Back-testing the Solar – Sea Level Relationship

Guest post by David Archibald

This is a little bit amusing. In February, I had a post on the solar – sea level relationship which quantified the sea level fall to come to the end of Solar Cycle 25:

http://wattsupwiththat.com/2012/02/03/quantifying-sea-level-fall/

The site “Skeptical Science” has to date carried two pieces in response to that February post: http://www.skepticalscience.com/Why_David_Archibald_is_wrong_about_solar_sea_level.html

and http://www.skepticalscience.com/Why_David_Archibald_is_wrong_about_solar_sea_level_1B.html

My February post was 624 words and 6 figures. The Skeptical Science responses to date total 3,446 words and 17 figures. The relationship I found between solar activity and sea level is 0.045 mm per unit of annual sunspot number. The threshold between rising and falling seal level is a sunspot amplitude of 40. Below 40, sea level falls. Above that, it rises.

So let’s apply that relationship to the know sunspot record back to the beginning of the Maunder Minimum and see what it tells us. This is the result:

clip_image002

Figure 1: Back-tested Sea Level from 1645

The figure shows sea level falling through the Maunder Minimum due to the lack of sunspots and then fluctuating in a band about 60 mm wide before increasing rapidly from 1934. It then shows sea level peaking in 2003 before declining 40 mm to 2040.

That is pretty much in agreement with the data from the last 150 years, as per this figure combining coastal tide gauge records to 2001 and the satellite record thereafter:

image

Figure 2: Sea Level Rise 1850 with a Projection 2040

The glaciers started retreating in 1859, with sea level responding with a rise of 1 mm per annum up to 1930. There was an inflection point in 1930 with the rate of sea level rise almost doubling to 1.9 mm per annum. Sea level also stopped rising from 2003. So the back-tested model and the sea level record are in agreement for at least the last 150 years.

Jevrejeva et al (http://www.psmsl.org/products/reconstructions/2008GL033611.pdf) reconstructed sea level back to 1700:

clip_image006

Figure 3: Global Mean Sea Level Reconstruction since 1700

This longer term reconstruction shows the rise of sea level once the glaciers started retreating. It also shows the acceleration of sea level rise from the early 1930s. As Solanki noted in 2004, the Sun was more active in the second half of the 20th Century than at any time in the previous 8,000 years: http://earthobservatory.nasa.gov/Newsroom/view.php?id=25538 A sea level response to that would be expected.

In summary, the sea level trend fluctuations driven by the internal variability of the ocean-atmosphere coupled system were overprinted by higher solar activity from 1933 to 2003. The period of best fit within that, from 1948 to 1987, has allowed the solar component of sea level rise to be elucidated.

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April 22, 2012 2:38 pm

Alvin says:
April 22, 2012 at 2:24 pm
How does the rabbit know it does not like to be eaten?
Evolution working its magic. The rabbits that do not run get eaten and leave fewer [or no] descendants.
The dog? It just chases anything.
Hoping to catch its food.

Alvin
April 22, 2012 2:41 pm

@Leif – Sunspot meeting to be shared at ICCC7?

P. Solar
April 22, 2012 2:41 pm

stevefitzpatrick says: The applied glacial rebound adjustment for sea level is ~+0.3 mm per year, much less than the measured rise.
No that is just the adjustment for the deepening of the oceanic basins. The land correction to tidal gauges is a separate adjustment.
>>
The rate of rebound near Hudson Bay in Canada is still ~12.5 mm per year…. easily measured by looking at how Hudson Bay’s shoreline changes over relatively short periods
>>
That’s fine if you have 12.5mm/a , you can see it clearly but you can not measure an effect using the shore line and then use it to correct the sea level! Circular reasoning. So although the “idea” of mantle rebound is fairly well accepted, this does not provide a way to measure it.
And while it may be possible to estimate land rises of the order of several feet per century the result is not going to be accurate the nearest mm which is what is needed to adjust a coastal tide gauge. It seems indemic in all areas touched by climate now to either totally ignore the uncertainly or to provide estimates which would cause howls of laughter in serious science or engineering. The claimed argo accuracy is a prime example. The idea that 10,000 temps in different places entitles you to divide the uncertainty by 100 is based on the fallacy that you have 10,000 measurements of the same quantity.
Whoever does that is either incompetent or a lier (or both).
>>
The main motivation for taking many thousands of temperature profiles was to characterize how military sonar waves would be influenced by the temperature (and so density) profile. There is no reason to believe that temperature profile data from the 1950′s, 60′s, and 70′s was somehow compromised by a desired outcome.
>>
So the data may be sufficiently accurate to make an adjustment to sonar propagation , that does not mean that they are sufficiently precise in temperature or coverage characterise the global heat content at 0.1C level. In reality the uncertainty is greater than the effect.

