years' difference between the ages of the sisters, yet
Madge's affection was always maternal in its protecting
thoughtfulness. To marry well would be to secure a home for Viola.
Sir Nugent was but a feeble staff to lean upon.
'I have no objection to marrying well whenever a fair opportunity
arises, Lady Cheshunt,' she said, firmly; 'but I will never marry a
man whom I cannot respect and like.'
'Of course not, my poor pet,' murmured the widow, soothingly;
'but, fortunately, there are so many men in the world one can like
and respect. It is that foolish sentimental feeling called love which
will only fit one person. In the meantime, Madge, take my advice,
and don't let people talk about you and Mr. Penwyn.'
'I don't know why they should talk about us.'
'Yes, you do, Madge—in your heart of hearts. You know that you
have sat together in corners, and that you have a knack of blushing
when he comes into the room. It won't do, Madge, it won't do. That
young fellow has nothing except what he can earn himself. I know
his mother had a struggle to bring him up, and if he hadn't been an
only son could hardly have brought him up at all. He was a Blue-coat
boy, I believe, or something equally dreadful. It is not to be thought
of, Madge.'
'I do not think of it, Lady Cheshunt,' replied Miss Bellingham,
resolutely, 'and I wish you would not worry yourself and me about
imaginary dangers.'
'Your visitors are beginning to come; go and receive them, and
leave me in my corner. Mr. Penwyn is to be here, I've no doubt.'
'I don't know. He knows that Saturday is our night.'
'Mr. Churchill Penwyn!' announced a footman at the door of the
larger room.
'I thought so,' said Lady Cheshunt, 'and the first to arrive, too.
That looks suspicious.'
CHAPTER V.
'IL NE FAUT PAS POUSSER AU BOUT LES
MALHEUREUX.'
Churchill Penwyn was one of those men who are sure to obtain a
certain amount of notice in whatsoever circle they appear—a man
upon whom the stamp of good blood, or good breeding, had been
set in a distinct and palpable manner—a man who had no need for
self-assertion.
It would have been difficult for any one to state in what the
distinction lay. He was not particularly good-looking. Intellect, rather
than regularity of feature, was the leading characteristic of his
countenance. Already, though he was still on the sunward side of his
thirtieth birthday, the dark brown hair grew thinly upon the broad
high brow, showing signs of premature baldness. His features were
sharply cut, but by no means faultless, the mouth somewhat
sunken, the lips thin. His light grey eyes had a keen, cold lustre; only
those who saw Churchill Penwyn in some rare moment of softer
feeling knew that those severe orbs could be beautiful. Mr. Penwyn
was a barrister, still in the uphill stage of his career. He got an
occasional brief, went on circuit assiduously, and did a little in the
literature of politics—a hard, dry kind of literature, but fairly
remunerative—when he got it to do. He had contributed hard-
headed statistical papers to the Edinburgh and the Westminster, and
knew a good deal about the condition of the operative classes. He
had lectured in some of the northern manufacturing towns, and
knew the black country by heart. People talked of him as a young
man who was sure to make his mark by and by; but by and by might
be a long way off. He would be fifty years of age, perhaps, before he
had worked his way to the front.
Churchill Penwyn went a great deal into society, when it is
considered how hard and how honestly he worked; but the houses
in which he was to be found were always houses affected by the
best people. He never wasted himself among second-rate circles. He
was an excellent art critic; knew enough about music to talk of it
cleverly, though he had hardly the faculty of distinguishing one tune
from another; waltzed like a Viennese; rode like a centaur; spoke
three Continental languages perfectly. It was his theory that no man
should presume to enter society who could not do everything that
society could require him to do. Society was worth very little in itself,
according to Churchill Penwyn, but a man owed it to himself to be
admired and respected by society.
'I see a good many men who go into the world to stare about
them through eye-glasses,' said Churchill. 'If I couldn't do anything
more than that I should spend my evenings in my own den.'
Churchill Penwyn went into the gay world with a definite aim—
some of the people he met must needs be useful to him sooner or
later.
Ohne Hast, ohne Rast—without haste, without rest—was his
motto. He had it engraved on his signet ring, instead of the Penwyn
crest. He was never in a hurry. While striving for success he had the
air of a man who had already succeeded. He occupied a third floor in
the Temple, and lived like an anchorite, but his tailor and bootmaker
were among the best in London, and he was a member of the
Travellers' and the Garrick. He was to be seen sometimes lunching at
his club, and occasionally entertained a friend at luncheon, but he
rarely dined there, and was never seen to drink anything more costly
than a pint of La Rose, or Medoc. No man had ever mastered the art
of economy more thoroughly than Churchill Penwyn, and yet he had
never laid himself open to the charge of meanness.
Miss Bellingham received him with a bright look of welcome,
despite the dowager's warning, and their hands met, with a gentle
pressure on Churchill's part. Viola was discreetly occupied in showing
Mrs. Noyce a new photograph, and only gave the visitor a bow and a
smile. So he had a fair excuse for seating himself next Madge, on
the divan by the fireplace, where there was just room for those two.
'I did not think you would come to-night,' said Madge, opening
and shutting her large black fan, with a slightly nervous movement.
'Why not?'
'I saw your name in the paper, at Halifax, or somewhere,
hundreds of miles away.'
'I was at Halifax the day before yesterday, but I would not miss
my Saturday evening here. You see I have come a quarter of an
hour in advance of your people, so that I might have you to myself
for a few minutes.'
'It is so good of you,' faltered Madge, 'and you know I am
always glad.'
'I should be wretched if I did not know it.'
This was going further than Mr. Penwyn's usual limits. The man
was the very soul of prudence. No sweet words, no tender promises,
had ever passed between these two, and yet they knew themselves
beloved. Madge knew it to her sorrow, for she was fain to admit the
wisdom of the dowager's warning. It would never do for her to
marry Churchill Penwyn.
Happily for her, up to this time Churchill had never asked her to
be his wife.
'He is too wise,' she said to herself, with the faintest touch of
bitterness. 'Too much a man of the world.'
But that this man of the world loved her she was very sure.
For just ten minutes they sat side by side, talking of indifferent
things, but only as people talk who are not quite indifferent to each
other. And then more visitors were announced. Sir Nugent and his
friends came upstairs; the rooms began to fill. Musical people
arrived. A German with long rough hair, bony wrists, and an eye-
glass, seated himself at the piano, and began a performance of so
strictly classical a character that he had the enjoyment of it all to
himself, for nobody else listened. Minor chords chased one another
backwards and forwards about the middle of the piano as if they
were hunting for the melody and couldn't find it. Little runs and
arpeggio passages went under and over each other, and wriggled in
and out and up and down in a distracted way, still searching for the
subject, and finally gave up the quest in utter despair, appropriately
expressed by vague grumblings in the bass, which slowly faded into
silence. Whereupon every one became enthusiastic in their
admiration.
After this a young lady in pink sang an airy little chanson, with
elaborate variations—using her bright soprano voice as freely as if
she had been Philomel, trilling her vespers in the dusky woods of
June. And then Madge Bellingham sat down to the piano, and played
as few young ladies play—as if her glad young soul were in the
music.
It was only an Hungarian march that she played. There were no
musical fireworks—no difficulties conquered; none of those passages
which make the listeners exclaim, 'Poor girl! how she must have
practised!' It was but a national melody—simple and spirit-stirring—
played as if the soul of a patriot were guiding those supple fingers.
The graceful figure was bent a little over the key-board—the dark
eyes followed the swift flight of the hands over the keys. She
seemed to caress the notes as she struck them—to play with the
melody. Pride, love, hope, rage, every passion expressed itself by
turns as she followed that wild strange music through the mazes of
its variations, never losing the subject. It sounded like the war-cry of
a free people. Even Churchill Penwyn, who in a general way cared so
little for music, listened entranced to this. He could hardly have
recalled the air half an hour later, but for the moment he was
enchanted. He stood a little way from the instrument, watching the
player, watching the beautiful head, with its dark rippling hair wound
into a Greek knot at the back, the perfect throat, with its classic
necklet of old Wedgwood medallions set in plainest gold; the
drooping lashes, as the downcast eyes followed the flying touch. To
hear Madge play was delightful, but to see her was still better. And
this man's love had all the strength of a passion repressed. He had
held himself in check so long, and every time he saw her he found
her more and more adorable.
The evening wore on. People came in and out. Madge played the
hostess divinely, always supported by Lady Cheshunt, who sat in the
smaller drawing-room as in a temple, and had all the best people
brought to her. Some came to Cavendish Row on their way
somewhere else, and were careful to let their acquaintance know
that they were 'due' at some very grand entertainment, and made
rather a favour of coming to Sir Nugent. The last of the guests went
about half an hour after midnight, and among the last Churchill
Penwyn.
'May I bring you that book after church to-morrow?' he asked.
The book was a comedy of Augier's lately produced at the Français,
which he had been telling her about.
Madge looked embarrassed. She had a particular wish to avoid a
tête-à-tête with Mr. Penwyn, and Sunday was an awkward day. Sir
Nugent would be at Hurlingham, most likely, and Viola was such a
foolish little thing, almost as bad as nobody.
'If you like' she answered. 'But why take the trouble to call on
purpose? You might bring it next Saturday, if you come to us.'
'I shall bring it you to-morrow,' he said, as they shook hands.
That tiresome Viola was in a hopeless state of headache and
prostration next morning, so Madge had to go to church alone.
Coming out of the pretty little Anglican temple she found herself face
to face with Churchill Penwyn. He had evidently been lying in wait
for her.
'I was so afraid I might not find you at home,' he said, half
apologetically, 'so I thought I might as well walk this way. I knew
this was your church. I've brought you the play we were talking
about.'
'You're very kind, but I hope you don't think I read French
comedies on Sundays?'
'Of course not; only Sunday is my leisure day, and I thought you
would not shut your door upon me even on Sunday.'
The church was only five minutes' walk from Cavendish Row.
When Sir Nugent's door was opened Mr. Penwyn followed Miss
Bellingham into the house as a matter of course. She had no help
for it but to go quietly upstairs to her fate. She almost knew what
was coming. There had been something in his manner last night that
told her it was very near.
'Prudence, courage,' she whispered to herself, and then, 'Viola!'
The last word was a kind of charm.
The rooms looked bright and gay in the noontide sunlight,
tempered by Spanish blinds. The flowers, the feminine prettiness
scattered about, struck Churchill's eye, they gave such a look of
home.
