Chapter 2 - The Historical Setting
2.5 The Role of Observations in Oceanography
The brief tour of theoretical ideas
suggests that observations are essential for understanding the oceans. The
theory describing a convecting, wind-forced, turbulent fluid in a rotating
coordinate system has never been sufficiently well known that important features
of the oceanic circulation could be predicted
before they were observed. In almost all cases, oceanographers resort to observations
to understand oceanic processes.
At first glance, we might think that the
numerous expeditions mounted since 1873 would give a good description of
The results are indeed
impressive. Hundreds of expeditions have extended into all oceans. Yet, much
of the ocean is poorly explored.
By the year 2000, most areas of the ocean
will have been sampled crudely from top to bottom only once. Some areas,
such as the Atlantic, will have been sparsely sampled
four times: during the Meteor Expedition from 1925 to 1925, during the International
Geophysical Year in 1959, during the Geochemical Sections cruises in the early
1970s, and during the World Ocean Circulation Experiment from 1991 to 1996.
All areas will be vastly under sampled. This is the
sampling problem (See box below). Our samples of the
are insufficient to describe the ocean well enough to predict its variability
and its response to changing forcing. Lack of
sufficient samples is the largest source
of error in our understanding of the ocean.
The lack of observations has led to a very important and widespread conceptual
The absence of evidence was taken as evidence
of absence The great
observing the ocean meant that when a phenomenon was not observed, it was
assumed it was not
present. The more one is able to observe the ocean, the more the complexity
and subtlety that
As a result, our understanding of the ocean is often too simple to be correct.
Sampling error is caused by a set of samples (measurements) not representing
the population of the variable being measured. A population
set of all possible measurements, and a sample is the sampled subset of the population.
We assume each measurement is perfectly accurate.
To determine if your measurement
has a sampling error, you must first completely specify the problem you wish
to study. This defines the population. Then, you must determine if the samples
represent the population. All steps are necessary.
Global Warming Example
- The Problem:
Suppose your problem is to
measure the annual-mean sea-surface temperature of the ocean to determine
if global warming is occurring.
- The Population: For this
problem, the population is the set of all possible measurements of surface
temperature, in all regions in all months. If the sample mean is to equal
the true mean, the samples must be uniformly distributed throughout the
year and over all the area of the ocean, and sufficiently dense to include
all important variability in time and space. This is impossible.
- The Sample: Ships
avoid stormy regions such as high latitudes in winter, so ship sample tend
not to represent the population of surface temperatures. Satellites may
not sample uniformly throughout the daily cycle, and they may not observe
temperature at high latitudes in winter because of persistent clouds, although
they tend to sample uniformly in space and throughout the year in most
regions. If daily variability is small, the satellite samples will be more
representative of the population than the ship samples.
From the above, it should be clear
that oceanic samples rarely represent the population we wish to study. We always
have sampling errors.
Sampling and Instrument Error
In defining sampling error, we must clearly distinguish
between instrument errors and sampling errors.
- Instrument errors are due to
the inaccuracy of the instrument.
- Sampling errors are due to a failure to make
- An example: Consider the example above: the determination of mean
- If the measurements are made by thermometers on
ships, each measurement has a small error because thermometers are not
perfect. This is an instrument error.
- If the ships avoids high latitudes
in winter, the absence of measurements at high latitude in winter is
a sampling error.
Meteorologists designing the Tropical Rainfall Mapping Mission have
been investigating the sampling error in measurements of rain. Their results
are general and may be applied to other variables. For a general description
of the problem see North & Nakamoto (1989).
Selecting Oceanic Data Sets
Much of the existing oceanic data have been organized into large data sets. For
example, satellite data are processed and distributed by groups working with
NASA. Data from ships have been collected and organized by other groups. Oceanographers
now rely more and more on such collections of data produced by others.
use of data produced by others introduces problems:
- How accurate are the
data in the set?
- What are the limitations of the data set? And,
- How does the set compare with other similar sets?
