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17
Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
DOI: 10.4408/IJEGE.2016-01.O-02
C
live
H. BeST
(*)
& R
oBeRTo
MADRIGALI
(*)
(*)
Independent scientist
Corresponding author: C.H. Best (clive.best@gmail.com)
EVIDENCE OF A TIDAL EFFECT ON THE POLAR JET STREAM
EXTENDED ABSTRACT
Le variazioni di velocità e direzione del Jet Stream Polare influenzano direttamente le condizioni atmosferiche a livello mondiale,
e nello specifico abbiamo esaminato gli effetti in tutta Europa e Nord America. Le variazioni del Jet Stream regolano e costruiscono
lo sviluppo delle onde di Rossby planetarie (D
iCkinSon
, 1978), influenzate dalla variazione della forza di Coriolis con la latitudine. In
questa ricerca scientifica mostriamo che l’aumento delle maree atmosferiche indotte dalla variazione della forza gravitazionale (tides)
correlate alla variazione dell’orbita lunare e solare rispetto alla Terra, inducono delle interferenze sul fluido d’aria (flusso troposferico)
con lo sviluppo di onde di Rossby ed effetti più marcati in maniera particolare durante i mesi invernali. Queste interferenze del tides sul
Jet Stream cambiano la direzione e la velocità del fluido d’aria, con effetti più o meno marcanti a seconda delle dimensioni delle onde, la
loro propagazione e persistenza nel tempo. Questa modifica della variazione della corrente a getto della libera atmosfera viene misurata
dalla Oscillazione Artica. La AO altro non è che la misura della variazione della pressione fra le latitudini artiche e le medio-alte lati-
tudini, indotte dalla modifica di velocità e direzione del Jet Stream Polare, che nella sua limitazione in latitudine, delimita l’estensione
del Vortice Polare. Anche se le forze di marea orizzontali sono molto piccoli (107 più piccole della gravità), esse agiscono su vaste aree
interferendo e trascinando il flusso del Jet Stream verso sud in impulsi regolari durante la rotazione della terra. La forza di Coriolis e
la forza mareale interferiscono sul Jet Stream, provocando cambiamenti importanti atmosferici. In più va evidenziato che le variazioni
periodiche del Jet Stream erano già riportate in pubblicazioni scientifiche, citando di variazioni del fluido d’aria a cadenza mensile,
con step settimanali. Questa cadenza risulta essere in correlazione evidente con il ciclo lunare, poiché il periodo sinodico di 28 giorni
si combina con le variazioni mensili del Jet Stream. I dati provenienti da otto ultimi inverni sono stati studiati osservando le variazioni
della Artic Oscillation e si è rilevato che l’AO è anti-correlato alla componente orizzontale “trazionale” delle maree che agiscono tra
la latitudine 45N e 60N. Il ciclo di 28 giorni lunare osservato con le variazioni del flusso del getto ha rivelato un significato numero
statistico > 99%. Una ulteriore ricerca statistica tra tutti i dati giornalieri della AO dal 1950 e la forza di marea di trazione, mostra sta-
tisticamente un significativo valore in anti-correlazione con un ritardo di ~5 giorni nella sua propagazione di effetto. Le correlazioni più
forti con più grandi escursioni della AO sono state osservate durante l’inverno 2005/6 - un anno con un valore di massimo fermo lunare.