'If I could afford to give her as good a home as this!' he thought.
He shut the door carefully behind him, and glanced round the
room to make sure they were alone, and went close to Madge as
she stood by one of the small tables, fidgeting with the clasp of her
prayer-book.
'I think you know why I came to-day,' he said.
'You have told me about three times,—to bring me "La
Quarantaine."'
'I have come to tell you a secret I have kept more than a year.
Have you never guessed it, Madge? Have I been clever enough to
hide the truth altogether? I love you, dearest. I, penniless Churchill
Penwyn, dare to adore one of the belles of the season. I, who
cannot for years to come offer you a house in May Fair. I, who at
most can venture to begin married life in a Bloomsbury lodging,
supported by the fruits of my pen. It sounds like madness, doesn't
it?'
'It is madness,' she answered, looking full at him with her
truthful eyes.
The answer surprised and humiliated him. He fancied she loved
him—would be ready to face poverty for his sake. She was so young,
and would hardly have acquired the wisdom of her world yet awhile.
'I beg your pardon,' he said, a curious change coming over his
face, a sudden coldness that made those definite features look as if
they had been cut out of stone. 'I have been deceiving myself all
along, it seems. I did not think I was quite indifferent to you.'
The eyelids drooped over the dark eyes for a moment, and were
then lifted suddenly, and the eyes met Churchill's. That one look told
all. She loved him.
'I have been learning to know the world while other girls are
allowed to dream,' she said. 'I know what the burden of debt means.
Poverty brings debt as a natural sequence. If you were a woodcutter
and we could live in a hovel and pay our way, there would be
nothing appalling in marriage. But our world will not let us live like
that. We must play at being fine ladies and gentlemen while our
hearts are breaking, and our creditors being ruined. Ever so long ago
I made up my mind that I must marry a rich man. If I have ever
seemed otherwise to you than a woman of the world, bent upon
worldly success, I humbly beg you to forgive me.'
'Madge,' cried Churchill, passionately, 'I will forgive anything if
you will only be frank. Were my luck to turn speedily, through some
unlooked-for professional success, for instance, would you have me
then?'
'If I stood alone in the world, if I had not my sister to consider, I
would marry you to-morrow. Yes, though you were a beggar,' she
answered, grandly.
He clasped her to his breast and kissed those proud lips. The
first lover's kiss that had ever rested there.
'I will be rich for your sake, distinguished for your sake,' he said
impetuously, 'if wealth and fame are within the reach of man's
effort.'
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Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery

  • 1. Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery download https://ebookultra.com/download/data-analysis-methods-in- physical-oceanography-2nd-edition-w-j-emery/ Explore and download more ebooks or textbooks at ebookultra.com
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  • 5. Data Analysis Methods in Physical Oceanography 2nd Edition W. J. Emery Digital Instant Download Author(s): W. J. Emery, Richard E. Thomson ISBN(s): 0444507574 Edition: 2 File Details: PDF, 36.04 MB Year: 2001 Language: english
  • 8. Preface Numerous books have been written on data analysis methods in the physical sciences over the past several decades. Most of these books lean heavily toward the theoretical aspects of data processing and few have been updated to include more modern techniques such as fractal analysis and rotary spectral decomposition. In writing this book we saw a clear need for a practical reference volume for earth and ocean sciences that brings established and modern techniques together under a single cover. The text is intended for students and established scientists alike. For the most part, graduate programs in oceanography have some form of methods course in which students learn about the measurement, calibration, processing and interpretation of geophysical data. The classes are intended to give the students needed experience in both the logistics of data collection and the practical problems of data processing and analysis. Because the class material generally is based on the experience of the faculty members giving the course, each class emphasizes different aspects of data collection and analysis. Formalism and presentation can differ widely. While it is valuable to learn from the first-hand experiences of the class instructor, it seemed to us important to have available a central reference text that could be used to provide some uniformity in the material being covered within the oceanographic community. Many of the data analysis techniques most useful to oceanographers can be found in books and journals covering a wide variety of topics ranging from elementary statistics to wavelet transforms. Much of the technical information on these techniques is detailed in texts on numerical methods, time series analysis, and statistical tech- niques. In this book, we attempt to bring together many of the key data processing methods found in the literature, as well as add new information on data analysis techniques not readily available in older texts. We also provide, in Chapter 1, a description of most of the instruments used today in physical oceanography. Our hope is that the book will provide instructional material for students in the oceanographic sciences and serve as a general reference volume for those directly involved with oceanographic research. The broad scope and rapidly evolving nature of oceanographic sciences has meant that it has not been possible for us to cover all existing or emerging data analysis methods. However, we trust that many of the methods and procedures outlined in the book will provide a basic understanding of the kinds of options available to the user for interpretation of data sets. Our intention is to describe general statistical and analytical methods that will be sufficiently fundamental to maintain a high level of utility over the years.
  • 9. xii Data Analysis Methods in Physical Oceanography Finally, we believe that the analysis procedures discussed in this book apply to a wide readership in the geophysical sciences. As with oceanographers, this wider community of scientists would likely benefit from a central source of information that encompasses not only a description of the mathematical methods but also considers some of the practical aspects of data analyses. It is this synthesis between theoretical insight and the logistical limitations of real data measurement that is a primarily goal of this text. WilliamJ. Emery and Richard E. Thomson Boulder, Colorado and Sidney, BC
  • 10. Acknowledgments Many people have contributed to this book over the years that it has taken to write. The support and encouragement we received from our colleagues while we were drafting the manuscript is most gratefully acknowledged. Bill Emery began work on the book during a sabbatical year at the Institut ft~rMeereskunde (IFM) in Kiel and is grateful for the hospitality of Drs Gerold Siedler, Wolfgang Kraus, Walter Zenk, Rolf Kas~, Juergen Willebrand, Juergen Kielman, and others. Additional progress was made at the University of British Columbia where Mrs Hiltrud Heckel aided in typing the handwritten text. Colleagues at the University of Colorado who helped with the book include Dr Robert Leben, who reviewed the text, contributed advice, text and figures, and Mr Dan Leatzow, who converted all of the initial text and figures to the Macintosh. The author would like to thank Mr Tom Kelecy for serving as the teaching assistant the first time that the material was presented in a course on "Engineering Data Analysis". Bill Emery also thanks the students who helped improve the book during the course on data analysis and the National Space and Aeronautics Administration (NASA) whose grant funding provided the laptop computer used in preparation of the manuscript. The author also thanks his family for tolerating the ever growing number of files labelled "dampo" on the family computer. Rick Thomson independently began work on the book through the frustration of too much time spent looking for information on data analysis methods in the literature. There was clearly a need for a reference-type book that covers the wide range of analysis techniques commonly used by oceanographers and other geoscientists. Many of the ideas for the book originated with the author's studies as a research scientist within Fisheries and Oceans Canada, but work on the book was done strictly at home during evenings and weekends. Numerous conversations with Drs Dudley Chelton and Alexander Rabinovich helped maintain the author's enthusiasm for the project. The author wishes to thank his wife and two daughters (Justine and Karen) for enduring the constant tapping of the keyboard and hours of dark despair when it looked as if the book would never come to an end, and his parents (John and Irene) for encouraging an interest in science. The authors would like to thank the colleagues and friends who took time from their research to review sections of the text or provide figures. There were others, far too numerous to mention, whose comments and words of advice added to the usefulness of the text. We are most grateful to Dudley Chelton of Oregon State University and Alexander Rabinovich of Moscow State University who spent considerable time criticizing the more mathematical chapters of the book. Dudley proved to be a most impressive reviewer and Sasha contributed several figures that significantly improved
  • 11. xvi Data Analysis Methods in Physical Oceanography the section on time series analysis. George Pickard, Professor Emeritus of the University of British Columbia (UBC), and Susumu Tabata, Research Scientist Emeritus of the Institute of Ocean Sciences (IOS), provided thorough, and much appreciated, reviews of Chapters 1 and 2. We thank Andrew Bennett of Oregon State University for his comments on inverse methods in Chapter 4, Brenda Burd of Ecostat Research for reviewing the bootstrap method in Chapter 3, and Steve Mihaly for reviewing Appendix A. Contributions to the text were provided by Libe Washburn (University of California, Santa Barbara), Peter Schlussel (IFM), Patrick Cummins (lOS), and Mike Woodward (lOS). Figures or data were generously provided by Mark E. Geneau (Inter-Ocean Systems, Inc.), Gail Gabel (G.S. Gabel Associates), R. Lee Gordon (RD Instruments, Inc.), Diane Masson, Humfrey Melling, George Chase, John Love, and Tom Juhfisz (lOS), Jason Middleton and Greg Nippard (University of New South Wales), Doug Bennett (Sea-Bird Electronics, Inc.), Dan Schaas and Marcia Gracia (General Oceanics), Mayra Pazos (National Oceanic and Atmospheric Admini- stration), Chris Garrett (University of Victoria), David Halpern (Jet Propulsion Laboratory), Phillip Richardson (Woods Hole Oceanographic Institution), Daniel Jamous (Massachusetts Institute of Technology), Paul Dragos (Battelle Ocean Sciences), Thomas Rossby (University of Rhode Island), Lynne Talley (Scripps), Adrian Dolling and Jane Eert (Channel Consulting), and Gary Hamilton (Intelex Research). The authors would also like to thank Anna Allen for continued interest in this project from the time she took over until now. There were a great many delays and postponements, but through it all she remained firm in her support of the project. This continued support made it easier to work through these delays and gave us courage to believe that the project would one day be completed. Lastly, we would like to thank our colleagues who found and reported errors and omissions in the first printing of the book. Although the inevitable typos and mistakes are discouraging for the authors (and frustrating for the reader), it is better that we know about them so that they can be corrected in future printings and revisions. Our thanks to Brian Blanton (University of North Carolina), Mike Foreman (Institute of Ocean Sciences), Denis Gilbert (Institute Maurice-Lamontagne), Jack Harlan (NOTkA, Boulder, Colorado), Clive Holden (Oceanographic Field Services, Pymbla, New South Wales), Frank Janssen (University of Hamburg), Masahisa Kubota (Tokai University), Robert Leben (University of Colorado), Rolf Lueck (University of Victoria), Andrew Slater (University of Colorado), and Roy Hourston (WeatherWorks Consulting, Victoria).
