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International Journal of Astronomy and Astrophysics, 2021, 11, 279-341
ISSN Online: 2161-4725
ISSN Print: 2161-4717
10.4236/ijaa.2021.112015 Jun. 29, 2021 279 International Journal of Astronomy and
Changes in Barents Sea Ice Edge Positions in
the Last 442 Years. Part 2: Sun, Moon and
Jan-Erik Solheim1*, Stig Falk-Petersen2, Ole Humlum3,4, Nils-Axel Mörner5
1Retired, Department of Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway
2Akvaplan-niva, The Fram Centre, Tromsø, Norway
3The University Centre on Svalbard (UNIS), Longyearbyen, Svalbard, Norway
4Department of Geosciences, University of Oslo, Oslo, Norway
5Deceased, Paleogeophysics & Geodynamics, Stockholm, Sweden
This is the second paper in a series of two, which analyze the position of the
Barents Sea ice-edge (BIE) based on a 442-
year long dataset to understand its
time variations. The data have been collected from ship-logs, polar expedi-
tions, and hunters in addition to airplan
es and satellites in recent times. Our
main result is that the BIE position alternates
between a southern and a
northern position followed by Gulf Stream Beats (GSBs) at the occ
urrence of
deep solar minima. We decompose the low frequency BIE position variations
in cycles composed of dominant periods which are related to the Jose period
of 179 years, indicating planetary forcings. We propose that the mechanism
transferring planeta
ry signals into changes in BIE position is the solar wind
(SW), which provides magnetic shielding of the Earth in addition to geo-
magnetic disturbances. Increase in the solar wind produces pressure which de-
celerates the Earth’s rotation. It also transfers electrical energy to the ring cur-
rent in the earth’s magnetosphere. This current magnetizes the earth’s solid
core and makes it rotate faster. To conserve angular momentum the earth’s
outer fluid mantle rotates slower with a delay of about 100 years. In add
will geomagnetic storms, initiated by solar coronal mass ejections (CMEs) pe-
netrate deep in the Earth’s atmosphere and change pressure pattern in the Arc-
tic. This effect is larger during solar minima since the magnetic shielding then
is reduced. The
Arctic may then experience local warming. The transition of
solar activities to a possibly
deep and long minimum in the present century
may indicate Arctic cooling and the BIE moving south th
is century. For the
North Atlantic region, effects of the BIE expanding southward will have noti-
ceable consequences for the ocean bio-production from about 2040.
How to cite this paper:
Solheim, J.-E
-Petersen, S., Humlum, O. and Mörner,
.-A. (2021)
Changes in Barents Sea Ice
Edge Positions in the Last 442 Years. Part 2:
Sun, Moon and Planets
International Jou
nal of Astronomy and Astrophysics
April 26, 2021
June 26, 2021
June 29, 2021
Copyright © 20
21 by author(s) and
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
Open Access
J.-E. Solheim et al.
10.4236/ijaa.2021.112015 280
International Journal of Astronomy and Astrophysics
Barents Sea Ice Edge Position, Cyclic and Non-Linear Changes, Lunar and
Solar Forcing, Planetary Orbit Synchronization
1. Introduction
The Arctic ice cover is a particularly important factor for the Earth’s climate.
Expanding ice cover leads to severe living-conditions for aquatic and land re-
lated life in the region. Diminishing and thinning ice cover has increased the to-
tal phytoplankton and ice-algae production with increased secondary produc-
tion (herbivorous zooplankters) followed by an increase in fish and mammal
stocks. The seasonal and decadal climate changes have a larger amplitude in the
Arctic than elsewhere, wherefore climate trends and shifts may potentially be
easier discovered. However, the amplitude of chaotic noise is also larger and may
mask the underlying pattern.
1.1. Background
The ice cover is modulated by several forces as described in our first paper [1].
The temperature difference between the warm equator regions and the cold po-
lar regions is the prime driving force for the global weather patterns. Heat from
the equator regions is transported towards the poles by advection in the atmos-
phere and by ocean currents. The source of the heat is the Sun. If radiation from
the Sun is diminished by less solar energy production or absorbed and reflected
én route to the surface or atmosphere of the Earth, by aerosols or increasing
clouds, ice and snow, the result will be less heat transport to the Arctic and a
larger ice cover.
The Barents Sea (BS) is an Arctic shelf sea with partly ice-free ocean during
winter in the present climate (Figure 1). The northward flowing Atlantic Water
(AW) that keeps the BS partly ice-free, also keeps the Greenland Sea mostly
ice-free during winter. These regions provided the first observations of decad-
al-scale oscillations in the air-ice-ocean system [2]. Warm AW is entering the
shallow BS through the Barents Sea Opening (BSO) or the Fram Strait (FS) via
the West Spitzbergen Current (WSC) [3] [4]. The AW heat flow into FS is twice
as big in the winter as in the summer, with an estimated heat flow into FS vary-
ing from 28 TW in summer to 46 TW in the winter. The heat transport to BS via
BSO is steadier, about 70 TW [5]. A rapid warming in the Eastern FS has re-
sulted in a temperature increase of ≈2˚C ocean temperature since about 1850
and a temperature > 1.5˚C higher than in the Medieval Climate Anomaly
(MCA) [6].
In glacial times when the BS was covered by a grounded ice sheet, reducing
the inflow of AW through the BS, most of the northward flowing AW would
have entered the Arctic Ocean through the FS [7]. However, the warm and salty
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Figure 1. Barents Sea map with depth contours. Circulation of the main water masses is
depicted by the arrows (Atlantic water: red; Arctic water: blue; Norwegian Coastal Cur-
rent: green; Barents Sea Waters: purple). Polar Front: PF, (solid line); BSO: Barents Sea
Opening; Ø KS: Kola section; SBD: Svalbard; FJL: Frans Josef Land; FS: Fram Strait; Isfj:
Isfjorden; H; Hornsund; L: Longyearbyen (modified from Oziel
et al.
AW is heavier than the fresh water on the surface, which keeps freezing water
temperature in the upper 80 to 100 m [8]. Only in areas with upwelling of AW
along the ice edges with wind from northeast and along the shelf break [9] can
the AW heat result in melting ice. Fridtjof Nansen [10] observed during his
crossings of the Artic Basin that the Sun melted ice from the top while it was still
freezing at the bottom in June. We should therefore expect that solar variations
should be detectable in the BIE position variations.
Ikeda [2] suggested a positive feedback to oscillations driven by a weak exter-
nal forcing as the solar activity. The feedback mechanism worked like this: “the
increased cyclonic wind-stress curl associated with the atmospheric circulation
enhances the exchange of cold Arctic water, including sea ice, and warm Atlantic
water, and reduces the amount of Barents Sea ice. The reduced ice cover encou-
rages heat flux from the Barents Sea to the atmosphere, tending to reinforce the
low pressure in the Arctic.” This we may call the wind-mechanism.
1.2. Hypothesis
A review of potential long-period forcings on the sea ice cover is presented in
[1]. Our hypothesis is that cyclic changes in movement of the Sun in its bary-
centric orbit due to the planets, will be transmitted to the Earth as fluctuations in
insolation and in the solar wind, and be identified in climatic patterns as shown
in [1] Figure 91. In addition to solar energy effects, we have also investigated the
effects of short-term perturbations of the Sun’s orbit by the planets. A high fre-
quency signal from the planets will most likely disappear in the rapid changing
1This is a reference to Figure 1 in [1].
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and at times chaotic weather-pattern, but low frequency fluctuations may sur-
vive as climate modulations. This underscores the importance of long, homoge-
neous, time series.
In this paper we present an analysis of a time-series of BIE yearly positions,
obtained from ship logbooks, scientific reports, aerial surveys, and satellite ob-
servations updated from [9]. The observations cover a period of 442 years, with
completeness increasing from 34 to 66 per cent per century from the beginning
in 1579. The position estimates refer to the summer ice position during the last
two weeks of August between the Svalbard archipelago and Frans Josef land,
which is named the Western Barents Sea. The data set is unique in the sense that
it covers the two last grand solar minima, the Maunder Minimum (1640-1720)
and the Dalton Minimum (1790-1820) [12], in addition to the coldest decade
(1690-1700) in the last millennium in the Northern Hemisphere [13]. During
grand solar minima the BIE position frequently has been southernly at 76˚N la-
titude. This corresponds to periods with stronger cold Arctic water currents.
This weakens the warm AW transport to the Arctic and may result in the Gulf
Stream beat (GSB) between two branchesthe northern or southern branch
[14] as illustrated in [1] Figure 1.
We investigate the hypothesis that there is a stable or stationary signal from
the planets which synchronize the natural oscillations of the position of BIE. If a
prolonged low position is reached, the GSB switches to the southern mode (type
b and c in [1] Figure 5) leading to a cold climate in the North Atlantic region.
Our main hypothesis is that this is related to the solar wind (SW) acting on the
rotation speed of the Earth making measurable changes in the length of day
(LOD). Our starting hypothesis is that the beat itself originates in the switch be-
tween Earth rotation acceleration during solar minima and deceleration during
solar maxima [1] Figure 4.
We compare the BIE positions with other climatic and solar time series and
investigate phase relations. An identical phase indicates identical forcing, differ-
ent phases may give a clue to what may be cause and effect. We find that the BIE
position changes in concert with NH-climate in phase with long solar cycles and
the Jose planetary cycles. The BIE movement north was rapid after the deep
Maunder Minimum, but slow after the Dalton minimum, using more than a
century to gather momentum. This may be explained by a “tired Sun” in the
1800s, after high activity in the 1700s, related to a bicentennial cycle [15].
1.3. Organization of the Paper
The structure of this paper is as follows: We describe the BIE data set in Section
2. In Section 3 we analyze the data and search for fingerprints. Then in Section 4
we compare with other climate data sets. In Section 5 we compare with orbital,
solar and lunar forcings; in Section 6 we investigate signs of planetary influence.
In Section 7 we have a discussion, and finally the conclusion in Section 8. In Ta-
ble 1 we present a list of acronyms and explain some of them.
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International Journal of Astronomy and Astrophysics
Table 1. Acronyms and explanations.
Geomagnetic activity index: difference
between two antipodal geomagnetic observatories
GCR Galactic cosmic rays: particles
from exploding stars
NH-SST Northern Hemisphere sea surface
ACRIM Active Cavity Radiometer Irradiance
Monitor: series of satellites measuring TSI
Hale Solar magnetic period:
about 22 years (SH)
Nyquist-Shannon sampling theorem:
limit for frequencies
ACSYS Arctic climate system studies INAO Integrated NAO P04 Period 04: program for harmonic
periods analysis
AMO Atlantic multidecadal oscillation: A
sea surface temperature index for the North Atlantic
Insolation: radiation energy received
from the Sun
QBO Quasi-biennial oscillation: a tropical,
downward propagating zonal wind
ArcT Arctic land temperature: from stations
north of 60˚N INAO Integrated NAO SC Solar cycle
AW Atlantic water IZI Integrated ZI SCL Solar cycle length
BIE Barents Sea ice edge: positions in last part
of August
Jose Period of 179 years: a common period
for many of the solar system planets (PJo) SIM Sun inertial motion
BS Barents Sea KolaT Kola section sea temperatures
0 - 200 m depth SMM/I Special Sensor Microwave/Imager
BSO Barents Sea opening LIA Little ice age: cold period
CE 1350 - 1850 (1900 in Arctic)
SSMIS Special Sensor Microwave
CE Common Era, secular equivalent of AD anno
Domini LIG latitudinal insolation gradient SMMR Scanning Multichannel
Microwave Radiometer
CET Central England temperature series LOD change of the length of day (ms/year) SN Sunspot number (
CME Coronal mass ejection: burst of plasma
from the solar corona
MCA Medieval climate anomaly:
a warm climate period about 1000 CE SST Sea surface temperature
Coif3 Wavelet function for time series analysis Morlet wavelet function for time series analysis
SW Solar wind
DMSP Defence meteorological satellite program
NAO The North Atlantic Oscillation: Index of
atmospheric pressure difference at sea level
between the Icelandic Low and the Azores High
SWS Solar Wind Speed
Ekman transport: water transported to the right
angle of the wind direction in the NH hemisphere
NB Northern Branch: northern branch of the
Gulf Stream also called the Norwegian Current TSI Total solar insolation
FS Fram Strait NDSIDC National Snow and
Ice Data Center, Boulder, USA
VLBI Very long baseline
inter-ferometry(radio astronomy)
FT Fourier transform: converting time series
to frequencies NH Northern Hemisphere WSC West Spitsbergen Current
GSB Gulf stream beat: a change between
northern and southern branch of Gulf stream
ZI Zonal wind index: pressure difference
between 35˚N and 55˚N
2. The BIE-Data
The Arctic seas were for a long time a terra incognito for European sea travelers,
but the wish to find an eastern sea route north of the Eurasian continent led to
expeditions which found rich animal life at the edge of the sea ice, and hunters
went north. The English Muscovy Company was founded as early as 1555,
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International Journal of Astronomy and Astrophysics
opening trade with Russia via Archangel. Around 1580 the Dutch joined the
White Sea trade and became frequent travelers in the area. The whale-hunting
north of Svalbard became a profitable industry which occupied many ships from
the middle of the 17th century [1] (Figure 14 and Section 7.1.) This resulted in
information about sea-ice conditions. Most whaling took place in late summer.
A time series of the estimated position of the August ice edge in the sector
between 20˚E and 45˚E, covering the western Barents Sea between Svalbard and
Frans Josef Land (Figure 2) was collected and presented by Torgny Vinje [16].
