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<!DOCTYPE html>
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<head>
<link rel="stylesheet" type="text/css" href="sst_review_style.css">
<title>3.2.2 Uncorrelated and Systematic Measurement Errors</title>
</head>
<body>
<div class="row">
<div class="column side">
<p></p>
</div>
<div class="column middle">
<p>
<a href="3.2.1.html">Previous - 3.2.1 Uncorrelated Measurement Errors</a> <a href="index.html">Index</a> <a href="3.2.3.html">Next - 3.2.3 Summary of Individual Observational Errors</a>
</p>
<h1>3.2.2 Uncorrelated and Systematic Measurement Errors</h1>
<p>
Kent and Berry [2008] and Kennedy et al. [2011a, 2011b] decomposed the observational
errors into uncorrelated and systematic components. Brasnett [2008] and Xu and Ignatov
[2010] implicitly used the same error model their analyses output the same statistics
produced by Kent and Berry [2008] and the results are indeed very similar (Figure 3).
Estimates are summarized in Table 4. The possibility of correlated measurement errors
is also implicitly allowed for by Ishii et al. [2003] and Hirahara et al. [2013] who
merge observations from a single ship into a super observation before calculating
uncertainties. Adding the uncertainties in quadrature gives a combined observational
uncertainty of between 1 and 1.5 K, consistent with earlier estimates (Table 1) that
did not differentiate between the two.
</p>
<p>
<img src="http://www.metoffice.gov.uk/hadobs/hadsst3/uncertainty_review/Figure_3.png">
</p><p>
<i><b>Figure 3</b>: Distributions of estimated measurement errors and uncertainties
from ships. (a) distributions of systematic measurement errors for all entries (2003-2007)
in Kennedy et al. [2011a], Brasnett [2008], Berry and Kent [2008] and Xu and Ignatov [2010].
(b) distributions of uncorrelated measurement error uncertainties (expressed as variances)
from the same analyses as in the top left panel and Atkinson et al. [2013]. (c) as for top
left except each ship now has only a single entry so the analyses are directly comparable.
(d) scatter plot showing systematic measurement errors estimated by Brasnett [2008] and
Berry and Kent [2008] showing the good correlation between the estimates.</i>
</p>
<p>
In most of the studies listed in Table 4, the systematic component of the error was assumed to be
different for each ship, but this does not on its own capture the effects of pervasive
systematic errors. Chan and Huybers [2019] showed that there are systematic errors at the level of
nations and decks in ICOADS. They argue for the inclusion of a systematic component that
operates at this level. The data from Kent and Berry [2008], Brasnett [2008] and Xu and Ignatov
[2010] also show that the systematic observational error component for some ships varies
from month to month suggesting that the partitioning of systematic and uncorrelated effects
is also a function of the time period considered.
</p>
<center>
<table>
<tr><th><b>Reference</b></th><th><b>Platform type</b></th><th><b>Uncorrelated</b></th><th><b>Systematic</b></th><th><b>Notes</b></th></tr>
<tr><td>Chan and Huybers [2019] Table 3</td><td>Ship</td><td>0.55±0.15K<sup>2</sup></td><td>0.78±0.12K<sup>2</sup></td><td>After accounting for national level effects</td><tr>
<tr><td>Chan and Huybers [2019] Table 3</td><td>Ship</td><td>0.42±0.15K<sup>2</sup></td><td>0.80±0.12K<sup>2</sup></td><td>After accounting for deck level effects</td><tr>
<tr><td>Kent and Berry [2008] pg 11 Table 5a</td><td>Ship</td><td>0.7 K</td><td>0.8 K</td><td>From comparison with Numerical Weather Prediction fields provided with VOSClim data</td></tr>
<tr><td>Pg 12 Table 5c</td><td> Drifter</td><td>0.6 K</td><td>0.3 K</td><td></td></tr>
<tr><td>Pg 11 Table 5b</td><td> Mooring </td><td>0.3 K</td><td>0.2 K</td><td></td></tr>
<tr><td>Kennedy et al. [2011a, 2011b] pg 86</td><td>Ship</td><td>0.74 K</td><td>0.71 K</td><td>From comparison with Along Track Scanning Radiometer SST retrievals</td></tr>
<tr><td>Pg 86</td><td>Drifter</td><td>0.26 K</td><td>0.29 K</td><td></td></tr>
<tr><td>Brasnett [2008] values estimated for present study by author</td><td>Ship</td><td>1.16 K</td><td>0.69 K</td><td>From comparison with interpolated fields</td></tr>
<tr><td>Xu and Ignatov [2010] values estimated for present study by author</td><td>Ship</td><td>0.81 K</td><td>0.53 K</td><td>From comparison with multisensor satellite SST fields</td></tr>
<tr><td>Kennedy et al. [2011a, 2011b] method using Atkinson et al. [2013] whitelist</td><td>Ship</td><td>0.56 K</td><td>0.37 K</td><td>From comparison with multisensor satellite SST fields</td></tr>
<tr><td>Gilhousen [1987] Table 6 pg 104 </td><td>Mooring</td><td>0.22 K</td><td>0.13 K</td><td>Comparison of moored buoys</td></tr>
</table>
<p class="caption"><i><b>Table 4</b>: List of estimates of measurement error uncertainties for all platforms for studies where the measurement error uncertainty is decomposed into uncorrelated and systematic components.</i></p>
</center>
<p>
The addition of a systematic component has a pronounced effect on the uncertainty of
large-scale averages comprising many observations. Kennedy et al. [2011b] estimated
that the effect of the correlations between errors in individual ship measurements was
to increase the uncertainty of
the global annual average SST anomaly due to measurement error from 0.01 K (uncorrelated
case) to more than 0.05 K in the 19th Century and to more than 0.01 K even in the
well-observed modern period when millions of observations contribute to the annual
global average (see Figure 8). The Deck-level and nation-level systematic errors
identified by Chan and Huybers [2019] would likely lead to an increase in the uncertainty
of large scale averages in unadjusted data. However, it is not clear to what extent existing bias
adjustment methods deal with the global and regional biases arising from systematic errors
at this level.
