<p>Question: &quot;Would someone help to understand the accuracy of the calculated 'Delta T' against the numbers provided on the websites.&quot;</p>
<p>The nature of Delta T (ΔT) reflects an irregularly-fluctuating natural phenomenon: it is a quantity that fundamentally has to be observed and measured, rather than calculated.</p>
<p>Evidence suggesting that mean solar time is after all somewhat irregular -- and not uniform as had been long believed -- began to be accumulated from about the mid-19th century onwards. During the 1920s and 1930s the evidence for this irregularity came to be generally accepted as convincing. The first timescale independent of the fluctuations of mean solar time (&quot;Ephemeris Time&quot;) was devised in the late 1940s. The Wikipedia article on <a href="https://en.wikipedia.org/w/index.php?title=Ephemeris_time&amp;oldid=686852474" rel="nofollow noreferrer">Ephemeris Time</a> gave (as of late 2015) a reasonably good account of the history. Some of the linked articles are also useful, including the article on <a href="https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)" rel="nofollow noreferrer">Delta T</a>, but the current version of the article on Delta T has unfortunately been amended to include a misleading suggestion that Delta T is a product of calculation -- some older versions, still accessible through the history tab, were more accurate.</p>
<p>Since the fundamental values of Delta T are products of observation, of course these intrinsically belong to the past -- even if sometimes a very recent past. The historical values of Delta T vary in accuracy, from very high accuracy for the past few decades, maybe to 0.0001 second as at the US Naval Observatory website, to much lower accuracies for centuries-old dates, for which Delta T had to be estimated (recently) from a variety of old historical observations. (See especially the historical work of Stephenson, Morrison and Hohenkerk, e.g. at (<a href="http://astro.ukho.gov.uk/nao/lvm/" rel="nofollow noreferrer">http://astro.ukho.gov.uk/nao/lvm/</a>)).</p>
<p>Naturally, present-day time-users tend to wish for current quantities rather than history. So, attempts are regularly made to predict Delta T for the near future. The results of these attempts are at best approximate. This can be seen from graphs that compare past predictions with what then turned out to be the actual measured quantities.</p>
<p>An example is the second out of three graphs shown at the web-page for <a href="https://asa.hmnao.com/SecK/DeltaT.html" rel="nofollow noreferrer">&quot;Delta T : Past, present and Future&quot;</a> on the &quot;Astronomical Almanac Online&quot; website <a href="https://asa.hmnao.com/" rel="nofollow noreferrer">here</a>. This shows &quot;Current values and short term predictions of Delta T&quot; from 2000 to 2022 -- including the odd and unexplained fact that in the interval 2020-2022 the measured values of Delta T stopped trending upwards, and have even slightly diminished. The graph shows clearly how quickly and how much the actual measurements began to deviate from both of two sets of calculated predictions. One set is of IERS predictions made for about 2006 onwards (which turned out lower than actual, about 2 seconds lower by 2022). Another set is a series of USNO predictions (which turned out higher than actual, over 2 seconds higher by 2022).</p>
<p>For a long time, the US Naval Observatory website was a good source of the latest data and predictions about Delta T. But in the last two years and more, its webpages were sometimes inaccessible, and data for latest measured values and most recent predictions seemed to be updated either seldom or not at all. But recently I found that I could again access updates, now via (<a href="https://www.cnmoc.usff.navy.mil/Organization/United-States-Naval-Observatory/Earth-Orientation-Department/USNO-Earth-Orientation-Products/Long-term-Delta-T/" rel="nofollow noreferrer">https://www.cnmoc.usff.navy.mil/Organization/United-States-Naval-Observatory/Earth-Orientation-Department/USNO-Earth-Orientation-Products/Long-term-Delta-T/</a>) and its links to:</p>
<p><a href="https://maia.usno.navy.mil/ser7/deltat.data" rel="nofollow noreferrer">&quot;Monthly values of (TT - UT1) since 1973. Updated quarterly&quot;</a> -- here are the latest few entries at the time of writing this:</p>
<pre><code>&gt;    Date      (TT-UT1, secs)
&gt;  2021 10  1     69.2893
&gt;  2021 11  1     69.2880
&gt;  2021 12  1     69.2908
&gt;  2022  1  1     69.2945
&gt;  2022  2  1     69.2913 
</code></pre>
<p>and to the latest <a href="https://maia.usno.navy.mil/ser7/deltat.preds" rel="nofollow noreferrer">&quot;Predictions of (TT-UT1) from the present through 2027. Updated annually.&quot;</a> -- here are a few entries for the period about the time of writing this:</p>
<pre><code>&gt;  Year      TT-UT1 (s)   Uncertainty (s)
&gt; 2021.25    69.358221    0.000004
&gt; 2021.50    69.351422    0.000003
&gt; 2021.75    69.41        0.12
&gt; 2022.00    69.48        0.16
&gt; 2022.25    69.57        0.22
&gt; 2022.50    69.63        0.27
&gt; 2022.75    69.65        0.33
&gt; 2023.00    69.73        0.40
</code></pre>
<p>It can be seen, even from these two brief table-quotes, that even the expert predictions, maybe only about a year or two old, have already begun to deviate appreciably from the actuals.  The IERS website gives essentially the same data, but it divides Delta T into components given on different web-pages. The USNO combined format -- when available -- seems much the most convenient.  I suggest that websites showing values other than these, however they may have been calculated, should be regarded as approximations; but the best of them include some very useful approximations for past Delta T values, for example calculated by formulae that define a collection of spline-curve segments, saving the volume and inconvenience of large lookup tables while losing negligible amounts of accuracy.</p>