The ice edge position was based on ship-logs before 1900, from whalers and seal
hunters who systematically observed and logged sea-ice conditions and ice edge
locations. Small islands that appeared or disappeared due to variations in sea ice
extent helped in locating the position of the ice edge. Whaling was first a Dutch
industry, but also English and French hunters participated. These observations
are the base for the ice edge location estimates before 1800.
After 1800 data came from Norwegian trappers who then started wintering on
the islands of the Svalbard archipelago, with annual seal-hunting along the ice
edge between Denmark Strait and Novaya Zemlya from 1853. Information on
the ice conditions around Svalbard 1850-1922 were collected by Prof. Otto Sver-
drup and Capt. A. Hermansen from altogether 285 ship-logs in connection with
planning of coal shipping from Spitsbergen [17]. Since then, Norwegian Polar
Figure 2. The BIE position 1579-2020. From 1979 the ice edge is defined as 15% median
value of ice.
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Institute has collected information from all kinds of shipping activities in the
area. After about 1950 ice-maps were made from observations by US, Russian
and Norwegian airplanes. Images from US satellites were included from 1966.
The data have been supplemented from other sources, quality controlled, and
made available in ACSYS historical Ice Chart Archive [18] as monthly or yearly
ice charts. In this series the ice edge is defined as the outer boundary reported by
sealers or whalers, which is estimated to be about 30% ice covered. In the optical
image satellite period, the edge was defined as >10% ice coverage. From 1979
data from satellite microwave sensors were available [18]. The minimum sea-ice
extent (August-September), is calculated using monthly mean sea-ice concentra-
tion from the National Snow and Ice Data Center (NSIDC) [19]. This data set is
generated from satellite-based, brightness temperature data derived from the
following sensors: Nimbus-7 Scanning Multichannel Microwave Radiometer
(SMMR), the Defense Meteorological Satellite Program (DMSP)-F8, -F11 and
-F13 Special Sensor Microwave/Imagers (SSM/I) and the DMSP-F17 Special
Sensor Microwave Imager/Sounder (SSMIS). These data are provided in the po-
lar stereographic projection at a grid cell size of 25 × 25 km for the period
The recent version of the passive microwave data set [20] determines the rela-
tive ice area pixelwise and defines the ice edge as the median value of pixels with
more than 15% of ice. We have used the average position of the ice edge in the
two last weeks of August to compare with historical data.
The ice cover is determined with automated algorithms which classify types of
ice and open water [21]. However, in the summer melting season temporary
melt-water-pools may appear on the surface of sea ice, and this may lead to sys-
tematic underestimates of the ice area. In an attempt to recalibrate pre-satellite
Arctic ice cover data sets, to fit with the satellite observations, the average annual
ice-covered area had to be reduced with ~1.5 mill∙km2 (or ~11%) before 1979
[22]. For the BIE positions (Figure 2) the lower latitude of 76˚N seems to be a
common minimum for 300 years and is probably a natural limit. The northern
limits have been more variable.
2.1. A Revised BIE Data Set
An updated and revised version of the data set was published by Falk-Petersen
[9]. In this set, updated positions from satellite maps were used from 1996. In
the revision presented in this paper, old data have been corrected and the series
has been updated including 2020. It was discovered that in some cases data were
extrapolated from adjacent areas (seas) or from other months. These data have
been deleted. Our revised data set (Figure 2) has passive satellite radiometer
measurements from 1979.
Comparing the old and new data from the overlapping period 1977-90
(Figure 3), we find that there is a systematic position difference of +1.2˚N for
the revised part of the BIE data set. We have not corrected for this difference in
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Figure 3. BIE position data 1952-2020. This revised version (red) and overlapping part of
earlier version (blue) before satellite microwave sensor data was used for the period
1979-1996. The black bars are trend lines for the two last decades.
the data before 1977 since the difference is of the same order as the uncertainty
of the data.
The estimated ice edge positions (Figure 2) vary between 75.5˚N (1616,
1667-68) and 83.35˚N (2013). The data show two long latitudinal minima
1625-1662 and 1785-1812. The first corresponds to the early part of the solar
Maunder Minimum 1640-1720 and the second to the beginning of the Dalton
Minimum 1790-1820. However, several times between 1660 and 1710 we find ice
edge estimates north of 80˚N. From 1850 the ice edge is almost always north of
78˚N, except in the period 1902-17. After 1990 the August ice edge has always
been north of 80˚N, except in 2003. The data show no trend in the last 10 years
with an average value of 82.5 N.
2.2. BIE Position Data Coverage
The first 402 years of the series have many missing data points. From 1579 to
1678 the coverage is 39 per cent. For the next hundred years 1679-1778 the cov-
erage is only 34 per cent, and there is a large gap 1708-22. The last part of the
1600s was the coldest in Europe in the Little ice age (LIA) [1] (see Figure 12),
and several strong storms destroyed many ships in the Netherlands, where most
whalers came from [23], and, presumably, fewer ships were then able to obtain
observations for some years.
For the whaling in the Arctic most Dutch ships gathered in the deeper part of
the Waddenzee near the coast of the island of Vlieland. Here the ships were rea-
died for the whaling expeditions and waited for a favorable wind to be able to
cross the North Sea. The Dutch whaling ships were not able to cruise against the
wind. When the wind came from the north and northwest they had to waitoften
many weeks, sometimes months [24].
From 1779-1878 the coverage improved to 58% and in the following hundred
years to 66%. From 1979 we have 100 per cent coverage due to the use of satellite
passive radiometer microwave measurements. In total we have 238 data points
spanning 442 years, or an average coverage of 54%.
In Figure 4 we show the distribution of ice edge position estimates for four
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Figure 4. Distribution of BIE position estimates in half degree bins for four centuries.
The distribution is binominal with one peak around 76˚N and one between
79˚N and 80˚N. This is true for all centuriesexcept for the 1800s with a single
peak in the distribution at 77.5˚N. Comparing the extreme values with the map
in Figure 1, we find that when the BIE position is 76˚N - 77.5˚N, then the east
coast of Spitzbergen is ice covered. When it is 80˚N - 82˚N the entire northern
and eastern coasts are ice free.
The binominal distribution suggests two semi-stable positions of the ice edge,
that may be related both to the inflow of warm AW on decadal and centennial
scale as well as the prevailing winds influencing the ice drift on a much shorter
scale. The vessel Fram’s drift (1893-1896), showed the existence of a wind-driven
polar ice drift from the Siberian shelf over the deepest part of the Arctic Ocean
through the FS [25].
In addition to the ice transport through the FS there is a substantial, but vari-
able, inflow of sea ice to the BS between Nordaustlandet (Svalbard) and Frans
Josef Land. The interannual variation of the sea ice extent in the BS can exceed
the annual variation [26]. This wind driven ice drift can further be transported
up the west coast of Spitsbergen with the cold East Spitsbergen Current [27] as
far north as Hornsund and Isfjorden.
The long-term variation in ice cover is related to GSBs [1] [28] and the vo-
lume and the temperature of the AW into the Arctic Ocean [29], while prevail-
ing winds affect the ice distribution on scales of days, months, years, and dec-
ades [25]. Prevailing easterly wind north of Spitsbergen and Frans Josef Land
will lead to an off-shelf Ekman transport of ice and surface water and upwelling
of warm AW along the shelf break and onto the shelf itself [9] [30]. A prevailing
northerly wind transports sea ice far south into the BS and up along the west
coast of Spitsbergen [25]. In his analysis T.Vinje [16] tried to separate wind- and
ocean effects and concluded “that the variation of ocean temperature and its
positive or negative correlation with wind direction seems to be of crucial im-
portance for the variation in the ice extent”.
When we compare the BIE-positions with a simple harmonic model based on
four significant periods (Figure 5), we find that the scatter in the observational
difference from the model is less than ±1.5 degrees after 1750, but considerably
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Figure 5. Residuals between BIE positions and a harmonic model.
more before this date. This may be due to higher intrinsic variability and/or less
precise estimates. It is also worth noting that the scatter is not reduced in the sa-
tellite era beginning in 1979. The two most positive deviating positions are in
1660 (+4.8 deg) and 1690 (+3.4 deg)in the coldest period in the Maunder
Minimum. The most negative deviations are in 1695 (−3.1 deg) and 1962 (−3.05
2.3. BIE Extreme Positions
The binominal nature of the data (Figure 3) derives from intervals with almost
stable positions, but with rapid changes in between (Figure 2). Our series starts
with positions around 79˚N in the years 1579-1608. The next year the position
moves to 76˚N and stays there until 1676, only with a few deviations: 1622
(80˚N), 1664 (82˚N) and 1671 (79˚N). In the period 1683-1707 the position is far
north (78.5˚N - 82.5˚N), with one exception: 1695 (76˚N).
We have a gap in the data 1708-1722, but from 1723 to 1780 the position is
generally far north, except for a dip in 1734-1743. It is again below 78˚N
1785-1839, except for the years 1802-1803 (78.4˚N). Then it moved north of
78˚N for most of the period 1844-1864, before a slow decline to a minimum at
76˚N 1909-1913 and moving north to a maximum of 81˚N in 1938-1939. Then,
we observe a short dip in 1962 (76.5˚N), before moving to a northern maximum
in 2013 (83.35˚N). The last decade (2011-2020) the trend is near zero with aver-
age position 82˚N. The previous decade the trend was slightly negative (Figure
3). However, there was a position jump from 2009 to 2013, creating a difference
of 0.7 degrees between the mean of the two decades. Since 1981 BIE has moved
north with an average of ≈0.5 degrees per decade.
The most extreme change of 7 degrees expansion south happened 1690-1695
in the coldest decade of the last millennium. The last large southern advance was
2013-2014 with 4.5 degrees.
3. AnalysisA Search for Fingerprints
The BIE position during the period 1579-2020 (Figure 2) can be described as
fairly stable around 79˚N before 1610, then a long minimum about 76˚N be-
tween 1620 and 1660. Then we have large variations 1660-1750, and a long
minimum around 77˚N 1780-1830. Then it went north for a few decades fol-
lowed by a period with much ice 1870-1915. Then the ice cover decreased until
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International Journal of Astronomy and Astrophysics
1940, followed by a period with a slight increase in ice cover until 1980. Then the
ice sheet again decreased. In this section we will analyze the spectra of the oscil-
lations and compare with expected periods as described in [1]. We search for
stable periods forced by external forces.
3.1. Harmonic Analysis
The program Period 04 (P04) [31] is developed to handle series of data with
gaps. With this program it is possible to delete false periods which appear due to
aliasing because of gaps. Frequencies determined by Discrete Fourier Transform
are fitted into the data in the time domain, by determination of phase and am-
plitude. Sinusoids are then subtracted from the observed time series, one at a
time manually. Amplitudes are evaluated against a false-alarm detection limit.
Significant periods are subtracted until one ends up with a white noise spectrum.
The first analysis with P04 gives four significant periods
) with ampli-
): (
): [(252 ± 7, 1.2); (490 ± 30, 1.0); (83 ± 1.0, 0.7) and (151
± 5, 0.6)], with a residual (least square error) of 1.19 degrees. These 4 periods are
harmonically related:
years, with
= 1/2, 1, 5/3 and 3. We define the
periods 500, 250 and 150 years as the centennial periods. In addition, we include
two weaker periods [(19.7, 0.40); (14.0, 0.38.)]. The result is shown in Figure 6.
The residual is now reduced to 1.12 degrees. However, the analysis of the
BIE-position series may contain errors because of increased noise before 1750
(Figure 4) and diverging edges because of a strong trend. The normal procedure
is therefore to detrend the time series before analyzing for periodic variations.
The time series contain three intervals with deep minima: around 1650, 1800
and 1900. We find that the series from 1579 to 1890 show a negligible trend
(−0.0009 deg/year) and from 1890-2020 a trend 0.035 deg/year. This means we
have a breakpoint around 1890.
Figure 7 shows the BIE-position series with these trends (a) and detrended
(b). In (c) a spectrum of the whole series detrended is shown and in (d) for the
period 1750-2020 only. Panel (c) shows the following significant periods and
amplitudes (
): [(176 ± 6, 0.73); (84.8 ± 1.6, 0.59); (245 ± 14, 0.55] in addition
to the following not-significant periods [22.3, 0.39; 13.9, 0.39]. A model position
curve based on these 5 periods and amplitudes is shown as a red curve in Figure
7(b). This model gives a residual 1.16 degrees. The same analysis of the BIE po-
sitions from 1750-2020 gave a spectrum shown in panel (d) with the following
significant periods: [(86 ± 2.5, 0.61); (20.2 ± 0.2, 0.44); (43.4 ± 0.9, 0.42), (120 ±
7, 0.36)]. A model based on these four periods is shown in blue in Figure 7(b).
The residual is now 0.97 degrees, verifying the improvement of the data after
1750. In these series all periods are related to the Jose period of
= 178.38 years
, with
= 3/2, 2, 4, and 9. This corresponds to the formulae found
for periods in the solar motion around the solar system barycenter by N. Scafetta
[32] (Equation (8)). We consider this as an argument for a solar-planetary con-
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Figure 6. Harmonic analysis of BIE positions with four significant periods (thick red line)
and two weaker periods (thin line).
Figure 7. (a) BIE-position series with zero trend 1579-1890, and a linear trend 1990-2020;
(b) BIE-position series detrended with the trends in (a); (c) Spectrum of the whole de-
trended series; (d) Spectrum of the detrended series 1750-2020. In (b) are also harmonic
models with 4 periods (blue) and 5 periods shown (red).