  • 12. C HAPTER 1 Data Acquisition and Recording 1.1 INTRODUCTION Physical oceanography is an evolving science in which the instruments, types of observations and methods of analysis have undergone considerable change over the last few decades. With most advances in oceanographic theory, instrumentation, and software, there have been significant advances in marine science. The advent of digital computers has revolutionized data collection procedures and the way that data are reduced and analyzed. No longer is the individual scientist personally familiar with each data point and its contribution to his or her study. Instrumentation and data collection are moving out of direct application by the scientist and into the hands of skilled technicians who are becoming increasingly more specialized in the operation and maintenance of equipment. New electronic instruments operate at data rates not possible with earlier mechanical devices and produce volumes of information that can only be handled by high-speed computers. Most modern data collection systems transmit sensor data directly to computer-based data acquisition systems where they are stored in digital format on some type of electronic medium such as a tape, hard- drive, or optical disk. High-speed analog-to-digital (AD) converters and digital-signal- processors (DSPs) are now used to convert voltage or current signals from sensors to digital values. With the many technological advances taking place, it is important for oceano- graphers to be aware of both the capabilities and limitations of their sampling equipment. This requires a basic understanding of the sensors, the recording systems and the data-processing tools. If these are known and the experiment carefully planned, many problems commonly encountered during the processing stage can be avoided. We cannot overemphasize the need for thoughtful experimental planning and proper calibration of all oceanographic sensors. If instruments are not in near- optimal locations or the researcher is unsure of the values coming out of the machines, then it will be difficult to believe the results gathered in the field. To be truly reliable, instruments should be calibrated on a regular basis at intervals determined by use and the susceptibility of the sensor to drift. More specifically, the output from some instruments such as the piezoelectric pressure sensors and fixed pathlength trans- missometers drift with time and need to be calibrated before and after each field deployment. For example, the zero point for the Paroscientific Digiquartz (0- 10,000 psi) pressure sensors used in the Hawaii Ocean Time-series (HOT) at station "Aloha" 100 km north of Honolulu drifts about 4 dbar in three years. As a con- sequef~ce, the sensors are calibrated about every six months against a Paroscientific
  • 13. 2 Data Analysis Methods in Physical Oceanography laboratory standard, which is recalibrated periodically at special calibration facilities in the United States (Lukas, 1994). Our experience also shows that over-the-side field calibrations during oceanic surveys can be highly valuable. As we discuss in the following chapters, there are a number of fundamental requirements to be considered when planning the collection of field records, including such basic considerations as the sampling interval, sampling duration and sampling location. It is the purpose of this chapter to review many of the standard instruments and measurement techniques used in physical oceanography in order to provide the reader with a common understanding of both the utility and limitations of the resulting measurements. The discussion is not intended to serve as a detailed "user's manual" nor as an "observer's handbook". Rather, our purpose is to describe the fundamentals of the instruments in order to give some insight into the data they collect. An under- standing of the basic observational concepts, and their limitations, is a prerequisite for the development of methods, techniques and procedures used to analyze and interpret the data that are collected. Rather than treat each measurement tool individually, we have attempted to group them into generic classes and to limit our discussion to common features of the particular instruments and associated techniques. Specific references to particular company products and the quotation of manufacturer's engineering specifications have been avoided whenever possible. Instead, we refer to published material addressing the measurement systems or the data recorded by them. Those studies which compare measurements made by similar instruments are particularly valuable. The emphasis of the instrument review section is to give the reader a background in the collection of data in physical oceanography. For those readers interested in more complete information regarding a specific instrument or measurement technique, we refer to the references at the end of the book where we list the sources of the material quoted. We realize that, in terms of specific measurement systems, and their review, this text will be quickly dated as new and better systems evolve. Still, we hope that the general outline we present for accuracy, precision and data coverage will serve as a useful guide to the employment of newer instruments and methods. 1.2 BASIC SAMPLING REQUIREMENTS A primary concern in most observational work is the accuracy of the measurement device, a common performance statistic for the instrument. Absolute accuracy requires frequent instrument calibration to detect and correct for any shifts in behavior. The inconvenience of frequent calibration often causes the scientist to substitute instrument precision as the measurement capability of an instrument. Unlike absolute accuracy, precision is a relative term and simply represents the ability of the instrument to repeat the observation without deviation. Absolute accuracy further requires that the observation be consistent in magnitude with some absolute reference standard. In most cases, the user must be satisfied with having good precision and repeatability of the measurement rather than having absolute measurement accuracy. Any instrument that fails to maintain its precision, fails to provide data that can be handled in any meaningful statistical fashion. The best
  • 14. Data Acquisition and Recording 3 instruments are those that provide both high precision and defensible absolute accuracy. Digital instrument resolution is measured in bits, where a resolution of N bits means that the full range of the sensor is partitioned into 2N equal segments (N = 1, 2, ...). For example, eight-bit resolution means that the specified full-scale range of the sensor, say V = 10 volts, is divided into 28 = 256 increments, with a bit-resolution of V/256 = 0.039 volts. Whether the instrument can actually measure to a resolution or accuracy of V/2 N units is another matter. The sensor range can always be divided into an increasing number of smaller increments but eventually one reaches a point where the value of each bit is buried in the noise level of the sensor. 1.2.1 Sampling interval Assuming the instrument selected can produce reliable and useful data, the next highest priority sampling requirement is that the measurements be collected often enough in space and time to resolve the phenomena of interest. For example, in the days when oceanographers were only interested in the mean stratification of the world ocean, water property profiles from discrete-level hydrographic (bottle) casts were adequate to resolve the general vertical density structure. On the other hand, these same discrete-level profiles failed to resolve the detailed structure associated with interleaving and mixing processes that now are resolved by the rapid vertical sampling of modern conductivity-temperature-depth (CTD) profilers. The need for higher resolution assumes that the oceanographer has some prior knowledge of the process of interest. Often this prior knowledge has been collected with instruments incapable of resolving the true variability and may only be suggested by highly aliased (distorted) data collected using earlier techniques. In addition, theoretical studies may provide information on the scales that must be resolved by the measurement system. For discrete digital data x(ti) measured at times ti, the choice of the sampling increment At (or Zk~cin the case of spatial measurements) is the quantity of import- ance. In essence, we want to sample often enough that we can pick out the highest frequency component of interest in the time-series but not oversample so that we fill up the data storage file, use up all the battery power, or become swamped with a lot of unnecessary data. We might also want to sample at irregular intervals to avoid built-in bias in our sampling scheme. If the sampling interval is too large to resolve higher frequency components, it becomes necessary to suppress these components during sampling using a sensor whose response is limited to frequencies equal to that of the sampling frequency. As we discuss in our section on processing satellite-tracked drifter data, these lessons are often learned too latemafter the buoys have been cast adrift in the sea. The important aspect to keep in mind is that, for a given sampling interval At, the highest frequency we can hope to resolve is the Nyquist (or folding)frequency, fx, defined as fN = 1/(2At) (1.2.1) We cannot resolve any higher frequencies than this. For example, if we sample every 10 h, the highest frequency we can hope to see in the data isfN = 0.05 cph (cycles per hour). Equation (1.2.1) states the obvious--that it takes at least two sampling intervals (or three data points) to resolve a sinusoidal-type oscillation with period 1/fN (Figure
  • 15. 4 Data Analysis Methods in Physical Oceanography 1.2.1). In practice, we need to contend with noise and sampling errors so that it takes something like three or more sampling increments (i.e. _>four data points) to accurately determine the highest observable frequency. Thus,fx is an upper limit. The highest frequency we can resolve for a sampling of At - 10 h in Figure 1.2.1 is closer to 1~3At ~ 0.033 cph. An important consequence of (1.2.1) is the problem ofaliasing. In particular, if there is considerable energy at frequencies f > fN--Which we obviously cannot resolve because of the At we pickedmthis energy gets folded back into the range of frequen- cies, f < fN, which we are attempting to resolve. This unresolved energy doesn't disappear but gets redistributed within the frequency range of interest. What is worse is that the folded-back energy is disguised (or aliased) within frequency components different from those of its origin. We cannot distinguish this folded-back energy from that which actually belongs to the lower frequencies. Thus, we end up with erroneous (aliased) estimates of the spectral energy variance over the resolvable range of fre- quencies. An example of highly aliased data would be 13-h sampling of currents in a region having strong semidiurnal tidal currents. More will be said on this topic in Chapter 5. As a general rule, one should plan a measurement program based on the frequencies and wavenumbers (estimated from the corresponding periods and wavelengths) of the parameters of interest over the study domain. This requirement then dictates the selection of the measurement tool or technique. If the instrument cannot sample rapidly enough to resolve the frequencies of concern it should not be used. It should be emphasized that the Nyquist frequency concept applies to both time and space and the Nyquist wavenumber is a valid means of determining the fundamental wavelength that must be sampled. 1.2.2 Sampling duration The next concern is that one samples long-enough to establish a statistically significant picture of the process being studied. For time-series measurements, this amounts to a requirement that the data be collected over a period sufficiently long that 1.0 0.4 ~" 0.2 = 0.0 o .m ca -0.2 = -0.4 [.l., -0.6 -- ~ 9 True value 0.8 -- .If "~"~, o Measured value *i 0.6 -- t - j -0.8 -l.o j 0 0 4 8 12 16 20 24 Time (n) Figure 1.2.1. Plot of the function F(n) = sin (27m/20 + 4~)where time is given by the integer n - -1, O, .... 24. The period 2At =l/fN is 20 units and ~ is a random phase with a small magnitude in the range +0.1. Open circles denote measured points and solid points the curve F(n). Noise makes it necessary to use more than three data values to accurately define the oscillation period.