CC BY-SA 4.0
2022-04-11T21:45:02.013Z
2022-04-11T21:45:02.013Z
terry-s
<p>IERS Bulletin D reports DUT1 to the nearest tenth of a second. Do not use Bulletin D if you want finer values of DUT1. DUT1 is now estimated with an accuracy in the tens of microseconds. Be very careful regarding mixing and matching across various IERS products. The one exception regarding mixing and matching is DUT1 across leap second boundaries.</p>
<p>I recommend you use the EOP 14 C04 (IAU2000A) series and interpolate, taking care when interpolating across leap second boundaries. Also don't go overboard on the interpolating polynomial. A cubic interpolating polynomial is probably good enough and will avoid ringing due to Runge's phenomenon. Even a simple linear interpolation might be good enough, depending on your needs.</p>

CC BY-SA 4.0
2022-04-09T11:42:53.863Z
2022-04-09T11:48:03.067Z
2022-04-09T11:48:03.067Z
David Hammen
<p><span class="math-container">$\Delta$</span>T is defined as the 'measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time'.</p>
<p>I tried to calculate <span class="math-container">$\Delta$</span>T corresponding to October 17, 2003 05:30:30 UT. This calculation of <span class="math-container">$\Delta$</span>T is achieved through the following equations.</p>
<p>1.) <code>UTC = UT1 - DUT1</code>.</p>
<p>We have UT1 = October 17, 2003 05:30:30 UT.</p>
<p>From IERS Bulletin D (No. 89), DUT1 from April 3, 2003 0 hour UTC up to further notice is -0.4 seconds. Bulletin D No. 90 was issued on March 24, 2004. Therefore, DUT1 = -0.4 seconds.</p>
<p>UTC = UT1 - (-0.4 seconds) = UT1 + 0.4 seconds. This provides UTC = October 17, 2003 05:30:30.4</p>
<p>2.) <code>TAI = UTC + Delta AT</code>.</p>
<p>'<span class="math-container">$\Delta$</span>AT' from 1999-01-01 to 2005-12-31 was +32.0 seconds. This provides TAI = October 17, 2003 05:31:2.4</p>
<p>3.) <code>TT = TAI + 32.184 seconds</code>.</p>
<p>This provides TT = October 17, 2003 05:31:34.584</p>
<p>4.) <code>Delta T = TT - UT1</code></p>
<p>This provides <span class="math-container">$\Delta$</span>T = 00:01:4.584 = 64.584 seconds.</p>
<p>Thus, the computed value of '<span class="math-container">$\Delta$</span>T' for October 17, 2003 05:30:30 UT is 64.584 seconds.</p>
<p>This calculated value of '<span class="math-container">$\Delta$</span>T' needs to be compared with the literature.</p>
<p>1.) From 2003-1-1 to 2003-12-1, the website
'http://maia.usno.navy.mil/ser7/deltat.data' provide 64.4734 to 64.5654 seconds.</p>
<p>2.) From 2003-1-1 to 2004-01-01, the website
'https://www.stjarnhimlen.se/comp/time.html' provide +64.47 to +64.57 seconds.</p>
<p>Would someone help to understand the accuracy of the calculated 'Delta T' against the numbers provided on the websites.</p>