3.2. Morlet Wavelet Analysis and the 60-Year Period
Visual inspection of climate data series often suggests the existence of one or
several recurrent variations. However, describing the character (persistence, pe-
riod, and amplitude) of such cyclic patterns is difficult, as the variations quite
often come and go, lasting only for a limited period at each appearance. For this
reason, they may prove difficult to characterize fully from a normal Fourier
power spectrum. Especially the dynamics over time of the individual cycles, can
be difficult to analyze. However, despite such shortcomings, Fourier analysis
remains an extremely valuable tool for the identification of such recurrent natu-
ral climate variations.
To overcome the problem encountered when cyclic variations change their
period and amplitude, we here also employ wavelet analysis to identify and de-
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scribe oscillating variations in climate series as a supplement to the Fourier
analysis. Wavelet analyses can pick up even oscillations that last for a relatively
short time and change their phase between one appearance and the next. Thus,
wavelets transform represents an analysis tool well suited to the study of
non-stationary processes occurring over finite spatial and temporal domains.
Among other things, this technique is well suited to visualize the frequency con-
tent of a signal as it varies through time. Since its introduction by Jean Morlet
[33], wavelet analysis has gradually found application in several fields of
sciences, such as, e.g., seismic signal detection, turbulence, fractal research, etc.
By this, wavelet analysis is becoming a common tool for analyzing localized var-
iations of power within time series.
Many data series contain cyclic variations that are non-stationary, varying in
both amplitude and frequency over long periods of time, which makes identifi-
cation of such variations difficult. However, by decomposing time series into
time/frequency space by wavelet analysis, it becomes possible to extract infor-
mation on both the amplitude and variation over time of any periodic signal
within the series, but only for that part of the signal which can be decomposed
into sinusoidal components. An overall trend affecting the whole time series
considered will therefore not be identified by this technique. The resulting
wavelet diagram provides information on periodic behavior in the data series,
making it possible to determine both the dominant modes of variability and how
these modes vary with time. This, in turn, provides an important tool for under-
standing the nature of the main drivers behind observed cyclic variations of dif-
ferent phenomena.
Three types of wavelet types may be considered for analysis of time series: the
Paul-, the Gauss Deriv- and the Morlet wavelet. For a given count of evident os-
cillations in the wavelet, the Morlet offers the best frequency localization, the
Gauss Deriv wavelet is slightly less efficient, and the Paul wavelet is the least effi-
cient in this respect [34]. Here we chose to make use of the Morlet wavelet, be-
cause superior frequency localization is essential to determine the most likely
physical origin of the oscillations identified. At the same time, the Morlet wave-
let still provides good localization of the oscillations in the time domain.
To avoid wraparound effects that arise because of non-periodicity in both the
data and the response function (daughter wavelet), zero padding is needed equal
to the half the length of the non-zero elements in the daughter wavelet's fre-
quency response. Usually, zero padding to twice the data length, ensures that no
wraparound effects are possible anywhere in the spectrum. Sufficient zero pad-
ding wraparound effects are eliminated but a different issue then arises, as it is
likely that a discontinuity is introduced at the end of the data series. This zone of
edge effects is known as the cone of influence, outside which spectral informa-
tion is not likely to be as accurate regardless of whether zero padding is used.
Here we used zero padding and computed the cone of influence using e-folding
distances as described by [35].
In general, according to the Nyquist-Shannon sampling theorem [36] only
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frequencies lower than
should be considered in the analysis, where
representing the sampling frequency. As an example, for data series representing
annual values, only frequencies lower than 0.5 yr−1 should be considered, cor-
responding to periods longer than two years.
The results of a Morlet wavelet analysis of the BIE position series are shown in
Figure 8. The first impression is that no stable short periods are present inside
the cone of influence. The closest to stable periods are a cluster of periods be-
tween 14 and 20 years, which fades away after 1900. This is most likely the
14-year period detected in the P04-analysis. A 33-year period is present from the
beginning until about 1850. A 60-year period is present through the whole se-
ries, just outside the cone of influence. Before 1800 we observe the 60-year cycle
with harmonics 30, 14.5, and 7.5 years. The harmonics pattern is a proof that the
60-year cycle is real in this period. After 1800 the 60-year period is still present,
but its harmonics disappear, except a 19.8-year period which appears after 1900.
When harmonics appear, this indicates that the basic period is strongly forced.
There is also a period P~104 years present through the whole series. This may
be the 104-year solar modulation potential (φ) period determined from cosmo-
genic radionuclides 10Be and 14C [37] and is a harmonic of the 208-year de Vries
cycle. The 33-year period may be a harmonic of this. The 60-year and 104-year
periods are indications of planetary and solar forcings.
3.3. Analysis with a coif3 Wavelet Function
The BIE position series have also been analyzed with a coif3 [38] [39] wavelet
function. This wavelet provides phase information and handles variable ampli-
tudes in contrast to the Morlet wavelet and the Fourier Transform analysis.
Figure 8. Morlet wavelet analysis based on de-trended data. The black, broken line de-
fines the cone of influence where most accurate periods are found.
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Missing yearly data points were provided by cubic spline interpolation. Figure 9
shows the wavelet power spectrum. The four high peaks and the valleys show the
extreme values of a bicentennial period: (
): [(1643,
), (1725,
) (1851,
), (1986,
)] where
means minimum and maximum values. The
valley bottoms represent the (+, 0) and (−, 0) phase times. The differences be-
tween the extreme values are half periods of duration 83, 126 and 135 years, in-
dicating a period of the order 200 years. In Figure 9 we also have peaks of a
sub-centennial period.
In Figure 10 we show O-C-diagrams for some of the dominating periods. In
this type of diagrams, we compare the phase with expected phase from a clock
running with a fixed frequency. If the observed period is the same as the
clock-period, we get a straight line parallel with the x-axes. If the period is con-
stant but different, we get a straight line in some other direction.
The top panel shows the bicentennial peaks relative P = 252 years clock pulses.
The O-C-diagram shows P = 145 years before 1740 and P = 266 years thereafter.
The lower panel shows that a sub-centennial period of 82 years has a stable
phase between 1670 and 1910, but then a phase shift takes place between 1910
Figure 9. Wavelet power spectrum of the BIE-series with values of peaks and valleys (provided by H. Yndestad [38]).
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Figure 10. O-C diagram for phase-points marked in the wavelet power spectra in Figure
9, shown relative clock pulses of P = 252 years for the bicentennial and P = 82 years for
the sub-centennial periods.
and 1940. The lack of stability before 1740 may be due to less precise observa-
tions (see also Figure 5). The phase shift between 1910 and 1940 may be related
to the rapid warming in this period.
3.4. Conclusions on the Fingerprint Search
The 268-year period is ~3PJo/2 and the 145 year period ~4PJo/5, which are signs
of planets.
Sub-harmonics of the 60-year cycle with periods 120, 240 and 480 years are
also detected, as predicted in [1] (see Figure 13 and Section 10.2), but not as do-
minant periods. The 82-year period is close to the basic solar period found by
[38]. We have detected signatures of the Sun and planets.
4. Comparison with Other Climate Data Sets
The BIE position is a result of many driving factors: The freezing of new ice
during the winter, the melting in the summer, the sea temperature, the strength
of the wind pattern, the solar activity, tidal effects from the Moon and the Sun,
and pollution by dust etc. In the following we present some linear correlations
based on data from the same year before we present some correlations based on
averaged data. Goodness of fit (
) explains how much of the variation can be
explained by the calculated linear relation.
4.1. Central England Temperature (CET) Series
The Central England surface air temperature series is the longest existing me-
teorological record based on thermometer readings. It is constructed from sta-
tions with a minimum urban heating [40] and updated by the Hadley Centre
Climate is defined from 30-year averages. Correlating 30-year averages of CET
and BIE positions we get the goodness of fit
= 0.79 as shown in Figure 11, left
panel, with the relation
= 3.62 * CET + 44.6˚N. This shorter data set was
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Figure 11. BIE positions compared with CET. The left panel shows the correlation be-
tween 30 years averaged values (1778-2018). The right panel shows 5-year running mean
of CET converted to latitude by the relation shown in the left panel (red) and the BIE po-
sitions (blue dots) 1659-2020.
selected because of being less noisy than earlier data. This relation was used to
convert 5 years running mean CET-values to BIE-latitudes in the right panel and
compared to BIE position estimates.
CET is decreasing from 1659 to 1695 during the coldest period in the LIA.
The CET and BIE positions follow quite well also on shorter time scales. A CET
peak in the 1680’ies corresponds to a BIE position 82.5˚N, and a sharp tempera-
ture drop in the 1690’ies to a rapid BIE expansion to 76˚N. The temperature
peak in the 1730’ies is followed by BIE retreat to almost 82˚N. A CET peak in
1830 is followed by BIE retreat in the 1840’ies etc.
4.2. Nordic Arctic Sector Summer Sea-Ice Coverage
From 1979 both the Arctic summer ice cover in the Nordic sector [22] and the
BIE position, have been estimated from satellite observations. In this period the
BIE position varied between 79˚N and 83˚N and the ice sheet area in the Nordic
Arctic sector between 1.5 and 1.0 Mkm2. We find a goodness
= 0.61. The cor-
relation is shown in Figure 12. Based on a linear least square relation between
the summer ice cover shown in the left panel, we show the best fit in the right
panel. The residual is flat curve, showing that the summer ice cover and August
ice-edge position are well correlated these 40 years. Also including summer ice
estimates with other methods back to 1900, gave
= 0.22, indicating less precise
However, the correlation between the Arctic summer temperature in the Nor-
dic sector and the ice edge position is poor (
= 0.08) for the period 1979-2015
and is reduced to
r2 =
0.03 when we include data back to 1900. This is because
the summer temperatures in the Arctic show small variations from year to year,
while the winter temperatures, and thereby annual temperatures, show large
variations. For the Nordic sector ice and Arctic summer temperature correla-
tions we have used data from a recalibration of Arctic ice extent by [22].
4.3. Correlations with Arctic Land and Sea Temperatures
Since BIE runs from Svalbard to Frans Josefs Land, we expect a correlation
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Figure 12. Correlation between the summer sea-ice area in the Nordic Arctic sector and
the position of BIE 1979-2015 (left). The right panel shows the summer sea-ice area (red)
and the BIE position (blue).
between the BIE position and Longyearbyen air temperatures [42] and Kola sec-
tion sea temperatures (KolaT) [43]. Longyearbyen is situated in a fjord on the
western coast of Svalbard where a branch of the AW keeps the coast ice free in
most winters (see Figure 1). The winter temperature is dependent of the winter
ice conditions. Longyearbyen temperature measurements are available from
1898. KolaT series were provided by the Polar Research Institute of Marine Fi-
sheries and Oceanography (PINRO), Murmansk, Russia [44]. The data used here
are yearly temperature values from the upper 200 m of the Kola section, along
the 33˚13.0'E meridian from 70˚13.0'N to 72˚13.0'N in the Barents Sea.
The relations are shown in Figure 13 panels (a) and (d). Both temperature se-
ries peaks around 1920 and 1930 and show a rise from mid 1980-ties, which fol-
lows the BIE position quite well. Correlation between BIE position and Lon-
gyearbyen temperature gives
= 0.48 and with the KolaT
= 0.29. The devel-
opment in KolaT follows the same trend as described for the BSO by [4] where
the increase in the temperature started in mid 1980ties. We have also compared
with Arctic and NH land-temperatures based on rural stations (Figure (b) & (c)
in [45]). The Arctic land mean temperature (ArcT) (North of the Arctic Circle)
was around 0˚C from 1830-1920, and then increased 3 degrees in 30 years. This
is well correlated with the BIE position (
= 0.55) (Figure 13 panel (b)). Also,
the Longyearbyen temperature, has a steep rise around 1920 and peaks in 1940
or 1950. The NH-land temperature (panel (c)) has the same steep rise around
1920 but peaks 10 years later than the Longyearbyen temperature and ArcT.
As the ocean is a main transporter of heat to the Arctic, we should expect a
correlation between the NH sea temperature and BIE position. The relation is
shown in Figure 13 panel (e). The correlation is the same as for the NH rural
temperature and somewhat lower than for Arctic land temperature. We interpret
this as the land stations and BIE have an equal or larger contribution from air-
borne heat flow, maybe related to solar variations (TSI or GCR-induced clouds).
The sea surface temperature measurement is quite variable before 1900 but
tracks the BIE-position quite well after 1900. It seems to give a better fit than the
KolaT (
= 0.44 versus
= 0.29). The KolaT peaks in 1935, about 10 years be-
fore the NH-SST. Table 2 shows a summary of the correlations.
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Figure 13. Correlations between temperature series (red lines) and BIE positions (blue
dots) based on yearly data. (a) Longyearbyen T; (b) ArcT; (c) NH rural stations; (d) Ko-
laT; (e) NH-SST.
Table 2. Summary of correlations with BIE position.
Series Years no.
CET 30years mean 1779-2018 8 0.89 3.62 * X + 44.6
CET yearly 1659-2018 285 0.37 0.98 * X + 69.6
Nordic sector summer ice 1979-2015 37 0.78 6.83 * X + 90.0
Nordic sector summer ice 1900-2015 90 0.46 7.66 * X + 89.9
Nordic sector summer temp 1979-2015 37 0.28 0.39 * X + 80.8
Nordic sector summer temp 1900-2015 90 0.18 0.50 * X + 79.5
Longyearbyen air temp 1899-2018 94 0.69 0.55 * X + 82.9
Arctic land temp 1832-2014 124 0.74 1.54 * X + 79.1
NH rural land temp 1883-2014 100 0.66 2.84 * X + 79.0
KolaT 1901-2014 89 0.54 1.67 * X + 79.7
NH-SST (HadCRUT3) 1850-2018 124 0.66 3.95 * X + 79.6
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4.4. Cyclic Variations after 1800
In [1] we proposed that external forcings work through Earth’s rate of rotation
(LOD) and by the ocean surface and atmosphere circulation [1] (see Figure 7
and Figure 9). In the following we will investigate the period and phase relations
between LOD, BIE and other climate series and investigate how BIE position se-
ries fit in the SW concept [46] and [1] (Section 9.5).
