Guest Post by Willis Eschenbach
I came across a curious graph and claim today in a peer-reviewed scientific paper. Here’s the graph relating sunspots and the change in sea level:
And here is the claim about the graph:
Sea level change and solar activity
A stronger effect related to solar cycles is seen in Fig. 2, where the yearly averaged sunspot numbers are plotted together with the yearly change in coastal sea level (Holgate, 2007). The sea level rates are calculated from nine distributed tidal gauges with long records, which were compared with a larger set of data from 177 stations available in the last part of the century. In most of the century the sea level varied in phase with the solar activity, with the Sun leading the ocean, but in the beginning of the century they were in opposite phases, and during SC17 and 19 the sea level increased before the solar activity.
Let me see if I have this straight. At the start of the record, sunspots and sea level moved in opposite directions. Then for most of the time they were in phase. In both those cases, sunspots were leading sea level, suggesting the possibility that sunspots might affect sea level … except in opposite directions at different times. And in addition, in about 20% of the data, the sea level moved first, followed by the sunspots, suggesting the possibility that at times, the sea level might affect the number of sunspots …
Now, when I see a claim like that, after I get done laughing, I look around for some numerical measure of how similar the two series actually are. This is usually the “R2” (R squared) value, which varies from zero (no relationship) to 1 (they always move proportionately). Accompanying this R2 measure there is usually a “p-value”. The p-value measures how likely it is that we’re just seeing random variations. In other words, the p-value is the odds that the outcome has occurred by chance. A p-value of 0.05, for example, means that the odds are one in twenty that it’s a random occurrence.
So … what did the author of the paper put forwards as the R2 and p-value for this relationship?
Sad to relate, that part of the analysis seems to have slipped his mind. He doesn’t give us any guess as to how correlated the two series are, or whether we’re just looking at a random relationship.
So I thought, well, I’ll just get his data and measure the relationship myself. However, despite the journal’s policy requiring public archiving of the data necessary for replication, as is too common these days there was no public data, no code, and not even a Supplementary Online Information.
However, years of messing around with recalcitrant climate scientists has shown me that digitizing data is both fast and easy, so I simply digitized the graph of the data so I could analyze it. It’s quite accurate when done carefully.
And what did I find? Well, the R2 between sunspots and sea level is a mere 0.13, very little relationship. And even worse, the p-value of the relationship is 0.08 … sorry, no cigar. There is no statistically significant relationship between the two. In part this is because both datasets are so highly auto-correlated (~0.8 for both), and in part it’s because … well, it’s because as near as we can tell, sunspots [or whatever sunspots are a proxy for] don’t affect the sea level.
My conclusions from this, in no particular order, are:
• If this is the author’s “stronger effect related to solar cycles”, I’m not gonna worry about his weaker effect.
• This is not science in any sense of the word. There is no data. There is no code. There is no mathematical analysis of any kind, just bald assertions of a “stronger” relationship.
• Seems to me the idea that sunspots rule sea level would be pretty much scuttled by sunspot cycles 17 and 19 where the sea level moves first and sunspots follow … as well as by the phase reversal in the early data. At a minimum, you’d have to explain those large anomalies to make the case for a relationship. However, the author makes no effort to do so.
• The reviewers, as is far too often the case these days, were asleep at the switch. This study needs serious revision and buttressing to meet even the most minimal scientific standards.
• The editor bears responsibility as well, because the study is not replicable without the data as used, and the editor has not required the author to archive the data.
So … why am I bothering with a case of pseudo-science that is so easy to refute?
Because it is one of the papers in the Special Issue of the Copernicus journal, Pattern Recognition in Physics … and by no means the worst of the lot. There has been much disturbance in the farce lately regarding the journal being shut down, with many people saying that it was closed for political reasons. And perhaps that is the case.
However, if I ran Copernicus, I would have shut the journal down myself, but not for political reasons. I’d have closed it as soon as possible, for both scientific and business reasons.
I’d have shut it for scientific reasons because as we see in this example, peer-review was absent, the editorial actions were laughable, the authors reviewed each others papers, and the result was lots of handwaving and very little science.
And I’d have shut it for business reasons because Copernicus, as a publisher of scientific journals, cannot afford to become known as a place where reviewers don’t review and editors don’t edit. It would make them the laughing stock of the journal world, and being the butt of that kind of joke is something that no journal publisher can survive.