CC BY-SA 4.0
2022-04-09T10:01:16.207Z
T can be temperature, period, time, kinetic energy ... 
Always name your symbols. They don't necessarily self-explain. Also put your problem into context what you try to do. Here it obvously is some time (difference). But what is the actual problem you try to solve?
planetmaker
CC BY-SA 4.0
2022-04-09T10:28:41.527Z
I have done the edit, and changed Delta T to $\Delta$T. I may take some time to incorporate the same to the equations as well. Thank you.
Smarty
CC BY-SA 4.0
2022-04-09T12:00:17.567Z
@planetmaker It was fairly clear even without the edit that the OP was asking about time, in particular, the difference between Terrestrial Time (TT) and Universal Time (UT1). This time difference is called $\Delta \text T$. Link: https://en.wikipedia.org/wiki/ΔT_(timekeeping).
David Hammen
CC BY-SA 4.0
2022-04-09T12:13:14.983Z
To help with those who aren't familiar with the complexities of timekeeping, TAI is International Atomic Time. The acronym works with French, but the acronym is TAI even in languages such as Chinese or Arabic. TAI is what an atomic clock at sea level would read. Times for dates in the past do not change their TAI timestamp. (continued)
David Hammen
CC BY-SA 4.0
2022-04-09T12:13:44.383Z
TT (Terrestrial Time) is  essentially what an ideal atomic clock at sea level would read, but offset from TAI by about 32.184 seconds. Realizations of TT are released yearly. Times for dates in the past can change their TT timestamp with subsequent updates, but only at the sub-millisecond level.
David Hammen
CC BY-SA 4.0
2022-04-09T12:18:24.423Z
Universal Time comes in a number of flavors. Coordinated Universal Time (UTC; the acronym doesn't work in any language) is TAI plus or minus an integral number of leap seconds. The intent of leap seconds is to keep UTC more or less in sync with the Earth's rotation (UT1). The Earth's rotation is measured by UT0, UT1, the now defunct UT2, and multiple other convoluted measures. Timekeeping is a mess. A rather hot mess.
David Hammen
CC BY-SA 4.0
2022-04-09T12:45:10.130Z
FWIW, Horizons gives TDB-UT=64.182398 s. https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=YES&COMMAND=10&EPHEM_TYPE=OBSERVER&CENTER=%403&QUANTITIES=%2730,31%27&REF_SYSTEM=ICRF&CAL_FORMAT=BOTH&CSV_FORMAT=YES&TLIST=%272003-Oct-17%205:30:30%27
PM 2Ring
CC BY-SA 4.0
2022-04-09T12:54:49.573Z
Wikipedia has a brief article on [DUT1](https://en.wikipedia.org/wiki/DUT1), but it's not linked from many of its other pages on time scales.
PM 2Ring
CC BY-SA 4.0
2022-04-09T13:20:28.540Z
@DavidHammen obviously it is about time. But it is never a good idea to not even *mention* what you are talking about, but keep talking only in symbols. It's a bad habit done, but it doesn't help anyone understand questions etc. Especially not in question titles
planetmaker
CC BY-SA 4.0
2022-04-09T13:42:16.617Z
@planetmaker Your edit to the title is misleading. The TT (Terrestrial Time) scale is a count of seconds, it has no concept of days, although we generally write TT values using customary date & time notation for convenience. Please see [A Brief History of Time Scales](https://www.ucolick.org/~sla/leapsecs/timescales.html). I'm not totally happy with my version of the title, but I think it's an improvement. ;)
PM 2Ring
CC BY-SA 4.0
2022-04-09T14:17:27.233Z
@PM2Ring If you read the description to which you linked, "TDB-UT" is the difference Barycentric Dynamic Time (TDB) and Coordinated Universal Time (UTC): "Times AFTER 1962 are in UTC, the current civil or "wall-clock" time-scale." TDB is yet another time scale. It differs from TT by up to a couple of milliseconds. As I wrote earlier, time is a hot mess.
David Hammen
CC BY-SA 4.0
2022-04-09T14:22:08.137Z
@PM2Ring I agree with your title change. $\Delta\text T$ essentially is the cumulative change in length of day (LOD), so the title change by planetmaker was not correct.
David Hammen
CC BY-SA 4.0
2022-04-09T14:26:54.000Z
@David Yes, I realise that TDB (really, [JPL's $T_{eph}$](https://en.wikipedia.org/wiki/Ephemeris_time#JPL_ephemeris_time_argument_Teph)) *isn't* TT, so Horizon's Delta T isn't quite what the OP wants to calculate. I just posted it as a data value that's closely related. ;)
PM 2Ring
CC BY-SA 4.0
2022-04-09T14:32:12.393Z
@PM2Ring TDB was redefined to essentially be JPL's $\text T_{\text{eph}}$ sometime after the release of DE405. JPL later stopped estimating $\text T_{\text{eph}}$ with each release of their Development Ephemerides, using TDB as is instead. Accurate timekeeping is not just a hot mess. It is a white hot mess.
David Hammen
CC BY-SA 4.0
2022-04-09T14:49:40.270Z
Timekeeping is arguably one of the oldest scientific activities, and has been closely linked with astronomy for thousands of years. You'd think that by now we'd be able to do it properly. ;) But it's a complex mess with lack of consensus between the various interested parties.
PM 2Ring
CC BY-SA 4.0
2022-04-09T15:59:11.287Z
@PM2Ring I changed the $\Delta T$ in the title to ΔT (plain text). The reason I did this was we have been advised to not use MathJax in titles.
David Hammen
<time><positional-astronomy><ephemeris>
Calculation of Terrestrial and Universal time scale difference, ΔT
Smarty
# Calculation of Terrestrial and Universal time scale difference, ΔT

