[LEAPSECS] Comments on predictions for this century
Matsakis, Demetrios
demetrios.matsakis at usno.navy.mil
Fri Jan 16 13:53:12 EST 2015
Tom,
I don't have any special predictive insights, but when I look at the data things appear to be fairly flat. Although the length of day (LOD) has dropped below 86400 in the recent summers, it didn't last year. As my viewgraphs indicate, the best predictor for this kind of variation is that the LOD will increase by the "recent" historical tidal amount from where it has been over the last few years - not from where 20th century models had predicted it to be at this time. The LOD could just as easily increase or decrease from that baseline. There is a common belief (not your belief) that after a decadal fluctuation the Earth will rapidly slow down or speed up to "catch up" in its rotation angle. But that's not how it works. If a pendulum is made to suddenly turn slower, say by changing its length, it will simply go back to its old rate once its length is restored. It won't try to catch up its phase/position to where it would have been. Another way to put it is that the physics is in the motion of the Earth, not in its rotational position/angle.
Poul-Henning,
I think you are on the right track with the sea level computations. The Chapanov and Gambis paper agrees that the melting of ice is very important, although they find thermal expansion of the seawater to be fairly negligible. As you and many on this listserve know, the picture is complicated because as the glacial ice melts, the arctic land masses bear less weight. So over centuries the Earth's magna pushes them up , leading to glacial rebound. The matter pushing them up is coming from just below, but it in turn is replenished by magna from below the equatorial areas - so that the Earth gets rounder and therefore speeds up just like a twirling ballerina does when she brings in her arms. So while the Earth is being slowed by the redistribution of water from arctic to ocean, it is being sped up by the motion of much heavier material from the equator. At least that's the hand-waiving argument for less-than-expected long-term LOD increase. I am unaware of any authoritative computations about whether the very recent rotational speed-up is due to what is loosely called "global warming" or if it is a classical decadal fluctuation related to the motion of the Earth's core. Also of interest might be changes in the net velocity of the upper atmosphere winds - the December 2014 Scientific American had an interesting article about the effects of the jet stream on the weather over the last few years. I'm not the authority here.
Steve,
I have pasted your email at the very end of this one. It's a shame that in this regard your extensive and lovingly worked-out web pages may spread disinformation. You are right that predictions are hard when they are about the future. But if you really feel the need to show those models, perhaps you could add a prominent note indicating that they are all wrong about the near future - and that one reasonable analysis predicts that the effect would be < 1 minute by 2100. Unfortunately, my finding is too trivial to put in a refereed journal, and yes, I too could be wrong either way.
All,
Let me apologize if I have talked down to many of you. And by the way, the opinions and ideas expressed here are my own and not necessarily those of my employer or the US government.
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Poul-Henning Kamp writes:
> That reminds me, has anybody tried to do the math on climate change ?
>
> The main effect is (probably?) going to be the thermal expansion of
> the worlds oceans.
>
> I did a quick back of the envelope calculation modeling the earth as a
> sphere radius 6367 km, covered by a 4 km thick shell of water.
>
> Increasing the thickness of the water by one meter but retaining its
> mass, I get a realtive change in angular momentum of 6e-11 which is in
> the order of a millisecond per year.
Below is a posting from last year; two plots are attached. It guesses long-term climate LOD variations are on the order of 200 ms (that's leap second every week territory).
/tvb
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From: "Tom Van Baak" <tvb at LeapSecond.com>
To: "Leap Second Discussion List" <leapsecs at leapsecond.com>
Sent: Tuesday, April 15, 2014 7:32 AM
Subject: Re: [LEAPSECS] Earth speeding up?
> I'm not a geophysicist, but I too have noted what Tom reports. I've
> attached a plot that by coincidence I just made last week.
>
> The best hand-waiving arguments I've heard for these recent "decadal fluctuations"
> is that the oblateness of the Earth is changing, possibly due to the ice caps changing.
> Short-term fluctuations are much better understood, and they correlate
> very strongly with the atmospheric angular momentum.
>
> Demetrios,
Thanks for sharing that one. Now, do you dare join the club and predict the year when we hit 86400.000?
For a longer-term view, attached are two plots from a 2010 paper "Long-Periodical Variations of Earth Rotation, Determined from Reconstructed Millennial-Scale Glacial Sea Level" by Chapanov & Gambis translating mean sea level to excess LOD.
See also the 2003 Nature paper "Sea-level fluctuations during the last glacial cycle" by Siddall & Rohling.
One of these papers is from "New challenges for reference systems and numerical standards in astronomy"
http://syrte.obspm.fr/jsr/journees2010/pdf/
Or I can email you copies. I have the raw data here somewhere too.
/tvb
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>From Steve Allen's email:
People have liked to suppose that the change of Length of Day is linear over time, a constant deceleration.
See the first plot of Length of Day on
http://www.ucolick.org/~sla/leapsecs/dutc.html
The LOD change since Alexander the Great is not linear.
It is only approximately matched by any of the three lines.
Matsakis points out that looking only at the past two centuries the LOD is pretty much a random walk. This is clearly visible in the zoomed plots on that web page.
A linear change in Length of Day results in a quadratic accumulation of Delta T. See the penultimate plot on http://www.ucolick.org/~sla/leapsecs/deltat.html
The Delta T since Alexander the Great is not quadratic.
It is only approximately matched by any of the three parabolae.
> Who is right?
The short term LOD variations (weeks or less) have been very well modelled by weather in the atmosphere since I was doing VLBI at JPL in the 1980s. Big snowstorms make visible changes.
Richard Gross at JPL has a model of ocean currents which does pretty good at modelling the annual variations which are conventionally described in the equations for UT2-UT1. That's weather too.
The decadal fluctuations have been huge and must be caused by changes in the body and or core of the earth.
There's a quote (where academics argue about its attribution) "Prediction is hard, especially about the future."
Being "right" means predicting the weather in the core of the earth for the next century. I make no such claim. I have merely plotted out the numbers in the literature. Pick your favaorite number.
--
Steve Allen <sla at ucolick.org> WGS-84 (GPS)
UCO/Lick Observatory--ISB Natural Sciences II, Room 165 Lat +36.99855
1156 High Street Voice: +1 831 459 3046 Lng -122.06015
Santa Cruz, CA 95064 http://www.ucolick.org/~sla/ Hgt +250 m
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