The Nodal Tidal Cycle and a firm belief in the impossible

I've not paid much attention to the prognostications of Prof. Nils-Axel Mörner in the past, but recently his claims concerning global sea-level have been featured on several blogs, most notably Jo Nova. Several things struck me while reading the latter post, so I downloaded his paper entitled, rather uncompromisingly "Sea level is not rising" to give it a once-over. I focus here on this section with an accompanying chart:

French Guyana and Surinam

From this region, there is a very good tide-gauge record covering three 18.6-year tidal cycles (Fig. 14). The cycles vary symmetrically around a stable, horizontal zero-level. Satellite altimetry gives a rise of 3 mm/year in the same area. Facts and fiction seem to clash.

Figure 14. Changes in mean high-water level (cm: left axis) measured by tide gauges at the coast of French Guyana and Surinam (Gratiot et al., 2008; Mörner, 2010b). The record is dominated by the 18.6-year tidal cycle, which swings up and down around a long-term zero trend (the arrowed line), indicating that sea level has been quite stable over the last 50 years. However, satellite altimetry in the same region gives a rise of 3.0 mm/year – another revealing example of the difference between recorded facts and “reprocessed” satellite data.

I'll ignore for the moment that the graphic doesn't represent a tide-gauge record, that it doesn't show mean sea-level (which is what's under discussion here) and that it doesn't cover three tidal cycles. Instead I'll look first at what Gratiot et al., 2008 actually says about the nodal tidal cycle (henceforth NTC) and its manifestations and effects, and whether it affects mean sea-level (MSL) at all. The paper "Signifcant contribution of the 18.6 year tidal cycle to regional coastal changes" can be found here - it concerns itself with the effects of MHWL or mean high water level on erosion and sedimentation along the north-west coast of South America.

MHWL or mean high water level is the average of high water level (maximum tidal height) over the period under consideration. MHWL is accompanied by MLWL, mean low water level, and mean sea level is approximately half way between. The main conclusions of Gratiot et al. aren't disputed here; it seems perfectly logical that higher tidal levels cause greater shoreline erosion and that the nodal tidal cycle, which amplifies and reduces MHWL over an 18.6-year cycle has a significant effect. However, the last paragraph of the paper introduces another topic entirely; a claimed link between the NTC and mean sea level.

What I find amusing is that it isn't even necessary to understand the NTC. what causes the NTC to amplify tidal cycles worldwide, or even the extent of that amplification, to use the accompanying chart in Gratiot et al. to disprove their supplementary (and alarming) claim. However a brief description of the NTC might make things a little clearer. The Moon's orbit is inclined relative to the Earth's orbit around the Sun, which means that the Moon and the Sun pull on the oceans at a slight angle to one another. The lunar nodes are the points where the Moon's orbit crosses the plane of the Earth's orbit. When the Moon is at one of these nodes the Moon and Sun exert their pulls along the plane of Earth's orbit, and the total is greater than at other times. High water is at its highest during that part of the 18.61-year cycle, low water is at its lowest. 9.3 years either side, the effect is opposite, high water is reduced, low water increased. Back to Gratiot et al.

This study confrms the hypothesis that low tidal constituents are a major controlling factor in the evolution of the very gently sloping muddy coastal plain and shoreface of the Guyanas. Although tides have no effect on the long-term sea-level trend, they induce important fluctuations of the MHWL, when considering decadal timescales. As this timescale is particularly important for shoreline management and for policy makers, it is crucial to highlight the shoreline fluctuations associated with the 18.6 year cycle. From now to 2015, the coast of the Guyanas is expected to retreat by about 150m, 60% of this retreat resulting from the effect of the low-frequency tide constituents and 40% from sea-level rise due to global change. The nodal tidal cycle has a predictable effect on the tidal amplitude everywhere. It modulates the tidal amplitude by about 3% so that regions experiencing macro-tidal regimes are particularly concerned. Over the next decade, many coastal areas in Australia, Canada, China, England and France will experience a sea-level rise of several tens of centimetres due to the 18.6 tidal cycle (Fig. 3). This rise will contribute significantly to coastal erosion generated by global sea-level rise.

After having said that "tides have no effect on the long-term sea-level trend", they then say that "many coastal areas in Australia, Canada, China, England and France will experience a sea-level rise of several tens of centimetres due to the 18.6 tidal cycle". They mean of course that the mean sea-level will rise due to the increase from the low phase of the cycle in 2006 (see the chart above) to a high point some 9 years later. Here is their Fig.3, though from the preprint version of the paper - in the published version the title has vanished.

Figure 3 Predicted shifting of the MHWL under the 18.6 year nodal cycle for the next decade. (Adapted from the global map of tidal amplitude proposed by ref. 29 by considering a modulation of signal of 3%.) Grey areas correspond to locations of decrease or negligible rise. The black box (48W-62W-2N-12N) delimits the mud bank system of the Guyanas, South America.

Ref. 29 is Simon, B. La Marée Océanique Côtière (Institut Océanographique, Paris, 2007) if anyone's inclined to follow it up. Babel Fish translates "La Marée Océanique Côtière" as "The coastal ocean tide" which makes sense, if not good grammar, whereas Google Translate mangles it into "Tide Ocean Resort", which has a distinctly commercial flavour to it.

Note however how "Predicted shifting of the MHWL" in the caption becomes "sea-level rise" in the text. Note also that the sign of the "sea-level rise" is always positive; the scale has no negative part. This chart therefore must represent global sea-level rise due to a modification of tidal cycles. It demands the question - where does the water come from to generate this global rise? A second question - where did the water go to generate the implied previous 9-year low? A third question - why do none of the areas claimed as most affected show any part of such a large rise since 2006, nor any similarly large dip of "several tens of centimetres" over the previous 9 years? Their original chart is presumably based on a version of this one

Source: Aviso

.... which shows the lunar component of the global tides.