To me, it’s a huge tragedy, for two reasons. One is that I and other skeptical researchers get tarred with the same brush. The media commentary never says “a bunch of fringe pseudo-scientists” brought the journal down. No, it’s “climate skeptics” who get the blame, with no distinctions made despite the fact that we’ve falsified some of the claims of the Special Issue authors here on WUWT.
The other reason it’s a tragedy is that they were offered an unparalleled opportunity, the control of special issue of a reputable journal. I would give much to have the chance that they had. And they simply threw that away with nepotistic reviewing, inept editorship, wildly overblown claims, and a wholesale lack of science.
It’s a tragedy because you can be sure that if I, or many other skeptical researchers, got the chance to shape such a special issue, we wouldn’t give the publisher any reason to be unhappy with the quality of the peer-review, the strength of the editorship, or the scientific quality of the papers. The Copernicus folks might not like the conclusions, but they would be well researched, cited, and supported, with all data and code made public.
Ah, well … sic transit gloria monday, it’s already tuesday, and the struggle continues …
w.
PS—Based on … well, I’m not exactly sure what he’s basing it on, but the author says in the abstract:
The recent global warming may be interpreted as a rising branch of a millennium cycle, identified in ice cores and sediments and also recorded in history. This cycle peaks in the second half of this century, and then a 500 yr cooling trend will start.
Glad that’s settled. I was concerned about the next half millennium … you see what I mean about the absence of science in the Special Edition.
PPS—The usual request. I can defend my own words. I can’t defend your interpretation of my words. If you disagree with something I or anyone has written, please quote the exact words that you object to, and then tell us your objections. It prevents a host of misunderstandings, and it makes it clear just what you think is wrong, and why.
Let me chime in with what I hope with become an “open question” in this topic, though perhaps not providing an answer in its own right amongst the actual specific issue of sunspots and lunar cycles.
We have two cyclical phenomena, right? The two appear to be slowly (over time) sliding from out-of-phase -> to in phase -> to (perhaps) back out-of-phase with each other.
Should we not question the relationship – but be ready at the same time to admit that the two may not, in fact, related at all? After all, sunspots are themselves only a “symptom” of the underlaying solar currents and local magnetic fields in localized “storms” on the sun’s surface. That the sunspots change over time is obvious, but that the sunspots themselves cause anything to change elsewhere is a “coincidence” of two “grandchildren” or two “cousin” effects being changing in phase (or out-of-phase or lagging-in-certain-phases) because the original “grandparent” cause is pulling their chains slightly differently. Should we not be willing to look very, very closely for the cause of the “original change” in the original effect that the sunspots themselves merely highlight?
For example, if I try to link the “cause” of the moon with tides, surely I’d first get a number of tidal charts from a number of different cities around the world, then plot the moon’s position overhead locally with the tides at those spots, right?
Doesn’t work to well though. London is upstream from the Thames outlet to the English Channel, Halifax is on the south side of a coastline mere few miles from the highest tides on the planet, the River Seine behaves differently that does the Sacramento River dumping into San Francisco’s Bay, Portland and Vancouver behave differently over the year but both are on bays on the Pacific Northwest, and finally New Orleans is completely out-of-phase with the Mississippi river and its irregular flood season and nearby hurricanes – completely different from Pensacola or Mobile right nearby on the Gulf Coast.
Just in this simple analogy, you need to separate irregular hurricane tides from the sun’s neap tides from river back-flooding in spring (maybe, or maybe not, or maybe twice) from the basic and initial not-quite-two-tides-a-day lunar effect. All of that with the reverse flooding and ebbing in the surrounding large bay or Channel (Chesapeake, Fundy, San Francisco, Med. etc) On a problem this simple, could you spot the very small change due to the sun’s position with respect to the moon each month?
OK, thanks for the code. Much quicker as you say.
Firstly sunspot daily data runs from 1877 and was similar to the period used in fig2. You are using all the data back to 1700. Cropping to 1887 got the phase of the first peak similar to my plot, however, the overall envelop is still like your plots not with modulation max in middle . It seems that is due to differences in sunspot data. I need to look in more detail to find out why. Could be a fundamental difference between SS area and SSN, or a result of the Svalgaard ‘correction’.
Next question is waht does R do when you give it monthly data and tell it frequency=1 ?
