Rotational Eustasy as Understood in Physics

Global sea level has today become widely understood merely in terms of glacial eustasy and thermal expansion. Although this is good in theory, it is not enough to explain observational facts in nature. We know that the 17 century was characterized by cold climate, Little Ice Age conditions, and low solar activity during the Maunder Grand Solar Minimum. In contrast, the 18 century was characterized by warm climate conditions and a Grand Solar Maximum (with the Polar front located north of Svalbard). In terms of glacial eustasy, one would expect to find a low sea level in the 17 century and a high sea level in the 18 century. This is not the case in the equatorial regions, however. In the Indian Ocean and the Pacific, there was a 60 70 cm higher sea level in the 17 century, and a sea level well below the present one in the 18 century. This can only be understood in terms of “rotational eustasy”. This is a novel concept, here for the first time addressed with respect to physical interpretation. It is shown that planetary beat affects Earth’s rate of rotation and that this leads to oscillations of the equatorial water bulge with amplitudes of up to ±70 cm.


Introduction
The theory of sea level change includes glacial eustasy, ocean volume changes, geoidal eustasy, thermal-hyaline expansion/contraction of the water column, and changes of the rotational ellipsoid of the globe [1]- [6]. In the discussion of present and future sea level changes, the issue has generally become limited to glacial eustasy and thermal expansion [7]. Only observational facts in nature itself are good enough for a trustworthy picture, however.
Past sea level positions can be measured by watermarks, tide gauges, satellite How to cite this paper: Mörner, N.-A.
(2019) Rotational Eustasy as Understood in logical information. All of these factors have their limitations and margins of error, however (e.g. [8]).
There are more than 2000 tide gauge stations [9], but there are only a few long and continuous records. In formerly glaciated areas, the tide gauge records are dominated by glacial isostatic uplift. In other areas of the globe, the tide gauge records are usually affected by subsidence because the tide gauges are located at river-mouths where the accumulation of sediments has induced subsidence. The extraction of water from beneath cities generates sediment compaction and hence subsidence. Furthermore, many tide gauges are attached to heavy harbour constructions, which generate site-specific compaction (i.e. subsidence). Many tide gauge records are, in fact, fragmentary. Gaps in the recording may not be so serious. Gaps due to destruction (e.g. by storms and tsunamis) may generate serious discontinuities, however. This is certainly the case with relocations of the actual site of measurements. Such discontinuities invalidate straight-line trend analyses (e.g. [10]). There are also cycles to consider; the 18.6 lunar-tidal cycle and longer "lunar-tidal super cycles". Finally, there is the problem with the search for "global mean sea level change", when, in fact, eustatic sea level is a regional factor to be determined separately from region to region [11]. How can the personal selection of 6 sites [12] or 184 sites [13] provide anything but meaningless average values?
Satellite altimetry (e.g. [14]) is a new and important tool of recording sea level changes starting in late 1992. Whilst NOAA [15] gives a mean sea level rise of +2.9 ± 04 mm/yr, UC [16] gives a means sea level rise of 3.3 ± 0.4 mm/yr. Both values are strongly affected by subjective "corrections" or "manipulation" [17], however. Remove these improper "calibrations" and the values change to +0.45 and +0.65 mm/yr, respectively [18].
In this paper, I will focus on shore morphology and stratigraphy, the latitudinal differences in sea level changes during the last 500 years, the occurrence of a +60 -70 cm high sea level in the equatorial regions during the Little Ice Age in the 17 th century, a low sea level (peat and buildings below present sea level) in the warm period of the 18 th century, and the concept of "rotational eustasy" and its interpretation with respect to physics. The concept of "rotational eustasy" has been identified and successively built up on the basis of extensive field observations in the Indian Ocean and the Pacific [19]. In the true sense of science, it presents the logical steps from observations, via interpretations, to conclusions.
A complementary review of the observational facts is presented separately [19], and an additional a special account on biological and shore morphological criteria in [20].

