FIGURE 1: DATA FOR GMSL AND EMISSIONS

FIGURE 2: CORRELATION: 30-YEAR SLR & 30YR EMISSIONS: 1880-2013

FIGURE 3: CORRELATION: 35-YEAR SLR & 35YR EMISSIONS: 1880-2013

FIGURE 4: CORRELATION: 40-YEAR SLR & 40YR EMISSIONS: 1880-2013

FIGURE 5: CORRELATION: 45-YEAR SLR & 45YR EMISSIONS: 1880-2013

FIGURE 6: CORRELATION: 50-YEAR SLR & 50YR EMISSIONS: 1880-2013

FIGURE 7: CORRELATION: SUMMARY OF RESULTS

FIGURE 8: TEST OF THE CLARK HYPOTHESIS: Clark, Peter “Sea-level commitment as a gauge for climate policy.” Nature Climate Change 8.8 (2018) [LINK] 

[LIST OF POSTS ON THIS SITE]

1. Climate science tells us that the fossil fuel emissions of the industrial economy have caused an artificial global warming measured as a rising temperature trend “since pre-industrial times” that is not explained by usual interglacial dynamics. It is further claimed that this artificial warming of the industrial economy is responsible for the observed rise in global mean sea level (GMSL) since pre-industrial times. The importance of the relationship between global warming and sea level rise is that if fossil fuel emissions are not drastically reduced or eliminated, the artificial sea level rise caused by fossil fuel emissions of the industrial economy will have catastrophic consequences particularly in low lying coastal areas such as Florida and Bangladesh as well as in low lying islands and atolls in the Indian and Pacific oceans labeled as “vulnerable” by climate science. The important conclusion to be drawn from these relationships is that reducing fossil fuel emissions will moderate the rate of sea level rise as measured by the GMSL (SLR) and thereby prevent the catastrophic consequences projected for “vulnerable” places like Florida, Bangladesh, and the Maldive and Pacific islands.
2. It has been proposed that acceleration in SLR provides evidence of the human cause of SLR. Yet, sea level rise and acceleration in sea level rise are seen in prior interglacial events in the pre-industrial era as in the Eemian  [LINK] and the Younger Dryas [LINK] .  It should be obvious that SLR is constant only if a surface temperature above 0ºC is constant. In a warming period where the temperature is rising, the rate of sea level must also rise. Thus, since rising surface temperature is normal in interglacials, acceleration in SLR without human cause, is also normal in interglacials as evident in prior interglacial events where no human cause by way of fossil fuel emissions could have existed [LINK] [LINK] . Human cause of sea level rise by way of fossil fuel emissions must therefore be established by other means that involves the rate of fossil fuel emissions.
3. Here we propose that a testable implication of the proposed relationships that imply human cause of sea level rise is that if reducing emissions is expected to slow the rate of SLR, there ought to be a correlation, net of shared trends, between emissions and the rate of SLR at an appropriate time scale at which this causation can occur. This post is an empirical test of this hypothesis with the GMSL reconstruction provided by CSIRO (Commonwealth Scientific and Industrial Organization) [LINK] . These data are available as annual means for the sample period 1880 to 2013. The time scale for the causal relationship is not well defined. The emissions to warming time scale is estimated to be a decade by Ricke and Caldeira 2014 but the relationship between warming and ice melt is usually cited as multidecadal. The Nerem (2018) paper that claimed to show human cause in terms of acceleration in sea level rise used a 25-year study period of 1993-2018 and we use that as a reference to conclude that the time scale  for the slow process of converting emissions to sea level rise should be at least 25 years or perhaps longer. of In view of these considerations, five different time scales in the range of 30 years to 50 years are studied for the relationship between emissions and the rate of SLR. They are 30, 35, 40, 45, and 50 years.
4. A prior study carried out on the same basis by Peter Clark of Oregon State University found a strong correlation between emissions and sea level rise and concluded that emissions cause sea level (by way of warming) and that therefore, reducing emissions should reduce the rate of sea level rise. This study is discussed in a related post [LINK] where it is shown that the correlation between cumulative values used in the Clark study (and depicted graphically in Figure 8 above) is spurious. This is because the time series of cumulative values of another time series contains neither time scale nor degrees of freedom. This study extends the Clark study by inserting finite time scales so that the correlation can be tested for statistical significance.
5. The GMSL and emissions data used in the study are depicted graphically in Figure 1 above. The rate of SLR is computed as the linear regression coefficient of GMSL against time in years over time spans corresponding with the five time scales used, viz: 30, 35, 40, 45, and 50 years. These SLR rates are then compared with the total fossil fuel emissions in gigatons of carbon equivalent (GTC) in the duration of the time scale. We then study the correlation between emissions and the rate of SLR at each of the five time scales.
6. The correlation between the rate of SLR and the rate of emissions at time scales of 30, 35, 40, 45, and 50 years are depicted graphically in Figure 2, Figure 3, Figure 4, Figure 5, and Figure 6 respectively. The left panel of these figures show the correlation in the source data that includes the contribution of shared long term trends to correlation. The right panel shows the correlation between the detrended series in which the contribution of shared long term trends is removed and only the responsiveness at the time scale of interest remains. The necessity of this procedure is explained in a related post [LINK] . What we see in these charts is that though significant correlations are seen in the source data no correlation is apparent in the detrended data.
7. The observed correlations are tabulated in Figure 7 and the source data and detrended correlations are compared in a chart below the tabulation. These results show that the observed correlation in the source data derive from shared upward trends of the two time series. The zero to negative correlations in the detrended series imply that there is no evidence that the rate of sea level rise is responsive to the rate of fossil fuel emissions. This result is inconsistent with the proposition that climate action in the form of reducing fossil fuel emissions will moderate the rate of sea level rise.
8. CONCLUSION: Detrended correlation analysis of the relationship between the rate of fossil fuel emissions and the rate of sea level rise observed in the global mean sea level reconstruction 1880-2013 provided by the CSIRO does not show the responsiveness of the rate of SLR to the rate of emissions needed to support the climate action proposition that reductions in fossil fuel emissions will moderate the rate of sea level rise. 
9. The proposition by climate science that sea level rise can be attenuated with the prescribed climate action of reducing fossil fuel emissions  (Figure 9), is not supported by the data. 

THE CLIMATE MY FRIEND IS CHANGING

How many roads must a man walk down

Before he can see the climate change

How many seas must a white dove sail

Before the sea levels rise

Yes, and how many times must the airliners fly

Before they’re forever banned

The climate, my friend, is changing with the wind

The climate is changing with the wind

Yes, and how many years can deniers exist

Before they come back to sanity

Yes, and how many years must the science exist

Before they let consensus be

Yes, and how many times can a man turn his head

And pretend that he just doesn’t see

The climate, my friend, is changing with the wind

The climate is changing with the wind

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