Anyone who uses public
or private data sets is wise to obtain answers to such questions.
you plan to use data from others, here are some guidelines.
- Use well documented data sets. Does
the documentation completely de-scribe the sources of the original measurements,
used to process the data, and all criteria used
to exclude data? Does the data set include version numbers to identify
changes to the set?
- Use validated data. Has accuracy of
data been well documented? Was accuracy determined by comparing with different
measurements of the
same variable? Was validation global or regional?
- Use sets that have been
used by others and referenced in scientific papers. Some data
sets are widely used for good reason. Those who produced the
sets used them in their own published work and others trust the data.
don't use a data set just because it is handy. Can you document
the source of the set? For example, many versions of the digital, 5-minute
sea-floor are widely available. Some date back to the first sets produced
by the U. S. Defense Mapping Agency, others are from the ETOPO-5 set.
on a colleague's statement about the source. Find the documentation. If
it is missing, find another data set.
Designing Oceanic Experiments
are exceedingly important
for oceanography, yet observations are expensive because ship time and satellites
are expensive. As a result, oceanographic experiments must be carefully planned.
While the design of experiments may not t well within an historical chapter,
perhaps the topic merits a few brief comments because it is seldom
mentioned in oceanographic textbooks, although it is prominently described in
texts for other scientific fields. The design of experiments is particularly
important because poorly planned experiments lead to ambiguous results, they
may measure the wrong variables, or they may produce completely useless data.
first and most important aspect of the design of any experiment is to determine
why you wish to make a measurement before deciding how you will
make the measurement or what you will measure.
- What is the purpose of the
observations? Do you wish to test hypotheses or describe processes?
accuracy is required of the observation?
- What temporal and spatial resolution
is required? What is the duration of measurements?
Consider, for example,
how the purpose of the measurement changes how you might measure salinity
or temperature as a function of depth:
- If the purpose is to describe water
masses in an ocean basin, then measurements with 20-50m vertical spacing
and 50-300 km horizontal spacing, repeated once per 20-50 years in
deep water are required.
- If the purpose is to describe vertical mixing in the
open equatorial Pacific, then 0.5-1.0mm vertical spacing and 50-1000
km spacing between locations repeated
once per hour for many days may be required.
Accuracy, Precision, and
While we are on the topic of experiments, now is a good time to introduce
three concepts needed throughout the book when we discuss experiments: precision,
accuracy, and linearity of a measurement.
Accuracy is the difference between
the measured value and the true value.
Precision is the difference among
The distinction between accuracy and precision is
usually illustrated by the
simple example of firing a rifle at a target. Accuracy is the average distance
from the center of the target to the hits on the target. Precision
is the average distance between the hits. Thus, ten rifle shots could be clustered
within a circle 10 cm in diameter with the center of the cluster located
20cm from the center of the target. The accuracy is then 20 cm, and the precision
Linearity requires that the output of an instrument
be a linear function of the input. Nonlinear devices rectify variability to
a constant value.
So a nonlinear response leads to wrong mean values. Non-linearity
can be as important as accuracy. For example, let
Output = Input +0.1 (Input)2
Input = a
Output = a sin ωt + 0.1 (a
Output = a sin ωt
+ 1/2 a2 -
1/2 a2 cos 2ωt
Note that the mean value of the input is zero, yet the output of this non-linear
instrument has a mean value of 0.5 a2 plus
an equally large term at twice the input frequency. In general, if input has
frequencies ω1 and ω2,
then output of a non-linear instrument has frequencies ω1 ± ω2.
Linearity of an instrument is especially important when the instrument
must measure the mean value of a turbulent variable. For example, we require
linear current meters when measuring currents near the sea surface where wind
and waves produce a large variability in the current.
Sensitivity to other variables
Errors may be correlated with
other variables of the problem. For example, measurements of conductivity
are sensitive to temperature. So, errors in the measurement of temperature
in salinometers leads to errors in the measured values of conductivity or