# Correlation Between Cumulative Emissions and Cumulative Sea Level Rise

Posted September 14, 2018

on:FIGURE 1: EMISSIONS & SEA LEVEL TIME SERIES

FIGURE 2: CORRELATIONS BETWEEN EMISSIONS AND SEA LEVEL RISE

FIGURE 3: RANDOM EMISSIONS AND RANDOM SEA LEVEL RISE: WITH SIGN CONSTRAINTS

FIGURE 4: RANDOM EMISSIONS AND RANDOM SEA LEVEL RISE: WITHOUT SIGN CONSTRAINTS

**2018: Clark, Peter U., et al. “Sea-level commitment as a gauge for climate policy**.”*Nature Climate Change*8.8 (2018): 653. ABSTRACT: A well-defined relationship between global mean sea-level rise and cumulative carbon emissions can be used to inform policy about emission limits to prevent dangerous and essentially permanent anthropogenic interference with the climate system. AUTHOR STATEMENT: When we pump more carbon into the atmosphere, the effect on temperature is almost immediate but sea level rise takes a lot longer to respond to that warming. If you take an ice cube out of the freezer and put it on the sidewalk, it doesn’t melt immediately. The same is true for ice sheets. It takes time for them to melt so that the resulting sea level rise will continue for hundreds to thousands of years after we’re done emitting carbon. Since the beginning of the Industrial Revolution – about 1750 – people have emitted roughly 600 billion tons of carbon into the atmosphere, resulting in an increase of roughly one degree (Celsius) in overall global temperature. The global pace today is 10 billion tons of carbon annually, which means we’re on track to reach the 2-degree threshold in about 60 years. We now know how much more carbon we can emit to keep below a certain temperature. One way to begin looking at it from a policy standpoint is to ask the question, ‘how much sea level rise can we tolerate?’. It becomes a fairly simple exercise from there. The more carbon we emit, the more sea level rise we are committed to. We need to ask if there is a target for sea level rise – much like the 2-degree threshold that was established for global warming. Keeping sea level rise to 3-9 meters – or roughly 10 to 30 feet – over several thousand years is likely too optimistic unless society finds ways to quickly reach zero emissions and lower the CO2 in the atmosphere. If cumulative CO2 emissions rise to 3,000 billion tons, it likely will result in sea level rise of between 30 and 40 meters. The sea level rise we’ve seen thus far is just the tip of a very large iceberg. The big question is whether we can stabilize the system and find new energy sources. If not, we’re on the way to a slow-motion catastrophe. The question becomes: What do we owe our grandchildren, and their grandchildren? Economic losses in the world’s largest coastal cities due to coastal flooding in 2005 – the year of Hurricane Katrina – reached $6 billion – a figure that is estimated to grow to $1 trillion by 2050. Losses could be reduced to $60 billion through construction of coastal defenses, but “such well-intended short-term efforts neglect the long-term horizon of sea level rise. You can build a one-meter seawall, but what do you do when sea levels rise by two, or five, or 10 meters? Rising sea levels haven’t really alarmed people yet because their response time is much longer than temperature. Smart countries will use that to their advantage and begin adaptation strategies over time. Many of those people depend directly or indirectly on the oceans for their livelihood – and we don’t know all the ways they will be affected. “But you don’t have to look far away to see the devastating impact of extreme events like the hurricanes in Puerto Rico and Texas that will take decades to recover from.- The “author statement” quoted above was provided by the Oregon State University Newsroom [
**LINK].** - This work is a critical review of Clark et al 2018 described above. In the paper the authors use the proportionality between cumulative emissions and cumulative sea level rise to develop a functional and causal relationship that they then use to relate sea level rise to emissions and then to forecast future sea level rise scenarios and their consequences. The relationship is then used to evaluate the Paris Agreement in terms of sea level rise.
- We show here that the paper’s conclusions are specious because they are derived from a spurious correlation. A critical evaluation of the TCRE (Transient Climate Response to Cumulative Emissions) was presented in a previous post: [
**TCRE: Transient Climate Response to Cumulative Emissions**]. There it was shown that the near perfect “proportionality between cumulative warming and cumulative emissions seen in the data is an artifact of a fortuitous sign constraint contained in the data in which emissions are always positive and warming is mostly positive. When this fortuitous constraint in the data is removed the stable proportionality of the TCRE coefficient vanishes. It was concluded in that study that correlations between cumulative values are spurious and that the only information contained in such a stable proportionality is that it happens to contain the necessary sign constraints. - The TCRE analysis applies exactly to the use of correlations between cumulative emissions and cumulative sea level rise.
**Figure 2**shows that although no correlation is found between emissions and sea level rise at an annual time scale (left frame of Figure 2), a strong proportionality is seen between their cumulative values (right frame of Figure 2). In Figures 3 and Figure 4 we show that the only interpretation of this correlation is that the data contain a fortuitous sign constraint in which emissions are always positive and sea level rise values are mostly positive. **Figure 3**shows correlations between random emissions and random sea level rise values that follow the sign constraint described above where emissions are always positive and sea level rise values are mostly positive. Here as we take samples from these random numbers, we find strong proportionality between cumulative sea level rise and cumulative emissions just as we saw in the data in Figure 2. And yet, these are random numbers that are generating these correlations and statistically significant regression coefficients.- What happens when the sign constraint is relaxed so that a random fraction of both emissions and sea level rise are allowed to be negative? The answer to that question is demonstrated in
**Figure 4**where we find that the strong and stable proportionality seen in Figure 3 is not seen when the sign constraint is removed. We conclude from Figure 3 and Figure 4 taken together that correlations between cumulative values of time series data that do not exist in the source data at any finite time scale, are spurious and artifacts of sign constraints. Their only information content is that the needed sign constraint is found in the data. Such correlations have no interpretation in terms of causal relationships between the two variables at the time scale of interest. - The theoretical argument for the spuriousness of correlations between cumulative values is that the multiplicity in the use of the data for constructing cumulative values removes the available degrees of freedom in the data. The time series of cumulative values of another time series contains neither time scale nor degrees of freedom. No statistic computed with such a time series contains any causation interpretation because they contain no information except for the existence of a fortuitous sign constraint.
- It is of course not feasible that sea level should respond to emissions at an annual time scale but a time scale must be specified from theory so that a testable implication and its empirical test can be carried out. In a prior work, time scales of twenty to sixty years were tried but no correlation between emissions and sea level rise was found. The full text of this work is available for download at
**SSRN.COM or ACADEMIA.EDU.** - The conclusions presented above are supported by prior studies of correlations between cumulative values with full text download available at both SSRN.COM and ACADEMIA.EDU:
**SSRN1****SSRN2****SSRN3 SSRN4 SSRN5 ACADEMIA1 ACADEMIA2 ACADEMIA3 ACADEMIA4 ACADEMIA5 .**A related work on the proportionality between cumulative emissions and cumulative warming may be found here:**TCRE: Transient Climate Response to Cumulative Emissions.**

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