To compare the oscillating patterns, we have compared detrended and 11
years running mean values of BIE position (1800-2020), with KolaT (1900-2015)
[44], Arctic land temperature (ArcT) [45], AMO (1856-2018) [47], NAO
(1800-2018) [48] [49] and LOD [50] series. LOD is determined by observations,
mostly solar eclipses and occultation timings from ancient Babylonian, China,
and the Arab and European worlds through early telescope observations to
modern Very Long Baseline Interferometry (VLBI) observations after 1962 [50].
The BIE-positions have been detrended as shown in Figure 7 with a break in
1890. Since the BIE-series has many gaps of variable length, we have made run-
ning mean values based on 11 successive numbers. In the other series with yearly
values, we have calculated running mean of 11 yearly numbers. The result is
shown in Figure 14. The general impression is that all series, except NAO and
LOD, have maxima between 1930 and 1960, and minima 1900-1920, and 1960-1980.
NAO and LOD have maxima and minima some years earlier.
All the series show periodic variations 50 < P < 100 years. LOD, AMO and
NAO have periods 65 - 67 years. BIE has P~82 years with a phase shift between
1900 and 1950 (Figure 10). The KolaT P~77 years and ArcT P~82 years, are
closer to the BIE-period.
If we compare the dominating periods, we find the following phase shift se-
quence [-0] starting around 1900: LOD (1891) NAO (1902) ArcT (1914)
KolaT (1920) BIE (1921) AMO (1929). This may indicate LOD as driving
with NAO forcingresulting in ArcT, KolaT and BIE changing 15 - 30 years
later. In the next [-0] phase shift the sequence is slightly changed: LOD (1957)
NAO (1967) BIE (1980-90) ArcT (1996) AMO (1997). The sequence
again starts with LOD and NAO with the others 15 - 30 years later. Around 1850
the peak in BIE, ArcT and NAO are almost in phase.
The series have the following max values: LOD (1974) NAO (1983) KolaT
(2010?) BIE (2010-2020) AMO (2012) ArcT (2015 or later). The Lon-
gyearbyen temperature (not shown) lags BIE with ~5 years. The phase difference
LOD-NAO and LOD-negAMO is 0.3π, where neg means negative. This indi-
cates that LOD can be the driver of NAO and AMO, the most important period-
ic climate variations in the North Atlantic region. On the other hand, the BIE
position last century, is in antiphase with LOD 65-year period which has [0,-]
shift in 1926 and 1991, which is 5 or 3 years after BIE [-0] shifts.
The longer period Arctic temperature series (ArcT) has changed from being
in phase with LOD and NAO around 1850, to be in antiphase after 2000. The
opposite has happened with AMO and ArcT, which now are in phase. BIE posi-
tion and KolaT have gradually been phased to AMO.
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Figure 14. Oscillating pattern after detrending and 11 points running mean of (a) BIE
position; (b) KolaT; (c) ArcT; (d) AMO temperature index; and (e) NAO pressure index;
(f) LOD (not detrended).
The period pattern indicates decreasing BIE, AMO, ArcT and KolaT relative
the trends the next decades, while LOD and NAO are increasing. The next BIE
minimum relative the trend is about 2050. It should be remembered that a main
component responsible for the trend is the 268-year period found in Section 3.3.
This period had maximum in 1986 and is decreasing this century. A decreasing
KolaT is also predicted by [43].
4.5. The Stadium Wave Pattern
In the Stadium wave concept [1] [46] (see Section 9.5 and Appendix 1), various
periodic or quasi-periodic climate phenomena are found to vary in phase and
given membership in distinct temporal groups (TG). Anomaly of NHT, AMO,
negLOD and ArcT were all assigned to TG IV with maxima around 1938 and
1998. Cool Atlantic sea-surface temperatures (negAMO) correlated strongly
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with positive sea ice extent of the Greenland and Barents Seas. This means that
we should expect AMO in phase with BIE far north positions.
Our analyses (Figure 14) places AMO in TG I with maxima around 1945 and
2012 and NAO in TG II with maximum in 1983, while ArcT has a longer period
and moves from TG II in 1933 to TG I in 2015. It is now in phase with AMO.
Wyatt & Curry [46] analyzed boreal winter indices of NAO and the Arctic Os-
cillation (AO) and found that they behave differently from their yearly counter-
parts, and co-varied within TG II. We have used the yearly version of NAO in
our analysis. That may explain the difference.
The BIE position varies from TG III in 1938 to TG -I in 2011. This means that
the BIE position and ArcT are not at fixed positions in the Stadium wave but
moves relative to the pattern. Periods longer than the Stadium wave period may
be due to external forces as the Moon, Sun and planets as indicated in [1]. We
will explore this in Section 5.
4.6. BIE and NAO
When NAO is in its positive phase, the subtropical high-pressure center is
stronger than usual, and the Icelandic low-pressure center is deeper. The positive
phase is associated with stronger-than-average westerlies across mid-latitudes,
warm and wet winters in Northern Europe, dry winters in Southern Europe,
cold and dry winters in Northern Canada and Western Greenland, and mild and
wet winter conditions in Eastern USA. The negative phase is associated with the
opposite anomalies
A study of the ice edge anomaly and winter NAO-index by [51] demonstrated
a nearly anti-phase behavior indicating that positive NAO with increased north-
ern meridional circulation, promote a retreat of the ice cover. They found the
strongest NAO-effect on the ice cover in the Greenland Sea and western Barents
Sea with a correlation coefficient
= −0.5 to −0.6. The variations suggested
presence of a 60 - 80-year variability in the BIE position.
Vinje [16] investigated the relation between the change in NAO winter-index
) and the April ice extent and found a correlation
= −0.97 with in the
eastern area of the Nordic Sea. A sequence of southern winds (positive NAO
change) reduced the ice, while northern winds (negative NAO change) increased
the ice. For the western area he found a negative correlation
= −0.60, and for
the Newfoundland-Labrador area a positive correlation
= 0.61. This demon-
strated the “seesaw effect” between eastern and western areas [52].
et al.
[53] reported that the relationships between NAO and key
North Atlantic climate parameters like the sea surface temperature, surface air
temperature, and sea level pressure are not as stable as the accepted paradigm of
relations. For example, the ice-decline the last decades is accompanied with neg-
ative NAO-index, as demonstrated in Figure 14, while the ice-declines previous
decades have been accompanied with positive NAO-index and with high at-
mospheric cyclonicity. A possible interpretation of this reverse relation is that
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we are in the starting phase of a deep solar minimum.
4.7. Integrated Effects (LOD and INAO)
The detrended values for BIE position correlate with the detrended negLOD
(Figure 14). In [1] we have proposed LOD as the mechanism to transfer internal
and external forcings to the ocean surface and atmospheric circulation [1] (Fig-
ure 7). Since negLOD correlates with SST [54], it is a good candidate to transfer
the solar and planetary forcings to the Arctic ice cover by the geostrophic (zonal)
wind which is set up by the temperature difference between the tropics and
Earth’s poles. The temperature difference generates the pressure difference as
defined by NAO. The variation of wind speed (∆Ug) is related to the integrated
zonal index (IZI) or integrated NAO (INAO). Mazzarella and Scafetta [55] pro-
posed the following relation: IZI ~ INAO ~ ∆Ug ~ negLOD and showed that
SST was well correlated with INAO and negLOD, at least from 1840, and used
this to hindcast SST back to 1700. They assumed that the trend after 1840 also
was present before that date. This resulted in a SST temperature minimum 1.0˚C
- 1.5˚C colder than today [55].
In Figure 15 we show the linear least square fit of BIE position to INAO and
LOD for the period 1800-2018. The fit is quite good, except that INAO and BIE
are diverging after 2000 and LOD has a less steep trend after 1960. Hindcasting
before 1800 does not work since the trend in BIE then is zero as shown in Figure
The failure of hindcasting with respect to BIE position may be related to the
two negative GSB events 1687-1703 and 1808-1823, which has a period of posi-
tive GSB in between. The positive GSB 1703-1808 brings warm water to the
North Atlantic and may push BIE north.
Figure 15. 11-Point running mean BIE position (black), INAO (top, red) and negLOD
(bottom, red).
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4.8. Summary of Oscillating and Integrated Internal Effects
The strong correlations between the BIE position and other climate parameters
as the Nordic Sector summer ice, Longyearbyen air temperature, ArcT, NH-SST
and KolaT, show that the BIE position is related to other regional climate fac-
tors. The most important observation is the near linear change in BIE position
from 1900 (
= 0.61). The trend before 1900 is near zero. This may be an effect
of the GSB events 1676-1703 and 1808-1821.
Compared to cyclic changes after 1800 in the Stadium wave 60-year period
group, AMO, NAO, and LOD show the same periods, with AMO in antiphase of
LOD and NAO. BIE position, KolaT and ArcT oscillate with a longer period, but
with the same phase. However, the difference in periods means that the phase
similarity is only temporal.
INAO is clearly in antiphase with LOD. Both correlate well with BIE position
and have linear trends after 1800.
5. Forcing by the Sun and the Moon
The Arctic ice cover shows dramatic changes during the year. The major reason
for ice and snow melting in the summer season is the presence of the Sun. When
the first rays from the Sun hit the ice edge after the long period of no Sun in the
winter, ice melting starts, first slow, then fasteruntil minimum ice is reached at
the end of August or early September, when cold nights again start the freezing
cycle. It is important to notice that the melting season starts when temperature
rise above −5˚C. The yearly cycle is clearly a function of how the solar insolation
changes during the year.
In addition to direct solar insolation the ice cover is also modified by the in-
flux of warm Atlantic water which heats the Arctic atmosphere. A simulation
with the forced global ocean model NorESM20CR, aided by hydrographic ob-
servations shows a poleward ocean heat transport last century of 68 TW, with
typical variations 40 TW over time scales 5 - 10 years, due to thermohaline and
wind stress forcings [56]. In the model simulations 45 TW entered through BSO
and 15 TW through the FS. The rest of the heat transport came through the Da-
vis and Bering straits. The observed heat transport through BSO is about 70 TW,
and the seasonal difference is small, with a winter volume transport of 1.7 Sv and
a summer mean of 1.3 Sv.
Since the insolation changes with Earth’s orbit and the solar energy output va-
ries with solar cycles, we may expect that the BIE position mirrors solar and or-
bital variation. This is also true for the ocean currents which transport heat from
tropical oceans with a delay of decades. We may therefore expect both direct so-
lar signals and solar signals with short and long delays. In the following we will
take a closer look at orbital and solar variations, and, in Section 6, investigate if
there are relations to the orbits of the planets.
5.1. Orbital Forcing (The Milanković Cycles)
There are three orbital forcings: the change of ellipticity, axial inclination and
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orbital precession. Figure 16 shows the integrated total summer insolation
(ITSI) during the summer at 60˚N during the last 13,000 years [57]. The summer
season is defined as the time between spring and autumn equinoxes. The de-
crease in insolation from the Holocene maximum until recent times is about
6.2% and is mainly due the change in obliquity. The wiggle in the curve (Figure
16) is due to the perturbation in the distance to the Sun because of the 18.6 years
lunar nodal precession period.
The reduction in ITSI from the Holocene Maximum in Figure 16 corresponds
to a reduction in ocean surface temperatures of about 4˚C - 5˚C to a LIA mini-
mum between 550 and 250 cal years BP, determined from high-resolution sedi-
ment cores from the Vøring Plateau in the Norwegian Sea at 67
N [58] as shown
in Figure 17.
Biochemical proxy records from Icelandic lake sediments show the same evo-
lution, a millennium scale cooling after the Holocene warm period, a ~0.5˚C
summer cooling the first millennium, with stronger cooling starting ~1450 CE,
reaching maximum cooling of 1˚C shortly after 1850 CE. Model simulations
with CESM1.1 state-of-the-art global climate model show Arctic-wide cooling
from 1 CE to 1900 CE and a following sharp rise in temperature, the Medieval
warm episode from 950 CE to 1250 CE, the LIA 1300-1850 CE and abrupt cool-
ing in response to major explosive eruptions [59].
Figure 16. Integrated daily insolation for the astronomical summer at 60˚N for a con-
stant Sun and no atmospheric absorption (calculated by R.G. Cionco [57]).
Figure 17. Reconstructed SST for the Vøring Plateau at 67˚N in the Nordic Sea based on
high-resolution sediment cores (modified from [58]).