  • 16. Data Acquisition and Recording 5 repeated cycles of the phenomenon are observed. This also applies to spatial sampling where statistical considerations require a large enough sample to define multiple cycles of the process being studied. Again, the requirement places basic limitations on the instrument selected for use. If the equipment cannot continuously collect the data needed for the length of time required to resolve repeated cycles of the process, it is not well suited to the measurement required. Consider the duration of the sampling at time step At. The longer we make the record the better we are to resolve different frequency components in the data. In the case of spatially separated data, AJc, resolution increases with increased spatial coverage of the data. It is the total record length T = NAt obtained for N data samples that: (1) determines the lowest frequency (the fundamental frequency) fo = 1/(NAt) = 1/T (1.2.2) that can be extracted from the time-series record; (2) determines the frequency resolution or minimum difference in frequency Af = If2-fll = 1~NAt that can be resolved between adjoining frequency components, fl and f2 (Figure 1.2.2); and (3) determines the amount of band averaging (averaging of adjacent frequency bands) that can be applied to enhance the statistical significance of individual spectral esti- mates. In Figure 1.2.2, the two separate waveforms of equal amplitude but different frequency produce a single spectrum. The two frequencies are well resolved for Af = 2~NAt and 3~2NAt, just resolved for Af--1~NAt, and not resolved for Af = 1~2NAt. In theory, we should be able to resolve all frequency components,f, in the frequency rangefo <_f <_fN, wherefx andfo are defined by (1.2.1) and (1.2.2), respectively. Herein lies a classic sampling problem. In order to resolve the frequencies of interest in a time-series, we need to sample for a long time (T large) so that fo covers the low end of the frequency spectrum and Af is small (frequency resolution is high). At the same time, we would like to sample sufficiently rapidly (At small) so thatfN extends beyond all frequency components with significant spectral energy. Unfortunately, the longer and more rapidly we want to sample the more data we need to collect and store, the more time, effort and money we need to put into the sampling and the better resolution we require from our sensors. Our ability to resolve frequency components follows from Rayleigh's criterion for the resolution of adjacent spectral peaks in light shone onto a diffraction grating. It states that two adjacent frequency components are just resolved when the peaks of the spectra are separated by frequency difference Af =fo = 1~NAt (Figure 1.2.2). For example, to separate the spectral peak associated with the lunar-solar semidiurnal tidal component M2 (frequency - 0.08051 cph) from that of the solar semidiurnal tidal component $2 (0.08333 cph), for which Af - 0.00282 cph, requires N - 355 data points at a sampling interval At - 1 h or N = 71 data points at At = 5 h. Similarly, a total of 328 data values at 1-h sampling are needed to separate the two main diurnal constituents Kl and O1 (Af - 0.00305 cph). Note that iffN is the highest frequency we can measure and fo is the limit of frequency resolution, then fX/fo = (1/2At)/(1/NAt) = N/2 (1.2.3) is the maximum number of Fourier components we can hope to estimate in any analysis.
  • 17. 6 Data Analysis Methods in Physical Oceanography (a) ~ -- Af ----q (b) wb 0 ra~ (c) Frequency (d) t ~ Combined spectra Figure 1.2.2. Spectral peaks of two separate waveforms of equal amplitude and frequencies f z and f2 (dashed and thin line) together with the calculated spectrum (solid line). (a) and (b) are well-resolved spectra; (c) just resolved spectra; and (d) not resolved. Thick solid line is total spectrum for two underlying signals with slightly different peak frequencies. 1.2.3 Sampling accuracy According to the two previous sections, we need to sample long and often if we hope to resolve the range of scales of interest in the variables we are measuring. It is intuitively obvious that we also need tolsample as accurately as possible--with the degree of recording accuracy determined by the response characteristics of the sensors, the number of bits per data record (or parameter value) needed to raise measurement values above background noise, and the volume of data we can live ~ith. There is no use attempting to sample the high or low ends of the spectrum if the instrument cannot respond rapidly or accurately enough to resolve changes in the parameter being measured. In addition, there are several approaches to this aspect of data sampling including the brute-force approach in which we measure as often as we can at the degree of accuracy available and then improve the statistical reliability of each data record through post-survey averaging, smoothing, and other manipulation. 1.2.4 Burst sampling versus continuous sampling Regularly-spaced, digital time-series can be obtained in two different ways. The most common approach is to use a continuous sampling mode, in which the data are sampled at equally spaced intervals tk -- to + kAt from the start time to. Here, k is a positive integer. Regardless of whether the equally spaced data have undergone internal averaging or decimation using algorithms built into the machine, the output to the data storage file is a series of individual samples at times tk. (Here, "decimation" is used in the loose sense of removing every nth data point, where n is any positive integer, and not in the sense of the ancient Roman technique of putting to death one in ten soldiers in a legion guilty of mutiny or other crime.) Alternatively, we can use a
  • 18. Data Acquisition and Recording 7 burst sampling mode, in which rapid sampling is undertaken over a relatively short time interval AtB or "burst" embedded within each regularly spaced time interval, At. That is, the data are sampled at high frequency for a short duration starting (or ending) at times tk for which the burst duration Atn << At. The instrument "rests" between bursts. There are advantages to the burst sampling scheme, especially in noisy (high fre- quency) environments where it may be necessary to average-out the noise to get at the frequencies of interest. Burst sampling works especially well when there is a "spectral gap" between fluctuations at the high and low ends of the spectrum. As an example, there is typically a spectral gap between surface gravity waves in the open ocean (periods of 1-20 s) and the 12-hourly motions that characterize semidiurnal tidal cur- rents. Thus, if we wanted to measure surface tidal currents using the burst-mode option for our current meter, we could set the sampling to a 2-min burst every hour; this option would smooth out the high-frequency wave effects but provide sufficient numbers of velocity measurements to resolve the tidal motions. Burst sampling enables us to filter out the high-frequency noise and obtain an improved estimate of the variability hidden underneath the high-frequency fluctuations. In addition, we can examine the high- frequency variability by scrutinizing the burst sampled data. If we were to sample rapidly enough, we could estimate the surface gravity wave energy spectrum. Many oceanographic instruments use (or have provision for) a burst-sampling data collection mode. The "duty cycle" often used to collect positional data from satellite-tracked drifters is a cost-saving form of burst sampling in which all positional data within a 24-h period (about 10 satellite fixes) are collected only every third day. Tracking costs paid to Service Argos are reduced by a factor of three using the duty cycle. Problems arise when the length of each burst is too short to resolve energetic motions with periods comparable to the burst sample length. In the case of satellite-tracked drifters poleward of tropical latitudes, these problems are associated with highly energetic inertial motions whose periods T = 1/(2f~ sin 0) are comparable to the 24-h duration of the burst sample (here, f~ = 0.1161 • 10-4 cycles per second is the earth's rate of rotation and 0 =_ latitude). Since 1992, it has been possible to improve resolution of high- frequency motions using a 1/3 duty cycle of 8 h "on" followed by 16 h "off". According to Bograd et al. (1999), even better resolution of high-frequency mid-latitude motions could be obtained using a duty cycle of 16 h "on" followed by 32 h "off". 1.2.5 Regularly versus irregularly sampled data In certain respects, an irregular sampling in time or nonequidistant placement of instruments can be more effective than a more esthetically appealing uniform samp- ling. For example, unequal spacing permits a more statistically reliable resolution of oceanic spatial variability by increasing the number of quasi-independent estimates of the dominant wavelengths (wavenumbers). Since oceanographers are almost always faced with having fewer instruments than they require to resolve oceanic features, irregular spacing can also be used to increase the overall spatial coverage (funda- mental wavenumber) while maintaining the small-scale instrument separation for Nyquist wavenumber estimates. The main concern is the lack of redundancy should certain key instruments fail, as often seems to happen. In this case, a quasi-regular spacing between locations is better. Prior knowledge of the scales of variability to expect is a definite plus in any experimental array design. In a sense, the quasi-logarithmic vertical spacing adopted by oceanographers for bottle cast (hydrographic) sampling of 0, 10, 20, 30, 50, 75, 100, 125, 150 m, etc. represents a "spectral window" adaptation to the known physical-chemical structure
  • 19. 8 Data Analysis Methods in Physical Oceanography of the ocean. Highest resolution is required near the surface where vertical changes are most rapid. Similarly, an uneven spatial arrangement of observations increases the number of quasi-independent estimates of the wavenumber spectrum. Digital data are most often sampled (or subsampled) at regularly-spaced time increments. Aside from the usual human propensity for order, the need for regularly-spaced data derives from the fact that most analysis methods have been developed for regular-spaced data. However, digital data do not necessarily need to be sampled at regularly-spaced time increments to give meaningful results, although some form of interpolation between values may eventually be required. 1.2.6 Independent realizations As we review the different instruments and methods, the reader should keep in mind the three basic concerns of accuracy/precision, resolution (spatial and temporal), and statistical significance (statistical sampling theory). A fundamental consideration in ensuring the statistical significance of a set of measurements is the need for inde- pendent realizations. If repeat measurements of a process are strongly correlated, they provide no new information and do not contribute to the statistical significance of the measurements. Often a subjective decision must be made on the question of statistical independence. While this concept has a formal definition, in practice it is often difficult to judge. A simple guide suggested here is that any suite of measurements that is highly correlated (in time or space) cannot be independent. At the same time, a group of measurements that is totally uncorrelated, must be independent. In the case of no correlation, the number of "degrees of freedom" is defined by the total number of measurements; for the case of perfect correlation, the redundancy of the data values reduces the degrees of freedom to one for scalar quantity and to two for a vector quantity. The degree of correlation in the data set provides a way of roughly estimating the number of degrees of freedom within a given suite of observations. While more precise methods will be presented later in this text, a simple linear relation between degrees of freedom and correlation often gives the practitioner a way to proceed without developing complex mathematical constructs. As will be discussed in detail later, all of these sampling recommendations have statistical foundations and the guiding rules of probability and estimation can be carefully applied to determine the sampling requirements and dictate the appropriate measurement system. At the same time, these same statistical methods can be applied to existing data in order to better evaluate their ability to measure phenomena of interest. These comments are made to assist the reader in evaluating the potential of a particular instrument (or method) for the measurement of some desired variable. 1.3 TEMPERATURE The measurement of temperature in the ocean uses conventional techniques except for deep observations where hydrostatic pressures are high and there is a need to protect the sensing system from ambient depth/temperature changes higher in the water column as the sensor is returned to the ship. Temperature is the ocean property that is easiest to measure accurately. Some of the ways in which ocean temperature can be measured are:
  • 20. Data Acquisition and Recording 9 (a) Expansion of a liquid or a metal. (b) Differential expansion of two metals (bimetallic strip). (c) Vapor pressure of a liquid. (d) Thermocouples. (e) Change in electrical resistance. (f) Infrared radiation from the sea surface. In most of these sensing techniques, the temperature effect is very small and some form of amplification is necessary to make the temperature measurement detectable. Usually, the response is nearly linear with temperature so that only the first-order term is needed when converting the sensor measurement to temperature. However, in order to achieve high precision over large temperature ranges, second, third and even fourth order terms must sometimes be used to convert the measured variable to temperature. 1.3.1 Mercury thermometers Of the above methods, (a), (e), and (f) have been the most widely used in physical oceanography. The most common type of the liquid expansion sensor is the mercury- in-glass thermometer. In their earliest oceanographic application, simple mercury thermometers were lowered into the ocean with hopes of measuring the temperature at great depths in the ocean. Two effects were soon noticed. First, thermometer housings with insufficient strength succumbed to the greater pressure in the ocean and were crushed. Second, the process of bringing an active thermometer through the oceanic vertical temperature gradient sufficiently altered the deeper readings that it was not possible to accurately measure the deeper temperatures. An early solution to this problem was the development of min-max thermometers that were capable of retaining the minimum and maximum temperatures encountered over the descent and ascent of the thermometer. This type of thermometer was widely used on the Challenger expedition of 1873-1876. The real breakthrough in thermometry was the development of reversing thermo- meters, first introduced in London by Negretti and Zambra in 1874 (Sverdrup et al., 1942, p. 349). The reversing thermometer contains a mechanism such that, when the thermometer is inverted, the mercury in the thermometer stem separates from the bulb reservoir and captures the temperature at the time of inversion. Subsequent temperature changes experienced by the thermometer have limited effects on the amount of mercury in the thermometer stem and can be accounted for when the temperature is read on board the observing ship. This "break-off' mechanism is based on the fact that more energy is required to create a gas-mercury interface (i.e. to break the mercury) than is needed to expand an interface that already exists. Thus, within the "pigtail" section of the reversing thermometer is a narrow region called the "break-off point", located near appendix C in Figure 1.3.1, where the mercury will break when the thermometer is inverted. The accuracy of the reversing thermometer depends on the precision with which this break occurs. In good reversing thermometers this precision is better than 0.01 ~ In standard mercury-in-glass thermometers, as well as in reversing thermometers, there are concerns other than the break point which affect the precision of the temp- erature measurement. These are: (a) Linearity in the expansion coefficient of the liquid. (b) The constancy of the bulb volume.