</p><p>
Berry and Kent [2017] used an error model that combined both uncorrelated and systematic
effects to assess the adequacy of the marine observing network. They found that metrics
which rely solely on counts of observations in a grid cell or similar area (Zhang et al.
2006, Zhang et al. 2009) typically can
misestimate the adequacy of the network because they do not take into account the
effect of systematic biases. They found that simply increasing observation counts for SST
was not the best way of reducing uncertainty and that increasing the number of ships or
buoys was better.
</p><p>
Systematic errors could also have a pronounced effect
on reconstructions when they project onto large-scale modes of variability, or on the
estimation of EOFs. However, because of the assumed independence of the errors between
ships, the correlated component of the uncertainty remains relatively unimportant for
the analysis of long-term trends of large-scale averages. Pervasive systematic errors,
which are correlated across a large proportion of the global fleet, (section 3.2) are far
more important from that point of view. Systematic errors at deck-level or nation-level
(Chan and Huybers, 2019) could also affect regional and global trends as these are likely
to have large scale effects over multiple years.
</p><p>
One of the difficulties with estimating the uncertainties associated with systematic errors
from individual ships is that not all observations in ICOADS can be associated with an
individual ship. Some of the reports have no more information than a location, time and SST
measurement. Kennedy et al. [2011b] had to make estimates of how the uncertainty arising
from systematic errors behaved as the number of observations increased by considering the
behavior at times when the majority of reports contained a ship name or call-sign. They
assumed that observations without call signs behaved in the same way. Kent and Berry [2008]
suggested that only ship reports with extant metadata be used in climate analyses of the modern
period to minimize such ambiguities. For earlier periods, the gains in improved quantification
of uncertainty would need to be balanced against the increased uncertainty arising from reduced
coverage.
</p><p>
Carella et al. [2017] developed an algorithm to assemble ship tracks from marine reports
that have missing, non-unique, incorrect or otherwise confusing ID information in ICOADS.
They found that they could significantly increase the fraction of observations assigned to
coherent tracks for much of the record. They note that the new track assignments could be
used to improve estimates of measurement error uncertainty, help with bias adjustment, quality
control and data assimilation.
</p><p>
Many gridded SST data sets and analyses, as well as the studies that depend on them, assume
that the observational errors are normally distributed, but this is not necessarily the case
for individual observations. Kennedy et al. [2011a] investigated the properties of observations
that had been quality controlled using the procedures described in Rayner et al. [2006]. They
found that in comparisons with satellite observations the distributions of errors were 'fat-tailed'
with the distribution of errors having a positive kurtosis. Chan and Huybers [2019] note that the
kurtosis is reduced when spatial heterogeneity of matched observations is taken into account.
</p><p>
In the creation of gridded data sets
from SST observations, the effects of outliers can be minimized somewhat by the use of resistant
or robust statistics such as Winsorised, or trimmed means (see e.g., Rayner et al. [2006]).
The effect of outliers is further reduced in large scale averages and the distribution of
errors in large scale averages tends towards a normal distribution as the number of observations
increases [Kennedy et al., 2011a].
</p>
<p>
<a href="3.2.1.html">Previous - 3.2.1 Uncorrelated Measurement Errors</a> <a href="index.html">Index</a> <a href="3.2.3.html">Next - 3.2.3 Summary of Individual Observational Errors</a>
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