About the accelerated sea-level rise due to global warming

A new work about the possible dramatic rise of the world sea level as been published in PNAS " Proceeding of the National Academy of Sciences of the United States of America", the paper can be read here:

Climate-change–driven accelerated sea-level rise detected in the altimeter era

http://www.pnas.org/content/early/2018/02/06/1717312115

or as PDF
http://www.pnas.org/content/pnas/early/2018/02/06/1717312115.full.pdf

This data was quoted and taken as a basis for several publications worldwide, e.g.
https://www.sciencedaily.com/releases/2018/02/180212150739.htm

With the following conclusion:

" If sea level continues to change at this rate and acceleration, sea-level rise by 2100 (∼65 cm) will be more than double >the amount if the rate was constant at 3 mm/y."

65 cm Rise of sea level by the year 2100 seems in deed very dramatic and would lead to catastrophic consequences, so it is worth to take a closer look to that work and investigate how accurate is that “prediction”.
The researches collected 25 years of data to come to that conclusion. The data is obtained from satellite measurements.
All in all, the data measured shows that sea levels increased by 7cm over the last 25 years, which is 2.8 mm per year. If we would simply linearly extrapolate, we would achieve:

82 years x 2.8 mm/ year = 78.4 mm = 24.6 cm

82 years is the number of years to go from now on till the year 2100.

Hm… did we read 65 cm increase above and we “just” calculated 24.6 cm . That’s a big difference of 3 times. That´s the difference between moderate and catastrophic.. isn’t it ?

And our “extrapolation” was nothing else that a linear progression, which basic assumes that:

• We know that the sea rises “for the next 82 years” with the same rate (how do we know?)
• The rise rate never change and stay the same (how do we know ?)

The results of this very simple math are puzzling. We do quite weird assumptions (same rate, linear, extrapolation of the same behavior over 82 years) and even with such uncertainties we still can not explain why the researches calculates 65 cm increases (!)

The “magic” lies in a third assumption those honorable researches did: the “increase” is not “linear”, but “quadratic”. So double time period -> 4 times bigger effect (2*2). And if we take the time period 4 times longer, we come to exactly 8 times bigger effect and so on. The researchers are applying simple school math here.

The difference between a "linear" (= a simple line..) and "quadratic", means that instead of having the same increase per year, we have an increase that "increase" itself with the time proportional to the square of that time interval.

https://en.wikipedia.org/wiki/Quadratic_function

Same behaviour as free fall. The velocity of a stone falling to the earth increases "quadratic" and gets faster and faster.

Does it make sense ? we just measure 25 years and assume, the next 25 years will be exactly the same, and the next 25 years the same.. and so on. And thats with a "quadratic" increase ? Does "extrapolation" is a useful methodology when analyzing complex processes like climate, melting of ice poles and increase of sea level ?

Unfortunately the experience told us something differently. Extrapolating temperatures in the morning does not provide those on the night. Extrapolating the weather in the summer, does not lead to the weather in winter. Extrapolating the weather in 2018 does not provide that of 2100. Science knows very well that weather and climate can not be just be predicted by simple "extrapolations".

Our next question is obviously:

1. Why do the researches assume a “quadratic” increase and not linear (when linear was already a weird assumption!)
2. Why do the researches assume that they can extrapolate this behavior over a period of time which is 3 times larger as the period they measured (82 years / 25 years = 3.28). A puzzling assumption, isn’t it ?

The answer to 1) is given by the Fig 1 of the publication mentioned above. They assume a “quadratic” increase since a quadratic function “fits” quite well to the data over the last 25 years.

Calculation of Acceleration. We perform a least-squares fit of a quadratic using a time epoch of 2005.0 (the midpoint of >the altimeter time series), where acceleration is twice the quadratic coefficient. All of the data were weighted equally––>weighting the data based on error estimates from tide-gauge differences did not appreciably change the results.”

Well, if I would assume that logic to the growth curve of my child, I would come to the conclusion that he is going to be the tallest man of earth in his 50ties, assuming that he will grow for the next 50 years as he grew from 0 to 5 years. However the “Fit” of the growth data of my child between 0 – 5 years would be accurate. Only my “predictions” would be not. If I would apply the logic used by that researchers, I would argue that I have measured my child laser-precise and correspondingly, the data is extremely accurate. Sure, the data would be ok, only my “predictions” would be nonsense.

So what is wrong with that "quadratic fit" ? Nothing with the fit itself, but be carefully with the “predictions” originated from that fit. If they would fit the data for 25 years and predict the behavior in the next 5 nothing wrong with that. However measuring 25 years and predicting the next 82 is gently speaking, “ little bit exaggerated” as they do not know:

• Why it is quadratic
• If would remain as it is in the next 82 years

Common sense says that extrapolations are ok in a given context, especially when the extrapolated range is lower as the measured one. However trying to get conclusions of the next 82 years based on pure speculation that the rate will not change, is just that: speculation.

Interestingly the researches did a very careful “error analysis” on the possible error sources of their data, which is great. However their biggest error source is not the quality of the data but on their own assumptions extrapolated over a very long period of time.