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  • 22. 'If you come to that, I'll invite the whole company!' cried the spoiled child of fortune. The curtain came down at this moment, and Mr. Elgood returned to the green-room, unbuckling his sword-belt as he came along. 'I waited to remind you of your promise to sup with us to-night, Mr. Elgood,' said James. 'My dear sir, it is not an engagement to be forgotten. I shall be there.' 'Will half-past eleven be too early?' 'No; "The Stranger" has played quick to-night, and the afterpiece is short. I shall be there.' 'Miss Elgood will accompany you, I hope?' 'Thanks, no. The proprieties would be outraged by her appearance at a bachelor's table. The only lady present.' 'We could easily remedy that, if any other lady of the company would honour us.' 'Upon my word you are very kind; and I know the child would consider it a treat. If you put the question in such a friendly manner I feel sure that Mr. and Mrs. Dempson would be delighted to join us.' 'Pray bring them. Is Mrs. Dempson also dramatic?' 'You have seen her to-night in one of her greatest parts—Mrs. Haller.' 'I thought the lady was a Miss Villeroy.' 'Her professional name, merely. Joe Dempson and Miss Villeroy have been united in the sacred bonds of matrimony for some years.' 'I shall be charmed to make the lady's acquaintance. You know your way to the "Waterfowl?" 'It is familiar to me as the path of my infancy.' 'And you'll be sure to bring Miss Elgood?'
  • 23. 'Judy shall come without fail.' 'Judy?' 'The pet name chosen by affection. She was christened Justina. Pardon me if I leave you hastily, I play in the next piece.' Mr. Elgood hurried away. James Penwyn glanced at his friend with the glance of triumph. 'Out of leading-strings, you see, Maurice,' he said. Maurice Clissold shrugged his shoulders and turned away with a sigh. James, more touched by silence than reproof, put his arm through his friend's with a gay laugh, and they went out of the green-room and out of the theatre together, arm-in-arm, like brothers who loved each other.
  • 24. CHAPTER III. 'ÉVEILLONS LE PLAISIR, SON AURORE EST LA NUIT.' The supper at the 'Waterfowl' was a success. Every one, except perhaps Clissold, was in the humour to be pleased with everything, and even Clissold could not find it in his heart to make himself vehemently disagreeable amidst mirth so harmless, gaiety so childishly simple. To an actor, supper after the play is just the one crowning delight of life—that glimpse of paradise upon earth which we all get in some shape or other. A supper at a comfortable hostelry like the 'Waterfowl,' where the landlord knew how to do things in good style for a customer who could pay the piper, was certainly not to be despised. In this northern district there was a liberal plenty, a bounteous wealth of provision hardly known elsewhere. Tea at Eborsham meant dinner and breakfast rolled into one. Supper at Eborsham meant aldermanic barn-door fowls, and a mighty home-cured ham, weighing five-and-twenty pounds, or so— lobsters nestling among crisp green lettuces—pigeon pie—cheese- cakes—tarts—and, lest these lighter trifles should fail to satisfy appetite, a lordly cold sirloin by way of corps de reserve, to come in at a critical juncture, like Blucher at Waterloo. Mr. Dempson made himself the life of the party. The small melancholy man who had bewailed the decline of the drama, vanished altogether at sight of that plenteously-furnished table, and in his place appeared a jester of the first water. So James Penwyn thought at any rate, as he laughed—with youth's gay silver-clear laughter—at the low comedian's jokes. Even Miss Villeroy was sprightly, though she had a worn look about the eyes, as if she had aged herself prematurely with the woes of Mrs. Haller, and other
  • 25. heroines of tragedy. Justina sat next to James Penwyn, and was supremely happy, though only an hour ago she had shed tears of girlish shame at the idea of coming to a supper party in her threadbare brown merino gown—last winter's gown—which she was obliged to wear in the warm glad spring for want of fitter raiment. No one thought of her shabby gown, however, when the pale young face brightened and flushed with unwonted pleasure, and the large thoughtful eyes took a new light, and darkened to a deeper grey. James Penwyn did his uttermost to make her happy and at ease, and succeeded only too well. There is no impression so swift and so vivid as that which the first admirer makes upon a girl of seventeen. The tender words, the subdued tones, the smiles, the praises, have such a freshness. The adulation of a Cæsar in after years would hardly seem so sweet as these first flatteries of commonplace youth to the girl on the threshold of womanhood. Mr. Elgood saw what was going on, but was by no means alarmed by the aspect of affairs. He felt himself quite able to take care of Justina, even if Mr. Penwyn had been a hardened libertine instead of a kind-hearted youth fresh from the university. He had no desire to stifle admiration which might mean very little, but which would most likely result in liberal patronage for his own benefit, and a trifling present or two for Justina, a ring, or a bracelet, or a box of gloves. 'I don't want to stand in Justina's light,' mused Mr. Elgood, as he leaned back in his chair and sipped his last glass of champagne, when the pleasures of the table had given way to an agreeable sense of repletion. 'What did that gipsy woman mean by the line of life, and the planets?' asked Justina. She had lost all sense of shyness by this time, and she and James were talking to each other in lowered voices, as much alone as if the rest of the party had been pictures on the wall. Maurice marked them as he sat a little way apart from the others, smoking his black-muzzled pipe.
  • 26. 'Pshaw, only the professional jargon. What does she know of the planets?' 'But she stared at your hand in such a curious way, and looked so awful that she frightened me. Do tell me what she meant.' James laughed, and laid his left hand in Justina's, palm upwards. 'Look there,' he said; 'you see that line, a curved channel that goes from below the first finger to the base of the thumb—that is to say, it should go to the base of the thumb, but in my hand it doesn't. See where the line disappears, midway, just by that seam left by my pocket-knife. You can see no line beyond that scar, ergo the line never travelled further than that point.' Justina closely scrutinized the strong unwrinkled palm. 'What does that mean?' she asked; 'I don't understand even now.' 'It means a short life and a merry one.' The rare bloom faded from Justina's cheek. 'You don't believe in that?' she said, anxiously. 'No more than I believe in gipsies, or spirit-rappers, or the cave of Trophonius,' answered James, gaily. 'What a silly child you are to look so scared!' Justina gave a little sigh, and then tried to smile. Even this first dawn of a girlish fancy, airy as a butterfly's passion for a rose, brought new anxieties along with it. The gipsy's cant was an evil omen that disturbed her like a shapeless fear. Women resemble those mediæval roysterers of whom the old chronicler wrote. They take their pleasure sadly. The moon was at the full. There she sailed, a silver targe, above the distant hill-tops. James looked up at her, looked into that profound world above, which draws the fancies of youth with irresistible power. The room opened on the garden by two long
  • 27. windows, and the one nearest to Mr. Penwyn's end of the table stood open. 'Let us get away from the smoke,' he said, vexed to see Clissold's eye upon him, fixed and gloomy. The room was tolerably full of tobacco-smoke by this time, and Mr. Elgood was urging Mr. Dempson to favour the company with his famous song, 'The Ship's Carpenteer.' 'Come into the garden, Maud,' said James, gaily, flinging a look of defiance at his monitor. Justina blushed, hesitated, and obeyed him. They went out into the moonlit night together, and strolled side by side across the rustic garden, a slope of grass on which the most ancient of apple-trees, and pear-trees, big enough to have been mistaken for small elms, cast their crooked shadows. It was more orchard than garden, a homely, useful place altogether. Potherbs grew among the rose- bushes on the border by the boundary hedge, and on one side of the inn there was a patch of ground that grew cabbages and broad- beans; but all the rest was grass and apple-trees. At the end of that grassy slope ran the river, silver-shining under the moon. Eborsham, seen across the level landscape, looked a glorified city in that calm and mellow light. The boy and girl walked silently down to the river's brim and looked at the distant hills and woods, scattered cottages with lowly thatched roofs and antique chimney-stacks, here and there the white walls of a mansion silvered by the moon, and, dominating all in sublime and gloomy grandeur, the mighty towers of the cathedral, God's temple, rising, like fortalice and sanctuary, above all human habitations, as of old the Acropolis. Justina gazed and was silent. It was one of those rare moments of exaltation which poets tell us are worth a lifetime of sluggish feeling. The girl felt as if she had never lived till now. 'Pretty, isn't it?' remarked James, very much in the tone of Brummel, who after watching a splendid sunset was pleased to observe, 'How well he does it!'