(Asked by: username_0 on 2022-04-09)

$\Delta$T is defined as the 'measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time'.

I tried to calculate $\Delta$T corresponding to October 17, 2003 05:30:30 UT. This calculation of $\Delta$T is achieved through the following equations.

1.) `UTC = UT1 - DUT1`.

We have UT1 = October 17, 2003 05:30:30 UT.

From IERS Bulletin D (No. 89), DUT1 from April 3, 2003 0 hour UTC up to further notice is -0.4 seconds. Bulletin D No. 90 was issued on March 24, 2004. Therefore, DUT1 = -0.4 seconds.

UTC = UT1 - (-0.4 seconds) = UT1 + 0.4 seconds. This provides UTC = October 17, 2003 05:30:30.4

2.) `TAI = UTC + Delta AT`.

'$\Delta$AT' from 1999-01-01 to 2005-12-31 was +32.0 seconds. This provides TAI = October 17, 2003 05:31:2.4

3.) `TT = TAI + 32.184 seconds`.

This provides TT = October 17, 2003 05:31:34.584

4.) `Delta T = TT - UT1`

This provides $\Delta$T = 00:01:4.584 = 64.584 seconds.

Thus, the computed value of '$\Delta$T' for October 17, 2003 05:30:30 UT is 64.584 seconds.

This calculated value of '$\Delta$T' needs to be compared with the literature.

1.) From 2003-1-1 to 2003-12-1, the website
'http://maia.usno.navy.mil/ser7/deltat.data' provide 64.4734 to 64.5654 seconds.

2.) From 2003-1-1 to 2004-01-01, the website
'https://www.stjarnhimlen.se/comp/time.html' provide +64.47 to +64.57 seconds.

Would someone help to understand the accuracy of the calculated 'Delta T' against the numbers provided on the websites.