My guess is a straight annual average, which is not legit resampling. Could be producing aliasing that would produce spurious longer cycles.
I’ll look closer at whether it’s due to the different solar data.
Willis Eschenbach:
In your post at January 26, 2014 at 3:24 pm you say
Yes. And that is why I have been pressing the coherence issue and not the correlation issue.
As you note, Ian Schumacher has been very helpful on the ‘echo’ idea. However, despite his kind help, I remain unconvinced mainly because I have no idea what an ‘echo’ would be (which is why I have consistently put the word ‘echo’ in inverted commas).
Please read my post at January 26, 2014 at 3:08 pm which is here
I do not want to mislead by implying that I think there is any solar effect on SLR: I don’t. But I keep an open mind on possibilities and the synchronicity idea is plausible but – so far as I can see – not useful except as a spur to determine what could be a connection between solar variation and SLR.
Richard
” – but be ready at the same time to admit that the two may not, in fact, related at all? ”
Indeed. I’m still not convinced the link is strong. However, the cross-correlation looks very structured with the sunspot area data I used.
http://climategrog.wordpress.com/?attachment_id=760
RACookPE1978:
re your post at January 26, 2014 at 4:24 pm.
Yes, there may be no connection at all. Indeed, at present all we have is the analysis which Willis has conducted which indicates there is no direct causal relationship. (If you check up the thread you will see I had an unpleasant interaction with someone who refused to accept this.)
So, the present discussion is about finding ways in which the finding by Willis may be incorrect although his analysis has not been faulted.
Personally, I don’t think there is a relationship between solar cycle and SLR variation but – as in all things – I would welcome being shown to be wrong.
Richard
Willis Eschenbach,
“But what does a “sunspot echo” look like or consist of? And what is it bouncing off of?”
Well I’m speculating of course and know almost nothing about climate science, so humor me on the details.
Where does the PDO come from? Where do any of the ocean oscillations come from? I don’t mean it as a trick question. I hear PDO talked about all the time, but no one talks about why it exists in the exact form that it does (not that I have seen anyway). For the sake of argument I’m going to assume that there is some sort of delayed feedback (as that’s how most oscillations occur) through evaporation and ocean mixing. Evaporation creates a heavy salty layer, which reaches a threshold and falls deeper into the ocean bringing up cold water to replace it. Or at least ‘something’ like that. Presumably there are several of these types of oscillations all over the climate and this is just one we have noticed.
What are sunspots supposed to ‘do’ that alters climate. Well maybe they warm the Earth directly through increased insolation, or maybe the increase in cosmic rays create more clouds and so on. The end result is that ‘somehow’ there is supposed to be a corresponding change in energy.
Where does an increase in energy go? Well it should make the world a little warmer immediately of course, (unless it’s some really exotic mechanism like melting ice, or evaporating water directly through high-energy photons, that would be cool, pun intended), but also it goes into driving a slight increase in the amplitude of Earth’s natural oscillations and it’s disappearance of this extra energy allows the system to decay back to a previous level. Or maybe not. We can’t tell with chaos. It may require an off phase event to bring it back, or it may never come back. Anyways, that’s the ‘echo’ – the delayed response to a previous signal. Sunspots could change amplitude of existing cycles.
Now again, just guessing, but I bet these oscillation dynamics are non-linear. A particularly strong sunspot event may evaporate water faster than a weaker sunspot event (assuming that is the correct mechanism) and may actually speed up the PDO frequency for a time. That’s a different kind of echo. We are effecting how the system operates in the future by some event now. Depending on amplitude, sunspots could temporarily or permanently alter frequency and/or phase of existing cycles.
On a different note, even though many people on WUWT appear to treat PDO as sacrosanct. It may, in it’s current form, be a completely temporary phenomenon. Chaotic systems occasionally switch into a temporarily stable oscillation all the time, only to suddenly go off wildly with no warning into a different temporarily stable oscillation (think Lorentz butterfly – see http://en.wikipedia.org/wiki/Butterfly_effect in the unlikely event anyone reading this doesn’t know what I’m talking about). There are probably ‘butterfly’ equivalents all over the climate system.
I hope that was adequate. Chaos theory is a hobby of mine and I’m not an expert. I have a background in mathematical modeling and signal processing.
