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Tide gauge location and the measurement of global sea level rise

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Abstract

The location of tide gauges is not random. If their locations are positively (negatively) correlated with sea level rise (SLR), estimates of global SLR will be biased upwards (downwards). Using individual tide gauges obtained from the Permanent Service for Mean Sea Level during 1807–2010, we show that tide gauge locations in 2000 were independent of SLR as measured by satellite altimetry. Therefore these tide gauges constitute a quasi-random sample, and inferences about global SLR obtained from them are unbiased. Using recently developed methods for nonstationary time series, we find that sea levels rose in 7 % of tide gauge locations and fell in 4 %. The global mean increase is 0.39–1.03 mm/year. However, the mean increase for locations where sea levels are rising is 3.55–4.42 mm/year. These findings are much lower than estimates of global sea level (2.2 mm/year) reported in the literature and adopted by IPCC (2014), and which make widespread use of imputed data for locations which do not have tide gauges. We show that although tide gauge locations in 2000 are uncorrelated with SLR, the global diffusion of tide gauges during the 20th century was negatively correlated with SLR. This phenomenon induces positive imputation bias in estimates of global mean sea levels because tide gauges installed in the 19th century happened to be in locations where sea levels happened to be rising.

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Fig. 1
Fig. 2
Map 1
Fig. 3
Map 2
Fig. 4
Map 3

Notes

  1. Standard statistical tests based on the normal distribution (t, chi-square and F tests) assume that the data are stationary. Obviously, these tests cannot be used to test for stationarity.

  2. Failing to prove guilt is not equivalent to proving innocence, and vice-versa.

  3. Sowell (2002) has suggested a one-step estimator by maximum likelihood, which, however, is difficult to apply. Two-step estimators estimated the power spectrum or periodogram in the first stage, and then estimated by an OLS regression involving the estimated frequencies obtained from the first stage.

  4. We avoid here the decision by the government regarding the precise location of the tide gauges it constructs.

  5. For example, in Jevrejeva et al. (2006) the base year is 1810 and in Church and White (2006) it is 1870.

  6. Examples of split tide gauges may be seen in the Graphical Appendix: Neuville (Canada) in Fig. 5, Vancouver in Fig. 6, Brest and Swinousjcie (Poland) in Fig. 8.

    Fig. 2
    figure 2

    Distribution of missing values

  7. We omit 24 tide gauges whose classification varied across segments. For the remaining 325 tide gauges with multiple segments we use a weighted average in Fig. 3.

  8. Unlike the more popular estimator or Geweke and Porter-Hudak (1983), Robinson’s estimator is consistent for \(\hbox {d} > 1\).

  9. Also known as Tobit regression. Censored regression assumes that the dependent variable is continuous if it is not zero.

  10. Data sources are provided in an Appendix 1.

  11. Satellite data do not cover Arctic and Antarctic coasts.

  12. Douglas (2001) writes (p. 56), “It is that the longer the period of sea level variation, the greater the spatial extent of that signal. Thus very long records do not require the coverage needed by the shorter ones to establish a value of global change.” This statement assumes incorrectly that the tide gauge locations providing these long records are uncorrelated with SLR.

  13. The Fifth Review has adopted the thesis of Vermeer and Rahmsdorf (2009) who attribute global sea level rise to global warming. However, our results question whether global sea levels are in fact rising.

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Acknowledgments

We acknowledge the useful and insightful comments of two anonymous referees.

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Correspondence to Daniel Felsenstein.

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Handling editor: Ashis SenGupta.

Appendix 1: Data

Appendix 1: Data

1.1 Tide gauges

The data are obtained from PSMSL’s website. This dataset consists of a monthly calendar record per tide-gauge of mean sea level. While each station supplies its own record on a metric scale (also known as the raw data) PSMSL coverts these data using a joint datum for all stations. These datum reductions create a Revised Local Reference measure to which we apply Peltier’s VM2 GIA correction (Peltier 2001). RLR measures deviations in millimeters from the 7,000 mm below mean sea level datum (Figs. 5, 6, 7, 8).

Fig. 5
figure 5

Scatter plots by ID: no trend (KPSS)

Fig. 6
figure 6

Scatter plots by ID: positive trend (KPSS)

Fig. 7
figure 7

Scatter plots by ID: negative trend (KPSS)

Fig. 8
figure 8

Scatter plots by ID: historic stations

1.2 Data for Table 3

Data on GDP per capita were taken from the World Bank (Indicators: GDP Current US$ and Population, total) and the United Nations (Per capita GDP at current prices—US$ and Total population). We used the World Bank as the primary source of data and supplemented it with the UN’s records to fill missing values where applicable.

1.3 Data for Map 2

The data on satellite altimetry reported in Map 2 is obtained using the gridded, multi-mission Ssalto/Duacs data since 1993 available on the AVISO website. The data on coastline lengths is from http://chartsbin.com/view/ofv.

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Beenstock, M., Felsenstein, D., Frank, E. et al. Tide gauge location and the measurement of global sea level rise. Environ Ecol Stat 22, 179–206 (2015). https://doi.org/10.1007/s10651-014-0293-4

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  • DOI: https://doi.org/10.1007/s10651-014-0293-4

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