  • 28. 'It is too beautiful,' said Justina. 'Why too beautiful?' 'I don't know. It hurts me somehow, like actual pain!' 'You are like Byron's Lara,— "But a night like this, A night of beauty, mocked such breast as his." I hope it is not a case of bad conscience with you, as it was with him?' 'No, it is not my conscience. The worst I have ever done has been to grumble at the profession; and though father says it is wicked, the thought of my wickedness has never troubled me. But to me there's something awful in the beauty of night and stillness, a solemnity that chills me. I feel as if there were some trouble hanging over me, some great sorrow. Don't you?' 'Not the least in the world. I think moonlight awfully jolly. Would you much mind my lighting a cigar? You'll hardly feel the effects of the smoke out here.' 'I never feel it anywhere,' answered Justina, frankly. 'Father hardly ever leaves off smoking.' There was a weeping willow at the edge of the garden, a willow whose lower branches dipped into the river, and just beside the willow a bench where these two seated themselves, in the full glory of the moon. A much better place than the dusky summerhouse, which might peradventure be a harbour for frogs, snails, or spiders. They sat by the river's brim, and talked—talked as easily as if they had a thousand ideas in common, these two, who had never met until to-day, and whose lives lay so far apart. They had youth and hope in common, and that bond was enough to unite them.
  • 29. James asked Justina a good many questions about stage life, and was surprised to find the illusions of his boyhood vanish before stern truth. 'I thought it was such a jolly life, and the easiest in the world,' he said. 'I've often fancied I should like to be an actor. I think I could do it pretty well. I can imitate Buckstone, and Charles Mathews.' 'Pray don't think of it,' exclaimed Justina. 'You'd be tired to death in a year.' 'I dare say I should. I'm not much of a fellow for sticking to anything. I got "ploughed" a year ago at Oxford, and now I've been trying to read with Clissold walking through England and Wales, and putting up at all the quietest places we can find. Clissold is a first- rate coach, and it won't be his fault if I don't get my degree next time. How do you like him?' 'I don't know. I haven't thought about him, answered the girl, simply. This younger and fairer stranger had made her oblivious of Maurice Clissold, with his tall, strong frame, dark, penetrating eyes, and broad brow. Too manly a man altogether to be admired by a girl of seventeen. 'He is as good a fellow as ever breathed; a little bitter, perhaps; but most wholesome things are bitter,' said James. 'He has his crotchets. One is that I am to be a model master of Penwyn by and by, go into Parliament, marry an heiress, set up as a fine old English gentleman, in fact. Rather a wearisome métier, I should think. The worst of it is, he keeps it continually before my mind's eye, is always reminding me of how much I owe to Penwyn Manor and my race, and won't let me get much enjoyment out of youth's brief holiday. He's a good fellow, but I might love him better if I didn't respect him so much. He was a great favourite of my poor mother's. A romantic story, by the way. She was engaged to Maurice's father some years before she married mine. He was a captain in the East India Company's service, and fell fighting the niggers at Goojerat. Years afterwards, when my father was dead and gone, Clissold and I met
  • 30. at Eton. My mother burst into tears when she heard my schoolfellow's name, and asked me to bring him to see her. Of course I obeyed, and from that time to the day of her death my mother had a second son in Maurice. I think she loved him as well as she loved me.' 'And you were never jealous?' 'No, I was too fond of both of them for that. And then my dear mother was all love, all tenderness. I could afford to share her affection with my adopted brother. And now tell me something about your own life.' 'There is so little to tell,' answered the girl, drearily. 'Ever since I can remember we have lived the same kind of life—sometimes in one town, sometimes in another. When father could afford the money he used to send me to a day school, so I've been a little educated somehow, only I dare say I'm very ignorant, because my education used to stop sometimes, and by the time it began again I had forgotten a good deal.' 'Poor child,' murmured James, compassionately. 'Is your mother still living?' 'She died seven years ago. She had had so much trouble, it wore her out at last.' And Justina paid her dead mother the tribute of a hidden tear. 'I say, Jim, do you know that it is half-past two o'clock, and that Mr. Elgood is waiting for his daughter?' asked the voice of common sense in the tones of Maurice Clissold. The two children started up from the bench by the willow, scared by the sudden question. There stood Mr. Clissold, tall and straight, and severe-looking. 'I heard the cathedral clock a few minutes ago, and I am quite aware of the time. If Mr. Elgood wants his daughter he can come for her himself,' replied James.
  • 31. Mr. Penwyn was resolved to make a stand against his mentor, and he felt that now was the time for action. Mr. Elgood and Mr. Dempson came strolling out into the garden, cigars in their mouths. Penwyn's choicest brand had been largely sacrificed at the altar of hospitality. 'Judy, have you forgotten the time?' asked the heavy father, with accents that had a legato sound—one syllable gliding gently into another,—a tone that was all sweetness and affection, though indistinct. 'Yes, father,' answered the girl, innocently. 'It's so beautiful out here.' 'Beautiful,' echoed the father, thickly. '"Look how the floor of heaven is thick inlaid with—what's its names—of bright gold." Come, Jessica—Judy—put on your bonnet and shawl. Mrs. Dempson has been fast asleep for the last half-hour. "But look! The morn, in russet mantle clad, walks o'er the dew of yon high eastern hill," which reminds me that we have nearly a mile to walk before we get home.' 'I'll go with you,' said James. 'I want to arrange about to- morrow. We must make up a jolly party for the races. I'll get a roomy carriage that will hold all of us.' 'I haven't seen a race in anything like comfort for the last fifteen years,' responded Mr. Elgood. 'We'll make a day of it. Clissold and I will come to the theatre in the evening.' 'Make your own engagements if you please, James, and allow me to make mine,' said Mr. Clissold. 'I shall not go to the races to- morrow—or if I do, it will be by myself, and on foot; and I shall not go to the theatre in the evening.' 'Please yourself,' answered James, offended. They were all ready by this time. Mrs. Dempson had been awakened, and shaken out of the delusion that she had fallen asleep
  • 32. on the sofa in her own lodgings, and somewhat harshly reminded that she had a mile or so to walk before she could obtain complete repose. Mr. Dempson had finished his cigar, and accepted another as solace during the homeward walk. Justina had put on her shabby little bonnet and mantle. Every one was ready. The players took their leave of Maurice Clissold, who was but coldly civil. James Penwyn went out with them, and gave his arm to Justina, as if it were the most natural thing in the world. These two walked on in front, the other three straggling after them—walked arm in arm along the lonely footpath. The low murmur of the river sounded near—the stream showed silvery now and again between a break in the screen of alders. They talked as they had talked in the garden—about each other —their thoughts—and fancies—hopes—dreams—imaginings. Oh youth! oh glamour! Strange world in which for the first bright years we live as in a dream! Sweet dawn of life, when nothing in this world seems so real as the hopes that are never to know fruition!
  • 33. CHAPTER IV. 'LOVE'S A MIGHTY LORD.' Sir Nugent Bellingham was one of those men who are born and reared amidst pecuniary difficulties, and whose existence is spent upon the verge of ruin. Yet it seems a tolerably comfortable kind of life notwithstanding, and men of Sir Nugent's type hardly realize the meaning of the word deprivation. Sir Nugent had never known what it was to be out of debt. The Bellingham estate was mortgaged up to the hilt when he inherited it. Indeed, to be thus encumbered was the normal condition of all Bellingham property. Of course Sir Nugent had from time to time possessed money. He hardly could have drifted on so long without some amount of specie, even in such an easy-going world as that patrician sphere in which he revolved. He had inherited a modest fortune from his mother, with which he had paid his creditors something handsome on account all round, and made them his bondslaves for all time to come, since they cherished the hope of something more in the future. Sir Nugent had received legacies from an aunt and uncle or two, and these afforded further sops for his Cerberus, and enabled the baronet's dainty little household to sail gaily down the stream of time for some years. When the amelioration of manners brought bankruptcy within the reach of any gentleman, Sir Nugent Bellingham availed himself of the new code, and became insolvent in an easy, gentleman-like fashion. And what with one little help and another, the bijou house in May Fair, where Sir Nugent lived with his two motherless girls, was always kept up in the same good style. The same dinners—small and soigné—the same lively receptions after the little dinners. The best music, the newest books, the choicest hothouse flowers, were
  • 34. always to be found at No. 12, Cavendish Bow, May Fair. There were only a dozen houses in Cavendish Bow, and Sir Nugent Bellingham's was at the corner, squeezed into an angle made by the lofty wall of Lord Loamshire's garden—one of those dismal, awe-inspiring London gardens, grey and dull and blossomless, which look like a burial- ground without any graves. Seen from the street, No. 12 looked a mere doll's house, but the larger rooms were behind, abutting upon Lord Loamshire's garden. It was an irregular old house, full of corners, but, furnished after the peculiar tastes of Miss Bellingham, was one of the most charming houses in London. No upholsterer had been allowed to work his will—Madge Bellingham had chosen every item. The chairs and tables, and sofas and cabinets, were the cheapest that could be had, for they were all of unstained light woods, made after designs from Miss Bellingham's own pencil. The cabinets were mere frames for glass doors, behind which appeared the Bellingham collection of bric-a-brac, upon numerous shelves covered with dark-green silk. Madge's own clever hands had covered the deal shelves; and the bronzes, the Venetian glass, the Sèvres, Copenhagen, Berlin, Vienna, and Dresden porcelains looked all the better for so simple a setting. There were no draperies but chintz, the cheapest that could be bought, but always fresh. The looking-glasses had no frame save a natural garland of ivy. The floors were beeswaxed only, a Persian carpet here and there offering accommodation for the luxurious. The one costly object in the two drawing-rooms, after that bric-a-brac upon which the Bellingham race had squandered a small fortune, was the piano, a Broadwood grand, in a case made by a modern workman out of veritable Louis Seize marqueterie. The old ormolu mountings, goat's head, festoons, and masques, had been religiously preserved, and the piano was a triumph of art. It occupied the centre of the back drawing-room, the largest room in the house, and when Madge Bellingham sat before it, girl and piano made a cabinet picture of the highest school. 'People know we are out at elbows,' Madge said to her father when they began housekeeping in Cavendish Row. 'If we have
  • 35. expensive furniture every one will be sure we haven't paid for it; but if you let me carry out my ideas, the bills will be so light that you can pay them at once.' 'I can give the fellows something on account, at any rate,' replied Sir Nugent. Lady Bellingham's death, which occurred soon after the birth of Viola, the second daughter, had left Sir Nugent free to lead the life of a bachelor, for the most part in other people's houses, while his girls were in his sister's nursery or at school. When they grew to womanhood—and a very lovely womanhood, for good looks were hereditary in the Bellingham family—Sir Nugent found it incumbent upon him to provide them with a home; so he took the house in Cavendish Bow, and brought home the Bellingham bric-a-bric, which had been left him by the aforesaid aunts and uncles, and lodged at the Pantechnicon pending his settlement in life. He began housekeeping at five-and-forty years of age, and gave his little dinners at home henceforward, instead of at one or other of his clubs, and cherished high hopes of seeing his daughters splendidly established by and by. 'I think you have seen enough of what it is to be tormented by a set of harpies to teach you the value of money, Madge,' said Sir Nugent one morning, pointing to a small heap of letters which he had just now opened and dismissed with a glance. The harpies in question were his creditors, who expressed an unwarrantable eagerness for something more 'on account.' 'With your knowledge of life you are not likely to marry a pauper,' pursued Sir Nugent, dipping into a Strasburg pie. 'No, papa, not with my knowledge of life,' answered Madge, with ever so slight and upward curl of the firm lip. Miss Bellingham fondly loved her father, but it is possible that respect may have been somewhat lessened by her experience of that financial scramble in which his life was spent.