On a side-note and not to step on too many toes, PDO to me looks really noisy. I’m not actually convinced it’s a stable periodic phenomenon at all [http://en.wikipedia.org/wiki/File:PDO1000yr.svg ]
Willis,
It was hard work, but I think you managed to convince almost everyone here (including me) that the correlation (in every sense of the word) is too weak to be meaningful.
I downloaded the sunspot data from the link you recently posted took one look at the noisy sea level data and threw it away. The only signal in there I can see is the obvious one – ocean level is increasing over time. In many ways it feels like statistics has ruined science. When you can’t ‘see’ a signal and need to perform many dubious processing steps to tease out what you think should be there, the chance that you are just seeing an artifact of one of your processing steps is immense and difficult to completely compensate for.
RACookPE1978 says:
“Should we not question the relationship – but be ready at the same time to admit that the two may not, in fact, related at all?”
Is there something in the Universe that affects both Earth and the Sun? It’s a possible but very exotic theory 😉 What would be the other external thing be? Can we measure it? If you can measure it then you have a way to test your theory.
“The only signal in there I can see is the obvious one – ocean level is increasing over time. ”
Ian , you should read the Jevrejeva papers 😉
Willis, I’ve run Leif’s reworked SSN , 1877 onwards, through the same processing I did with sunspot area and get essentially the same result (just one minor peak moved from 16.75 to 17.4).
so the huge difference in form of the cross-correlation is in the processing not the data….
I said: ” Cropping to 1887 got the phase of the first peak similar to my plot, however, the overall envelop is still like your plots not with modulation max in middle .”
No. I’ve now got essentially the same x-correl plot from my code with data from 1750 on (earliest common date) .
Earlier incorrect report because setting start=1877.5 did not seem to do anything different and apparently still used all the data. That’s basically why I stopped using R. I had to spend more time double checking it did what I asked than I spent doing the job I itself.
thespots=ts(read.csv(“SIDC Sunspots.csv”)[,2],start=1877.5,frequency=1)
thesea=ts(read.csv(“jevrejeva sea level.csv”)[,2],start=1877.5,frequency=1)
ccf(diff(thesea),thespots, lag.max=60 , main=”Cross-Correlation, Sunspots and # Jevrejeva Sea Level”,
ylab=”Correlation”,col=”salmon”,lwd=3)
Now if you look at the jevre’ data there is a sudden doubling of the magnitude of variation pre-1900. This may be sampling errors or real climate variation: SST shows much larger variations too as does BEST land data.
Now I take the point made in your red noise tests about the solar cycle coming through, however this does not reproduce the 70 year envelop.
How about putting lag.max=100, limiting the data to 1877-ish, and seeing whether any random runs can produce anything like it? I rather doubt that will happen.
Ok, please allow me try to recapitulate:
1. We have that picture above, with clearly visible approx 11 year cycles in both data sets.
2. Actually, from first thought, doubt arises not whether a relationship exists, but much more why it appears to be so strong. Who would have thought that ?
3. For McIntyre this appears to be, offhand, the best decadal matching of any two climate variables.
4. Then, we have various analysis, applying methods which prima facie are not able to extract that 11 year pattern.
5. Correlation cannot handle the 1 or 2 major phase jump and also the amplitude mismatches.
Quote Willis Eschenbach says: January 23, 2014 at 8:05 pm : “… which just reveals the weakness of the method.”
6. Lagged correlation can’t do either.
7. Same problem with phase jumps and Fourier.
8. Then we have a discussion about a lacking physical explanation for small lags, which, due to noisy data and other influences working on sea level, may be totally explainable, and making that physical explanation redundant from the start..
9. Then there are comments, appearing to better address the visible relationship, but remaining totally ignored.
10. Shaviv 2008 reports to have improved correlation to 0.54 and p value to 0.0001 by removal of secular trends. How did he do that ?
11. I get a similar correlation value (for Shaviv 2008), if I remove the first 19 years of data, which may also be the most unreliable part of the data set.
12. Paul Westhaven reports an interesting strategy to extract a signal (by “forcing into correlation” and “examining the residuals”)…
Manfred says:
January 26, 2014 at 7:09 pm
10. Shaviv 2008 reports to have improved correlation to 0.54 and p value to 0.0001 by removal of secular trends. How did he do that ?
It seems to me that the secular trend would be the most important aspect of the whole matter. That would be the first-order response. Who would care about a small second-order wiggle on top of the dominant long-term trend?