La variazione della declinazione lunare con le forze di marea alle alte latitudini è la causa proposta riguardo una correlazione climatica
nel ciclo di 18,6 anni (periodo completo di rotazione del piano lunare nello spazio) con il riscontro di periodi anomali di precipitazioni o
siccità. Uno studio dettagliato di l
inDzen
(1981) spiega che le variazioni gravitazionali(maree atmosferiche) interagiscono in alta quota
per la componente orizzontale “di trazione”responsabile delle correnti di marea negli oceani come venti di marea nell’atmosfera supe-
riore (corrente a getto-flusso troposferico). Durante l’inverno il Jet Stream si rafforza e si sposta dal grande nord verso sud. I meandri
o onde di Rossby (D
iCkinSon
, 1978) si propagano dagli oceani verso i continenti e la loro forza è maggiore con minimo solare (periodo
invernale). Ci sono due onde di marea ogni mese siderale, che coincidono con la luna nuova e la luna piena. E’ stato riscontrato che
l’onda di marea gravitazionale più marcante in inverno coincide con la luna nuova, mentre nel periodo estivo con la luna piena. Due
volte l’anno in coincidenza degli equinozi a tutte le latitudini le maree sono approssimativamente uguali. Sovrapposto a questo effetto si
combina anche il ciclo di 18,6 anni della precessione lunare che modula la dipendenza in latitudine di questa ampiezza gravitazionale sul
Jet Stream. Il Tides varia la componente a getto in velocità, ampiezza, propagamento e direzione, influendo sulle tempeste invernali che
si scatenano sul nord Atlantico per lo scontro di aria calda del Golfo e aria polare fredda da terranova. Questo gradiente di temperatura
produce instabilità baroclina, generando tempeste atmosferiche che si muovono da ovest verso est in Atlantico. Il Jet Stream è l’artefice
di queste tempeste ed è il vero dominatore meteorologico e climatico mondiale.
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C.H. BEST & R. MADRIGALI
18
Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
ABSTRACT
Variations in the Polar Jet Stream directly affect weather
across Europe and North America (F
RanCiS
et alii, 2012). Jet
Stream dynamics are governed by the development of planetary
Rossby waves (D
iCkinSon
, 1978) driven by variation of the Co-
riolis force with latitude. Here we show that increasing atmos-
pheric tides can induce the development of Rossby waves, espe-
cially during winter months. This changes the flow and position
of the Jet Stream, as measured by the Arctic Oscillation (AO)
(H
igginS
et alii, 2002). Although horizontal tidal forces are tiny
(10
7
smaller than gravity), they act over vast areas dragging the
Jet Stream flow southwards in regular pulses as the earth rotates.
This induces a changing Coriolis torque, which then distorts the
Jet Stream flow. The data from eight recent winters are studied
indicating that the AO is anti-correlated to the horizontal “trac-
tional” component of tides acting between latitude 45N and 60N.
The observed 28 day cycle in Jet Stream flow and extent has a
statistical significance > 99%. A cross-correlation between all
daily AO data since 1950 and the tractional tidal strength shows a
small but statistically significant anti-correlation with a lag time
of ~5 days. The strongest correlation and largest excursions of
the AO are observed during winter 2005/6 - a maximum lunar
standstill year. This declination dependence of tidal forces at high
latitudes is the proposed cause of many previous reports of an
18.6-year dependence of continental rainfall and drought (C
uR
-
Rie
, 1983; 1984).
K
eywords
: climate, tides, jet stream
INTRODUCTION
Varying tidal forces act both on the oceans and atmosphere
particularly at high latitudes. A detailed study (l
inDzen
, 1981) of
atmospheric tides finds that gravitational lunar tidal winds are more
important at high altitudes. The horizontal or so called “tractional”
component of net tides is responsible for tidal currents in the ocean
and for tidal winds in the upper atmosphere. During northern win-
ters the Jet Stream strengthens and shifts northwards. Meanders or
Rossby waves (D
iCkinSon
, 1978) develop near the eastern edges
of continental landmasses and oceans. Solar insolation falls each
winter to zero inside the Arctic Circle and consequently the diurnal
solar ‘expansion’ tide disappears over Polar Regions. Gravitational
atmospheric tides now dominate near the poles.
There are two ‘spring’ tides each sidereal month, namely
that coincident with the new moon and that coincident with
the full moon. Seasons modulate the difference between both
spring tides depending on latitude. The larger the latitude the
larger is the asymmetry during the summer or winter solstice.
At the equator both spring tides are always equal, but for the
northern hemisphere the new moon tide is largest during win-
ter, whereas that coincident with the full moon is largest dur-
ing summer. Twice a year at the spring and autumn equinoxes
both spring tides are approximately equal at all latitudes. This
seasonal change causes a 6 monthly phase shift of ~14 days in
the maximum tractional tidal force. Superimposed onto this is
an 18.6 year cycle of the lunar precession which modulates the
latitude dependence of this amplitude. The tractional tidal force
therefore varies in magnitude, latitude and time, and so is not a
single frequency harmonic.