April 22, 2012 2:52 pm

Alvin says:
April 22, 2012 at 2:41 pm
@Leif – Sunspot meeting to be shared at ICCC7?
Our workshop takes place during the same days 21-25 May in Brussels, Belgium, so I guess not.

P. Solar
April 22, 2012 2:53 pm

https://www.dmr.nd.gov/ndgs/ndnotes/Rebound/Glacial%20Rebound.htm
>>
Brevik concluded that the tilt of the Herman strandline, when combined with the effects of the Lake Agassiz sediments, represents crustal depression of between 95 and 350 meters, figures which correspond to ice-thickness values of 280 to 1,040 meters, respectively. He therefore concluded that the actual ice thickness along the North Dakota-Minnesota border must have been somewhere between the two extremes that he calculated.
>>
That illustrates my point quite nicely . These values for mantle rebound are ball park, back of envelope numbers. And the guy got a master’s degree for that work so we have to think that’s about best that can be done.

LazTeenager
April 22, 2012 3:15 pm

Correlation is not causation as usual.
The correlation also seems to breakdown just prior to 1800. A peak in the sunspots meets a dip in the sealevel.

LazTeenager
April 22, 2012 3:21 pm

RobW says:
April 22, 2012 at 8:23 am
Can someone please expalin how in an La Nina year the global heat energy of the oceans is rising. Is this another example of data adjustments?
—————
Could it be because the warm surface waters have sunk and the cold deep waters have risen to the surface? Therefore more heat has been transferred to the deeps while the air temperature has cooled.

April 22, 2012 3:25 pm

why why matters.
I drop a ball from various altitudes on the earth. I see how long it takes. I fit a curve to these points. I don’t ask why. I dont break it down into “causes” . I dont have an accounting of gravity or understanding of it and I dont understand drag. I just have a curve that “works”
Can this predict how fast this ball will fall on earth? yup. Now, however, I try to generalize.
Can I use this “understanding” to predict how fast a giant flat plate will fall, an object with different drag? not very well. Can I use this “understanding” to predict how fast the same ball will
fall on the moon? nope. Why not? well because I have not understood the general law that underlies the phenomena that I can fit with a curve. I havent understood it with laws that hold over all space and time. Can I use my empirical model of ball falling on earth to send a rocket to the moon. Ask Harrison Schmidt.

April 22, 2012 3:27 pm

The dog? It just chases anything.
Hoping to catch its food
####
cars are not food as some dogs find out

Lew Skannen
April 22, 2012 3:32 pm

I was going to ask SS whether they were planning on applying the same scrutiny to Manns tree ring analysis but I realised that there was no chance of my comment being published.

LazTeenager
April 22, 2012 3:33 pm

SasjaL says
Is 2-8 m /6.5-26 ft sea level rise, because of (fictional) melting of ice, a real problem?
———-
I consider sea level rise the comedy aspect of global warming. I live well above sea level.
But then again if you live in Venice or Bangkok or any other low lying city you may not. The time scales are very long so people will move. But a large amount of our cultural heritage will be obliterated.

April 22, 2012 3:36 pm

Willis
‘You could improve your arguments greatly by doing a few things. The first is to actually calculate and report the R^2 of your claimed relationships (including the adjustment for autocorrelation), rather than just eyeballing it and claiming a “striking” correlation where only a very weak correlation exists.
The second is to cite your sources. For example, in Figure 2 you say there are “coastal tide gauge records to 2001 and the satellite record” … which coastal tide gauge records? Which satellite record? With or without the inverted barometer correction?”
I’d go further. I’d say that WUWT should set a standard for blog articles. No data, no code, no post allowed.
All of the analytical choices that david made should be subject to quick audit. which series was selected, how were they merged, what happens if we make other equally rational decisions.. in short is the answer robust with respect to analyst choices.. Or not.

LazTeenager
April 22, 2012 3:36 pm

And I forgot to mentioning agricultural deltas. E.g. The nile delta and places like Bangladesh.

LazTeenager
April 22, 2012 3:45 pm

P.Solar says
Nobody has “measured” the ice mass. All techniques depend on estimates of mantle rebound. (GRACE satellites can not tell the difference between ice mass and land mass so their gravity measurements get… adjusted. )
———-
Yes buut they can pick up mass changes. Unless you want to claim that rock is disappearing you woudl need to attribute that to ice loss.

