FIGURE 1: LIST OF SEA LEVEL RISE DATA SOURCES

FIGURE 2: FOSSIL FUEL EMISSIONS 1814-2014

FIGURE 3: RESULTS FOR JEVREJEVA GMSL 1807-2010

FIGURE 4: RESULTS FOR KEY BISCAYNE 1913-2014

FIGURE 5: RESULTS FOR PORTLAND, MAINE 1910-2014

FIGURE 6: RESULTS FOR ATLANTIC CITY, NJ 1911-2014

FIGURE 7: RESULTS FOR CRISTOBAL 1907-2014

FIGURE 8: RESULTS FOR HALIFAX, NOVA SCOTIA 1919-2014

FIGURE 9: RESULTS FOR GALVESTON, TX 1904-2014

FIGURE 10: RESULTS FOR BREST, FRANCE 1846-2014

FIGURE 11: RESULTS FOR MARSEILLE FRANCE 1885-2014

FIGURE 12: RESULTS FOR GEDSER DENMARK 1891-2014

FIGURE 13: RESULTS FOR HORNBAEK, DENMARK 1891-2014

FIGURE 14: RESULTS FOR HONOLULU, HI 1905-2014

FIGURE 15: RESULTS FOR BALBOA 1907-2014

FIGURE 16: RESULTS FOR PRINCE RUPERT, BC 1909-2014

FIGURE 17: RESULTS FOR VICTORIA BC 1909-2014

FIGURE 18: RESULTS FOR SAN FRANCISCO, CA 1897-2014

FIGURE 19: RESULTS FOR SAN DIEGO, CA 1906-2014

FIGURE 20: SUMMARY OF ALL 16 STATIONS: FULL SPAN

FIGURE 21: SUMMARY OF ALL 16 STATIONS: FIRST HALF

FIGURE 22: SUMMARY OF ALL 16 STATIONS: SECOND HALF

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1. The anthropogenic global warming (AGW) hypothesis holds that fossil fuel emissions since the Industrial Revolution have created an unnatural warming of the climate and thereby caused an unnatural sea level rise at an accelerated rate. The UNFCCC’s international agreement to limit fossil fuel emissions is derived from this theory of causation and proposes that dangerous anthropogenic sea level rise can be moderated by reducing emissions. This work is an empirical test of the causal relationship between emissions and sea level rise on which the UNFCCC emission reduction plan is based. A necessary condition for the effectiveness of the proposed intervention to attenuate sea level rise is that the rate of sea level rise and the rate of emissions must be correlated and that the correlation must be positive and must be statistically significant at the appropriate time scale. Here we test sea level data for the evidence of responsiveness of sea the rate of sea level rise to the rate of fossil fuel emissions at nine different time scales ranging from 20 years to 60 years using both a global mean sea level reconstruction for the period 1807 to 2010 (Jevrejeva, 2014) and observational data from sixteen Northern Hemisphere sea level measurement stations in the Pacific and Atlantic oceans. Figure 1 is a list of all sea level data sources and their time spans. Figure 2 displays the emissions data used in the study.
2. A  consideration in the study of sea level rise is the complexity of ocean dynamics that creates spatial and temporal differences that are natural and that therefore have no interpretation in terms of an external or artificial cause. AGW does not force SLR at the same rate everywhere. Rather, there are spatial variations of SLR superimposed on a global average rise. These variations are forced by ocean circulations, variations in temperature and salinity, mass re-distributions, changing gravity, and the Earth’s rotation and shape. These effects form unique spatial and temporal patterns in SLR that appear to be random” (Landerer, 2007) (Levermann, 2005) (Schleussner, 2011). Therefore no single tide gauge time series data has an interpretation in terms of a trend in global mean eustatic sea level. 
3. These issues are addressed in this study in several ways. First, only very long continuous time series of a century or more are used. Second, multiple measurement stations are selected over a wide geographical area and latitude span. Nine different time scales are used ranging from two to six decades for assessing the anthropogenic forcing of sea level change. The smaller time scales, less than 35 years, are likely to contain some noise from known multi-decadal cycles in ocean dynamics but the longer time scales of 40, 45, 50, 55, and 60 years are expected to detect an anthropogenic forcing if it exists. The reliability of the correlation between SLR and emissions is checked using a procedure patterned after the Cronbach split-half test. The two halves of the time series, overlapping in most cases, are compared and the reliability of the full span correlation is judged based on their consistency (Cronbach, 1947). The standard deviation of the correlation coefficient is estimated using Bowley’s procedure (Bowley, 1928) and degrees of freedom are adjusted for multiplicity of data use in moving windows (Munshi, Illusory Statistical Power in Time Series Analysis, 2016).
