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<!DOCTYPE html>
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<title>General classification of uncertainties</title>
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<p><a href="1.html">Previous - Introduction</a> <a href="index.html">Index</a> <a href="3.html">Next - The current state of uncertainty in in situ SST analyses</a></p>
<h1>General classification of uncertainties</h1>
<p>
Throughout this review the distinction will be made between an error and an
uncertainty. The distinction between the two loosely follows the usage in the
Guide to the Expression of Uncertainty in Measurement (GUM) [BIPM, 2008]. The
error in a measurement is the difference between some idealized "true value" and
the measured value and is unknowable. The GUM defines the uncertainty of a measurement
as the "parameter, associated with the result of a measurement, that characterizes
the dispersion of the values that could reasonably be attributed to the measurand".
This is the sense in which uncertainty is generally meant in the following discussion.
This is not necessarily the same usage as is found in the cited papers. It is common
to see the word error used as a synonym for uncertainty such as in the commonly used
phrases <i>standard error</i> and <i>analysis error</i>.
</p><p>
Broadly speaking, errors in individual SST observations have been split into two groupings:
<b>uncorrelated observational errors</b> (often referred to as random or independent
errors) and <b>systematic observational errors</b>. Although this is a convenient
way to deal with the uncertainties, errors in SST measurements will generally share
a little of the characteristics of each. More recent literature, particularly
associated with satellite retrievals, also deals with <b>locally-correlated errors</b>
also known as synoptically-correlated errors.
</p><p>
<b>Uncorrelated observational errors</b> occur for many reasons: misreading of the thermometer,
rounding errors, the difficulty of reading the thermometer to a precision higher than
the smallest marked gradation, incorrectly recorded values, errors in transcription
from written to digital sources and sensor noise among others. Although they might
confound a single measurement, the independence of the individual errors means they
tend to cancel out when large numbers are averaged together. Therefore, the contribution
of uncorrelated/independent errors to the uncertainty on the global average SST is much
smaller than the contribution of uncorrelated error to the uncertainty on a single
observation even in the most sparsely observed years. Nonetheless, where observations
are few, uncorrelated observational errors can be an important component of the total
uncertainty.
</p><p>
<b>Systematic observational errors</b> are much more problematic because their effects become
relatively more pronounced as greater numbers of observations are aggregated. Systematic
errors might occur because a particular thermometer is mis-calibrated, or poorly sited.
No amount of averaging of observations from a thermometer that is mis-calibrated such that
it reads 1 K too high will reduce the error in the aggregate below this level save by chance.
However, in many cases the systematic error will depend on the particular environment
of the thermometer and will therefore be independent from ship to ship. In this case,
averaging together observations from many different ships or buoys will tend to reduce
the contribution of systematic observational errors to the uncertainty of the average.
</p><p>
In the 19th and early 20th century, the majority of observations were made using buckets to haul a
sample of water up to the deck for measurement. Although buckets were not always of a
standard shape or size, they had a general tendency under typical environmental conditions
to lose heat via evaporation or directly to the air when the air-sea temperature difference
was large. Folland and Parker [1995] provide a more comprehensive survey of the problem
which was already well known in the early 20th Century (see, for example, the introduction
to Brooks [1926]). <b>Pervasive systematic observational errors</b> like the cold bucket
bias are particularly pertinent for climate studies because the errors affect the whole
observational system and change over time as observing technologies and practices change.
The change can be gradual as old methods are slowly phased out, but they can also be abrupt,
reflecting significant geopolitical events such as the Second World War [Thompson et al., 2008].
Rapid changes also arise because the digital archives of marine meteorological reports (ICOADS
Woodruff et al. [2011]) are themselves discontinuous.
</p><p>
Generally, systematic errors are dealt with by making adjustments based on knowledge of the systematic
effects. The adjustments are uncertain because the variables that determine the size of the
systematic error are imperfectly known. The atmospheric conditions at the point where the measurement
was made, the method used to make the measurement ERI or bucket the material used in the
construction of the bucket if one was used, as well as the general diligence of the sailors making
the observations have not in many cases been reliably recorded. Part of the uncertainty can be
estimated by allowing uncertain parameters and inputs to the adjustment algorithms to be varied
within their plausible ranges thus generating a range of adjustments (e.g., Kennedy et al. [2011c]).
This parametric uncertainty gives an idea of the uncertainties associated with poorly determined
parameters within a particular approach, but it does not address the more general uncertainty arising
from the underlying assumptions. This uncertainty will be dealt with later as structural uncertainty.
</p><p>
Between uncorrelated and systematic errors sit <b>locally-correlated errors</b>. These are typically associated
with unknown, or poorly known, temporary atmospheric conditions which have a common effect on
measurements in a limited region. This is most commonly encountered in discussions of satellite SST
retrieval errors, but would also apply to measurements made with buckets which are sensitive to changing
atmospheric conditions. Between pervasive systematic errors and systematic errors, one finds a range
of different potential correlations. For example, the buckets and instructions issued by a ship's
recruiting country, were different for each country. It is important to identify these kinds of
correlations between errors because even small correlations between errors mean that they cancel less
rapidly as readings are aggregated and can therefore be an important component of the uncertainty in
large-scale averages.