“3. For McIntyre this appears to be, offhand, the best decadal matching of any two climate variables.”
I would not make too much of that comment which was clearly just an initial visual assessment. Note the “offhand” qualifier.
“7. Same problem with phase jumps and Fourier.”
Assuming there’s reason for the phase jumps spectral analysis will likely explain them.
One feature of interference patterns between close harmonics is an abrupt phase change. The point in the x-correl plot I marked at 38 years is a clear example.
http://climategrog.wordpress.com/?attachment_id=760
The 1975 flip in N. Pacific SST is another example but this gets lost when it is processed into PDO ” empirical orthogonal functions”.
lsvalgaard says:
January 26, 2014 at 7:27 pm
Manfred says:
January 26, 2014 at 7:09 pm
10. Shaviv 2008 reports to have improved correlation to 0.54 and p value to 0.0001 by removal of secular trends. How did he do that ?
It seems to me that the secular trend would be the most important aspect of the whole matter. That would be the first-order response. Who would care about a small second-order wiggle on top of the dominant long-term trend?
===
Detrending is similar to taking first difference since a linear “trend” becomes a constant and then would not affect the correlation. First diff would be a means of removing auto-correlation also. That would be a more justifiable strategy than arbitrarily subtracting an artificial linear trend from data that almost certainly has no reason to be displaying such linear behaviour.
I have not read Shaviv 2008 to see exactly what he did.
Greg Goodman says:
January 26, 2014 at 4:24 pm
OK, thanks for the code. Much quicker as you say.
Since both the Jevrejeva sea level data and the SIDC sunspot numbers went back to 1700, that’s what I used.
The function ts() in R converts a string of evenly spaced data into a timeseries object. The for annual data starting in 1700 like the sunspot data the syntax is something like
my_timeseries = ts(somedata, start= 1700.5, frequency = 1)
If you have monthly data that starts in March 2000, like the CERES data, the syntax would be
CERES_ts = ts(CERESdata, start = c(2000,3), frequency=12)
No, there’s no averageing or resampling. The ts() function doesn’t do anything at all to the data. It just adds an (invisible) time string to the data so you can window the data or plot it easily and without ambiguity. There’s another kind of object, a “zoo” object, for irregularly spaced data.
w.
Greg Goodman says:
January 26, 2014 at 7:40 pm
Detrending is similar to taking first difference since a linear “trend” becomes a constant and then would not affect the correlation.
Sometimes what is observed has an inherent trend. Let me give you a realistic example: it is generally accepted that magnetic fields on the Sun are the main cause of variations of TSI [the total Solar Irradiance, which a priori must have an influence on the climate]. Sunspots are manifestations of surface magnetic fields and so should have an influence on TSI [should make TSI smaller as spots are darker than the average surface]. This is observed, as TSI dips when a large spot is on the disk. Sunspots decay by having their magnetic field ‘shredded’ into many small ‘strands’ that are moving away from the spots. This creates an area around the spot where many such strands of magnetic field can be found. As the magnetic field in a strand exerts a pressure of its own, less gas is needed for pressure balance so we can see deeper into the partly evacuated atmosphere inside the strand [and in particular see the ‘hot walls’ inside the strand; this is also observed]. This makes the debris field brighter than the surrounding surface. In fact, outshines the deficit caused by sunspot by a factor of two, so on the whole, many spots + their debris fields increase TSI. This would create a solar cycle variation of TSI, as observed. Now, assume that there are an immensity of tiny [and therefore hard to observe] magnetic elements not directly associated with sunspots erupting all over the Sun and that their rate of eruption would be variable, perhaps on a longer time-scale [centuries or longer]. This would create a long-term, secular trend in TSI, potentially much larger than the variations due to sunspots and potentially of much larger importance for the climate. In fact, such a ‘background’ is a much discussed item in solar physics today [see http://www.leif.org/research/Long-term-Variation-Solar-Activity.pdf ]. We do not know if a background exists [personally I think not, but that is just my well-founded opinion], but some researchers claim so. So here you have a case where detrending could remove the real and important signal and thus critically alter the correlation between solar magnetism and climate. As I said: “Who would care about a small second-order wiggle on top of the dominant long-term trend?”