**Tags:** time, positional-astronomy, ephemeris
> **Comments:**
> **username_1**: T can be temperature, period, time, kinetic energy ...  Always name your symbols. They don't necessarily self-explain. Also put your problem into context what you try to do. Here it obvously is some time (difference). But what is the actual problem you try to solve?  
> **username_0**: I have done the edit, and changed Delta T to $\Delta$T. I may take some time to incorporate the same to the equations as well. Thank you.  
> **username_2**: @planetmaker It was fairly clear even without the edit that the OP was asking about time, in particular, the difference between Terrestrial Time (TT) and Universal Time (UT1). This time difference is called $\Delta \text T$. Link: https://en.wikipedia.org/wiki/ΔT_(timekeeping).  
> **username_2**: To help with those who aren't familiar with the complexities of timekeeping, TAI is International Atomic Time. The acronym works with French, but the acronym is TAI even in languages such as Chinese or Arabic. TAI is what an atomic clock at sea level would read. Times for dates in the past do not change their TAI timestamp. (continued)  
> **username_2**: TT (Terrestrial Time) is  essentially what an ideal atomic clock at sea level would read, but offset from TAI by about 32.184 seconds. Realizations of TT are released yearly. Times for dates in the past can change their TT timestamp with subsequent updates, but only at the sub-millisecond level.  
> **username_2**: Universal Time comes in a number of flavors. Coordinated Universal Time (UTC; the acronym doesn't work in any language) is TAI plus or minus an integral number of leap seconds. The intent of leap seconds is to keep UTC more or less in sync with the Earth's rotation (UT1). The Earth's rotation is measured by UT0, UT1, the now defunct UT2, and multiple other convoluted measures. Timekeeping is a mess. A rather hot mess.  
> **username_3**: FWIW, Horizons gives TDB-UT=64.182398 s. https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=YES&COMMAND=10&EPHEM_TYPE=OBSERVER&CENTER=%403&QUANTITIES=%2730,31%27&REF_SYSTEM=ICRF&CAL_FORMAT=BOTH&CSV_FORMAT=YES&TLIST=%272003-Oct-17%205:30:30%27  
> **username_3**: Wikipedia has a brief article on [DUT1](https://en.wikipedia.org/wiki/DUT1), but it's not linked from many of its other pages on time scales.  
> **username_1**: @DavidHammen obviously it is about time. But it is never a good idea to not even *mention* what you are talking about, but keep talking only in symbols. It's a bad habit done, but it doesn't help anyone understand questions etc. Especially not in question titles  
> **username_3**: @planetmaker Your edit to the title is misleading. The TT (Terrestrial Time) scale is a count of seconds, it has no concept of days, although we generally write TT values using customary date & time notation for convenience. Please see [A Brief History of Time Scales](https://www.ucolick.org/~sla/leapsecs/timescales.html). I'm not totally happy with my version of the title, but I think it's an improvement. ;)  
> **username_2**: @PM2Ring If you read the description to which you linked, "TDB-UT" is the difference Barycentric Dynamic Time (TDB) and Coordinated Universal Time (UTC): "Times AFTER 1962 are in UTC, the current civil or "wall-clock" time-scale." TDB is yet another time scale. It differs from TT by up to a couple of milliseconds. As I wrote earlier, time is a hot mess.  
> **username_2**: @PM2Ring I agree with your title change. $\Delta\text T$ essentially is the cumulative change in length of day (LOD), so the title change by planetmaker was not correct.  
> **username_3**: @David Yes, I realise that TDB (really, [JPL's $T_{eph}$](https://en.wikipedia.org/wiki/Ephemeris_time#JPL_ephemeris_time_argument_Teph)) *isn't* TT, so Horizon's Delta T isn't quite what the OP wants to calculate. I just posted it as a data value that's closely related. ;)  
> **username_2**: @PM2Ring TDB was redefined to essentially be JPL's $\text T_{\text{eph}}$ sometime after the release of DE405. JPL later stopped estimating $\text T_{\text{eph}}$ with each release of their Development Ephemerides, using TDB as is instead. Accurate timekeeping is not just a hot mess. It is a white hot mess.  
> **username_3**: Timekeeping is arguably one of the oldest scientific activities, and has been closely linked with astronomy for thousands of years. You'd think that by now we'd be able to do it properly. ;) But it's a complex mess with lack of consensus between the various interested parties.  
> **username_2**: @PM2Ring I changed the $\Delta T$ in the title to ΔT (plain text). The reason I did this was we have been advised to not use MathJax in titles.  

