## CET temperature trends

UK temperatures essentially show no obvious warming for July over the last  365 years. There has however been a small warming effect in  January since 1970, which may just be related to rapid population growth.

Comparison of CET values for the coldest month (January) and the warmest month (July) each year with a) England’s population growth and b) CO2 increases.

The Central England Temperature (CET) measurements is the longest continuous dataset in the world and covers a 360 year period from 1658 to 2016. Weather stations are concentrated within a roughly triangular area ranging from  Lancashire, Bristol and London. The results are usually presented as annual temperature ‘anomalies’ relative to a 30-year seasonal average as for example by Ed Hawkins. However we can also simply plot the average measured temperatures for each month to identify trends. The resultant figure, as shown above, demonstrates that for CET there is no obvious trend in July temperatures at all. Perhaps after 1980 July temperatures have been slightly warmer than the long term 10y average, but well within annual variability. For the average temperatures  in January the year to year variability is much larger still. Extreme cold winters occur throughout the CET record. In my lifetime I remember 1963(average -2C), 1979 (-0.5C) and 2010(+1C) standing out as being particularly cold, while the record coldest January  is held by 1795 (-3C). The 10 yearly January average shows two recent warm periods lasting firstly from 1890 to 1940 and secondly from 1970 to 2016.

Is there really any  evidence for anthropogenic global warming in CET? I think you would be hard pushed on the basis of this data to claim that CO2 alone is responsible for recent trends. If the second increase in 1970 to 2016 UK winter temperatures does indeed have an anthropogenic cause, then it is just as likely caused by rapid population growth as it is by CO2. Today some 50 million people in England warm their homes every January driving ~30 million vehicles on well lit roads in warm cities. That massive population growth has also mostly been concentrated within the CET triangle.

Posted in climate science, UK Met Office | Tagged , , | 5 Comments

## The forgotten Milankovitch effect – Tides

The obliquity of the earth’s spin axis varies over a 41000y cycle between 24.5 and 22.2 degrees. The canonical work on calculating Milankovitch cycles has been done by J. Laskar and his team at the Observatoire de Paris[1]. Changes in obliquity have been the main driver for glacial cycles for over 2 million years. Larger obliquity increases summer insolation to both poles. Eccentricity and precession just modulate the seasonal balance at each pole. For the last 800,000 years obliquity alone has been insufficient to end glaciations, and the reason for this is still not fully understood.

Top graph: Obliquity and Eccentricity of the earth’s orbit for the last million years ( Laskar2010 ). Bottom graph shows just how small eccentricity affects net annual insolation.

However, increased obliquity has another effect. It changes the amplitude of the lunar orbital precession. The lunar orbit is inclined at 5 degrees to the solar ecliptic and precesses with a period of 18.6 years. The maximum declination of the moon at ‘lunar standstill is currently 28.5 degrees and this occurs every 18.6 years, as shown in the diagram. However 7000 years ago the earth’s tilt was 24.3 degrees compared to the current 23.5 degrees.  The obliquity is also decreasing  so that in 12000 year time it will be only 22.6 degrees.

This means that lunar standstills reached 29.1 degrees around LGM, while in 12000 years time they will reduce to only 27.4 degrees. This significantly changes the maximum strength of tidal flows at large latitudes during a lunar standstill. It is the tractional (horizontal) component of the moon’s gravitational tide which draws the oceans into a tidal bulge. This maximum tractional force occurs at about 45 degrees to the tidal bulge, so increases the average traction acting on polar regions. I have calculated this effect using the lunar ephemeris published by IRME back to about 8000 years ago. A clear reduction of the amplitude of high latitudes, Lunar standstill tides with decreasing obliquity is observed.

The graph shows the 28 day average of daily calculations of lunar tractional acceleration acting at 65N over the last ~ 6000y. The ephemeris is provided by ELPC82 (Laskar et al.) [1]

Extreme tides at high latitudes have been  decreasing for the last 8000 years  in coincidence with the decreasing obliquity of the earth. The solar tidal component at perihelion has also reduced by about 5% due to the  decrease in eccentricity. At the LGM sea levels were 120m below current levels. As a result the edge of ice sheets were grounded around Northern Europe and the Arctic which strongly affecting  tidal dynamics.

