### A Sea Change in North Carolina

The state of North Carolina has been getting some press – mostly, bad press – lately over a proposed law that would affect how the state officially estimates the rate of sea level rise.

The proposed law has recently been changed to put a four-year moratorium on how the rate is calculated. However, prior to the change, the bill stated that the rate of sea level rise should be determined linearly based on observed rates since the year 1900, even though most climate scientists suggest that the rate of rise should accelerate with time. Assuming that the rate the sea will rise is linear effectively means a rise of about 8 inches (about 20 centimeters) over the next 100 years, while assuming that the rate increases over time would mean a rise of about 39 inches (1 meter).

The actual text of the original proposed law (House Bill 819) is not that difficult to read: it is only 3 pages, the first of which deals primarily with the definition of a ‘coastal area’.

It has gotten international attention recently, especially after comedian Stephen Colbert covered it on his show.

The most pertinent passage of the law is that part that reads:

“The Division of Coastal Management shall be the only State agency authorized to develop rates of sea-level rise and shall do so only at the request of the [Coastal Resource] Commission. These rates shall only be determined using historical data, and these data shall be limited to the time period following the year 1900. Rates of sea-level rise may be extrapolated linearly to estimate future rates of rise but shall not include scenarios of accelerated rates of sea-level rise.”

Colbert calls the scientifically accepted rates of sea-level rise a “feedback loop that accelerates” and many people have criticized this proposed law on the grounds that it ignores accepted science by assuming that the sea level will only rise 8 inches over the next 100 years and not 39 inches. This assumption of “less aggressive” sea level rise would presumably have meant that larger areas of coastal land would be available for commercial development. By supporting this law Republicans are supposedly ‘disregarding science’ and putting commercial interests ahead of environmental ones.

**But is this really the case?**

Simply by opening Microsoft Excel we can create a table that shows the estimated sea level rise over the next 100 years if the rate of increase is linear and the final result is 8 inches over 100 years. This means that the sea level must rise 8/100 inches per year.

However, if the rate of increase is “a feedback loop that accelerates”, then a simple model would be exponential growth. Every year, the sea level is some percentage higher than it was the previous year. Like money in a bank account drawing 3 percent interest (good luck with that), if we deposit $100, then at the end of a year we will have $103. In the second year, we will gain another $3 plus interest on the $3 we earned in the first year. Overall, the growth of the bank account (or sea level) will go up according to the formula:

where r is the growth rate and t is the amount of time that has elapsed.

If the rate of growth of the sea level is about 3.6% (for you math whizzes, ln(40)), then the sea level will rise 39 inches in 100 years.

If you are not following the math, then I have shown a graph below of the rise of the sea level assuming that the rate is linear (8/100 of an inch per year) and assuming that the rate is a feedback loop, growing at the rate of about 3.7% per year.

(click image to enlarge)

You can see that after 100 years, the linear model projects a sea level rise of 8 inches while the exponential model predicts a rise of 39 inches. But here you can see something very strange if you are the kind of person who has been taught that exponential growth is somehow “faster” than linear growth. From the present day to a time about 37 years from now, the exponential rate actually assumes that the sea level will rise *less* than the linear prediction.

So, by assuming that the rate is linear, North Carolina’s Republicans are actually assuming that the sea level rise will be *more aggressive* than climate scientists predict – at least for the next 37 years, when we will presumably have much more reliable data about what will happen in the next 100 years than we have now.

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**UPDATE, 23 July 2013:** A recent study has found that the rise in the global average sea level from 2005-2011 averaged 2.4 mm per year, or 240 mm per 100 years, which is about 9.5 inches.

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