[Geophysical Research Letters]
Supporting Information for
[Considerations for Estimating the 20th Century Trend in Global Mean Sea Level]
B.D. Hamlington1 and P.R. Thompson2
[1] {Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, USA.}
[2] {Department of Oceanography, University of Hawai‘i at Mānoa, Honolulu, Hawaii,
USA.}
Contents of this file
Text S1
Introduction
The file text01.pdf contains a description of the methods used for selecting, editing, and
analyzing the tide gauge data.
Text S1.
1.
Methods
We analyze the tide gauge datasets used in three recent sea level reconstructions:
Ray and Douglas [2011; RD2011 hereafter], Church and White et al. [2011; CW2011
hereafter], and Hay et al. [2015; H2015 hereafter]. All three studies begin with tide gauge
data from the Permanent Service for Mean Sea Level (PSMSL) Revised Local Reference
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(RLR) dataset, but each implements very different gauge selection choices and quality
control criteria when forming the historical tide gauge dataset used in their
reconstructions. We begin with monthly RLR data spanning 1900-2013 and form three
datasets by subsetting the RLR dataset based on the gauges used in each reconstruction.
This information was obtained online for CW2011 and via personal communication for
RD2011 and H2015. To isolate the effect of tide gauge selection, we apply a consistent
automated quality control procedure to the data from each set and then use the same
simple method to calculate GMSL for each case.
The quality control algorithm is consistent with Church and White et al [2004] and
Calafat et al. [2014]: (1) All monthly values flagged by PSMSL have been removed; (2)
Gaps of one to two months were linearly interpolated; (3) Continuous sections of data
shorter than two years were removed; (4) Records were split when a 250 mm month-tomonth jump occurs if that record has fewer than ten such jumps. The ICE-5G v1.3 glacial
isostatic adjustment (GIA) [Peltier et al., 2004] was applied to all of the tide gauge
records. No other correction for vertical land motion was made.
GMSL for each of the three sets is calculated via a simple arithmetic mean over the
tide gauge data in each set. We are primarily interested in the effect of gauge selection on
20th century trends and this method has been shown to be adequate when computing
global long-term trends. In addition, this method is linear and transparent, which allows
us to diagnose the effect of particular selection choices on the estimated trends. Due to
the lack of a consistent datum for all of the tide gauge records, the arithmetic mean is
applied to the first differences of monthly tide gauge data, which is then reintegrated to
form the GMSL time series.
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We estimate trends from these time series over the 1900-2013 period using a linear
least squares fit, and confidence intervals (95%) are obtained using a standard error
estimate [Acton, 1966]. The effective degrees of freedom have been estimated based on
the decorrelation timescale of the GMSL time series. We avoid a more thorough
treatment of the error, as it does not affect the conclusions of the manuscript, but note
some differences in our error estimate in comparison to the three reconstruction studies.
The errors provided for the reconstructions are intended to represent errors in the
accuracy of the reconstructions relative to the true trend in GMSL. In contrast, we are
concerned with the precision (not accuracy) of the trend given differences in gauge
selection. Thus, the standard error estimate based solely on the least squares fit serves the
purpose of this paper. A more realistic estimate of the error would involve accounting for
spatial correlations among the tide gauges, leading to a further reduction in the degrees of
freedom. This, however, is left for future work.
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