Bathymetry of the Arctic Ocean curtesy NOAA. The 100m contour shows the approximate sea level 20,000y ago and the 1000m contour shows the maximum depth of grounded sea ice. Note the much narrower access channel to the North Atlantic. Tidal flows were about 5 times greater than today [2]

The energy dissipation in the North Atlantic and Arctic have been estimated to be  five times stronger than today[2].  Furthermore the tidal tractional force at maximum lunar standstill was significantly stronger combined with enhanced spring tides from the solar component. Enhanced tides also drive the  meridional overturning circulation MOC which is sensitive to increased enhanced tidal dissipation in the deep ocean [3].

Are these ‘Milankovitch’ tides the primary cause of the rapid melt back of the ice sheets once Arctic summer insolation had peaked ~15,000 years ago?

[1] La2010: a new orbital solution for the long-term motion of the Earth,  J. Laskar et al. A&A 532, A89 (2011)

[2] The evolution of tides and tidal dissipation over the past 21,000 years, Wilmes, Sophie-Berenice; Green, Mattias,  Journal of Geophysical Research. 2014

[3] Green, J. A. M., and M. Huber (2013), Tidal dissipation in the early Eocene and implications for ocean mixing, Geophys. Res. Lett., 40, 2707– 2713

Posted in climate science, Science | 16 Comments

## Evidence of a tidal effect on the Polar Jet Stream

Preamble: Our  paper has finally been published in Italian Journal of Engineering Geology and Environment. It proved to be controversial with ACP, but I am 95% certain that lunar tides affect both weather and medium term climate.

C.H. Best and R. Madrigali

## Abstract

Variations in the Polar Jet Stream directly affect weather across Europe and North America (Francis et al., (2012)). Jet Stream dynamics are governed by the development of planetary Rossby waves (Dickinson, (1978)) driven by variation of the Coriolis force with latitude. Here we show that increasing atmospheric tides can induce the development of Rossby waves, especially during winter months. This changes the flow and position of the Jet Stream, as measured by the Arctic Oscillation (AO) (Higgins 2002). Although horizontal tidal forces are tiny (107 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 “tractional” 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 (Currie, 1983/84).

## 1        Introduction

Varying tidal forces act both on the oceans and atmosphere particularly at high latitudes. A detailed study (Lindzen, 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 winters the Jet Stream strengthens and shifts northwards. Meanders or Rossby waves (Dickinson 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 winter, whereas that coincident with the full moon is largest during 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 spawning 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 (Francis, 2012). Previous studies (Currie, 1983, Agosta, 2014, Currie, 1934, Clegg, 1984) have shown an 18.6-year cycle in rainfall across large continental zones implying a dependence of storm formation on the lunar precession. Others have speculated about a tidal influence on climate over decadal timescales (Ray 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 (Thompson, 1998) and corresponds to a low-pressure difference between the Icelandic Low and the Azores High resulting in a weaker Jet Stream with larger meandering loops. This allows cold air to spill down from the Arctic 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. It was striking how several of these storms also coincided with high spring tides, for example those of December 5th 2013 and January 5th 2014.

## 2        Results

[RA Madden 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 atmospheric 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 (Standish, 1990) and then compared these to the Arctic Oscillation (AO). During northern winters the maxima of tidal forces occur at each new moon 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 unaffected 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 (Higgins, 2002) as a measure of Jet Stream flow.

Figure 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.

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 correlation 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 maximum lunar standstill, which occurred in 2005/2006 and resulted in the largest monthly variations of tidal forces for Polar regions. 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 apparent 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 included a total eclipse of the sun on March 20th coincident with the 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.

Figure 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 coincident with maximum tractional tides.

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 (Figure 2c), where the effect is even more striking. Finally Figure 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.

## 3        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 underlying 28-day cycle but with irregular changes in phase combined 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 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.

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 calculated over 5 successive days avoids excessive noise. Maxima 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 correlation) by 3.7 $\sigma$ equating to a statistical significance of >99.7%.

Figure 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.

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.

Figure 4: 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.