Material and Methods
The concept of rotational eustasy is a direct product of the accumulation of new observational facts from a number of sites in the Indian Ocean and the Pacific. been presented separately in peer reviewed scientific papers. A summary is presented below (Section 3), and an extensive review is presented in [19]. In a separate paper [20], I have addressed evidence from biological criteria (trees, corals, etc.) and shore morphology, because these data do not lie and hence seem irrefutable.
In addition to my own field documentations and sea level reconstructions, I want to refer to additional investigations of 709 atoll islands in the Pacific and Indian Ocean summarized by Duvat [21]. It refers to the changes in size and area of the individual islands over the past decade ( Figure 1). It is based on independent studies by [21]- [34]. This database is interesting because it is totally objective with respect to my own. As illustrated in Figure 1 hardly any atoll has decreased in size (as would have been the case if sea level really was rising), and the vast majority have remained stable during the last decade, indicating stable sea level conditions [35].
This is consistent with a modern understanding of coastal dynamics [35] which implies that the shore (land/sea interface) can be deformed both vertically

Observational Facts
The concept of rotational eustasy is a direct product of the accumulation of new observational facts from a number of sites in the Indian Ocean and the Pacific. In order to not include an extensive review of all the field data in this paper, I limit myself to a short review of the main findings, and present a review of the observational material separately [19]. Studies in the Maldives revealed that the 18 th century was represented by a sea level below the present level with peat below sea level, dated at 1720-1790 BP Figure 1. Changes in size of 709 atoll islandsin the Pacific and Indian Ocean (from [35], redrawn in upside-down view from [21]), providing additional evidence that the equatorial eustatic component has remaind stable for the past decades. Figure 2. Coastal dynamics deform the shore laterally (horizontally), whilst the changes in sea level or land level deforms the shrelevel vertically according to Encyclopedia of Coastal Science [38]. . During the 17 th century, sea level was 50 -60 cm higher than at present. This was our first record suggesting opposed sea level changes in the Indian Ocean with respect to the general climatic changes [42]. The next place of sea level investigation was the coast of Bangladesh ( [43]; [19], Fig 9). The 18 th century is represented by a distinct sea level low [39] [41] [43] with salt kilns in submarine position [44].
In Goa, India, it was possible to reconstruct the sea level change during the last 500 years with a high precision ( [19]  This level is fresh and young (sub-recent) and recorded over the entire island. It is also seen in a sub-recent sandy shore level preceding at +70 cm. Figure 3 shows a former shore cliff with under-cut notches located 70 cm above the present high-tide level (HTL). The continuity between the present and +70 cm shore marks indicates a sub-recent age of the +70 sea level. But most impressive is a rock-cut shore platform 70 cm above the present HTL ( Figure 4). It is fresh, cut into the old reef deposits and lacking any sign of weathering, indicating a young or sub-recent age ( [19], . This level must correlate to the +70 cm sea level recorded in the Fiji Islands and dated to the 17 th century (just as was the case in the Maldives and in Goa, India).
In Figure 5, I summarize the observed sea level changes during the last 500 years as observed and documented in Bangladesh [43], Goa [41], the Maldives [39], Fiji [46], New Caledonia [35] and the present trend on a number of Pacific    Figure 18 in [19]). Therefore, we must seek a new explanation.

