An obvious clue from tidal data

One of the interesting traits of climate science is the way it gives away obvious clues. This recent paper by Iz

Iz, H Bâki. “The Effect of Regional Sea Level Atmospheric Pressure on Sea Level Variations at Globally Distributed Tide Gauge Stations with Long Records.” Journal of Geodetic Science 8, no. 1 (n.d.): 55–71.
shows such a breathtakingly obvious characteristic that it’s a wonder why everyone isn’t all over it.  The author seems to be understating the feature, which is essentially showing that for certain tidal records, the atmospheric pressure (recorded in the tidal measurement location) is pseudo-quantized to a set of specific values.  In other words, for a New York City tidal gauge station, there are 12 values of atmospheric pressure between 1000 and 1035 mb that are heavily favored over all other values.
One can see it in the raw data here where clear horizontal lines are apparent in the data points:

Raw data for NYC station  (Iz, H Bâki. “The Effect of Regional Sea Level Atmospheric Pressure on Sea Level Variations at Globally Distributed Tide Gauge Stations with Long Records.” Journal of Geodetic Science 8, no. 1 (n.d.): 55–71.)

and for the transformed data shown in the histogram below, where I believe the waviness in the lines is compensated by fitting to long-period tidal signal factors (such as 18.6 year, 9.3 year periods, etc).

Histogram for transformed data for NYC station  Iz, H Bâki. “The Effect of Regional Sea Level Atmospheric Pressure on Sea Level Variations at Globally Distributed Tide Gauge Stations with Long Records.” Journal of Geodetic Science 8, no. 1 (n.d.): 55–71.

The author isn’t calling it a quantization, and doesn’t really call attention to it with a specific name other than clustering, yet it is obvious from the raw data and even more from the histograms of the transformed data.

The first temptation is to attribute the pattern to a measurement artifact. These are monthly readings and there are 12 separate discrete values identified so that connection seems causal. The author says

“It was shown that random component of regional atmospheric pressure tends to cluster at monthly intervals. The clusters are likely to be caused by the intraannual seasonal atmospheric temperature changes, which may also act as random beats in generating sub-harmonics observed in sea level changes as another mechanism.”
Nearer the equator, the pattern is not readily evident. The fundamental connection between tidal value and atmospheric pressure is due to the inverse barometric effect
“At any fixed location, the sea level record is a function of time, involving periodic components as well as continuous random fluctuations. The periodic motion is mostly due to the gravitational effects of the sun-earth-moon system as well as because of solar radiation upon the atmosphere and the ocean as discussed before. Sometimes the random fluctuations are of meteorological origin and reflect the effect of ’weather’ upon the sea surface but reflect also the inverse barometric effect of atmospheric pressure at sea level.”
So the bottom-line impact is that the underlying tidal signal is viably measured even though it is at a monthly resolution and not the diurnal or semi-diurnal resolution typically associated with tides.
Why this effect is not as evident closer to the equator is rationalized by smaller annual amplification
“Stations closer to the equator are also exposed to yearly periodic variations but with smaller amplitudes. Large adjusted R2 values show that the models explain most of the variations in atmospheric pressure  observed at the sea level at the corresponding stations. For those stations closer to the equator, the amplitudes of the annual and semiannual changes are considerably smaller and overwhelmed by random excursions. Stations in Europe experience similar regional variations because of their proximities to each other”
So, for the Sydney Harbor tidal data the pattern is not observed

Sydney histogram does not show a clear delineated quantization

Whereas, I previously showed the clear impact of the ENSO signal on the Sydney tidal data after a specific transform in this post. The erratic ENSO signal (with a huge inverse barometric effect as measured via the SOI readings of atmospheric pressure) competes with the annual signal so that the monthly quantization is obscured. Yet, if the ENSO behavior is also connected to the tidal forcing at these long-period levels, there may be a tidal unification yet to be drawn from these clues.

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