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Magnitude of Tides


Q: If the Moon is slowly moving away from Earth presumably it was previously closer and had a stronger gravitational pull on our planet than it does at present. Does this mean that the tides were more extreme in the geological past? If so, what is the geological evidence for this, and what does it tell us about the magnitude of the tidal range at different periods of time?

From Mr Michael Rosenbaum (April 2010)

Reply by Dr Russ Evans (BGS)

Briefly, the geological record offers little if any direct evidence about the magnitude of the tidal range in the past. Nevertheless, there is geological evidence related to tidal periodicity that confirms results derived from astronomical and geodetic considerations. These calculations tell us that tides in the past, although on average a little greater than currently, were of similar magnitude to those we see today.

To elaborate, we must first remind ourselves of the relevant astronomy. The gravitational force exercised by the Moon on the Earth tries to pull its oceans (and with lesser success the solid Earth itself) into a slightly ellipsoidal shape. The rotation of the Earth means that this gives rise to two tides per lunar day at most locations. Because of the geometry of the ocean basins and the viscous response of the “solid” Earth this process dissipates the rotational energy of the Earth, which is therefore slowing down. Days are getting longer! The presence of friction means that the tidal “bump” in the Earth’s topography does not lie directly beneath the Moon. Since the Earth rotates in the same direction as the Moon orbits around it, the “bump” lies a little ahead of that point. Because of this, the Moon experiences a small but steady pull speeding it up, increasing its kinetic energy, causing it to move into a higher orbit, lengthening its orbital period and reducing its tidal pull on the Earth. The net loss of energy to the Moon is an additional factor slowing the Earth’s rate of rotation.

If no other event occurs to stop this process, the rotational period of the Earth will eventually come to match the orbital period of the Moon. This phenomenon (“tidal locking”) has already happened to the Moon itself, early in its history – it always presents the same face to the Earth. The same is true for many satellites in the solar and other stellar systems, for essentially the same reasons.

The rate of this process is, obviously, very slow. The distance between the Earth and Moon, as determined through lunar laser ranging, is currently increasing by 38 mm/y and the length of day is increasing by around 2 ms/century. Since the semi-major axis of the Moon’s orbit is 384,399 km, this means that the Earth-Moon distance is increasing by almost exactly one part in 10 billion per year. Because the gravitational force exercised by one body on another is inversely proportional to the square of the distance between them, for small changes in distance, the proportional change in force is twice the proportional change in distance. So the tidal force is decreasing by two parts in 10 billion per year. Clearly, geological timescales are required to effect significant changes in these figures.

Cycles are recorded in the geological record as “rhythmites”, bedding or lamination in rocks such as sandstone, siltstone or mudstone, and are classified according to the period of the phenomena that generated them. Rhythmites associated with annual cycles are often referred to as varves, and Milankovitch cycles are ascribed to very-long period cyclical phenomena. Tidal flows modulate currents in a marine environment, even where these contain a consistent sediment load, varying the amounts and distribution of particle sizes laid down from hour to hour. Thus tidal rhythmites can potentially develop in any situation where sedimentary processes are influenced by tides. They have been identified in a variety of marine environments ranging from the neighbourhoods of deepwater hydrothermal plumes through estuaries to the distal parts of a deltaic system. The latter are particularly favourable to generating lengthy sequences.

As far as I have been able to determine, no-one has yet found a way to use the data from rhythmites to determine tidal heights directly, and even if that were possible, measurement from a single location would tell us little if anything about global tidal behaviour, as tidal heights in marginal seas vary greatly throughout the modern world due to the shape of ocean basins, and we have no reason to believe that matters were any different in the past. Tidal rhythmites can, however, provide confirmation of the astronomical observations and the associated calculations can be used to determine the length of day, lunar distance, rate of lunar recession, and other features of this process.

Tides vary in intensity on a number of cyclical patterns determined by the orbit of the Moon, and these variations are recorded in the thicknesses of rhythmite layers. By subjecting measurements of layer thicknesses from very long rhythmite sequences to harmonic analysis, it is possible to determine the ratios between these cycles at the time the sediments were laid down. The astronomical theory outlined above can also be used to calculate the ratios for any given Earth-Moon distance. So, by comparing the geological observations with the theoretical results, it is possible to determine the Earth-Moon distance at that time quite accurately. Once the distance is known, values for the length of the month, the tidal forces and tidal heights can all be calculated very easily.

Based on information obtained from tidal rhythmites, Williams (2000) showed that at 620Ma the Earth-Moon distance was 0.965 of its present value, and that at 2450Ma it was 0.906 of its present value. These and other considerations regarding the Earth-Moon system (Williams, 2000; Varga et al. 2006) lead to the conclusion that the distance between the Earth and the Moon was perhaps only 20% or so less than its current value even at the start of their joint evolution 4+ billion years ago. This appears to be the current consensus view amongst geologists working on this matter. Williams’ results also imply that the rate of recession of the Moon has accelerated over that period.

In terms of tides, if the Earth-Moon distance has never been more than ~20% less than the present value, then tidal forces have never been much more than 40% greater than current values. Since tidal heights today vary far more than this, from less than 1m in the deep ocean (and much less in confined seas such as the Mediterranean) to 17m in the Bay of Fundy, it seems unlikely that tidal heights, even at unusual locations such as Fundy, or at any point in the past, were significantly more extreme than those seen today.


Williams, G.E. 2000. Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit. Reviews of Geophysics, v. 38, p. 37-60

Varga, P., Rybicki, K.R. and Denis C. 2006. Comment on the paper “Fast tidal cycling and the origin of life” by Richard Lathe. Icarus, v. 180, pp. 274-276