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At the BIE average position 78˚N we can study the difference in TSI at the NH
vernal and autumn equinoxes and summer solstice in Figure 18. The top panel
shows the reduction of TSI at summer solstice. This is an effect of the reduction
of the Earth’s axial tilt. This is partly compensated for in the spring, due to the
precession effect moving the Earth’s perihelion closer to the vernal equinox. The
lower panel shows the difference in TSI at the equinoxes. During the last 2000
years, TSI has increased at the vernal equinox, while it has declined at the au-
tumn equinox. From 1242 CE, when perihelion was aligned with the winter sols-
tice, it has advanced about two weeks to the first week of January. From then on,
the spring TSI is larger than the autumn TSI. This results in increased insolation
at the start of the melting season. Since the ice is 0.7 - 0.8 and open sea albedo is
less than 0.1, this means a huge change in the ability to absorb sunlight and ear-
lier melting of the ice and warming the sea. We may call this an Early spring ef-
fect [54]. This may be the main reason for the general movement of BIE to the
In situ measurements of solar and ground radiation on an expedition [26] to
81˚N shows solar insolation as high as 400 W/m2 at clear sky during the Arctic
summer, which means a transmission of almost 78%, while the average insola-
tion was of the order 100 - 200 W/m2 due to mostly cloudy conditions. The
longwave radiation was approximately −50 W/m2 during the expedition period.
With more open water during the melting season, more evaporation creates
more local clouds as the melting season develops. This means that the melting by
direct sunlight is more effective early in the spring.
5.2. The Equator-to-Pole Temperature Distribution and the
Latitudinal Insolation Gradient
The current annually averaged equator-to-pole temperature difference is about
Figure 18. TSI at summer solstice (top panel: red) and TSI at spring (green) and autumn
(black) equinoxes (lower panel) at 78˚N latitude. This is for a constant Sun (calculated by
Rodolfo G. Cionco [57]).
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40˚C. In the absence of dynamic transport this would have been about 100˚C
[60]. The atmospheric heat transport is believed to arise from baroclinic instabil-
ity, which again depends on the intensity of the Hadley circulation [61] (see Fig-
ure 8).
The difference in solar energy at low and high latitudes drives the climate sys-
tem on planetary scale through both atmospheric and oceanic different heat sto-
rage and release mechanisms. This has its origin in the difference in insolation at
different latitudes. The insolation received depends on the height of the Sun rel-
ative to the horizon and the Sun’s magnetic activity level. This changes with the
Earth’s orbit during the year and with the Milanković cycles and are demon-
strated in Figure 16 and Figure 18 for a constant Sun.
The temperature difference between latitudes originates in the latitudinal in-
solation gradient (LIG). The variation of LIG throughout the Holocene is calcu-
lated by [57] for low and high [62] frequency variations. LIG for the latitude dif-
ference 30˚N and 78˚N with variable solar TSI is shown in Figure 19. There are
at least sixteen different estimates for TSI since the 19th century and a few for
earlier periods [63]. For this work we have selected an estimate by [64], based on
the ACRIM reconstructions [65]. The green and red curves show the insolation
difference for spring (solar longitude 0 - 90 deg) and summer (solar longitude 90
- 180 deg), where the solar longitude is measured along the ecliptic from the
vernal point. Increasing LIG means stronger temperature gradient and stronger
wind forcing for moving air eddies and sea currents. The effect of steeper LIG in
the spring, means more advection of warm and humid air to the BIE, and earlier
start of the melting season. This is an important contribution to the BIE north-
ward displacement.
5.3. BiE and TSI Correlations
The Earth’s slow orbital variations lead to changes on centennial and millennial
time scales in the decreasing integrated TSI (black curve for constant solar out-
put) in Figure 20. A wiggle in the curve is due to perturbations from the lunar
Figure 19. The average daily latitude insolation difference (LIG) between 30˚ and 78˚N
for the spring period (green) and the summer (red). A TSI reconstruction by [64] based
on ACCRIM observations [65] is used for the calculation by R.G. Cionco [66].
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Figure 20. Integrated total summer (solar latitude 0 - 180 deg) insolation at 78˚N. The
black curve is for a constant Sun. The red curve is estimated TSI ACRIM-calibrated [64]
(calculated by R. G. Cionco [57]).
nodal cycle with a period of 18.63 years. In the same figure is drawn a red curve
which is the changing TSI due to solar magnetic activity. The wiggle in this
curve is due to the 11-year solar activity cycle, which is related to the 22 years
solar magnetic cycle, the Hale cycle. The downward trend due to the obliquity
change is more than compensated from the deep minimum 1650-1700 CE by the
increasing solar activity. It also tells us that the next deep solar minima may
produce less summer insolation than the previous due to the downward trend in
orbital variation (the grey curve).
Understanding the influence of solar variability on Earth’s climate requires
knowledge of solar variability, solar-terrestrial interactions and mechanisms de-
termining the response of the Earth’s climate system. A summary is given by
[67] and possible relations with solar cycles and BIE periods are discussed in [1]
(see Section 8.1).
The summer season melting power depends on atmospheric transparency,
clouds, and albedo. If we calculate insolation with 40% transmission and albedo
of 0.8 we get 440 MJ/m2 solar insolation available for melting in the summer.
The heat necessary to melt 1 kg ice is 0.334 MJ, which means that the available
insolation melts 1300 kg/m2 or 1.3 m thickness of ice. This should be sufficient
to melt the ice at 78 N each summer. The increase in insolation from 1690 to
2000 is about 0.5%, which translate to 6 mm more ice melted. An amplification
is therefore clearly needed to explain the increased melting from 76 N to 83 N. A
reduction of albedo by 0.1 and the cloud cover with 0.1, would nearly double the
summer melting. Comparing with 70 TW heat entering BSO by ocean currents:
insolation in the summer season with albedo 0.8 provides 38 TW for melting ice
with albedo 0.8 or 170 TW for heating open ocean with albedo 0.1producing
warm air or warm surface water which again melts ice. One should also remem-
ber that on top of the sea ice cover is a layer of snow, which also needs to be
melted before the ice-melting starts [68].
How the drift-ice is melting is described by [10] in the drawing shown as Fig-
ure 21. The Sun melts ice floats from the top, where freshwater melting-pools
absorb heat from the Sun and accelerate the melting. Solar irradiation also heats
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Figure 21. Ice melting off the East Coast of Greenland in 1882 (F. Nansen [10]).
the upper part of the sea which provide melting at sea level. At the same time the
temperature in the fresh top level sea water is below freezing and the ice float
grows in the deeper layerseven in the month of June when the insolation is
In Figure 22 we present correlations between two estimated TSI-series and
the observed BIE-positions. The top panel shows the correlation between the
summer insolation at 78˚N and BIE position. The peaks at 1750, 1850 and 1950
are well correlated, but the minima are not as deep and flat in the TSI-series as in
the BIE-observations. In the Hoyt-Schatten-ACRIM reconstruction [69] (lower
panel), the peaks fit better and the minima around 1800, 1900 and 1960 are bet-
ter reproduced. In both TSI reconstructions the BIE position is too far north af-
ter 2000 CE. We also notice that the correlation is much better for the
TSI-HS-record starting 1700 CE. Table 3 shows the correlations between TSI
and BIE positions.
The TSI-HS series also shows a high correlation with the Arctic and NH tem-
peratures (see [1] Figure 18) and both series show planet-related periods [32]. It
must be mentioned that the TSI reconstructions in Figure 22 are only two of at
least 16 various reconstructions presented and evaluated in [63].
5.4. BIE and Sunspot Cycle Length (SCL)
Another indication of the solar connection is the high correlation (
between SCL (low pass filtered with L12221) and the normalized mean of BIE
position in the first version of the BIE data set [70]. The low pass filtering means
that only periods longer than 30 years are investigated. They concluded that the
good fit between solar cycle length and BIE position was lost at the end of the
20th century and interpreted this as a possible sign of the appearance of another
forcing as for instance anthropogenic warming.
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Figure 22. Correlations between solar insolation and BIE position. The top panel shows
summer insolation at 78˚N based on the [64] TSI-estimates and the lower panel Hoyt-Schatten
TSI recently revised and updated by satellite observations [65]. (a) TSI-78N; (b) TSI-HS.
Table 3. Correlations with BIE positions.
Series period no. data
TSI78N 1579-2018 236 0.23 1.688 * X − 499.8
TSI-HS 1706-2018 191 0.41 0.967 * X − 1236.3
We have correlated the L12221 filtered updated SCL-series with the revised
BIE data set (11 points mean), shown in Figure 23, left panel. The goodness is
. Periods with long solar cycles correspond to BIE positions south and
short solar cycles to less ice. From 1950 the SCL-trend has shifted to longer solar
cycles and the BIE position followed until 1980, but thereafter the BIE position is
north of what is expected from the SCL-relation. The high correlation indicates a
possible low frequency relation between solar activity and the BIE position.
et al.
[71] found a correlation between the length of the previous solar
cycle and the mean temperature in the next cycle for certain observing stations.
This correlation was highest for stations bordering the North Atlantic. Figure 24
shows how much of the temperature variations (
) are explained by the length
of the previous solar cycle. For stations bordering the North Atlantic
r2 > 50%
This is a strong indication that there is a delayed solar heating of the North At-
lantic and the Barents Sea. This delay is at least the length of a solar cycle. Lans-
ner and Pepke Pedersen [72] showed that inland stations with little ocean influ-
ence, warmed up quickly around 1930, while both coastal and inland stations
warmed up during the 1990-2010 temperature peak. This indicates that the
warming by ocean was delayed 60 years or more.
It is observed that long solar cycles in general correspond to low BIE, and
short cycles as 1700-1800 and after 1900 corresponds to high values of BIE (see
Figure 2). It is shown [15] that SCL varies with periods 190 and 86 years. This
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Figure 23. BIE position (blue dots: 11 points mean) compared with low pass (L12221)
filtered SCL. The left panel shows the correlation and right panel the fit to the SCL curve
(red). Shorter solar cycles correspond to less ice.
Figure 24. Contribution (
) from the length of the previous solar cycle to the tempera-
ture in the next solar cycle (in percent) [71].
corresponds to planetary periods (Section 6). The longer cycles in the 19th cen-
tury means there are only 9 solar cycles in that century, while there are 10 in the
next. In addition to the cycle length, it should be noted that the solar activity,
described by sunspots, was very low in the 17th century (Maunder Minimum)
and in the period 1790-1820 (Dalton Minimum), and again around 1900 (see
Figure 25).
5.5. BIE, Sunspots, and Earth’s Rotation (LOD)
In [1] (see Section 7.3 and Figure 17) we proposed that the BIE position may be
related to a solar-planetary beat, synchronized by the orbits of the planets. One
forcing is direct solar irradiance modulated by the Earth’s orbit on Milanković
and shorter time scales as discussed in the previous section. The other route for
forcing is by solar wind which acts on the Earth’s magnetosphere. The wind
modifies (see [1] Figure 20) the magnetic shielding which protects the Earth
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Figure 25. (a) Group sunspot numbers (11-year running mean), grSN; (b) LOD; (c) BIE
position (11-points mean). Increasing LOD indicates cold and decreasing LOD indicates
warm periods.
from galactic cosmic rays (GCR) [1] Figure 4 and contributes to the magnetos-
pheric ring current which controls the momentum exchange with the Earth’s
magnetic core. This introduces a change in the Earth’s rotation which is ob-
served as Length of Day or LOD-changes.
In Figure 25, we show group sunspot numbers (A) (Gnbb2) [73] [74]. This
data set is a pure solar index and does not rely on input from other proxies. It
shows that the solar activity has risen from a low level between 1650 and 1700
(Maunder Minimum) and had three long maxima about the same level the last
300 years. The black curve is a P04-periodogram with three significant periods
(437, 213, 118 years). A weaker oscillation with P = 55 years is not included. The
most rapid increase happened between 1690 and 1730. There is also a deep short
minimum around 1800 (Dalton Minimum) and a longer, not so deep minimum
between 1880 and 1930. All these minima are observed in the BIE position (c).
Panel (b) shows LOD. Peaks in sunspot numbers correspond to the BIE peaks
around 1750, 1850 and 1975. Except for the peak in 1850, BIE always start mov-
ing north before the sunspot numbers increase. According to our hypothesis, we
expect warming when LOD decreases. Then the Earth is rotating faster. This is
marked with “Warm or W” in red under (b). When the Earth is rotating slower,
we expect cooling. This is marked with “Cold or C” in blue. We find that BIE
always respond to the LOD-changes if the trend in LOD lasts long enough. The
last LOD change around 2005 may have initiated the cooling in the North Atlan-
tic shown in [1] (see Figure 10), but the expected effect on BIE is not yet ob-
The correlation between sunspot numbers and BIE position from 1700 is only
= 0.01. We note that the sunspot minimum around 1900 was almost as deep as
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the during the Dalton minimum, and that BIE has not yet moved south after
2000 as it did during other deep sunspot minima. The correlation between
sunspot numbers and LOD is also low, only
= 0.03, which means that we can-
not link sunspots and Earth rotation directly. However, the correlation increases
= 0.08 for 11-year running mean sunspot numbers. In Figure 25, panel (a),
the black curve is a best fit harmonic model with periods 99, 53 and 65 years.
On the other hand, there is an anti-correlation between LOD and BIE for low
frequency variations as shown in Figure 25. In addition, the GSB-beats during
periods of low solar activity shown in [1] (see Figure 5), are an indication of a
connection with variations in LOD, which regulates the inflow of warm Atlantic
water to the Arctic. Increasing LOD means decreasing speed of rotation and in-
crease of warm water flow towards the Arctic. LOD-acceleration during deep
solar minima and deceleration (retarding) during maxima is predicted by
Mörner [75]. He proposed a simple mechanism: The solar wind intensity affects
Earth’s rotation. More intense solar wind gives more pressure and slows the
Earth’s rotation. When the Sun is less active, the solar wind decreases and the
Earth speeds up, as it has done since 1975 and BIE moves north.