Interpretation in Terms of Physics
The observations ( These changes in sea level are a novel finding for which I have coined the term "rotational eustasy" [5] [42] [45]. It refers to the north-south redistribution of water masses and the increase and decrease in the equatorial bulge as a function of changes in the Earth's rate of rotation ( Figure 6). If temperature continues to rise, sea level is likely to rise by about 10 cm up to year 2100 in the northern hemisphere and remain more or less stable in the equatorial region. If, on the other hand, we will face a new Grand Solar Minimum by about 2030-2050 [51] [52] [54], sea is likely to fall in the north and rise in the equatorial regions ( Figure 6).
For the period 1850-1930, there may have been a general glacial eustatic rise in sea level as a function of the temperature rise and ice melting after the Little Ice Ages (in Figure 6). In this case, the rise would have an internal cause as proposed before [4] [55].
The    [52]. The observed expansion/contraction changes are illustrated in Figure 8.
The changes in Earth's rate of rotation generating rotational eustatic changes in sea level are not internally but externally driven [56]. The changes in rotation were first observed in the beat of the Gulf Stream [57]. Later, it was understood that this beat (variability) ultimately had to be driven by changes in the Solar Wind [50]; i.e. solar variability. The changes in Solar Wind emission (and simultaneously also in solar irradiance emission) were found to be the function of planetary beat (the 60-yr cycle, the 84-yr Gleissberg cycle, etc.). Figure 9 gives an integrated system of the changes of planetary beat on the Sun, the Earth and the Earth-Moon system [42] [53] [58] [59].
Scafetta [60] showed that the 60-yr cycle is a prime cycle in solar variability and that it exhibits excellent correlation with the planetary cycle of the combined effect of 5 Jupiter (59.30 yr) and 2 Saturn (58.90 yr) rotations around the Sun. The same applies for the Gleissberg cycle, which is the combined effect of 7 Jupiter (83.02 yr), 3 Saturn (88.35 yr) and 1 Uranus (84.3 yr) revolutions around the Sun. Neptune (164.79 yr) and Pluto (248 yr) should also be integrated in the beat systems.
The planetary cycles have a direct effect on the Sun's position with respect to the centre of mass of our planetary system [61] [62], and the internal motions of planetary-Sun barycentre [59] [63]. Obviously, the planetary beat cycles drive both the 60-yr cycle and the Grand Solar Maxima/Minima cycles (besides longer-term cycles). The impact on the terrestrial system is manifold as illustrated in Figure 9.
Of course there are other planetary cycles, both longer and shorter, that are likely to affect ocean circulation and sea level changes. The Gulf Stream exhibits 30 pulses in the last 13,000 years with cycles varying in length between 230 and 1000 years [48]. This paper, however, is about rotational eustasy during the last 500 years.  . Integrated terrestrial effects (including rotational eustasy) as driven by planetary beat on the Sun, the Earth and the Earth-Moon system. Brown boxes give processes that are involved in the changes in sea level and ocean "oscillations" (3). The 60-yr geomagnetic field cycle (2) provides evidence of a back-ground in changes in Solar Wind [50]. The changes in Earth's shielding (1) are a well-known characteristic of Solar Wind interaction with the Earth's geomagnetic field.
The remarkable thing with respect to rotational eustasy is that the observed changes in sea level during the last 500 years now can be traced back to an origin in the motions of the planets around the Sun and the multiple planetary beats on the Sun, the Earth and the Earth-Moon system as illustrated in Figure 9.

Conclusions
The concepts of glacial eustasy and thermal expansion/contraction cannot explain the sea level changes observed in the equatorial belt of the Indian Ocean and the Pacific. This calls for an alternative explanation.
The explanation presented is termed "rotational eustasy" [35] [42] [45]. It implies that the water masses are re-located between the high latitudes and the equatorial region in response to changes in Earth's rotation. The changes in rotation originate from the planetary beat on the Sun generating variations in emission of Solar Wind which interacts with the Earth's magnetosphere, and direct planetary beat on the Earth and the Earth-Moon system [5] [42] [45] [59] as illustrated in Figure 9.
During Grand Solar Minima, the Earth's rate of rotation speeds up and the equatorial bulge increases generating sea level rises in the Pacific and Indian Ocean. The process may also be seen as a new type of "lunar-tidal super cycles". Besides the Grand Solar Maxima/Minima cycle, we also have the 60-yr cycle, which is a basic climatic-eustatic cycle [42] with an origin in the Jupiter-Saturn motions around the Sun [60].
The latitudinal changes in sea level during the last 400 years are summarized in Figure 6 and Figure 7. The north-south differentiation is obvious. The driving forces can only be understood in terms of rotational eustasy (Figure 8).
The concept of rotational eustasy is, of course, also valid for periods prior to the last 500 years here analysed. I leave this for future analyses, but just note that The concept is, of course, also valid for the future. Therefore, it is to be expected that sea level will rise in the equatorial regions during the next Grand Solar Minimum likely to occur at about 2030-2050 [54].

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.