</p><p>
There are a number of other uncertainties associated with the creation of the gridded data sets and SST analyses
that are commonly used as a convenient alternative to dealing with individual marine observations.
The uncertainties are closely related because they arise in the estimation of area-averages from a
finite number of noisy and often sparsely-distributed observations.
</p><p>
In Kennedy et al., [2011b] two forms of this uncertainty were considered: <b>grid-box sampling uncertainty</b>
and <b>large-scale sampling uncertainty</b> (which they referred to as coverage uncertainty). Grid-box
sampling uncertainty refers to the uncertainty accruing from the estimation of an area-average SST
anomaly within a grid box from a finite, and often small, number of observations. Large-scale sampling
uncertainty refers to the uncertainty arising from estimating an area-average for a larger area that
encompasses many grid boxes that do not contain observations. Although these two uncertainties are
closely related, it is often easier to estimate the grid-box sampling uncertainty, where one is dealing
with variability within a grid box, than the large-scale sampling uncertainty, where one must take into
consideration the rich spectrum of variability at a global scale.
</p><p>
Although some gridded SST data sets contain many grid boxes which are not assigned an SST value because they
contain no measurements, other SST data sets oftentimes referred to as SST analyses use a variety
of techniques to fill the gaps. They use information gleaned from data-rich periods to estimate the
parameters of statistical models that are then used to estimate SSTs in the data voids, often by
interpolation or pattern fitting. There are many ways to tackle this problem and all are necessarily
approximations to the truth. The correctness of the analysis uncertainty estimates derived from these
statistical methods are conditional upon the correctness of the methods, inputs and assumptions used
to derive them. No method is correct therefore analytic uncertainties based on a particular method will
not give a definitive estimate of the true uncertainty. To gain an appreciation of the full uncertainty
it is necessary to factor in the lack of knowledge about the correct methods to use, which brings the
discussion back to structural uncertainty.
</p><p>
There are many scientifically defensible ways to produce a data set. For example, one
might choose to fill gaps in the data by projecting a set of Empirical Orthogonal
Functions (EOFs) onto the available data. Alternatively, one might opt to fill the data
using simple optimal interpolation. Both are defensible approaches to the problem, but
each will give different results. In the process of creating any data set, many such
choices are made. <b>Structural uncertainty</b> [Thorne et al., 2005] is the term used
to understand the spread that arises from the many choices and foundational assumptions
that can be (and have to be) made during data set creation. The character of structural
uncertainty is somewhat different to the other uncertainties considered so far. The
uncertainty associated with a measurement error, for example, assumes that there is
some underlying distribution that characterizes the dispersion of the measured values.
In contrast, there is generally no underlying "distribution of methods" that can be
used to quantify the structural uncertainty. Furthermore, the diverse approaches taken
by different teams might reflect genuine scientific differences about the nature of
the problems to be tackled. Consequently, structural uncertainty is one of the more
difficult uncertainties to quantify or explore efficiently. It requires multiple,
independent attempts to resolve the same difficulties, it is an ongoing commitment,
and it does not guarantee that the true value will be encompassed by those independent
estimates. Nevertheless, the role that the creation of multiple independent estimates
and their comparison has played in uncovering, resolving, and quantifying some of the
more mystifying uncertainties in climate analyses is unquestionable. The most obvious
one might say, notorious examples are those of tropospheric temperature records made
using satellites and radiosondes [Thorne et al., 2011] and sub-surface ocean temperature
analyses [Lyman et al., 2010; Abraham et al., 2013].
</p><p>
Which leads finally to <b>unknown unknowns</b>. On February 12th 2002, at a news briefing at the US Department of Defense, Donald Rumsfeld memorably divided the world of knowledge into three quarters:
</p><blockquote>
<i>"There are known knowns. These are things we know we know. We also know there
are known unknowns. That is to say, we know there are some things we do not know.
But there are also unknown unknowns, the ones we don't know we don't know."</i>
</blockquote><p>
In the context of SST uncertainty, unknown unknowns are those things that have been overlooked. By their nature, unknown unknowns are unquantifiable; they represent the deeper uncertainties that beset all scientific endeavors. By deep, I do not mean to imply that they are necessarily large. In this review I hope to show that the scope for revolutions in our understanding is limited. Nevertheless, refinement through the continual evolution of our understanding can only come if we accept that our understanding is incomplete. Unknown unknowns will only come to light with continued, diligent and sometimes imaginative investigation of the data and metadata.
</p>
<p><a href="1.html">Previous - Introduction</a> <a href="index.html">Index</a> <a href="3.html">Next - The current state of uncertainty in in situ SST analyses</a></p>
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