Winter storms in the North Atlantic form at the interface
where warm Gulf air meets cold Polar air near Newfoundland.
This temperature gradient produces baroclinic instability spawn-
ing storms that move westward across the Atlantic. The track of
these storms follows the Jet Stream and their impact on Europe
depends both on their strength and the relative position of the
Jet Stream (F
RanCiS
& v
avRuS
, 2012). Previous studies (C
uR
-
Rie
, 1983; C
uRRie
, 1984; C
legg
& W
igley
, 1984; a
goSTa
, 2014)
have shown an 18.6-year cycle in rainfall across large continen-
tal zones implying a dependence of storm formation on the lu-
nar precession. Others have speculated about a tidal influence on
climate over decadal timescales (R
ay
, 2007). Changes in lunar
declination through the 18.6-year cycle mainly affect the strength
and sidereal rate of change of tidal forces with latitude.
The cold winter of 2010 resulted from a Jet Stream positioned
below the UK drawing cold air down from the North and East. A
negative value of the North Atlantic Oscillation (NAO) is related
to a negative AO (T
HompSon
& W
allaCe
, 1998) and corresponds
to a low-pressure difference between the Icelandic Low and the
Azores High resulting in a weaker Jet Stream with larger mean-
dering loops. This allows cold air to spill down from the Arc-
tic and Siberia into mid latitudes. During the winter of 2013/14
a strong Jet Stream was positioned directly over the UK and a
string of powerful storms caused extensive coastal flooding (m
eT
o
FFiCe
, 2014). It was striking how several of these storms also
coincided with high spring tides, for example those of December
5
th
2013 and January 5
th
2014.
RESULTS
m
aDDen
(2007) identified a free Rossby planetary wave
mode with a 28-day period during Northern Hemisphere winters
in NCEP/NCAR reanalysis data. He also noted that all such free
waves need “some kind of excitation in order to exist in the face
of dissipation by radiation and friction”. Could gravitational tides
in the atmosphere be responsible? It is the horizontal (tractional)
component of tides that produces deep ocean currents and atmos-
pheric pressure gradients in the atmosphere. Can these also disturb
the Jet Stream flow? To investigate this possibility further, we have
calculated the time dependence of tractional tidal forces acting at
different latitudes using the JPL ephemeris (S
TanDiSH
, 1990) and
then compared these to the Arctic Oscillation (AO). During north-
ern winters the maxima of tidal forces occur at each new moon
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EVIDENCE OF A TIDAL EFFECT ON THE POLAR JET STREAM
19
Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
and their strength depends on the relative positions of the earth,
moon and sun. Although these tractional forces are only about 10
-7
times the strength of the earth’s gravitational acceleration g, they
still dominate because they act perpendicular to and therefore un-
affected by the earth’s gravity. These changing tidal forces sweep
across the earth daily, generating a variable pull on the Jet Stream
of several tons per kilometre. We have used the daily values of
the Arctic Oscillation from 1950 to 2015 as calculated by NOAA
(H
igginS
et alii, 2002) as a measure of Jet Stream flow.
Figure 1 shows the variation of the AO index compared to
calculations of the tidal tractional forces acting at 60N and 45N
for the last 6 winters. (see Appendix A for details). These results
show a visual hint of an AO signal aligned with the lunar cycle,
although it is not always consistent in time. The approximate 28-
day cycle is still however rather striking. A calculation of the cor-
relation between AO and tidal force at 60N gives a value of -0.2
between October 2009 and March 2010.
To investigate further, we also looked at the recent maxi-
mum lunar standstill, which occurred in 2005/2006 and resulted
in the largest monthly variations of tidal forces for Polar re-
gions. If tractional tides affect the Jet Stream flow one would
expect to see a maximum correlation between AO and tidal
forces during the 2005/2006 winter months. Figure 2a shows
the result. There are indeed large swings in the AO, which again
appear anti-correlated with tractional tidal forces. In particular,
the coincidence with the 45N component is striking. This appar-
ent tidal effect may also provide an explanation for the many
reports that rainfall and droughts in northern continents follow
an 18.6-year cycle [3-5], since the path and strength of storms
depend on changes in the flow and direction of the Jet Stream.