Ian Schumacher says:
January 26, 2014 at 4:46 pm
Thanks for the interesting thoughts. Yes, there can be delayed actions, no question. What I was questioning was your specific example from signal analysis, an “echo”. And you showed examples.
It seems now that you didn’t mean an echo, but some other delaying mechanism involving the transformation of the energy into another form. You see, a sound echo comes back as sound. An electronic echo comes back as an electromagnetic signal.
It seems now that you’ve abandoned that, and are talking about a different concept, which is fine. I’m just trying to follow. The new concept is that something associated with sunspots somehow (electro-magnetically?) affects some unknown process on the earth in such a way as to suddenly flip the phase of the response to the sunspots from negative to positive …
I’m still not seeing it, Ian.
Regarding your speculations on the PDO, interesting ideas on an interesting issue. You might enjoy my analysis called “Decadal Oscillations Of The Pacific Kind” …
Finally, you say:
Ummm … that chart is a reconstruction of the PDO from tree rings … possible, but the error bars would go floor to ceiling. Which may be why there aren’t any … Take a look at my paper linked above, Figure 4 shows the cumulative PDO which is much clearer about the existence of the phenomenon.
My best to you,
w.
Greg Goodman says:
January 26, 2014 at 7:40 pm
Detrending is similar to taking first difference since a linear “trend” becomes a constant and then would not affect the correlation.
Another realistic example: solar activity modulates the flux of Galactic Cosmic Rays [GCRs] by a few percent. The Earth’s magnetic field shields us from much of that GCR flux. The Earth’s magnetic field is a much stronger modulator of GHCs than the Sun is. The field varies on timescales of centuries or longer and cause the flux of GCRs to vary an order of magnitude more than the sorry wiggles due to the Sun. If GCRs have an influence on the climate, detrending the GCR flux will remove that large, important and first-order effect and leave us to fight with the noise. As I said: “Who would care about a small second-order wiggle on top of the dominant long-term trend?”
Manfred says:
January 26, 2014 at 7:09 pm
I love the plan. Who would have guessed that you could actually improve the correlation by the simple expedient of throwing away the data that doesn’t agree with your theory! Brilliant!
… [/sarc] …
Manfred, I’ll take that as your convoluted way of saying you couldn’t reproduce Shaviv’s results. Hey, I couldn’t either, as I reported above.
w.
lsvalgaard says:
January 26, 2014 at 7:27 pm
Thanks, Leif. That’s what I was pointing at in the Parana river post when I said:
In that case, it inconveniently didn’t fit with their narrative, so they just subtracted out the secular trend and went on … I just shook my head.
w.
For the nitpickers: “The Earth’s magnetic field is a much stronger modulator of GCRs than the Sun is”
lsvalgaard says:
January 26, 2014 at 8:19 pm
Dang, I love the web, it’s like attending the best school EVAR!
Leif, do you have a link to some kind of long-term measurement of the geomagnetic field? The sucker has to be monstrously complex, being as how it’s a 3-d vector or maybe tensor field. Dang … that kind of thing can’t be boiled down to one number, so I suppose they do what? Measure field strength in othogonal directions? Makes a man’s head hurt … any references to data and descriptions would be appreciated.
w.
Greg Goodman says:
January 26, 2014 at 7:40 pm
Detrending is similar to taking first difference since a linear “trend” becomes a constant and then would not affect the correlation.
Yet another example: due to various geometric effects there are [weak] 22-year cycles both in GCRs and Geomagnetic Activity. These [tiny] second-order effects are supposed to cause 22-year cycles in climate and all kinds of other things. If they do, one would expect a much larger effect from the much larger first-order variations that dominate over those tiny 22-year variations. As I said: “Who would care about a small second-order wiggle on top of the dominant long-term trend?”
Willis Eschenbach says:
January 26, 2014 at 8:35 pm
Leif, do you have a link to some kind of long-term measurement of the geomagnetic field?
Lots of such links. The single quantity that is much used is simply the dipole moment [the strength of the main field]. That quantity determines, among other things, the size of the Earth’s magnetosphere [stronger diple, larger magnetosphere]. Here are some links: [Google is your friend] http://seismo.berkeley.edu/~rallen/eps122/lectures/L05.pdf and http://earthref.org/ERDA/973/ and an old [but still valid] Figure: http://www.leif/org/research/CosmicRays-GeoDipole.jpg