We have in Section 4.4 shown that BIE positions anti-correlate with detrended
= 0.40). This means that decreasing LOD, which means increasing
Earth’s speed of rotation leads to less ice or warmer Arctic. The geomagnetic in-
is a measure of the solar wind in the ecliptic plane, and a zonal wind in-
dex (ZI) is the pressure difference between 35˚N and 55˚N latitude circles. Maz-
zarella [76] finds a correlation (
= −0.97) between 23-year running mean, de-
trended integrated geomagnetic index (
) and integrated zonal index (IZI)
5 years ahead. This indicates that an increase in solar wind speed causes
a decrease in zonal atmospheric circulation with a delay of 5 years. IZI and LOD
appear inverse correlated (
= −0.87) with LOD 4 years after IZI. Mazzarella [76]
explains the relation between solar activity and LOD in the following way: When
solar activity increases the Sun ejects plasma (charged particles) both in the con-
tinuous solar wind and in hydrodynamic shock waves which interfere with the
Earth’s magnetosphere and create turbulent pressure waves which decelerate
atmospheric circulation and slows the Earth’s rotation. This cools the Earth.
When solar activity decrease, we observe a faster Earth rotation and BIE moving
north, as seen in Figure 25 since 1975. We may call this the direct SW-driven
Another explanation proposed by Duhau and Martinez [77] is that geomag-
netic storms in the solar wind modulate the magnetospheric ring current’s con-
trol of momentum exchange with the Earth’s interior. It is well known that short
periodic variations in LOD are due to exchange of angular momentum between
the atmosphere and the solid Earth’s core. Some of these periods may be excited
by geomagnetic storm variations following solar activity cycles. Longer periods
are related to torsional oscillations in the Earth’s liquid core. They may be ex-
cited by variations in the magnetic field carried with the solar wind as described
in [77]. Duhau and de Jager [78] (in their Figure 61.3) show that a bi-decadal
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period in LOD oscillates synchronous and anticorrelated with the sunspot num-
. A semi-secular period is also anticorrelated with
but with a lag of 94
years. This lag is a sign of a different mechanism. Signals in the decadal band
and below are exited in the mantle by atmospheric motions that appear to be
driven by solar activity (synchronous). Torsional oscillations have their sources
at the outer-inner core boundary and need nearly 100 years to travel to the sur-
face [77]. In addition, the amplitudes of both the bi-decadal and semi-secular
cycles are modulated with the Jose period of 179 years, indicating a relation to
the orbits of planets. This will be discussed in Section 6.
The anti-correlation and lag create the apparent lack of correlation between
sunspots and LOD in Figure 25. However, the figure shows a good correlation
between peaks in LOD and turning points of BIE movements. All the BIE peaks
are within periods of maximum sunspots and BIE moves south when the suns-
pot number decreases rapidly, as seen for the periods 1600-1650, 1790-1810, and
1870-1910. A repeat of this pattern indicates that we should expect a rapid move
of BIE south in the period 2010-2030.
The 66-year LOD period in Section 4.4 is also found for the AMO- and
NAO-variations and is also close to the Stadium wave period and is equal to the
solar magnetic period 3PH, where PH is the solar magnetic Hale period of 22
years. The dominating BIE sub-centennial period of 82 years is 5/4 of the period
Figure 26 shows the relation between inverted, and 94-year lagged 11 years
running mean sunspot numbers (
) and LOD as proposed by [77] and [78].
The blue curve shows observed LOD-values which follow closely
in the
period 1820-1970. If we shift the blue curve ±179 years, to indicate the planetary
period repetition (the Jose period), we get the blue (broken) curve. This also fits
well with the
curve around 1700 and 2020-2070. A peak at 2090 should
probably be moved to 2120 to follow
better. With this relation between
and LOD, we get an answer to the problematic relation between BIE and
sunspot number (
) around 1700, when we observe that BIE moves north before
Figure 26. LOD11: (11 years running mean, observed: blue, repeated and shifted ± 179
years: blue-broken) compared with group sunspot no, SN11: (11-year running mean, in-
verted and forwarded 94 years: red). (a) SN 11; (b) LOD 11.
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increases. Figure 26 shows that BIE gets a kick north by the LOD peaks forced
by the strong
pulse from 1720 and 1900. Figure 25 and Figure 26 indicate
that the BIE position around 1850 is so far south that an increasing LOD has lit-
tle effect. A longer cycle of ≈240 years was also found in LOD by [77]. This fol-
lows a similar cycle correlating with
with a lag of 74 years. This may be re-
lated to the BIE bi-centennial period of 266 years (see Figure 10). The hindcast-
ing of the LOD-pattern to the period 1600-1800 gives an indication of a LOD
acceleration 1670-90, which may the reason for the extreme BIE-estimates in this
period, before the cold period 1690-1730, which corresponded to a GSB type c
With declining averaged sunspot numbers from 1975 and Earth deceleration
from about 2000, we expect an effect on climate. A cooling in the north Atlantic
is already recorded in [1] (see Figure 10(a) and Figure 10(b)) and documented in
[79]. They show a trend-reversal from warming to cooling from 2004-2005 in
the north Atlantic which is a verification of this relation. This is also docu-
mented by [80]. However, if the 94 years forward effect of SN11 and the repeti-
tion of LOD-pattern, is correct, then the LOD will again accelerate from 2025 to
2040, with BIE increasing, before the large increase in LOD 2050-80 makes BIE
position decrease.
An analysis of the LOD changes since 1970 by [81] shows how a LOD-period
of 21.93 years correlate with the 11.06 years solar cycle: If the magnetic S-pole is
at the Sun’s north pole, the Earth’s rotation with a 21.93-year period will start to
accelerate. At the next sunspot maximum, the Earth’s rotation will start to dece-
lerate. The magnetic cycles are slightly biased to higher deceleration than acce-
leration, which means that the overall result of a complete magnetic cycle is de-
celeration. This supports the relation proposed by [75]. If the same relation
holds back to 1700, this means that a part of the linear trend in LOD may be ex-
plained by the systematic increase in LOD with the Hale cycle.
5.6. Magnetic Shielding and Cosmic Rays
In [1] (see Section 4), we wrote that the type-a circulation for the GSB is typical
for Grand Solar Maxima, while types b and c happen during Grand Solar Mini-
ma. The alteration between solar maxima and minima changes the Earth’s mag-
netic shielding capacity, both at the 22-year magnetic (Hale) cycle, described in
the previous section, and at longer cycles as the centennial sunspot cycles shown
in Figure 25, which lead to grand minima or maxima.
By using the method of singular spectrum analysis (SSA), Le Mouël
et al.
identified a rising trend and Gleissberg cycles of period ~90 years in the interna-
tional sunspot series 1700-2015. Four extended minima were identified, also
shown in Figure 24 with group sunspots numbers back to 1612. The rising trend
was quasi-monotonic with an acceleration around 1900. This compares well with
the trend in BIE (Figure 24). Their Gleissberg periods varied from 85 to 94
years, with an average of 90.5 years.
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To study modulations on longer time scales, one must use proxy data. Varia-
tions in solar activity leads to modulation of the flux of galactic cosmic rays en-
tering the terrestrial atmosphere, generating radionuclides such as 10Be and 14C
in ice cores and tree rings. In [1] (see Figure 4), the changing 14C production rate
is shown. This is anticorrelated with cosmic ray’s corpuscular radiation, which
may generate clouds which strongly affect the climate. The cooling periods, with BIE
moving south, as in the periods 1600-1700, 1780-1820, 1870-1900 and 1940-1950
are clearly present.
Figure 27 shows 10Be-flux measured in a Northern Greenland ice core [83]
compared with BIE estimated positions. We find that southern positions of BIE
correspond to high level of 10Be. We also notice that the 10Be level during the
Spörer minimum (1400-1520 CE) is about the same level as the maximum
around 1900.
The 10Be-flux as shown in Figure 27 is not available after 1994. To investigate
what happens in recent times we compare the BIE estimates with neutron counts
from the Oulu Observatory in Finland. The result is shown in Figure 28. In-
verted sunspot numbers (-
) follow the neutron counts. The BIE position fol-
lows the inverted neutron counts until about 1995. This is according to the hy-
pothesis that less galactic cosmic rays create less clouds, the Earth heats up and
the Arctic ice cover shrinks. However, this relation is broken after 1985. Then we
observe more neutron counts while BIE is still moving north. We interpret this
as a sign of a less shielded magnetosphere. This means that magnetic storms ori-
ginating from solar flares and CMEs penetrate easier the Earth’s magnetic shield.
This heats the polar region and increases the cyclonicity and moves BIE to the
north and explains the almost instant response of BIE to change in solar activity.
Two 9400-year-long 10Be data records and a 14C record of equal length was
analyzed by [84]. They found 15 significant periodicities between 40 and 2320
years and concluded that cosmic radiation is the primary cause for periods < 250
years, but for longer periods some terrestrial origins were possible. They found a
very stable (~0.5% variations) Gleissberg period of 87 years. They determined 26
Figure 27. Yearly average 10Be flux from the NGRIP (Northern Greenland) [83] ice core
with 11-year running mean (red) from 1389-1994 compared with BIE position estimates
(blue dots). The 10Be flux is increasing downwards.
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Figure 28. Oulu neutron counts 1964-2019 (lower panel with 11year running mean). The
upper panel shows BIE positions (blue) with inverted Oulu neutron counts (downloaded
Grand Minima like the Maunder Minimum, which appeared in groups of 2 - 7
Grand Minima with intervals of 800 - 1200 years between. Some periodicities
were harmonically related pairs (65 and 130 years), (75 and 150 years), and (104
and 208 years). The 208-year (de Vries) period was present during Grand Mini-
ma, and not detected outside those.
The transition between periods with Grand Minima and no-Grand Minima is
related to a super-modulation period of about 2300 years, called the Hallstatt
cycle, which may be the upper limit to periods associated with the solar dynamo
[85]. However, [86] has shown that the amplitude of the ~210-year oscillation
[1] (Figure 4the thin grey line) depends on the phase of the 2300-year varia-
tions in the dipole moment of the Earth’s geomagnetic field. They used empirical
mode decomposition and calculated a cross-spectrum which had as its most sig-
nificant feature a spectral line with period ~2300 years, confirming that this pe-
riod originates in the Earth’s magnetic field. This geomagnetic field component
had its minimum around 1450, which indicates maximum amplitude of the
~210-year oscillation, leading to the deep Spörer and Maunder minima. On the
other hand, direct observations of Earth’s magnetic field strength have shown a
10% decrease in dipole strength the last 180 years due to even longer period
components [87].
5.7. BIE and Solar Wind
Tails of bright comets visualize the wind from the Sun blowing evaporated ma-
terial away from the comets’ nuclei. We often observe two tails, one curved
composed of neutral particles, governed by gravitational laws, and one straight,
containing ionized particles forced by the streams of ionized particles from the
Sun. Since the Sun is a rotating body, the solar wind streams become curved like
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an expanding spiral, eventually hitting the Earth, passing through the stream
pattern, also called a Parker spiral after E.N. Parker [88] who first calculated its
The relation between the solar wind (SW) and the Earth is described by [89]
as follows: Magnetic fields produced by the dynamo mechanism in the interior
of the Sun, find their way to the surface and are leaked into the heliosphere with
the solar wind, which sustain the magnetosphere of the Earth. The solar wind is
classified as three basic flow types: the high-speed streams associated with co-
ronal holes and co-rotation interaction regions, the slow wind originating from
streamer belts and the transient flows related to interplanetary CMEs. Near
Earth the wind causes geomagnetic activity like magnetic disturbances and au-
roras. CMEs and burst of high-speed streams are more frequent near solar
et al.
[1] Figure 21 show estimated yearly mean solar wind speed
(SWS). It is between 250 and 400 km/s just before the Maunder Minimum. The
largest yearly variation is 300 to 600 km/s in the 1720 ies, otherwise it has been
between 400 and 500 km/s most of the time after 1740. The 11-year running av-
erage velocity curve of the solar wind is repeated in Figure 29. The velocity
curve after 1720 shows two small dips, one about 1820 and one about 1920. A
P04-periodogram gives a dominating 100-year period with a weak 52-year har-
monics. They are approximately the same periods as found for the suns-
pots-series (Figure 25 panel (a)).
We have also analyzed the solar wind series with the Morlet-wavelet as shown
in Figure 30. The similarity with the BIE Morlet-wavelet (Figure 8), is striking.
A 60-year period is present for both series, and a period 95 - 98 years is just out-
side the cone of influence for the SWS series matching the 104-year period for
BIE. The main difference between BIE and SWS is that BIE has many shorter
periods that may be internally or lunar driven.
Analysis of long 14C records has shown that a 900-year cycle has intensity 5 - 7
times the centennial cycle [90] and a 420-year cycle, much stronger than the
centennial and sub-centennial cycles [91]. The peaks found are 414, 216, 142,
and 85 years. Three of those are also in BIE spectrum: 82, 208/2, and 145 years.
The strongest cycle found is 11,500 years with intensity several times the centen-
nial and sub-centennial cycles [92]. In addition to the 11,500 years cycle they
Figure 29. Solar equator wind (11-year running mean), with harmonic model based on
data from 1720 (red).
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Figure 30. The solar wind analyzed with the Morlet wavelet.
found cycles of 1670, 1420, 1280, 924, 835, 787, 750, 663 and 545 years in various
long solar wind proxies. We suggest that the big dip in the SW-curve at the
Maunder Minimum is the result of this 545-year cycle and will return to this in
our discussion (Section 7).