DirkH
April 22, 2012 3:49 pm

LazTeenager says:
April 22, 2012 at 3:21 pm
“RobW says:
April 22, 2012 at 8:23 am
Can someone please expalin how in an La Nina year the global heat energy of the oceans is rising. Is this another example of data adjustments?
—————
Could it be because the warm surface waters have sunk and the cold deep waters have risen to the surface? Therefore more heat has been transferred to the deeps while the air temperature has cooled.”
Yeah sure. Also, Global Warming will make water flow uphill.

Gail Combs
April 22, 2012 4:04 pm

Leif Svalgaard says:
April 22, 2012 at 2:38 pm
….The dog? It just chases anything.
Hoping to catch its food.
__________________
Unless it is a retriever. Then it catches and dumps the live rabbits, rats and very annoyed woodchucks on your feet, or if you are really unlucky on your bed. (YUCK)

David Archibald
April 22, 2012 4:06 pm

Willis Eschenbach says:
April 22, 2012 at 12:15 pm
Willis, the only reason I get to publish anything on WUWT at all is that I am filling a vacuum. The work I have done here should have been done by the good and the great years ago. But they are still thrashing around in the weeds instead of looking to the stars, and one star in particular, our beloved Sun. I am very happy with this backtesting piece because it has nailed why sea level took off with a gallop from about 1930.
Anyone who is dismayed by the deficiencies in my work can displace it by doing better work and getting it into print before I do. So, viewed from that angle, the problem of this piece entering the public domain is not my fault, it is the fault of those who could have and should have done better work but failed to do so. So, look into your own hearts, those who hold to high levels of public discourse, the deficiencies of this piece are purely your own.
Let’s go back to that 1930s inflection point in the rate of sea level rise. It has been sitting in the data record for at least 50 years. Nobody was in the least bit curious as to why it was there. “Why was it a sharp inflection instead of a gentle curve” would have been a good question to ask. It took me and a simple model using sunspot numbers to find out why that inflection point exists. That in turn implies that the Sun had a big role in the climate of the second half of the 20th Century. I am happy, happy, happy to have done my bit to push back the darkness.

dp
April 22, 2012 4:35 pm

LazTeenager says:
April 22, 2012 at 3:36 pm
And I forgot to mentioning agricultural deltas. E.g. The nile delta and places like Bangladesh.

Delta regions exist because rivers empty into seas. That relationship exists for all expected levels of the sea.

stevefitzpatrick
April 22, 2012 4:36 pm

P. Solar,
“The idea that 10,000 temps in different places entitles you to divide the uncertainty by 100 is based on the fallacy that you have 10,000 measurements of the same quantity.”
“Whoever does that is either incompetent or a lier (or both).”
You would do better to stay away from insults; it reflects very poorly on you. I have worked in research and as a technical consultant for almost 40 years. I assure you I am neither technically incompetent nor a liar. I said nothing about how the uncertainty falls with increasing measurements. I said only that it most certainly does fall with increasing numbers of measurements.
The thing that is most interesting about the thermocline is that it is surprisingly similar over considerable distances, because movement of water along constant density lines is thousands of times (or even tens of thousands of times) faster than vertical transport (that is, perpendicular to the density gradient), so there is a reasonable argument to be made that shifts in the average profile (if that average come from a reasonable geographical sample) gives a pretty good estimate of changes in heat content. The uncertainty in the average temperature of the 0-700 meter level is not anywhere close to 0.1C. But more than the actual observations, the existing shape of the thermocline (an almost exponential fall in temperature with depth except at high latitudes) means that the measured warming of the surface of the ocean ought to (logically) lead to gradual heat accumulation via eddy driven diffusion down the thermocline. Which is why the Argo system was developed in the first place. The estimates of ocean heat accumulation will only become better as Argo accumulates more data. It is only fully in operation since ~2004 after all. Argo generates better quality data than most anything else in climate science, and estimates of OHC change will only improve. Argo represents the best way to constrain the credible range of climate sensitivity to GHG forcing.
“That’s fine if you have 12.5mm/a , you can see it clearly but you can not measure an effect using the shore line and then use it to correct the sea level! Circular reasoning. So although the “idea” of mantle rebound is fairly well accepted, this does not provide a way to measure it.”
You seem to have missed the point of my comment completely. I was trying to point out that measured changes in land altitude demonstrate very clearly the local magnitude of glacial rebound some 10,000 years after the ice melted. If the land is rising at about ~10 mm per year relative to sea level, and your globally averaged tide gauges say the sea level is increasing ~2 mm per year, then you can be pretty sure the land is rising about 12 mm per year. That is useful information if you are trying to understand how the Earth actually reacts to changing surface mass distribution. Is there some uncertainty around Hudson bay? Sure, but it is not huge. If you don’t like comparing to sea level, then you can put fixed GPS receivers on the ground and measure the local rate of rise independent of the ocean. The “models” of glacial rebound have been tested against exactly that kind of reasonably solid measurement, which is why I find them to be credible. Is the overall isostatic correction to sea level of 0.3 mm/yr absolutely certain? Heck no! It might be 0.2 mm or 0.4 mm. But there is no reason to believe it should be -0.5mm/yr, nor 0.8mm per year.
There are in fact lots of things in climate science which are very poorly known (or essentially unknown), like aerosol effects (direct and indirect), and net cloud amplification (negative or positive). There are some things that are reasonably well known (like GHG forcing levels), and some that fall between those two extremes, like measured ocean heat content and the influence of oceanic pseudocycles. Declaring that we know essentially nothing about sea level rise, ocean heat content, or glacial rebound is not accurate.