  • 36. Two or three evenings before the night which made James Penwyn acquainted with life behind the scenes of a small provincial theatre, Sir Nugent Bellingham gave one of his snug little dinners—a dinner of eight—the guests of choicest brands, like the wines. Lady Cheshunt, one of the most exalted matrons in the great world, kept the Miss Bellinghams in countenance. Madge was her pet protegée whose praises she was never tired of sounding among the chosen ones of the earth. Mr. Albert Noyce, a distinguished wit and littérateur, supplied the salt of the banquet. He was a small, mild- looking man, with a pretty, unoffending wife, and dined out perpetually during the London season. Mr. Shinebar, the famous barrister, made a fourth. Lord George Bulrose, a West of England man, a gourmet, and, in so far as after-dinner talk went, a mighty hunter, was the fifth; and Sir Nugent and his two daughters completed the circle. After dinner there was to be an evening party, and before the small hours of the morning a great many famous people would have dropped in at the corner house in Cavendish Row. The ladies had retired, leaving Sir Nugent and his chosen friends to talk about law, and horses, and the last new burlesque actress, as they drew closer in to the dainty round table, where the glass sparkled and the deep-hued blossoms brightened under the cluster of wax lights in the central chandelier. Viola and Lady Cheshunt went upstairs arm-in-arm, the girl nestling affectionately against the substantial shoulder of the portly matron. Mrs. Noyce tripped lightly after these two, and Madge followed, alone, with a grave brow, and that lofty air which so well became Sir Nugent Bellingham's elder daughter. Barely were sisters less alike than these two. Viola was a blonde, complexion alabaster, hair the colour of raw silk—plenteous flaxen hair, which the girl wound into a crown of pale gold upon the top of her small head; eyes of turquoise blue; figure a thought too slim, but the perfection of grace in every movement and attitude; foot
  • 37. and hand absolutely faultless: altogether a girl to be put under a glass case. 'I should admire the younger Miss Bellingham more if she were a little less like Sèvres china,' one of the magnates of society had observed. Madge was a brunette—hair almost black, and with a natural ripple—complexion a rich olive, eyes darkest hazel—features the true Bellingham type, clearly cut as a profile on an old Roman medal— figure tall and commanding, a woman born to rule, one would say, judging by externals—a woman with the stuff in her to make a general, Sir Nugent was wont to boast. But although she was of a loftier mould than the generality of women, there was no hardness about Madge Bellingham. In love or in anger she was alike strong. For hate she was too noble. The rooms were deliciously cool, the light somewhat subdued, the windows open to the warm spring night. There were flowers enough in the small front drawing-room to make it an indoor garden. The dowager seated herself upon the most comfortable sofa in this room, a capacious, square-backed sofa, in a dusky corner, fenced off and sheltered by a well-filled jardinière. 'Come here, Madge,' she cried, with good-natured imperiousness, 'I want to talk to you.—Viola, child, go and amuse yourself with Mrs. Noyce. Show her your photograph album, or parlez chiffons. I want Madge all to myself.' Madge obeyed without a word, and squeezed herself into the corner of the sofa, which Lady Cheshunt and Lady Cheshunt's dress almost filled. 'How big you are growing, child! there's hardly room enough for you!' remarked the matron. 'And now tell me the truth, Madge; what is the matter with you to-night?' 'I don't think there is anything the matter more than usual, Lady Cheshunt.'
  • 38. 'I know better than that. You were dull and distrait all dinner- time. True, there was no one to talk to but two married men, and that old twaddler, Bulrose; but a young lady should be always equally agreeable—that is one of the fundamental principles of good breeding.' 'If I seemed a little out of spirits you can hardly wonder. Papa's sadly involved state is enough to make me uneasy.' 'My dear, your papa has been involved ever since my first season —when my waist was only eighteen inches, and Madame Devy made my gowns. He is no worse off now than he was then, and he will go on being hopelessly involved till the end of the chapter. I don't see why you should be unhappy about it. He will be able to give you and Viola a tolerable home till you marry and make better homes for yourselves, which it is actually incumbent upon you to do.' This was said with a touch of severity. Madge sighed, and the slender foot in the satin shoe tapped the ground with a nervous, impatient movement. 'Madge, I hope there is no truth in what I hear about you and Mr. Penwyn.' A deep tell-tale glow burned in Miss Bellingham's cheek. She fanned herself vehemently. 'I cannot imagine what you have heard, Lady Cheshunt.' 'I have heard your name coupled with Mr. Penwyn's—the poor Mr. Penwyn.' 'I only know one Mr. Penwyn.' 'So much the worse for you, my dear. You know the wrong one. There is a cousin of that young man's who has a fine estate in Cornwall—the Penwyn estate. You must have heard of that.' 'Yes, I have heard Mr. Penwyn speak of his cousin's property.' 'Of course. Poor penniless young man; very natural that he should talk of it. Don't suppose that I have no feeling for him. He is
  • 39. next heir to the property, but no doubt the other young man, James Penwyn's son, will marry and have a herd of children. I knew James Penwyn, this young man's father, years ago. There were three brothers—George, the eldest, who was in the army, and was killed in a skirmish with some wild Indians in Canada—very sad story; James, who was in the church, and had a living somewhere near London; and Balfour, in the law, I believe, whose son you know.' 'Yes,' sighed Madge. She had heard the family history from Churchill Penwyn, but the dowager liked to hear herself talk, and did not like to be interrupted. 'Now, if by any chance the present James Penwyn, who is little more than a lad, were to die unmarried, Churchill Penwyn could come into the property under his grandfather's will, which left the estate to the eldest surviving son and his children after him. George died unmarried. James left an only son. Churchill is therefore heir presumptive. But it's a very remote contingency, my love, and it would be madness for you to give it a thought—with your chances.' Madge shrugged her shoulders despondently. 'I don't think my chances are particularly brilliant, Lady Cheshunt.' 'Nonsense, Madge! Everybody talks of the beautiful Bellinghams. And you refused a splendid offer only the other day—that Mr. Cardingham, the great manufacturer.' 'Who had only seen me four times when he had the impudence to ask me to marry him! He was old and ugly, too.' 'When the end is a good establishment one must not look at the means too closely. Poor dear Cheshunt was many years my senior, and no beauty, even in his wig. You must take a more serious view of things, my dear Madge. It will not do for you and your sister to hang fire. The handsomer girls are, the more vital it is for them to go off quickly. A plain little unobtrusive thing may creep through half a dozen seasons and surprise everybody by making a good match at
  • 40. last. But a beauty who doesn't marry soon is apt to get talked about. Malicious people put it down to too much flirtation. And then, my love, consider your milliner's bills; what will they be at the end of a few seasons?' 'Not very much, Lady Cheshunt. I cut out all my own dresses and Viola's too, and our maid runs them together. Viola and I help sometimes, when we can steal an hour from society. I couldn't bear to wear anything that wasn't paid for.' 'Upon my word you are an exemplary girl, Madge,' exclaimed Lady Cheshunt, astounded by such Roman virtue. 'What a wife you will make!' 'Yes, I think I might make a tolerable wife, for a poor man.' 'Don't speak of such a thing. You were born for wealth and power. You are bound to make a great marriage—if not for your own sake, for Viola's. See what a poor helpless child she is—sadly wanting in moral stamina. If you had a good establishment she would have a haven of refuge. But if you were to marry badly what will become of her? She would never be able to manage your papa.' Madge sighed again, and this time deeply. Love for her sister was Madge Bellingham's weakest point. She positively adored the fair fragile girl who had been given into her childish arms eighteen years ago, on that bitter day which made her an orphan. There was only four years' difference between the ages of the sisters, yet Madge's affection was always maternal in its protecting thoughtfulness. To marry well would be to secure a home for Viola. Sir Nugent was but a feeble staff to lean upon. 'I have no objection to marrying well whenever a fair opportunity arises, Lady Cheshunt,' she said, firmly; 'but I will never marry a man whom I cannot respect and like.' 'Of course not, my poor pet,' murmured the widow, soothingly; 'but, fortunately, there are so many men in the world one can like and respect. It is that foolish sentimental feeling called love which
  • 41. will only fit one person. In the meantime, Madge, take my advice, and don't let people talk about you and Mr. Penwyn.' 'I don't know why they should talk about us.' 'Yes, you do, Madge—in your heart of hearts. You know that you have sat together in corners, and that you have a knack of blushing when he comes into the room. It won't do, Madge, it won't do. That young fellow has nothing except what he can earn himself. I know his mother had a struggle to bring him up, and if he hadn't been an only son could hardly have brought him up at all. He was a Blue-coat boy, I believe, or something equally dreadful. It is not to be thought of, Madge.' 'I do not think of it, Lady Cheshunt,' replied Miss Bellingham, resolutely, 'and I wish you would not worry yourself and me about imaginary dangers.' 'Your visitors are beginning to come; go and receive them, and leave me in my corner. Mr. Penwyn is to be here, I've no doubt.' 'I don't know. He knows that Saturday is our night.' 'Mr. Churchill Penwyn!' announced a footman at the door of the larger room. 'I thought so,' said Lady Cheshunt, 'and the first to arrive, too. That looks suspicious.'