In 2006 there were net swings of the AO index through absolute
values of ~6 between consecutive new moons. Figure 2b shows
the same results for the recent winter 2014/15, which includ-
ed a total eclipse of the sun on March 20
th
coincident with the
Fig. 1 - Comparison of the Arctic Oscillation (AO) with tractional tidal forces acting at 60N(blue) and 45N(green) for the last six winters 2009-2014. The
red arrows show observed dips in the AO coincident with tidal maxima
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C.H. BEST & R. MADRIGALI
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Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
moon at perihelion (super-moon), resulting in exceptional high
tides. This strong anti-correlation for two successive total lunar
eclipses occurring at the March equinox is also striking. Such
perfect alignment of the sun and moon bring the highest spring
tides, especially with the moon at perigee.
A large negative swing in the AO occurred in coincidence with
the 2015 eclipse, with a regular anti-correlated beat beforehand. A
very similar situation can be observed for the total eclipse, which
occurred on March 7 1970, and which also happened to be near a
lunar standstill (Fig. 2c), where the effect is even more striking.
Finally, Fig. 2d shows the current winter 2015/16 at the time of
writing, which again shows the same pattern of negative AO at
times of maximum tides.
STATISTICAL ANALYSIS
How statistically significant are these observations? Figure
3 plots the composite of the last 10 years of daily AO signal
compared to calculated tidal forces. A pattern emerges of an un-
derlying 28-day cycle but with irregular changes in phase com-
bined with stochastic noise. This pattern becomes even more
apparent when comparing the differential of the AO to tides that
measures the rate of change. Figure 4 shows the 5-day averaged
rate of change of AO (DA/DT) compared to the tidal traction
force at 45N (T45) over a 65 year period. The differential cal-
culated over 5 successive days avoids excessive noise. Maxi-
ma and minima of DA/DT tend to coincide with maxima and
minima of the tidal force. The Spearman correlation coefficient
calculated between all values of DA/DT and T(45) evaluates to
2.4%, which although small still deviates from zero (no correla-
tion) by 3.7 σ equating to a statistical significance of >99.7%.
As a further test a cross-correlation analysis was also performed
between daily AO values, from 1950 to 2015, and the tractional
tidal acceleration at latitudes for both 45N and 60N each day.
This procedure calculates the correlation coefficient between
both signals as a function of the time lag ‘n’ between them by
systematically shifting one of the series by n-days. Both time
series cover well over 23,800 daily values. Figure 5 presents
this cross-correlation as a function of the tidal lag time. There
is again a small, yet still statistically significant, anti-correlation
of the AO which peaks at a time lag of ~5 days with the tides.
The effect is strongest for the 45N component.
By comparing lunar cycles with AO between December and
the end of March from figures 1 & 2, one can make a further
estimate of the statistical significance in winter. If there is no
effect then we can assume that each tidal maximum would co-
incide with either a dip or a rise in the value of AO. Then we
would expect a distribution of dips similar to simply tossing a
coin. However some 46 out of 56 lunar cycles in figures 1&2
show a visible drop in the value of the AO, coincident with
maximum tidal traction, as indicated by the arrows. The prob-
ability of this occurring by chance is . Maxima in tidal traction
mainly shift the AO towards negative values, which then relax
during tidal minima.
The three lines of evidence therefore for the statistical signifi-
cance of these result are as follows.
Correlation coefficient of maximum rate of change of AO
with maximum tides over 65 years of 0.024 with statistical
significance of 3.7 σ above zero.
A cross-correlation of daily values of tractional tides with AO
over 65 years shows an anti-correlation of -0.02 with an aver-
age time lag of 5 days.
A coincidence of declining values of AO with maximum trac-
tional tides for 10 recent winters. The probability of this being
a random occurrence is ~0.5x10
-6
.