4. The proposition that the rate of sea level rise can be moderated by reducing fossil fuel emissions is tested with detrended correlation analysis. Correlations between time series may derive from effects other than those at the time scale of interest particularly from an incidental common drift in time that is unrelated to the theory of causation at the proposed time scale (Shumway, 2011) (Prodobnik,2008) (Munshi, Spurious Correlations in Time Series Data, 2016) (Munshi, 2017). It is therefore necessary to separate the time scale effect from the common drift effect. In the hypothesis test for correlation, the alternate hypothesis is HA: ρ>0 and the corresponding null hypothesis is H0: ρ≤0. Here ρ represents the correlation in the underlying phenomenon that generated the time series sample data being studied. The sixteen correlations from the sixteen stations for each of the three time spans and for each time scale are assumed to be manifestations of the same underlying phenomenon but with natural geographical variability among stations and their average is taken “as a more accurate estimate of the population correlation” (Corey, 1998).
5. The results of detrended correlation analysis for the Jevrejeva global mean sea level reconstruction 1807-2010 are presented in Figure 3. No positive relationship between rate of emissions and the rate of sea level rise is found at any of nine time scales from 20 years to 60 years in the full span of the data 1807-2010 or in the most recent half-span 1909-2010. Some high positive correlations between r=0.628 to r=0.829 are found for time scales of 45 to 55 years are found in the early half-span of the data 1807-1908. This result is considered spurious in light of the complete absence of positive correlations in the full span and particularly in the recent half-span when fossil fuel emissions were an order of magnitude greater than in the early half-span. Total fossil fuel emissions 1807-1908 were 18.1 GTC (gigatons of carbon equivalent) while in the recent half-span 1909-2010 emissions were 345.7 GTC. If forcing by emissions drive the rate of sea level rise it should be more apparent in the recent half-span than in the early half-span. Thus, the results in Figure 3 do not present credible evidence that the proposed climate action intervention to attenuate sea level rise will be effective. It is noted that correlation is a necessary though not sufficient condition for causation.
6. The corresponding results for observational data from the sixteen measuring stations are presented in Figure 4 to Figure 19. As in the global mean sea level reconstruction, detrended correlation analysis is carried out for the full span as well as for the early half and the recent half of the available full span data series. The full span results for all sixteen stations are summarized in Figure 20 and the results for the early half and recent half are summarized in Figure 21 and Figure 22 respectively. Differences in the observed correlation among time scales in each of these Figures 20,21,&22 are expected but for any given time scale the sources of variance are assumed to be natural regional variation. In such cases “the correlation coefficient can be a highly variable statistic” (Corey, 1998). Although the time spans among stations don’t exactly correspond, we assume that the sixteen correlations from the sixteen stations for each of the three time spans and for each time scale are the manifestations of the same underlying phenomenon but with natural geographical variability among stations. Accordingly, we take their average as a better estimate of the population correlation (Corey, 1998). The average is shown in the bottom of each of the Figures 20,21,&22. For statistical significance, the standardized value of the average correlation would have to be much greater than unity. However, as seen in the charts in Figures 20,21,&22, the maximum standardized average correlation, found at time scales of 30 to 40 years, is tmax=0.1 for the full span (Figure 20), tmax=0.4 for the early time span (Figure 21), and tmax=0.53 for the recent time span (Figure 22). These results are consistent with the results for the 204-year sea level reconstruction data (Figure 3). We conclude that the data presented in Figures 20,21,&22 do not provide credible evidence that the rate of sea level rise can be moderated by reducing fossil fuel emissions as claimed by various authors (Hansen, 2016).
7. The (Clark 2018) paper that showed a correlation between cumulative sea level rise and cumulative emissions is discussed in a related post [LINK] . There we show that the correlation between cumulative  values is spurious because time series of the cumulative values of another time series contains neither time scale nor degrees of freedom (See also [TCRE] ). In our work this issue is addressed by using finite time scales less than the full span to insert both time scale and degrees of freedom in the correlation statistics and find that when the spuriousness of the correlation between cumulative values is removed, no correlation is found.

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