Wednesday, December 23, 2015

On The Origin of the Sea-level Seesaw - 2

Fig. 1 Seesaw / Sawtooth pattern of SLC
I have been doing some research concerning the "seesaw" or "sawtooth" pattern effect that tide gauge stations around the world tend to show us (Fig. 1, Fig. 2, PSMSL).

In so doing I ran across indications that a lot of myth, ignorance, and plain old "we don't know" are involved in some of the issues concerning both climate change and sea level change.

Fig. 2 Seesaw / Sawtooth pattern of SLC
I will not be at all surprised if the issue of what causes the seesaw / sawtooth pattern at tide gauge stations around the world is likewise a source of conflicting explanations.

I had addressed the issue, yesterday, in this manner:
I have been looking into the historical foundation for notions such as "El Niño," "La Nina," and "The Polar Vortex."

I am doing so because I think many aspects of current civilization's development of explanations is wrong headed.
(On The Origin of the Sea-level Seesaw). A while after writing that, and then getting back into the research, I ran across this statement:
"The truth is, no one knows what really causes El Niño."
(NOVA PBS, emphasis added). So, that puts the inquiry into the "valid questioning of an issue category," the zone where scientists themselves are not completely in agreement.

There is one thing, in that NOVA PBS post, about the physical aspects of an El Niño which intrigued me.

Not only that, the subject fits nicely into today's discussion even if it is a bit abstract:
In one sense, it's [El Niño is] like an iceberg; most of it is submerged, but part of it sticks out above the sea's surface, as the wedge floats in the surrounding ocean. Partly because warm water is less dense than cool water, and also partly because El Niño waters are less salty than normal seawater. (It's always raining over an El Niño, and the rainwater dilutes the sea.) Both of these conditions contribute to buoyancy. A sharp temperature and density change—called the thermocline—floats about 100 meters below the surface, and marks the bottom of this warm "iceberg." The top layer of water may protrude 150 or more centimeters above sea level. This isn't so hard to picture if you think about tides, which also pile water up above sea level.
(ibid, NOVA PBS, emphasis added). There is counter-intuitive material in this issue.

Counter-intuitive like in the issue of the gravity of sea level change (The Gravity of Sea Level Change).

Interestingly, there is even some disagreement about what seems to be a straight forward issue, which is: the movement of actual icebergs.

Yes, that can also cause differing views to be held by competent scientists.

For example, take the case of the iceberg that sank the Titanic (The Iceberg’s Accomplice: Did the Moon Sink the Titanic?).

In these cases it is often a good idea to begin a discussion based upon what aspects of the issue has more. or the most, agreement.

There is agreement that when melt water or an iceberg calves into the ocean from an ice sheet, there is immediate displacement of ocean water, there is immediate loss of mass of the ice sheet, and immediate mass increase of the ocean.

There may be some differing viewpoints, however, as to what happens next, and differing viewpoints as to how it happens.

How does the melt water of the ice sheet get relocated or redistributed in the ocean?

The same question goes for the iceberg melt water once it melts.

My hypothesis at this point is that the displacement and the transference of gravitational-energy, from the ice sheet to the ocean, is the ghost factor which behaves more like the tidal waves, the ocean tides.

Which are created by the gravity of the Moon and Sun, in terms of speed and shape.

But in principle, other than the speed involved, they are like a tsunami wave in the sense of being hidden for most of their early existence:
In the deep ocean, a tsunami wave may only be a few inches high.

\displaystyle  v \approx \sqrt{g b} \ \ \ \ \ (1)
where {b} is the depth of the ocean, and {g \approx 9.8 ms^{-2}} is the force of gravity. As such, tsunamis in deep water move very fast – speeds such as 500 kilometres per hour (300 miles per hour) are quite typical; enough to travel from Japan to the US, for instance, in less than a day. Ultimately, this is due to the incompressibility of water (and conservation of mass); the massive net pressure (or more precisely, spatial variations in this pressure) of a very broad and deep wave of water forces the profile of the wave to move horizontally at vast speeds. (Note though that this is the phase velocity of the tsunami wave, and not the velocity of the water molecules themselves, which are far slower.)

\displaystyle  A \propto \frac{1}{b^{1/4}} \ \ \ \ \ (2)
at least until the amplitude becomes comparable to the water depth (at which point the assumptions that underlie the above approximate results break down; also, in two (horizontal) spatial dimensions there will be some decay of amplitude as the tsunami spreads outwards). If one starts with a tsunami whose initial amplitude was {A_0} at depth {b_0} and computes the point at which the amplitude {A} and depth {b} become comparable using the proportionality relationship (2), some high school algebra then reveals that at this point, amplitude of a tsunami (and the depth of the water) is about {A_0^{4/5} b_0^{1/5}}. Thus, for instance, a tsunami with initial amplitude of one metre at a depth of 2 kilometres can end up with a final amplitude of about 5 metres near shore, while still traveling at about ten metres per second (35 kilometres per hour, or 22 miles per hour), and we have all now seen the impact that can have when it hits shore.
(What's New). When I finished reading that, I thought "that is wild."

Then I attributed some of the seesaw / sawtooth pattern to the mystery of the tsunami, until I read about the mystery of any wave, ocean type or not.

Once again, this potential solution also tends to be counter intuitive:
Waves are among the most familiar features in the ocean. All waves work similarly, so although we are talking about ocean waves here, the same information would apply to any other waves you might discuss in science classes.

Ocean waves transport energy over vast distances, although the water itself does not move, except up and down.
(Oceans in Motion: Waves and Tides, emphasis added). The writer is talking about the water itself not moving with the movement of wave energy over vast distances (in order to transfer that energy from point "A" to point "B").

In the application of this dynamic to ice sheets, the parts that cannot immediately become waves, the icebergs, are moved about slowly until they melt.

So, the sea level rise and fall caused by ice sheet mass-gravity energy loss, in Greenland and Antarctica, is primarily a function of a transfer of energy to a distant location by waves of various sorts, and far less so a relocation of the molecules of water (when the molecules are moved it is via ocean currents).

Those waves move at different speeds, and in different directions, eventually having an effect at tide gauge stations around the globe.

"The truth is in the trend line." - Dredd

The next post in this series is here, the previous post in this series is here.

The Ocean (lyrics here):

1 comment:

  1. Wow, good stuff Dredd! Your perspective equates SLC to energy transfer and attendant effects - very perceptive.