Fig. 2 - a) Variations in the AO which show an anti-correlation with
the tractional tidal forces at 45N(green) and 60N(blue) during
the Maximum lunar standstill (2005/6). b) A similar study for
the current Winter 2014/15. A steep drop in AO is observed
coincident with the solar eclipse on March 20. c) A previous
total eclipse, which occurred on March 7 1970 and produced a
similar steep drop in AO. Lunar declination in 1970 was near
maximum. d) The current winter (2015/2016) up until the end
of February 2016. The red arrows show dips in the AO coinci-
dent with maximum tractional tides
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EVIDENCE OF A TIDAL EFFECT ON THE POLAR JET STREAM
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Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
These results show that it is extremely likely that there is a
tidal influence on the Polar Jet stream flow. The strongest effect
occurs, on average, 5 days after a major spring tide and during
winter. The absolute values of the anti-correlation are small but
the observation of such a continuous signal over 28,300 daily val-
ues is still statistically convincing.
DISCUSSION
The evolution of the Jet Stream and generation of Rossby
waves is an immensely complicated process. Winter weather in
the northern hemisphere is dominated by the strength and flow
direction of the Jet Stream. The intensity of flow varies from one
year to another. The Arctic Oscillation is just one scalar measure-
ment of this evolution. Despite this, we have demonstrated that
there is strong statistical evidence of a small sidereal tidal effect
on the AO, especially during winter months. Strong atmospheric
tides increase the southward drag on the Jet Stream generating a
Coriolis torque as the tides sweep east-west around the rotating
earth, and play a role in triggering storms. It is noticeable how
many of the damaging UK winter storms of 2013/1411 also coin-
cided with high spring tides. The total effect depends both on the
maxima and on the rate of change of the tractional tidal compo-
nent. These both vary within the 18.6-year lunar precession cycle.
Ocean tidal variation may also indirectly affect surface pressure
and therefore AO. However, this possibility cannot be isolated
as it is in phase with any direct effect from atmospheric tides.
Fig. 3 - The last 10 years of daily AO data compared to tractional tidal forces calculated at 60N (black) and 45N (green). The greatest variance occurs
during winter months
Fig. 4 - A comparison between the differential of the Arctic Oscillation (DA/DT) as shown in grey with the tractional tidal force per unit mass at 45N in
blue. The correlation between the two shows a positive correlation of 0.02 with a significance above zero of 3.7 sigma
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C.H. BEST & R. MADRIGALI
22
Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
The work reported here provides strong evidence that increasing
tractional tidal forces can change the direction and speed of the
Jet Stream, especially during winter months with a lag time of
about 5 days. It is therefore proposed that the accuracy of medi-
um-range weather forecasting could be further improved by in-
cluding quantitative gravitational tidal forcing terms into Global
Circulation Models.
APPENDIX A: TRACTIONAL TIDES
The tractional (tangential) tidal force at any point a whose
position vector subtends an angle θ to the lunar position vector r
is defined as follows.
The net force per unit mass acting on point a, assuming F°
= 0
is simply
REFERENCES
a
goSTa
E.A. (2014) - The 18.6-year nodal tidal cycle and the bi-decadal precipitation oscillation over the plains to the east of subtropical Andes, South
America. Int. Journal Climatology, 35(5): 1606-1614.
Fig. 5 - Cross-correlation of the Arctic Oscillation with tractional Tidal
acceleration since 1950. The green values are for the tractional
acceleration at 45N and the gold values are those for 60N. Both
show a small anti-correlation to the AO with a time lag. The 45N
component in particular shows a lag time peaking at 5 days
However for finite angle the tidal force acquires a vertical
component.
The distance a-m is given by
Gravity acting on point a) is therefore
The tidal force now has 2 components
and
where
and
The tractional component (parallel to the surface) can be cal-
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vector for any given date and time. All computer software used is
available from the authors on request (see also supplementary in-
formation).
Note: A simulation of tractional tides experienced during the
winter period 2005/6 can be viewed at https://www.youtube.com/
watch?=v=rebJTFo3XQQ
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EVIDENCE OF A TIDAL EFFECT ON THE POLAR JET STREAM
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Italian Journal of Engineering Geology and Environment, 1 (2016)
© Sapienza Università Editrice
www.ijege.uniroma1.it
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. (1990) - The observational basis for JPL’s DE 200, the planetary ephemerides of the Astronomical Almanac. Astron. Astrophysics, 233:
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ay
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Received January 2016 - Accepted April 2016
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