Several studies have shown relations between winter climate at high northern
latitudes and the solar cycle [67]. Proposed drivers include TSI, solar UV, galac-
tic cosmic rays and energetic magnetic particles from the Sun. To identify the
drivers [93] analyzed the relation between different drivers and the phase of the
solar cycle. The geomagnetic activity and magnetospheric particle flux have a
maximum in the declining phase of the sunspot cycle while TSI and UV radia-
tion follow more closely the solar cycle. They analyzed 13 solar cycles (1859-2009)
and compared with winter temperatures and NAO-phases. This is interesting in
connection with BIE, since a low winter temperature means more ice to melt
next summer and a more southern BIE. The most significant relation was found
during the sunspot declining phase with temperature pattern resembling a posi-
tive NAO, suggesting that the solar wind and magnetic particle flux is the main
driver of winter temperature variations. Negative NAO and cooling in the Ba-
rents region were found in the increasing phase of the sunspot cycle. The same
pattern was found during low and high sunspot activity cycles, suggesting that
the pattern is independent of the level of solar activity. On the other hand,
maximum frequency of CMEs is found near peaks in the solar cycle.
Comparing winter (DJF) season ice cover with sunspot numbers during solar
cycle 21 - 24 [94] showed that during winters with low sunspot numbers, the BS
area is warmer than average, and the ice cover is decreasing. Cooling, on the
other hand is dominant over Scandinavia and Siberia. The largest warming hap-
pens at the surface because of enhanced exchange of sensible and latent heat flux
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from the open ocean to the atmosphere during low sea ice years. In the same pe-
riod the NH snow cover has been constant, proving that this relation is a
sun-ice-ocean relation.
Possible models suggested by Roy [94] (see her Figure 7), are either 1) a 6%
increase in UV-radiation in solar maximum years, creating more Ozone heating
in the upper stratosphere and a stronger jet stream in NH, which strengthen the
polar vortex. Perturbations are transported all the way down to the surface by
planetary waves and create a cold Arctic for solar maximum years. Or 2) the
stronger jet causes a poleward shift of the Ferrel cell and supports a cold polar
vortex leading to cold Arctic and more ice. Since 15 of the last 16 years have had
less than average sunspot numbers, this may explain less ice and BIE far north in
this period. The same may have happened during the Maunder and Dalton Mi-
nima, making West Svalbard unusually warm during the LIA. D’Andrea
et al.
[95] have determined a gradual warming in eastern FS CE 1600-1900 followed
by accelerated warming the last 120 years. Analysis of lake sediments from
Western Svalbard showed mild summers from CE 1600, even when the rest of
the Arctic was cooling. They interpreted this as increased heat transport into the
Arctic via the WSC from ca. CE 1600.
et al.
[96] have found a significant correlation between the solar wind
speed (SWS) and sea surface temperature in the region of the North Atlantic
Ocean for the NH winters from 1963 to 2010, based on 3-month seasonal aver-
ages. The correlation is dependent on
(the interplanetary magnetic field
component parallel to the Earth's magnetic dipole) as well as the SWS. It is
stronger in the stratospheric quasi-biennial oscillation (QBO) west phase than in
the east phase. The correlations with the SWS are stronger than with solar UV
inputs to the stratosphere. Sea surface temperature responds to changes in tro-
pospheric dynamics via wind stress, and changes in cloud cover affecting the ra-
diative balance. Suggested mechanisms for the solar influence on sea surface
temperature include changes in atmospheric ionization and cloud microphysics
affecting cloud cover, storm invigoration, and tropospheric dynamics. Such
changes modify upward wave propagation to the stratosphere, affecting the dy-
namics of the polar vortex. Also, direct solar inputs, including energetic particles
and solar UV, produce stratospheric dynamical changes. Downward propaga-
tion of stratospheric dynamical changes eventually further perturbs tropospheric
dynamics and the sea surface temperature.
From Russian rocket soundings in the Arctic, it has been found that the SW
contributes to the thermal regime of the polar middle atmosphere via delivering
electric current to the global electric circuit [97]. The passive element of this
circuit is the ionospheric E-layer and the conducting layer of the Earth’s surface.
It is observed that the temperature in the stratosphere increases with the distur-
bances if the conductivity of the ground is high and decreases if it is low (ice and
tundra). It is calculated that the Earth’s magnetopause can move from a distance
of 12RE to 6RE (Earth radius) during a magnetic storm, and this can dissipate an
amount of Joule heating comparable with the heating of the ozone layer by solar
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UV radiation. Such energy burst changes the atmospheric circulation and is en-
forcing cyclonic activity which is observed related to CMEs. Joule heating in-
cluded in a dynamical photo-chemical model of atmospheric circulations shows
that NH lower stratospheric temperature increase 1˚C - 3˚C during minimum of
the solar cycle [98].
Returning to the question of the trend in BIE from 1800 or 1900, this may be a
result of an integrated forcing. The melting in the summer depends primarily on
the heat available for melting, but also on the freezing previous winter, and the
left over from last summer etc. We have identified several processes which may
lead to increased melting and reduced freezing: The Early Spring Effect, the LIG
variations, increasing TSI, increasing solar activity, decreasing LOD, and INAO
(see Figure 15). There may also be an integrated effect of CMEs acting on the
Earth’s rotation and forces the Atlantic current to the north. Geomagnetic stor-
miness determines the average BIE position either with pressure bursts which
decelerate the Earth’s rotation or modulating the magnetospheric ring current’s
control of momentum exchange with the Earth’s interior
Since we the last 300 years observe a nearly flat SWS-curve, what happens in
the future depends on the evolution of the ongoing solar activity reduction,
whether this evolves into a deep minimum or not. In addition to deep minima,
shallow minima appear 100-year apart. In addition to the processes described
above we also must consider lunar modulations described in the next section.
5.8. The Lunar-Solar Tides, the Lunar-Nodal Cycle, Polar Tides,
and the Sun
We observe tidal effects on all levels of the planet: from the atmosphere to the
inner structure which has a fluid outer core surrounding the solid inner core of
the Earth. Luni-solar tides are the result of the Earth and Moon orbiting their
common barycenter, with perturbing effect of the Sun, and the Earth, Moon and
Sun orbiting the solar system barycenter.
The luni-solar tides have 9 main periodicities [99]: Twice daily, fortnightly, 27
days, 9.3, 18.6, 62, 93, 222 and 1500 years. The lunar nodal oscillation with pe-
riod LN = 18.61 years with several harmonics is observed in sea level changes and
analyzed by many researchers. Hansen
et al.
[100] analyzed 26 long-time
(1840-2015) tide-gauge series from the eastern North Sea and central Baltic re-
gion. They found a strong correlation (
= 0.94) between sea-level changes and
the sum of identified harmonic oscillations, corresponding to the lunar nodal
period and four multiples of it,
high amplitudes for
= 18.6, 60.5, and 76.1
years, and statistically less significant for
= 28.1 and 111.1 years. A purely ma-
thematical extension of the oscillations suggests the production of 223-year
pulses of quasi-oscillations which can be divided into 158-year periods (e.g.
1747-1905 and after 1970) with large oscillations, followed by 65-year periods
(e.g., 1905-70) with much smaller oscillations.
The main Atlantic current continues through the Faroe-Shetland Channel and
the Norwegian Sea before reaching the BSO or FS and arriving in the BS. Analy-
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sis of two 100 years long hydrographic series from the Faroe-Shetland Channel
and the Kola section by [101], shows dominant cycles in sea level, salinity and
temperature correlated to a sub-harmonic 74-year cycle of the nodal tide, with
an advective delay of two years between the Faroe-Shetland Channel and the
Kola section. In addition, correlations were found between dominant Atlantic
water temperature cycles and the LN period, and for the LN/2 = 9.3-year lunar
nodal phase tide [101]. Phase reversals of temperature and salinity curves took
place in 1925 and 1960 when the 74-year lunar nodal cycle changed phase [−0].
Analysis of time-series for the polar position, the extent of Arctic ice, sea level
at Hammerfest, Røst winter air temperature, and the NAO winter index with a
coiflet3-wavelet impulse function by [101] shows for all series a harmonic spec-
trum based on the LN-cycle with a stationary period, but with non-stationary
amplitudes and phases. The phase relation between the identified cycles indi-
cates a possible chain of events from lunar nodal gravity cycles to long-term
tides, polar motions, Arctic ice extent, NAO winter index, weather, and climate.
et al.
[101] explain this by the gravity force from the LN cycle which
affects the polar position (nutation) and the circulating water in the Arctic
Ocean. A stationary polar-position cycle forces the Arctic oceans and introduces
the Arctic oscillations which interacts with the Arctic ice extent, water tempera-
ture and atmospheric conditions. The LN cycle has harmonic and sub-harmonic
The Earth’s nutation is a predictable cycle of the Earth’s spin around its axis
with periods 18.6134 years, 9.3 years, half year and half month. Analysis of the
observed positions show dominant periods of 1.2, 6, 18 and 74 years [102]. The
LN -cycle is in phase with the nutation cycle in the y-direction from 1870 to 1950
but phase reversals take place when the 74-year cycle have minima at about 1865
and 1940. This shows that the phase is controlled by the 74-year cycle in the
y-direction. This is not the case in the x-direction.
5.9. Summary of Forcings by the Sun and the Moon
The 442-year BIE-position data set covers the coldest part of the LIA and the
recovery from it after 1900. The LIA may be due to a combination of less solar
irradiance because of decreasing obliquity of the Earth and a series of deep solar
minima. The recovery from LIA in the Arctic after 1900, is partly due to in-
creased solar activity and the precession of the Earth’s orbit providing an Early
Spring Effect and increased spring LIG at BIE-latitudes.
The correlation between solar cycle length and BIE position (
= 0.59) indi-
cates a strong solar forcing. A relation is established between the rotation of the
Earth, measured as LOD and the sunspot number -
with a lag of 94 years. This
is explained by an electric current brought with the solar wind, inducing mag-
netic torque on the solid core of the Earth, creating LOD-pulses, slowing the
Earth’s rotation. The LOD-pulses appear with a period of 66 years or three
magnetic solar cycles 3SH. In addition, we have pressure bursts from geomagnet-
ic storms slowing Earth’s rotation and cooling with a delay of about 15 years.
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Periodic variations of the BIE position are controlled by bi-centennial and
semi-centennial cycles. The bi-centennial cycle has a period of 145 years before
1750 and 268 years thereafter. The amplitude is constant, and the period is con-
trolled as 4/5 and 3/2 PJo, indicating planetary control. The semi-centennial pe-
riod has a quasi-stationary period of 82 years which is close to 4/3 of the 60-year
period. The amplitude of the semi-centennial period is variable with peaks
around 1587, 1696 and 2008. If the first two peaks indicate a maximum between
1590-1690 which declined to a minimum around 1935, this indicates a modula-
tion period of about 600 years. The disappearance for some time around 1650,
may be due to a GSB during the Maunder Minimum. The next GSB during the
Dalton Minimum did not affect the amplitude.
6. Planetary Influence
The focus of this paper is to investigate a possible relation between planetary
beats and climate variations as observed in the 442-year BIE series, as shown in
[1] Figure 9. A forcing can be transferred directly to the Earth or the Earth-Moon
system or it can be relayed via the Sun which then acts via irradiance or solar wind
as outlined in [1] Figure 20. A mechanism is presented in [1] (see Figure 7),
where an external force, like the solar wind, acts on the Earth’s rate of rotation,
which again results in sea level changes and ocean current variations, and in ex-
treme cases a GSB. The BIE variations can be split into a linear trend and various
oscillations. The linear trend is the dominating featureat least since 1900 (see
Figure 7). It may be due to an integrated effect, as investigated in Sections 4.9
(LOD and INAO) and 5.7 (ISW) or be a temporary linear part of a sum of long
period oscillations. In Table 4 we have listed some periods related to Moon, Sun
and planets which we may find in Earth’s climate.
Table 4. Some relevant periods with origin in the Moon, Sun, and planeta.
Name P (years) Type
SC 11.07 Schwabe Sunspot Cycle (variable)
PJ 11.86 Jupiter orbit
LN 18.61 Lunar nodal
PJS l9.86 Jupiter-Saturn synodic
SH 22.3 Hale solar magnetic (variable)
PS 29.46 Saturn orbit
PSU 45.36 Saturn-Uranus synodic
PU 84.01 Uranus orbit
PG 88±1 Solar Gleissberg (variable)
PJo 178.7 Jose Solar system (variable)
PdV 208 Solar deVries
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6.1. The Complex Synchronization of the Solar System
The planets move in fairly stable orbits, but their change of positions relative to
the Sun makes the Sun move in a complex orbit, also called solar inertial motion
(SIM), as demonstrated in Figure 31 for the period 1940-2040.
The SIM-pattern change between a “disordered like” and quasi-regular or
“orderly” state with a “tri-foliar-like pattern” that follows the Jupiter-Saturn or-
bits. Charvátová and Hejda [103] have shown that the orderly pattern lasts about
50 years and is followed by a mildly or strongly disordered period. During dis-
ordered states deep solar minima have appeared, and during orderly periods
long-term maxima of solar activity are possible. The pattern repeats with a pe-
riod of ~179 years: the Jose period [104]. In the last millennium chaotic patterns
were present 1270-1350, 1430-1520, 1620-1710, and 1787-1843. In these periods
we find deep solar minima and GSBs, as well as maximum ice (BIE minima).
The next disorderly phase started in 1985 and lasts until 2040. The lowest suns-
pot numbers in 200 years were observed in sunspot cycle 24 which ended in De-
cember 2019. High level of solar activity was observed in the orderly periods
1192-1241, 1370-1419, 1549-1598, 1727-1777 and 1906-1955.