P. Solar
April 22, 2012 4:52 pm

RobW says:
April 22, 2012 at 8:23 am
Can someone please expalin how in an La Nina year the global heat energy of the oceans is rising. Is this another example of data adjustments?
If you think La Nina = cold , it seems paradoxical, but you have not thought about it. La Nina is cold for surface temps, it does not mean cold for the bulk of the ocean.
A cold ocean surface means less evaporation, less radiative loss ie less heat going out that usual. This will not reduce the amount of heat absorbed so there is a net warming. OHC goes up. The opposite is the case for El Nino, it is a cooling event precisely because the surface is hotter.
This shows how ocean currents can actually cause planetary warming and cooling rather than just being “internal” variations of the system.

April 22, 2012 4:58 pm

Where do the numbers behind the graph in fig 1 come from? In particular the numbers for the years 1646-1726.

P. Solar
April 22, 2012 5:38 pm

stevefitzpatrick says:
April 22, 2012 at 4:36 pm
>>
P. Solar,
“The idea that 10,000 temps in different places entitles you to divide the uncertainty by 100 is based on the fallacy that you have 10,000 measurements of the same quantity.”
“Whoever does that is either incompetent or a lier (or both).”
You would do better to stay away from insults; it reflects very poorly on you. I have worked in research and as a technical consultant for almost 40 years. I assure you I am neither technically incompetent nor a liar.
>>
Steve, you did not say measurement uncertainties could be divided by 100 so my comment was not aimed at you. Don’t take it personally. Neither was I questioning your competence, You seem very knowledgeable.
However, you seem to credit argo with a degree of accuracy that may make it relevant to a meaningful assessment of OHC. That is why I brought up the spurious claims of accuracy that are quite simply dishonest coming from anyone with a scientific training.

P. Solar
April 22, 2012 5:56 pm

“Argo generates better quality data than most anything else in climate science,”
yes the individual instruments are very good.
“…and estimates of OHC change will only improve. ” Truism, does not say anything about the current state of play.
“Argo represents the best way to constrain the credible range of climate sensitivity to GHG forcing. ”
Only if you attribute a fantastic value for the measurement uncertainty. I think Argo is very interesting and will surely advance our knowledge of the oceans in coming decades.But the spacial and temporal coverage is wide of the mark to provide OHC to within an accuracy sufficient to tell us about GHG forcing.

edbarbar
April 22, 2012 6:02 pm

@Leif Svalgaard:
So it seems there are “adjustments” to the measurements. See, now I need to know whether you are a warmist, luke warmist, or denier before I can even begin to trust your slides (especially since they seem to lack lots of information, and I’m finding it increasingly hard to care).
I think from now on I will give greater trust to warmist studies that demonstrate “surprises” in their understanding of AGW (not in the “Oh, it’s going to get a a lot warmer than we thought”), because even after spending large amounts of time trying to understand “adjusted” data, etc., I am in no better position than when I started to know whether the “adjustments” are valid or not.
See what happens when science is abused?

April 22, 2012 6:19 pm

The last part of the chart looks like an upside down hockey stick. Then I see that you used different measurement before 2001 than after, and I am reminded of another hockey stick graph that used the same “trick”.