Their first mistake is assuming that the effect of the NTC is to amplify the tidal range by 3% globally; it does not. Several papers show the effect to be around +-5cm in the English Channel and North Sea, rather than the +-18-30cm their chart shows. The effect along the US Atlantic coast is greater than their chart shows, and the effect along the SW coast of Australia is also greater than their 3%, which I assume they calculated for their area of study, French Guyana and Surinam.

Their second mistake is a simple statistical one; if a range broadens, the difference between the mean of the range and the new maximum increases by only half the broadening. A range of 10-20 has a mean of 15, broadening to 10-30 increases the mean to 15. A range of 10-20 which broadens about its centre, the mean, produces no change in the mean at all. So even if the NTC produces an increase in the MHWL of 10cm, the mean can't increase by any more than 5cm. Even if they are correct in their assumption that an increase in MHWL produces a change in MSL, the latter can't possibly be equal to the former. In fact, tidal cycles expand and contract about their centre as I will show in detail in a later post, and as the NTC produces a simple broadening and shrinking of those cycles, it can't possibly cause any measurable change in MSL. I intend to write to the journal editors on the topic of the logical fallacies in the last paragraph in Gratiot et al., 2008.

A little background information here - It was this very topic, the Nodal Tidal Cycle, which got me interested in studying sea-level change several years ago. Having read of the claimed effect on local MSL, I decided to look for evidence in tide-gauge records. If the effect was as large as claimed, the effects should be obvious. I didn't expect to find that all sites would show it; I'd have been satisfied with a few clear examples. In short, I found none. I did find a few articles where the gauge record appeared to show some correlation for just a part of the record. Adjacent gauge sites I checked didn't show the effect at all, a fact curiously omitted by the authors. I even found a couple of published papers claiming to have found the effect. Their statistical "proof" was, to be candid, laughable. Most authors who refer to and study the effect of the NTC on MHWL, and its effect on erosion or some other phenomenon don't in general mention MSL; if they do, they don't link it with the NTC. Here's the abstract for one paper which does;

Nodal Tidal Cycle of 18.6 Yr.: Its Importance in Sea-Level Curves of the East Coast of the United States and Its Value in Explaining Long-Term Sea-Level Changes

Clifford A. Kaye and Gary W. Stuckey

The 18.6-yr cycle of the Moon's nodes dominates the annual means of high water, low water, and range at Boston and at other East Coast harbors. The maxima and minima of the high-water and range curves agree closely with the 180° and 0° long. yr, respectively, of the Moon's ascending node, and are fairly well accounted for by tide-prediction equations. The curve of annual mean sea level also reflects the cycle, but more weakly. Recognition of the cyclical nature of tidal data both simplifies and clarifies assessments of longer term sea-level trends and points to the need to include only multiples of entire cycles in the computations of these trends. When the curves of mean high water and range are used, it is possible to recognize long-term sea-level trends rapidly and to determine whether these are attributable to tidal or nontidal causes. The data suggest that the secular sea-level rise during the 20th century is tidal in origin and may be caused by vertical movement of the oceanic floor. This has the effect of reducing the volume of ocean basins, and, by changing basin geometry, alters the characteristics of terrestrial tidal constituents (standing waves).

Now I'd say that if the "secular sea-level rise during the 20th century" was caused by "vertical movement of the oceanic floor", then it's clearly not "tidal in origin". They also say that "The curve of annual mean sea level also reflects the cycle, but more weakly", while providing no proof in the text but for Boston, just one of the many sites they analysed. I'll be covering their assessment in a later post.

The realisation that the NTC simply amplified tidal cycles and didn't shift their mid-points soon dawned on me. Put simply, if high water increase due an effect on the gravitational pull of the moon, that water has to come from somewhere. The "somewhere" is in fact two "somewheres", the areas at right angles to the Earth-Moon axis along which the Moon exerts its pull. Those areas see lower tides as a result, and as the Earth rotates though the "tidal bulge" the point experiencing the higher tide experiences the lower tide some 6 hours later. The Gratiot et al. paper hasn't got a "somewhere" to act as a source for their claimed increases, ergo those worldwide increases can't happen, and Mörner's link between MHWL and sea-level is spurious.

I haven't actually provided any actual proof - you know graphs and stuff, that what I claim about the non-effect of the NTC on local mean sea-level is correct. That's for a later post, already in preparation. In the meanwhile, I'll return to my comment on Mörner's reproduced chart. The source is Fig. 1c in the Gratiot et al. paper (my bold in the caption)

c, Nodal cycles of the mhwl in Surinam and French Guiana. From 1958 to 1978, tidal gauge measurements in the mouth of the Surinam river ; from 1979 to the present, data from the tidal model of the Service Hydrographique et Océanographique de la Marine (SHOM, France www.shom.fr/ann_marees) obtained from tidal gauge measurements on Devil’s Islands (French Guiana). The corresponding phases of overall erosion and colonization reported by previous studies and in this work are shown as red and green patches. 

As I said, It's not a tide-gauge record and it doesn't show MSL but MHWL. I've never seen a tide-gauge record which looks like that, with a smooth multi-year cycle - no-one has. I'll overlook the fact that it's stitched-together from two sources. I'll even overlook that it doesn't cover "three 18.6-year tidal cycles". What I can't overlook is misrepresentation. Perhaps we sceptics should be more sceptical of what's claimed as proof - from "friends" as well as the "other side".