A theory for the relation between solar activity and its source, the solar dyna-
mo and GM-events has recently been proposed by [105], involving the storing
and releasing potential energy in the solar interior. In the SIM pattern shown in
Figure 31, the Sun moves in a prograde (counter-clockwise) orbit, except during
one of the tri-foliar loops (marked red). Detailed calculations by [106] show that
the process of storing and releasing potential energy starts about 40 years before
the angular momentum inversion and lasts about 80 years. Simulations show
Figure 31. Solar inertial motion (SIM) relative to the solar system barycenter (SSB) for
the period 1940-2040. The cross represents the SSB and the yellow filled circle the radius
of the Sun. The part with a retrograde orbit is marked red.
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that the angular momentum inversion is a rapid process that takes place in one
year. It has during the last millennium only happened at the epochs of Maunder
Minimum (1632), Dalton Minimum (1811) and in 1990 before the newly started
minimum. The reason for near barycenter passages 40 years before and after the
inversion pulse is the Saturn-Uranus synodic period of 45 years when a new qu-
asi-alignment happens. We also notice that the inversion events are 179 years
apart, again the Jose cycle of repeated planet positions.
In a study by Fairbridge
et al.
[107] of the pattern of the solar orbit, the angle
between tangents to two successive loops is defined as the Axym-angle. This fol-
lows the Saturn-Jupiter synodic period (PJS) of 19.9 years with a shift in angle of
117.4 degrees for each loop, returning to approximately the same part of the sky
after 59.7 years. Three full Axym-cycles make a Jose period of 179 years. Duhau
and de Jager [78] have calculated the difference in angle between two successive
orbits (Daxym) and found that it is modulated with a period of 45 years, which
is the Saturn-Uranus synodic period and 1/4 of the Jose period. They also ob-
served that 3 LOD periods of 60 years are close to the Jose period, and that the
amplitude in the LOD-oscillations followed the Daxym variations with a 94-year
delay in anti-phase of
. This is the reason for the repeated LOD pattern with
the Jose period shown in Figure 26. Duhau and de Jager [78] concluded that the
LOD amplitude modulation follows linearly solar system motions.
In Section 5.5 we have confirmed the anticorrelation with 94-year lag between
and LOD. We have also found the LOD period to be 66 years, or 3SH periods
instead of 3PSJ periods, not confirming the period found by [78]. Since the mag-
netic period is more likely to affect the solar wind’s interaction with the magne-
tospheric ring current, which can magnetize the core of the Earth, we find our
interpretation more likely.
Regarding timing of events, we notice that the phase change between 1900 and
1950 inversion happened during a rapid decrease of LOD and increasing solar
activity. Thereafter the solar activity is reduced and the cosmic rays count in-
creasing (Figure 28). A phase shift appeared in the BIE sub-centennial period
(Figure 10 lower panel) between 1900 and 1950. A rapid move of BIE happened
94 years after the 1632 -inversion and 94 years after the 1811-inversion. It may
happen again 94 years after the 1990-inversion,
from about 2085.
The bicentennial period which changes from P = 145 (4
/5) years to 266
/2) years is also a strong indication of planetary synchronization.
6.2. The Hale Cycle (SH)
The sunspot-cycle length varies between 8 and 15 years with an average of 11.06
years. The amplitude spectrum has 4 peaks at 9.97, 10.66, 11.01, and 11.83 years
[14]. The strongest peak at 11.01 years is close to the Venus-Earth-Jupiter recur-
rent cycle of tidal torque (
) which produce an increase in the rotation of the
outer layers of the Sun for 11.07 years and a decrease in the next 11.07 years,
making a full cycle of 22.14 years, which is close to the solar magnetic cycle of
= 22 ± 1 years [108]. The other peaks are interpreted as the Jupiter period
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11.86 years, and the spring (half synodic) tidal oscillation of Jupiter and Saturn
(PJS/2 ~ 9.93 years), and a minor peak at 10.57 years, also found in the periodo-
gram of the solar velocity variations [109].
A common objection against planetary tidal gravitational potential energy as
the source of solar irradiance variation, is that it is several magnitudes too small.
However, if the tidal massage of the Sun results in nuclear fusion variations in
the solar core, then one can expect a magnification factor of the order 4 × 106
and solar radiation fluctuations of the same order as observed with the ACRIM
satellite [110].
Since the dominant BIE sub-centennial and bicentennial periods show
PJo-harmonics, we conclude that the planets contribute to the synchronization of
BIE position oscillations in addition to the Moon and the Sun.
6.3. A 60-Year CycleDirectly from Jupiter?
In addition to presence in climate records, a 60-year cycle is also found in long
records of meteorite falls covering the period 619-1943 CE [111]. Since meteorite
falls are related to cosmic dust from comets, and their orbits in many cases are
changed by near passages of Jupiter, one may expect a relation between changes
in Jupiter orbit and the influx of cosmic dust at the Earth. Since atmospheric
dust modify the cloud cover on the Earth, the variation in cosmic dust may also
result in climate variations.
The orbital eccentricity of Jupiter shows a strong 60-year oscillation which is
correlated with several climatic records and with the 60-year cycle of meteorite
fall recordings [111]. One of the climate records well correlated is the climatic
variability of the North Atlantic based on
abundance variations
from 1650 to 1990 [112].
This is an example of possible direct planetary forcing, which don’t rely on
being transmitted via the Sun or the core of the Earth. The low amplitude sta-
tionary 60-year period detected with the Morlet-wavelet (Section 4.6) may be
explained by this direct forcing. However, the detection of a 19.9-year weak sig-
nal (Section 3.1), which can only be the PJS beat signal, indicates this as the
source of the 60-year signal, which is also found in the solar wind speed varia-
6.4. A 60-Year Cycle or a 66-Year Cycle?
The term “60-year cycle” is given somewhat imprecisely about cycles of the or-
der 60 to 70 years. We can construct two competing 60-year cycles, one being
subharmonics of the lunar nodal (
) cycle of 18.61 years and its spring cycle 9.3
years or the solar magnetic cycle of
= 22.1 years. Both create “65 - 66-year
2 = 65.1 and 3
= 66.3 years. The O-C diagram in Figure 10 shows
that BIE since 1700 has an 82-year cycle which may be composed of 3
= 88,
JS = 80, and
2 = 84 years cycles.
A high degree of coherence is found between global temperature series
(HadCRUT3) for periods of exactly 20 and 60 years and the speed of the Sun
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relative to the center of the mass of the solar system by [113]. They are related to
the PJS synodic period of 19.95 years. In the BIE record we observe this 60-year
cycle as a low amplitude signal, detected in the Morlet-analysis (Figure 8). This
signal is not dominating in our BIE-series, nor in the AMO, NAO and NH tem-
perature series we have analyzed. On the other hand, we observe sub-harmonics
of the 60-year cycle as weak 120, 240 and maybe 480-years periods forced by the
planets and Earth’s morphology into dominant, slightly longer periods as 82,
145, 266 and 490 years.
The fundamental difference from the global analysis is that our BIE-series is a
result of the local climate. The Arctic ice cover may influence the global climate,
at least if a GSB is initiated. What we observe are local changes to global signals
with the Moon and Sun as prime actors.
7. Discussion
This is the second in a series of two papers which analyze the BIE position based
on a 442-years long dataset covering the period 1579-2020, to understand its
time variations. Our first paper was a review of various oceanic and atmospheric
factors that may influence the BIE position. We concluded that the GSB with
respect to alternations in flow intensity and N-S distribution, plays a central role
in combination with external forcing from total solar irradiation (TSI), Earth’s
shielding strength, Earth’s geomagnetic field intensity, Earth’s rotation, jet
stream changes, etc.; all factors of which are ultimately driven by planetary beat
on the Sun, the Earth, and the Earth-Moon system.
Our working hypothesis is that the planetary gravity beat is somehow pre-
served as a weak signal through a chain of processes schematically shown in [1]
Figure 9 and in some cases amplified in local or regional synchronized systems:
especially Earth rotation [28] and the polar wobble [102]. In [1] we assumed that
the climate of the Northwestern coast of Europe and the position of the ice edge
in the North Atlantic Ocean are controlled by the Northern branch of the Atlan-
tic current (Gulf Stream) and by advection modulated by the Northern Jet
Stream, which both are controlled by the solar wind. The solar wind also acts on
the Earth’s speed of rotation, which again forces the ocean currents [1] Figure 7.
In this paper we have analyzed the BIE data set and correlated it with other
data sets, and in particular compared periods and phases of oscillations. We have
found that oscillations combine non-linearly with variable frequencies, ampli-
tudes, and phases. This makes predictions of future behavior difficult. However,
since some of the forcing signals are generated from planetary orbits which have
been quasi-stable for millions of years, we expect a high degree of synchroniza-
tion between planets, Sun, and Earth climate.
We have found that in addition to cycles, the BIE variations have a near linear
trend towards a more northerly position from about 1900. This must be the re-
sult of an integrated effect or a temporary near linear sum of oscillations. We
have investigated different possibilities. In the following we first discuss the data
set, then the oscillations, integrated effects, and possible falsifications/verifications.
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7.1. The Data Set
A time series of the estimated position for the last two weeks of August ice edge
in the sector between 20˚E and 45˚E, covering the western Barents Sea between
Svalbard and Frans Josef Land (see Figure 1) was originally collected and pre-
sented by T. Vinje [16]. The data have been collected from ship-logs, polar ex-
peditions, and hunters in addition to airplanes and satellites in recent times. In
particular has the European, mainly Dutch whaling that took place around Sval-
bard in the period 1600-1800 been a valuable source of information. The BIE
position has been defined as the occurrence of 15% ice and has been updated to
include the 2020 position. Since 1979 satellite data from microwave sensors have
been used. Comparing data from direct sightings with microwave data, we found
that the latter moved BIE 1.2 degrees north. We have not corrected the data set
for this discrepancy since it is comparable with the uncertainty in the data set.
The data coverage has increased from 34% in the first century to 100% after
1979 with satellite observations. The BIE position has varied between 75.5˚N and
83.4˚N, with a position far south 1625-1670 and 1784-1830,
before and dur-
ing the Maunder and Dalton solar minima. From about 1920, BIE has moved
north, except for a southward expansion between 1940 and 1970. The last ten
years the position has been variable around 82 N with no trend. The northern-
most position was recorded in 2013 with 83.37˚N. The data varies ±1.1 degrees
of an average value after 1740, but much more before. Satellite observations in
the last 40 years did not reduce the variations.
Sorting the data set in centuries (Figure 4) resulted in a binominal distribu-
tion with median values around 76˚N and 79˚N, except for the 19th century with
only one peak around 77.5˚N.
The binominal distribution may be related both to the inflow of warm AW on
decadal and centennial scales as well as the prevailing winds that influence the
ice drift on a much shorter time scale.
10 - 15
7.2. Correlations with Other Data Sets
Before we concluded on external forcings we checked possible internal forcings.
We have calculated Pearson correlations, assuming linear relations. A correla-
tion does not imply a causal relationwe also must find a physical relation. We
have done three types of correlations: Instant,
observed values for the same
year or smoothed (
11-year running mean) or long period mean values. We
use the
as a measure of goodness of fit,
calculated how much of the ob-
served variation can be explained by a linear trend. The best fit found was
0.79 for 30-year average values related to the longest instrumental temperature
series from Central England from 1659. The correlation with annual values gives
= 0.14.
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Another good correlation was with yearly estimates of the Arctic summer ice
cover (
= 0.62) after 1979 estimated from satellites. For data back to 1900 we
= 0.22. This means that BIE estimated by satellites gives a good estimate of
Arctic summer ice, but the estimates of ice cover and/or BIE are less precise at
earlier times.
BIE tracks NH-SST and land temperatures quite well (
= 0.43), which is bet-
ter than for the KolaT (
= 0.29). This may be due to less noise in the average
SST series but may also be a result of the warmer deeper AW under the colder
surface water in the Kola section data.
7.3. Planetary Orbit Fingerprints
We have searched for periodicities with the P04 period search program devel-
oped for gapped data, Morlet wavelet which gives precise frequencies, and coif3
wavelet for investigation of phase events. We did not find any stationary periods
in the bi-decadal range or shorter. Some periods with P < 50 years exist for some
decades. Only four low-frequency periods are necessary to explain the BIE secu-
lar variations. They are harmonically related with
years, with
= 1/2, 1,
5/3 and 3.
We found that the data set showed no trend before 1890, but a steep rise
(0.035 deg/year) thereafter. Analysis of the detrended data set showed the PJo =
179 years as the dominating period with other periods harmonically related to
We investigated amplitude and phase variations and found that the
semi-centennial period P = 82 years had a constant period, but with phase shifts
before 1700 and between 1900 and 1950. It is amplitude modulated with a nearly
zero amplitude between 1900 and 1950 and a maximum between 1600 and 1700,
but disappeared completely around 1650. A bicentennial period was on average
252 years but consisted of two periods: P = 145 years before 1750 and P = 266
years after, although with constant amplitudes. In addition, we found a low am-
plitude period of 60 years with 120 and 240 years weak sub-harmonics, as ex-
pected in [1] Figure 17.
7.4. Search for Mechanisms
Detrending BIE after 1800 and taking 11-point mean, we compared BIE with
KolaT, ArcT, AMO, NAO and LOD (Figure 14). BIE is in phase with ArcT, Ko-
laT, and AMO 1900-1950, but in antiphase with NAO and LOD. Analyzing the
sub-centennial periods, we found that LOD, AMO and NAO have periods 65 -