Tidal variations

Finally I have a working program which calculates the strength of tides based on the relative positions of the moon and the sun. This is based on the JPL ephemeris which is the most accurate available and is also used for space probes. The calculation is based on the relative distances of the moon and sun from the earth at any day over the last 60 years. The net tidal force is the vector sum of both components during their respective orbits. To sum these I take the dot product of the position vectors and apply a factor Mass/R^3 to both terms. Twice a month the earth experiences spring tides corresponding to the new moon and the full moon.  This is because the sun’s tidal force aligns more or less in the same direction to the moon’s tide at new moon and again slightly less at full moon. This is then amplified when the new moon coincides with perihelion of the earth’s orbit around the sun. These are perihelion spring tides and up to 4 times the strength of neap tides.

Fig 1. The net effect of the solar and lunar tides are reinforced  when they align  in the same plane. Maxima occur when the relative distances are minimised. Every 18000 y they coincide in a perfect plane with all distances minimised.


Now look carefully at just how much the earth’s eccentricity modulates the net tidal forces. This is because the sun’s mass is 27 million times larger than the moon and small changes in earth-sun distance can have large effects. Currently the eccentricity is 0.0167 and can reach as high as 0.057 during Milankovitch cycles leading to a rough doubling of the direct solar tide. This then must also amplify  the net vector lunar-solar tide as indicated  above significantly. Small changes in sun-earth distance are amplified with respect to those of the moon by a mass ratio of 2.7*10^7 caused by the  1/R^3 dependence of tidal forces.

Now consider the coastal flooding this winter which has mainly effected  western coastal regions of the  UK. The main reason for this are the unusually strong spring tides rather than global warming. These storms have tended to coincide with unusually extreme tides. Next winter such flooding is unlikely to re-occur. 


9 Responses to Tidal variations

  1. John F. Hultquist says:

    Very interesting – and I just read something related:

    The “Weekly Climate and Energy News Roundup” by SEPP on WUWT (Feb. 2) included a link to a paper regarding this place;
    Saint-Louis, Senegal [also called Ndar ]
    Put the above place-name as your search term in Google Earth
    (or use these: 16.0227, -16.5018 )
    The article linked to in the SEPP weekly report is here:

    A carefully reading of the article in contrast to the title reveals the place is a huge sand bar on the east coast of the Atlantic Ocean and is a problematic place for a large population (>175,000). The ‘images’ on the Web are also interesting.

    If I read Fig. 1 in this post correctly there would have been high, but somewhat less high, tides last spring (Apr/May) than currently (Jan/Feb). It looks like the UN should urge these folks to begin moving now or get moved by higher tides later.
    It is shameful that the UN and Nation-states have wasted so much money on the IPCC and CO2.

  2. Clive Best says:

    Regular tidal changes in sea level are far greater than any tiny increase due to global warming. Tides change sea level by upwards of 10 meters each day. Even using IPCC estimates AGW has caused at most a couple of cm increase. Furthermore tides vary enormously between neap tides, spring tides and perigrean spring tides. It would be far better to warn people when they should prepare for flooding especially if spring tides coincide with stormy weather.

    Another possibility is that large tides can actually spawn storms – but that is another story !

    I am traveling for 2 weeks so updates on this will have to wait.

  3. A C Osborn says:

    There is evidence to suggest that not only Water is affected but the Atmosphere as well.
    That would be another area to explore.

  4. A C Osborn says:

    Clive how does this paper fir in with what you have just found?

    • clivebest says:

      This definitely seems like an atmospheric tidal effect. These northern and southern “annular nodes” look to be related to the jet streams which determine weather patterns. The 18.6 year precession moves the tidal bulge further north (and south) which changes tidal patterns. Can the moon cause storms to form by tweaking the polar air front ?

      January 2014 was a particularly strange month which won’t occur again until 2018. There were 2 perigean spring tides – 1st January and 30th January. These are tides where the sun moon and earth line up in the same plane and both the earth and moon are at perigean (shortest distance) in their respective orbits. For a week or so either side of the new moon then we get strong high tides. Do strong tides also play a role in generating storms for example the recent ones over UK? When there is a severe storm then there are then two additional effects:

      1. The low pressure actually rises up the sea level – like in a vacuum pump. This recent low pressure was centered over cornwall.
      2. Strong on-shore winds whip up large waves which are driven over the tidal defenses.

  5. Nik Kelly says:

    Hi ! Slightly tangential, but does that tidal data indicate much bigger tidal ranges around the Dark ages and early Medieval period ? There was a lot of land lost to the sea around UK coast in a comparatively short period (‘geologically’ speaking ;-). eg Mount St Michael (& French equivalent) went from coastal to island.

    This may also account for those legendary maelstroms which, today, are wimpy except for Spring tides and storms…

  6. Gianni says:

    Hello. Very nice article. Is it possible to have a look at the code you used to make calculation?
    I’m trying to do something similar with JPL ephemeris, but with poor results: I’m a coder but I’m not an astronomer!

    Many thanks.

    • Clive Best says:

      The method of calculating the tidal forces is described in

      I have IDL code if you can use that. Otherwise I have a fortran interface to JPL ephemeris.
      This snippet derives maximum tides.

      for i=0, 98 do begin
      for j=0,364 do begin

      JPLEPHINTERP, pinfo, pdata, jstart, xearth, yearth, zearth,/EARTH
      JPLEPHINTERP, pinfo, pdata, jstart, xmoon, ymoon, zmoon,OBJECTNAME=’MOON’
      JPLEPHINTERP, pinfo, pdata, jstart, xsun, ysun, zsun,OBJECTNAME=’SUN’
      earth[0] = xearth*1000.
      earth[1] = yearth*1000.
      earth[2] = zearth*1000.
      moon[0] = xmoon*1000.
      moon[1] = ymoon*1000.
      moon[2] = zmoon*1000.
      sun[0] = xsun*1000.
      sun[1] = ysun*1000.
      sun[2] = zsun*1000.
      se = sun – earth
      me = moon-earth

      scal1 = sqrt(se[0]^2 + se[1]^2 + se[2]^2)
      scal2 = sqrt(me[0]^2 + me[1]^2 + me[2]^2)
      fcos = (me[0]*se[0]+me[1]*se[1]+me[2]*se[2])/(scal1*scal2)
      stide = 2.0*G*sunmass*rearth/scal1^3
      mtide = 2.0*G*moonmass*rearth/scal2^3

      if (fcos GT 0) then begin
      res = mtide/scal2*me + stide/scal1*se
      endif else begin
      res = mtide/scal2*me – stide/scal1*se
      tidetot = sqrt(res[0]^2 + res[1]^2 + res[2]^2)
      angle = asin(res(2)/tidetot)
      polang = 1.134464 – angle

      if (tidetot GT tmax) then begin
      tide[i] = tmax
      fdat[i] = jstart

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