---

## 2 answers

### Answer by username_4 on 2022-04-11. Score: 2

Question: "Would someone help to understand the accuracy of the calculated 'Delta T' against the numbers provided on the websites."
The nature of Delta T (ΔT) reflects an irregularly-fluctuating natural phenomenon: it is a quantity that fundamentally has to be observed and measured, rather than calculated.
Evidence suggesting that mean solar time is after all somewhat irregular -- and not uniform as had been long believed -- began to be accumulated from about the mid-19th century onwards. During the 1920s and 1930s the evidence for this irregularity came to be generally accepted as convincing. The first timescale independent of the fluctuations of mean solar time ("Ephemeris Time") was devised in the late 1940s. The Wikipedia article on Ephemeris Time gave (as of late 2015) a reasonably good account of the history. Some of the linked articles are also useful, including the article on Delta T, but the current version of the article on Delta T has unfortunately been amended to include a misleading suggestion that Delta T is a product of calculation -- some older versions, still accessible through the history tab, were more accurate.
Since the fundamental values of Delta T are products of observation, of course these intrinsically belong to the past -- even if sometimes a very recent past. The historical values of Delta T vary in accuracy, from very high accuracy for the past few decades, maybe to 0.0001 second as at the US Naval Observatory website, to much lower accuracies for centuries-old dates, for which Delta T had to be estimated (recently) from a variety of old historical observations. (See especially the historical work of Stephenson, Morrison and Hohenkerk, e.g. at (http://astro.ukho.gov.uk/nao/lvm/)).
Naturally, present-day time-users tend to wish for current quantities rather than history. So, attempts are regularly made to predict Delta T for the near future. The results of these attempts are at best approximate. This can be seen from graphs that compare past predictions with what then turned out to be the actual measured quantities.
An example is the second out of three graphs shown at the web-page for "Delta T : Past, present and Future" on the "Astronomical Almanac Online" website here. This shows "Current values and short term predictions of Delta T" from 2000 to 2022 -- including the odd and unexplained fact that in the interval 2020-2022 the measured values of Delta T stopped trending upwards, and have even slightly diminished. The graph shows clearly how quickly and how much the actual measurements began to deviate from both of two sets of calculated predictions. One set is of IERS predictions made for about 2006 onwards (which turned out lower than actual, about 2 seconds lower by 2022). Another set is a series of USNO predictions (which turned out higher than actual, over 2 seconds higher by 2022).
For a long time, the US Naval Observatory website was a good source of the latest data and predictions about Delta T. But in the last two years and more, its webpages were sometimes inaccessible, and data for latest measured values and most recent predictions seemed to be updated either seldom or not at all. But recently I found that I could again access updates, now via (https://www.cnmoc.usff.navy.mil/Organization/United-States-Naval-Observatory/Earth-Orientation-Department/USNO-Earth-Orientation-Products/Long-term-Delta-T/) and its links to:
"Monthly values of (TT - UT1) since 1973. Updated quarterly" -- here are the latest few entries at the time of writing this:
>    Date      (TT-UT1, secs)
>  2021 10  1     69.2893
>  2021 11  1     69.2880
>  2021 12  1     69.2908
>  2022  1  1     69.2945
>  2022  2  1     69.2913 

and to the latest "Predictions of (TT-UT1) from the present through 2027. Updated annually." -- here are a few entries for the period about the time of writing this:
>  Year      TT-UT1 (s)   Uncertainty (s)
> 2021.25    69.358221    0.000004
> 2021.50    69.351422    0.000003
> 2021.75    69.41        0.12
> 2022.00    69.48        0.16
> 2022.25    69.57        0.22
> 2022.50    69.63        0.27
> 2022.75    69.65        0.33
> 2023.00    69.73        0.40

It can be seen, even from these two brief table-quotes, that even the expert predictions, maybe only about a year or two old, have already begun to deviate appreciably from the actuals.  The IERS website gives essentially the same data, but it divides Delta T into components given on different web-pages. The USNO combined format -- when available -- seems much the most convenient.  I suggest that websites showing values other than these, however they may have been calculated, should be regarded as approximations; but the best of them include some very useful approximations for past Delta T values, for example calculated by formulae that define a collection of spline-curve segments, saving the volume and inconvenience of large lookup tables while losing negligible amounts of accuracy.


---

### Answer by username_2 on 2022-04-09. Score: 2

IERS Bulletin D reports DUT1 to the nearest tenth of a second. Do not use Bulletin D if you want finer values of DUT1. DUT1 is now estimated with an accuracy in the tens of microseconds. Be very careful regarding mixing and matching across various IERS products. The one exception regarding mixing and matching is DUT1 across leap second boundaries.

I recommend you use the EOP 14 C04 (IAU2000A) series and interpolate, taking care when interpolating across leap second boundaries. Also don't go overboard on the interpolating polynomial. A cubic interpolating polynomial is probably good enough and will avoid ringing due to Runge's phenomenon. Even a simple linear interpolation might be good enough, depending on your needs.


---