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 coincide 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 probability 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 significance 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 ? 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 average time lag of 5 days
• A coincidence of declining values of AO with maximum tractional tides for 10 recent winters. The probability of this being a random occurrence is ~0.5×10-6 .

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 values is still statistically convincing.

## 4        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 measurement 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 coincided with high spring tides. The total effect depends both on the maxima and on the rate of change of the tractional tidal component. 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. 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 medium-range weather forecasting could be further improved by including 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 ? to the lunar position vector r is defined as follows.

The net force per unit mass acting on point a, assuming  $\Phi = 0$ is simply

$\frac{Gm}{(r-R \cos \theta)^2} - \frac{Gm}{r^2} \cong \frac{2GmR \cos \theta}{r^3}$

However for finite angle $\Phi$ the tidal force acquires a vertical component.

The distance a-m is by Pythagorus

$\sqrt{R^2 \sin^2 \theta + (r - R \cos \theta)^2}$

$= \sqrt{R^2 +r^2 -2rR \cos \theta}$

Gravity acting on point a) is therefore

$\frac{Gm}{R^2 + r^2 -2rR \cos \theta}$

The tidal force now has 2 components

$Fx = Gm( \frac{ \cos \phi}{R^2 + r^2 - 2rR \cos \theta} - \frac{1}{r^2})$

$Fy = \frac{ -Gm \sin \phi}{R^2 + r^2 - 2rR \cos \theta}$

where

$\cos \phi = \frac{r-R \cos \theta}{\sqrt{R^2 + r^2 - 2rR \cos \theta}}$

and

$\sin \phi = \frac{R \sin \theta}{\sqrt{R^2 + r^2 - 2rR \cos \theta}}$

The tractional component (parallel to the surface) can be calculated using the JPL ephemeris to derive the net lunar-solar tidal vector for any given date and time. All computer software used is available from the authors on request (see also supplementary information).

Note: A simulation of tractional tides experienced during the winter period 2005/6 can be viewed at https://www.youtube.com/watch?v=rebJTFo3XQQ

## References

1. S. Lindzen (1981), Turbulence and stress owing to gravity wave and tidal breakdown, Journal of Geophysical Research: Oceans (1978–2012), Volume 86, Issue C10, pages 9707–9714, 20 October 1981

Dickinson, R E (1978), “Rossby Waves-Long-Period Oscillations of Oceans and Atmospheres”. Annual Review of Fluid Mechanics 10: 159

Francis, J. A. and S. J. Vavrus (2012): Evidence Linking Arctic Amplification to Extreme Weather in Mid-Latitudes, Geophys. Res. Lett., Vol. 39, L06801

Robert G. Currie (1983), Detection of 18.6 year nodal induced drought in the Patagonian Andes Geophysical Research Letters Volume 10, Issue 11, pages 1089–1092, November 1983

Eduardo Andros (2014) Agosta 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, 35,5,1606-1614,2014

RG Currie (1984) On bistable phasing of 18.6 year nodal induced flood in India Geophysical Research Letters. 1984; 11(1). DOI: 10.1029/GL011i001p00050

S.L. Clegg, T.M.L. Wigley, Periodicities in North-East China, 1470-1979, Geopys Res. Lett. Vol.11 Pages 1219-1222, Dec 1984

Standish, E. M., Jr. The observational basis for JPL’s DE 200, the planetary ephemerides of the Astronomical Almanac. Astron. Astrophysics. 233, 252-271 (1990)

Richard D. Ray, 2007: Decadal Climate Variability: Is There a Tidal Connection? J. Climate, 20, 3542–3560.

Thompson, David W. J.; John Michael Wallace (1998). “The Arctic oscillation signature in the wintertime geopotential height and temperature fields”. Geophys. Res. Letters 25 (9): 1297–1300.

Madden, R. A. (2007) Large-scale, free Rossby waves in the atmosphere – an update, Tellus, 59A, 571-590.

Higgins, R. W., A. Leetmaa, and V. E. Kousky, 2002: Relationships between climate variability and winter temperature extremes in the United States. J. Climate, 15, 1555-1572. Data: https://www.ncdc.noaa.gov/teleconnections/ao/

Met Office Report, Winter 2013/14

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