Tuesday, 23 June 2015

Variations On the rate of change of sea level rise

Global warming due to the build up of greenhouse gases, primarily carbon dioxide (CO2), causes the sea level to rise.

Here I will describe a flawed attempt by Nir Shaviv at attributing global warming on changes in solar activity. This case by looking at sea level rises rather than surface temperatures.

Shaviv posted to the Financial Post on June 16 2015 claiming “the sun raises the seas”. In that post (link to follow) he claims he has evidence to show that it is changes in solar activity that is the major factor in present day sea level rise. However his arguments do not disprove the consensus view that this sea level rise is primarily due to the enhanced Greenhouse Effect (GHE) due to human activities. It is however reasonable to consider sea level rises as most of the energy built up due to Global Warming is taken up by the oceans. It is this energy absorption that results in sea level rises.(figure 1)

Figure 1 Sea level rises CSIRO

If this sea level rise could be attributed to changes in the sun rather than greenhouse gases then this would be a way of undermining the GHE.
Previous attempts at showing that it is changes in the solar activity that has caused surface temperatures to change have failed:-

To raise the sea levels requires extra energy; energy obtained via the GHE. Most of this energy raises the temperature of the sea and cause the seas to expand. Some of the energy also results in net melting of land ice that also raises sea levels. This explains the trend in rising sea levels. The short term variations, however, may be due to natural variations such as changes in solar activity or in oceanic circulation patterns such as El Nino and La Nina; the later resulting in changes of rainfall and snowfall over land changing the amount of water removed from the oceans.

However Shaviv claims that the sea level data shows.....the rate of change of sea level “follows the sun”.....and then concludes that it the sun that it is the cause of sea level rise.

I will argue that the first point is very dubious but also show that even if it where the case the calculations he shows about rates of changes of sea level does not support the conclusion. Shaviv doesn’t explicitly say he has made the conclusion from that evidence, however in his post that is the only evidence he presents and so the very strong inference is made.

Figure 2 Shaviv

The lower graph in figure 2 shows sea level rises without uncertainties but otherwise similar to that of figure 1.

The upper graph shows the rate of change of sea level (blue line) and variations in solar flux (black line). We see these two superimposed graphs overlap well with similar amplitude phase and frequency and so superficially it may seem that the conclusion follows.

Let us assume for the moment that the rate of change of sea level follows the sun as in the upper diagram of fig 2 is true. Why does the conclusion not follow?

When manipulating data to tease out underlying causes, it is important that your conclusions are not really a result of the manipulations and not the data itself.

Shaviv manipulates the data by effectively removing the trend in sea level (explained later) and smoothing out the sea level to omit seasonal changes so he is only left with other natural variations. Nothing wrong so far. However one can no longer make conclusions about the solar activity and the trend in sea level rise but this is precisely what he seems to do.

Shaviv does not actually remove the trend; he simply hides it. If he were to remove the trend and the seasonal cycles we would be left with variations that would be more obviously related to ENSO cycles. Instead he finds the rate of change of sea level suitably smoothed so that a linear trend will be seen as a horizontal offset so when compared and plotted with another graph showing the solar cycle with an independent scale and origin he has effectively removed the trend for comparison purposes.

Perhaps simpler examples can clarify this and this is good reason to look at what is regarded as the main cause of modern day sea level rise.
Keeling curve:-

Figure 3 CO2 levels

This diagram plots the CO2 smoothed out to show the monthly changes (red curve) and yearly changes (blue curve). The monthly changes are due to the seasonal cycle whereby CO2 is absorbed by plants during the growing season in the NH and CO2 is released by decay over the winter months. The trend is due to the build up of from human activities mainly in the burning of fossil fuels.

When focussing on the rates of change, the annual rate of change of CO2 is completely dominated by the monthly rate of change clearly because the slow annual trend is smaller than the swings in concentration over each single year. A graph of the rate of change of the monthly concentration of CO2 would show positive and negative swings across the time axis off-set slightly due to the long term trend. (Similar to figure 4).

This Keeling curve can be approximately modelled by a straight line with a long term trend rate (given the value k) modulated by a sinusoidal wave.

CO2 = kt + asinwt + a constant

Rate of change of CO2 (wrt to t) =  k+awcoswt

Figure 4 rate of change of idealized CO2 concentration against time.

Figure 4 shows a sinusoidal wave with an average value k, that is offset by a value k, the long term trend rate. The higher the frequency, w, of noise or short term variations then the more the long term trend k is obscured by the amplitude, aw.

From the Keeling curve we can see that the rate of change of the CO2 concentration (as seen by the changing slope of the red graph) mainly follows the seasons but this is totally independent of the causes of CO2 build up due to human activities as seen by the long term trend.

Back to sea level rise:-
 Shaviv has smoothed and sampled the sea level data at appropriate intervals, just enough but not too much, ensuring the short term variations dominate the trend when looking at rates of change. (....too little and other variations would dominate the solar cycle....too much and variations over frequencies comparable to the solar cycle would disappear).

However what about the similar frequency and amplitude of the rate of change of sea level rise and solar flux as in the upper diagram of figure 2?

The frequencies are similar partly because they are chosen to be so by deciding how much smoothing is employed and partly because there may be some albeit small connection. However I can see about two or three times per decade (when looking at the sea level rise as in the lower graph of figure 2)  when the rate of change of sea level rise should swing between positive and negative which is not reflected in the upper graph.

The amplitudes are equally similar because again they are chosen to be so....the two graphs have independent scales and further the origin of each graph is changed so that the long term trend (k, of about 2 or 3 mm/year as seen in the average of the rate of change of sea level..blue graph) is overlapped by the solar flux.

The important conclusion I make here is that any resemblance of the rate of change of sea level rise to the solar variations have no bearing on the long term trend of sea level rise just as in the case of the CO2 variations. The causes of the short term variations and the long term trend in each of these graphs are different.

There is an obvious correlation here of course, and that is the consensus view, that the long term trend in CO2 is not only the cause of the long term trend in sea level but the correlation between them is excellent (graphs 1 and 3). Shaviv has discarded the obvious and made claims or inferences that could lead the reader to a false conclusion. 

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