Frequency analysis of Tide Data from Port Arthur, Tasmania

Some of you may remember the entertaining engagement I had with Dr John Hunter of the University of Tasmania, regarding his controversial reanalysis of the tide register of Thomas Lempriere in the 1840s.

Lempriere had, under the instruction of James Clark Ross, made a mark in a rock face at the Isle of the Dead, near Port Arthur in what is now Tasmania.

According to Lempriere, he made the mark at the “mean level of the ocean”. According to James Clark Ross in his sea log, Lempriere made the mark at the mean point of the ocean.

That mark is now above the mean level of the ocean.

According to John Hunter (pictured below with the mark), this is because Lempriere actually put the mark above high tide so as to avoid too much wave erosion.

After a lot of banter, John Hunter posted data that he and colleague Coleman had made in 2001-2004 by putting an electronic tide gauge in the same harbour as Lempriere, and recorded the sea level.

Here is the plot of the data (time axis in days from the beginning of the experiment, y-axis is height in mm above the mean):

As you can see, there is a gap in the data near the beginning where the electronic tide gauge failed. I assume John Hunter went over and kicked it into life. It must have worked.

The tide gauge recorded the water level every six minutes, but measured downwards to the level of the sea. In order to return the data to the more normal orientation, I computed the mean of the data, and then subtracted each data point from the mean.

Since I had a gap and intended to use Fourier Analysis, I truncated the data to just after the gap:

x-axis seconds, y-axis water level height from mean

The Fourier Analysis was done using MathCAD 14.0 and the results are as follows:


Fourier Spectrum of Port Arthur Tide data

The discrete frequencies correspond to the following resonances (all except ‘X’)


Species Symbol (hr)
Principal lunar semidiurnal M2 12.42
Principal solar semidiurnal S2 12
Larger lunar elliptic semidiurnal N2 12.66
Larger lunar evectional ν2 12.63
Variational MU2 12.87
Lunar elliptical semidiurnal second-order 2″N2 12.91
Lunar diurnal K1 23.93
Lunar diurnal O1 25.82
Lunar diurnal OO1 22.31
Solar diurnal S1 24
Smaller lunar elliptic diurnal M1 24.84
Smaller lunar elliptic diurnal J1 23.1
Larger lunar evectional diurnal ρ 26.72
Larger lunar elliptic diurnal Q1 26.87

However the resonance marked as “X” does not correspond to any astronomical forcing, and is distinct from the Solar Diurnal S1 as can be seen from the following close-up.

So I surmise that X corresponds to the tidal constant of the estuary. Apparently in that locale with the currents, sea floor geometry and wind directions, the sea washes in and out of the harbour every 23 hours and 37 minutes.

All of this was unknown to Thomas Lempriere, of course. The tidal constant being so close to one of the main astronomical forcings caused some very peculiar tide behaviour.

When I’ve analyzed Lempriere’s data from 1840-1842, we may be able to see how well Lempriere managed to record that data in the light of modern measurements.

More to follow.

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3 Responses to Frequency analysis of Tide Data from Port Arthur, Tasmania

  1. Gary says:

    I’ll be looking for the comparison. No doubt you will check for evidence of physical changes to the harbor basin over the last 170 years.

  2. John A says:

    According to (the late) John Daly, the harbour has barely changed in the intervening period. He took photographs to prove it.

    There are three confounding problems (1) sea level rise, (2) isostatic rebound and (3) sudden uplift in the 1880s following a series of earth tremors.

    But first, I want to see how good a tide recorder Thomas Lempriere really was.

  3. mondo says:

    Interesting stuff John. Well done for mentioning the confounding problems. Perhaps not at this location, but at many locations there are other confounding problems that can affect the observed result. These can include local subsidence due to extraction of ground water (Adelaide for example) or in the case of coral atolls subsidence or emergence driven by changes in the level of activity of the underlying volcanic edifice.

    It has intrigued me that the CSIRO (for example) can present information on sea level around Australia that simply averages reported results, without acknowledging these known confounding factors. I don’t have the information with me, but as I recall the CSIRO reporting of the Australian average sea level rise includes data for Adelaide and Port Adelaide (two stations in close proximity) in an area known to be subsiding due to groundwater extraction, data for Fremantle where subsidence is also thought to be happening, and Newcastle. If these outliers are removed, as I believe they should be, the average rise in Australian sea level falls to a much lower level than reported.

    Later data published as a map in The Australian shows sea level rise on the western seaboard being significantly higher than on the eastern seaboard. Why is that? Apparently nobody bothers to ask (and certainly not answer) the question.

    I am sure that similar anomalies occur in many places. Yet those arguing for alarming levels of sea level rise (due of course to man’s emissions of CO2!) never address these confounding factors which could explain most, if not all, of the observed rise (or fall in the case you are looking at).

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