  • 42. CHAPTER V. 'IL NE FAUT PAS POUSSER AU BOUT LES MALHEUREUX.' Churchill Penwyn was one of those men who are sure to obtain a certain amount of notice in whatsoever circle they appear—a man upon whom the stamp of good blood, or good breeding, had been set in a distinct and palpable manner—a man who had no need for self-assertion. It would have been difficult for any one to state in what the distinction lay. He was not particularly good-looking. Intellect, rather than regularity of feature, was the leading characteristic of his countenance. Already, though he was still on the sunward side of his thirtieth birthday, the dark brown hair grew thinly upon the broad high brow, showing signs of premature baldness. His features were sharply cut, but by no means faultless, the mouth somewhat sunken, the lips thin. His light grey eyes had a keen, cold lustre; only those who saw Churchill Penwyn in some rare moment of softer feeling knew that those severe orbs could be beautiful. Mr. Penwyn was a barrister, still in the uphill stage of his career. He got an occasional brief, went on circuit assiduously, and did a little in the literature of politics—a hard, dry kind of literature, but fairly remunerative—when he got it to do. He had contributed hard- headed statistical papers to the Edinburgh and the Westminster, and knew a good deal about the condition of the operative classes. He had lectured in some of the northern manufacturing towns, and knew the black country by heart. People talked of him as a young man who was sure to make his mark by and by; but by and by might be a long way off. He would be fifty years of age, perhaps, before he had worked his way to the front.
  • 43. Churchill Penwyn went a great deal into society, when it is considered how hard and how honestly he worked; but the houses in which he was to be found were always houses affected by the best people. He never wasted himself among second-rate circles. He was an excellent art critic; knew enough about music to talk of it cleverly, though he had hardly the faculty of distinguishing one tune from another; waltzed like a Viennese; rode like a centaur; spoke three Continental languages perfectly. It was his theory that no man should presume to enter society who could not do everything that society could require him to do. Society was worth very little in itself, according to Churchill Penwyn, but a man owed it to himself to be admired and respected by society. 'I see a good many men who go into the world to stare about them through eye-glasses,' said Churchill. 'If I couldn't do anything more than that I should spend my evenings in my own den.' Churchill Penwyn went into the gay world with a definite aim— some of the people he met must needs be useful to him sooner or later. Ohne Hast, ohne Rast—without haste, without rest—was his motto. He had it engraved on his signet ring, instead of the Penwyn crest. He was never in a hurry. While striving for success he had the air of a man who had already succeeded. He occupied a third floor in the Temple, and lived like an anchorite, but his tailor and bootmaker were among the best in London, and he was a member of the Travellers' and the Garrick. He was to be seen sometimes lunching at his club, and occasionally entertained a friend at luncheon, but he rarely dined there, and was never seen to drink anything more costly than a pint of La Rose, or Medoc. No man had ever mastered the art of economy more thoroughly than Churchill Penwyn, and yet he had never laid himself open to the charge of meanness. Miss Bellingham received him with a bright look of welcome, despite the dowager's warning, and their hands met, with a gentle pressure on Churchill's part. Viola was discreetly occupied in showing Mrs. Noyce a new photograph, and only gave the visitor a bow and a
  • 44. smile. So he had a fair excuse for seating himself next Madge, on the divan by the fireplace, where there was just room for those two. 'I did not think you would come to-night,' said Madge, opening and shutting her large black fan, with a slightly nervous movement. 'Why not?' 'I saw your name in the paper, at Halifax, or somewhere, hundreds of miles away.' 'I was at Halifax the day before yesterday, but I would not miss my Saturday evening here. You see I have come a quarter of an hour in advance of your people, so that I might have you to myself for a few minutes.' 'It is so good of you,' faltered Madge, 'and you know I am always glad.' 'I should be wretched if I did not know it.' This was going further than Mr. Penwyn's usual limits. The man was the very soul of prudence. No sweet words, no tender promises, had ever passed between these two, and yet they knew themselves beloved. Madge knew it to her sorrow, for she was fain to admit the wisdom of the dowager's warning. It would never do for her to marry Churchill Penwyn. Happily for her, up to this time Churchill had never asked her to be his wife. 'He is too wise,' she said to herself, with the faintest touch of bitterness. 'Too much a man of the world.' But that this man of the world loved her she was very sure. For just ten minutes they sat side by side, talking of indifferent things, but only as people talk who are not quite indifferent to each other. And then more visitors were announced. Sir Nugent and his friends came upstairs; the rooms began to fill. Musical people arrived. A German with long rough hair, bony wrists, and an eye- glass, seated himself at the piano, and began a performance of so
  • 45. strictly classical a character that he had the enjoyment of it all to himself, for nobody else listened. Minor chords chased one another backwards and forwards about the middle of the piano as if they were hunting for the melody and couldn't find it. Little runs and arpeggio passages went under and over each other, and wriggled in and out and up and down in a distracted way, still searching for the subject, and finally gave up the quest in utter despair, appropriately expressed by vague grumblings in the bass, which slowly faded into silence. Whereupon every one became enthusiastic in their admiration. After this a young lady in pink sang an airy little chanson, with elaborate variations—using her bright soprano voice as freely as if she had been Philomel, trilling her vespers in the dusky woods of June. And then Madge Bellingham sat down to the piano, and played as few young ladies play—as if her glad young soul were in the music. It was only an Hungarian march that she played. There were no musical fireworks—no difficulties conquered; none of those passages which make the listeners exclaim, 'Poor girl! how she must have practised!' It was but a national melody—simple and spirit-stirring— played as if the soul of a patriot were guiding those supple fingers. The graceful figure was bent a little over the key-board—the dark eyes followed the swift flight of the hands over the keys. She seemed to caress the notes as she struck them—to play with the melody. Pride, love, hope, rage, every passion expressed itself by turns as she followed that wild strange music through the mazes of its variations, never losing the subject. It sounded like the war-cry of a free people. Even Churchill Penwyn, who in a general way cared so little for music, listened entranced to this. He could hardly have recalled the air half an hour later, but for the moment he was enchanted. He stood a little way from the instrument, watching the player, watching the beautiful head, with its dark rippling hair wound into a Greek knot at the back, the perfect throat, with its classic necklet of old Wedgwood medallions set in plainest gold; the drooping lashes, as the downcast eyes followed the flying touch. To
  • 46. hear Madge play was delightful, but to see her was still better. And this man's love had all the strength of a passion repressed. He had held himself in check so long, and every time he saw her he found her more and more adorable. The evening wore on. People came in and out. Madge played the hostess divinely, always supported by Lady Cheshunt, who sat in the smaller drawing-room as in a temple, and had all the best people brought to her. Some came to Cavendish Row on their way somewhere else, and were careful to let their acquaintance know that they were 'due' at some very grand entertainment, and made rather a favour of coming to Sir Nugent. The last of the guests went about half an hour after midnight, and among the last Churchill Penwyn. 'May I bring you that book after church to-morrow?' he asked. The book was a comedy of Augier's lately produced at the Français, which he had been telling her about. Madge looked embarrassed. She had a particular wish to avoid a tête-à-tête with Mr. Penwyn, and Sunday was an awkward day. Sir Nugent would be at Hurlingham, most likely, and Viola was such a foolish little thing, almost as bad as nobody. 'If you like' she answered. 'But why take the trouble to call on purpose? You might bring it next Saturday, if you come to us.' 'I shall bring it you to-morrow,' he said, as they shook hands. That tiresome Viola was in a hopeless state of headache and prostration next morning, so Madge had to go to church alone. Coming out of the pretty little Anglican temple she found herself face to face with Churchill Penwyn. He had evidently been lying in wait for her. 'I was so afraid I might not find you at home,' he said, half apologetically, 'so I thought I might as well walk this way. I knew this was your church. I've brought you the play we were talking about.'
  • 47. 'You're very kind, but I hope you don't think I read French comedies on Sundays?' 'Of course not; only Sunday is my leisure day, and I thought you would not shut your door upon me even on Sunday.' The church was only five minutes' walk from Cavendish Row. When Sir Nugent's door was opened Mr. Penwyn followed Miss Bellingham into the house as a matter of course. She had no help for it but to go quietly upstairs to her fate. She almost knew what was coming. There had been something in his manner last night that told her it was very near. 'Prudence, courage,' she whispered to herself, and then, 'Viola!' The last word was a kind of charm. The rooms looked bright and gay in the noontide sunlight, tempered by Spanish blinds. The flowers, the feminine prettiness scattered about, struck Churchill's eye, they gave such a look of home. 'If I could afford to give her as good a home as this!' he thought. He shut the door carefully behind him, and glanced round the room to make sure they were alone, and went close to Madge as she stood by one of the small tables, fidgeting with the clasp of her prayer-book. 'I think you know why I came to-day,' he said. 'You have told me about three times,—to bring me "La Quarantaine."' 'I have come to tell you a secret I have kept more than a year. Have you never guessed it, Madge? Have I been clever enough to hide the truth altogether? I love you, dearest. I, penniless Churchill Penwyn, dare to adore one of the belles of the season. I, who cannot for years to come offer you a house in May Fair. I, who at most can venture to begin married life in a Bloomsbury lodging, supported by the fruits of my pen. It sounds like madness, doesn't it?'
  • 48. 'It is madness,' she answered, looking full at him with her truthful eyes. The answer surprised and humiliated him. He fancied she loved him—would be ready to face poverty for his sake. She was so young, and would hardly have acquired the wisdom of her world yet awhile. 'I beg your pardon,' he said, a curious change coming over his face, a sudden coldness that made those definite features look as if they had been cut out of stone. 'I have been deceiving myself all along, it seems. I did not think I was quite indifferent to you.' The eyelids drooped over the dark eyes for a moment, and were then lifted suddenly, and the eyes met Churchill's. That one look told all. She loved him. 'I have been learning to know the world while other girls are allowed to dream,' she said. 'I know what the burden of debt means. Poverty brings debt as a natural sequence. If you were a woodcutter and we could live in a hovel and pay our way, there would be nothing appalling in marriage. But our world will not let us live like that. We must play at being fine ladies and gentlemen while our hearts are breaking, and our creditors being ruined. Ever so long ago I made up my mind that I must marry a rich man. If I have ever seemed otherwise to you than a woman of the world, bent upon worldly success, I humbly beg you to forgive me.' 'Madge,' cried Churchill, passionately, 'I will forgive anything if you will only be frank. Were my luck to turn speedily, through some unlooked-for professional success, for instance, would you have me then?' 'If I stood alone in the world, if I had not my sister to consider, I would marry you to-morrow. Yes, though you were a beggar,' she answered, grandly. He clasped her to his breast and kissed those proud lips. The first lover's kiss that had ever rested there.
  • 49. 'I will be rich for your sake, distinguished for your sake,' he said impetuously, 'if wealth and fame are within the reach of man's effort.'
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