predicting leap seconds (was Re: [LEAPSECS] Where the responsibility lies)

From: Neal McBurnett <neal_at_bcn.boulder.co.us>
Date: Sat, 7 Jan 2006 16:26:14 -0700

On Wed, Jan 04, 2006 at 07:36:17AM +0100, Poul-Henning Kamp wrote:
> In message <20060104004053.GC2021_at_feynman>, Neal McBurnett writes:
> >On Tue, Jan 03, 2006 at 08:32:08PM +0100, Poul-Henning Kamp wrote:
> >> If we can increase the tolerance to 10sec, IERS can give us the
> >> leapseconds with 20 years notice and only the minority of computers
> >> that survive longer than that would need to update the factory
> >> installed table of leapseconds.
> >
> >Do you have any evidence for this assertion?
>
> It is an educated guess.
>
> The IERS have already indicated that they belive they could do prediction
> under the 0.9 second tolerance with two or three year horizon.

The Torino Colloquium had some discussion of this.

 Proceedings of the Colloquium on the UTC Timescale held by
 ITU-R SRG 7A
 http://www.ien.it/luc/cesio/itu/ITU.shtml

 Prediction of Universal Time and LOD Variation
 D. Gambis and C. Bizouard, (IERS)
 http://www.ien.it/luc/cesio/itu/gambis.pdf

After a bunch of nice graphs (not all of which were easy to interpret)
I found the periodogram (essentially a discrete Fourier transform of
the input data) interesting. The way I read it (expert advice
welcomed), the broad peaks at 26 years (0.6 ms/d) and 52 years (0.3
ms/d) suggest that the most common pattern is a gradual cycle a few
decades long of lengthening and shortening of the day, presumably
driven by movements in the earth's mantle and core.

Page 14 of the pdf has a table:

 Skill of the UT1 prediction statistics over 1963-2003

    Horizon Prediction accuracy in ms
    3 years 308
    2 years 163
    1 year 68
    180 days 36
    90 days 21
    30 days 7
    10 days 3

Perhaps these are worst cases? It would be nice to have confidence
intervals.

They presented these conclusions:

 Possibility to predict UT1 with a 1s accuracy at least over 4 years
 using a simple method : seasonal, bias and drift.

 New prediction methods are under investigation (Singular Spectrum
 Analysis, neural network,..)

 Possibility to use Core Angular Momentum prediction for decadal
 modeling

Steve Allen wrote:
> http://www.ucolick.org/~sla/leapsecs/McCarthy.html
>
> This deserves discussion and analysis and explanation.

I wrote Dennis McCarthy about that, and he said he'd look up the
details and get back to me next week. But he did remind me of this,
which I remember seeing in data they published via ftp years ago:

> Regarding the accuracy of these long-term predictions, the IERS
> Rapid Service and Prediction Center located at the U. S. Naval
> Observatory does make predictions of Delta-T in the IERS Annual
> Report. The algorithm for those predictions was determined
> empirically by testing a wide range of possibilities. It is
> essentially an auto-regressive model using the past ten years of
> data. The accuracy based on comparison of observations with what
> would have been predicted using that model is shown in the table
> below. Note that the accuracy estimates are 1-sigma estimates and
> that excursions of 2-sigma (or more) may not be unexpected.
>
> +-----------------------------------------+
> |Year in the Future|Accuracy (1s) (seconds|
> |------------------+----------------------|
> | 1 | .04 |
> |------------------+----------------------|
> | 2 | .08 |
> |------------------+----------------------|
> | 3 | .3 |
> |------------------+----------------------|
> | 4 | .8 |
> |------------------+----------------------|
> | 5 | 1. |
> |------------------+----------------------|
> | 6 | 2. |
> |------------------+----------------------|
> | 7 | 2. |
> |------------------+----------------------|
> | 8 | 3. |
> |------------------+----------------------|
> | 9 | 4. |
> +-----------------------------------------+

The http://www.iers.org/ points eventually to

 http://141.74.1.36/MainDisp.csl?pid=47-25786

but the links from there to the annual reports seem broken right now.

I still haven't seen any good data on predictions for periods of
longer than 9 years.

Neal McBurnett http://bcn.boulder.co.us/~neal/
Received on Sat Jan 07 2006 - 15:26:40 PST

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