Hate leap seconds? Imagine a negative one
Because the possibility just got slightly more plausible
You’d think that I’d be done writing about time, leap seconds and atomic clocks. Heck, *I* thought I was about done writing about those topics already too. But, alas, it was not meant to be. Earth has found a way to drag me back into this fascinating mess.
So here’s what brought me back to this mess — a simple line chart published by the International Earth Rotation and Reference Systems (IERS) organization:
This plot is the difference between UT1 and UTC in seconds. And to make sure we’re all on the same page in time scale terminology, a quick review:
If you already know what UT1, UTC, and UT1-UTC mean you can jump to the next section.
Time standard terminology, again
UT1, a.k.a. “Universal Time”, is the modern equivalent of “solar time” and is determined when a specific set of distant quasars pass specific points in the sky. Solar time used to be measured when the sun was directly overhead on the Prime Meridian, but giant blinding fuzzy balls of gas in the sky is harder to measure precisely than extremely distant quasars that essentially act as point sources. It’s important to know that there are exactly 86400 (24*60*60) UT1 seconds in a UT1 day. If the rotation of the Earth speeds up/slows down, the definition of a UT1 second changes since the number of seconds in a day is constant.
UTC, a.k.a. Coordinated Universal Time, is an atomic standard of time. It’s based off of TAI (International Atomic Time), which is atomic seconds (so the SI definition of 9,192,631,770 transitions of hyperfine states of cesium atoms from ground state). There are also 86400 atomic seconds in a TAI day. Here, atomic seconds are fixed by definition, as well as the day.
TAI and UTC “tick” exactly the same, they’re both atomic standards. The difference is that UTC includes the use of leap seconds to make sure the difference between UT1 and UTC are never more than 1 second apart. The reason for the difference between UT1 and UTC/TAI is because the earth’s rotation isn’t uniform. It slows and speeds up a tiny bit due to lots of factors like tides and earthquakes. This means that it is not necessarily true that there are 86400 atomic (TAI) seconds in a UTC day — there are occasionally leap seconds.
Imagine you had two identical tubes. You fill one tube (UTC) with exactly 1mL of water every clock tick, but you fill the other tube (UT1) with roughly 0.99999999mL every clock tick. You keep filling the tubes, but you have a rule that the two tubes should never be more than 1mL apart. Whenever the difference is about to get too big, you temporarily pause water flowing into the 1mL/tick tube (UTC) for a single tick, which let’s the UT1 tube pick up one extra drop and pull ahead of UTC. Then you resume everything again, tracking the new differences.
That process I just described is essentially what that UT1-UTC chart is showing. UTC is “paused” via the injection of a leap second, and it allows UT1’s value to jump slightly ahead of UTC. Over time, because UT1 is slowing down, UTC will eat away at UT1’s lead until a new leap second resets the chase.
Back to the graph, what’s so special about it
Data science time! Take a look at the graph, and then look at the last bits of it. Does it set off any alarm bells?
It’s going sideways and the predicted bit is going upwards slightly. That is highly not normal! The whole trend of the graph has always been a steady march downwards, only varying in slope here and there that’s interrupted by vertical lines that indicate leap seconds being inserted.
If instead of UTC, we plot against TAI (which doesn’t use leap seconds but is otherwise identical), you see the steady decline turn dead flat (the scale is such you can’t see any reversals)
So the graph is saying that the rotation of the Earth, relative to the fixed stars, has sped up and is predicted to continue to do so for a bit. The change is small, and there are cyclical components (often related to the tides) to UT1-UTC that are predicted to contribute to the speed-up in the short term.
So, do we know why yet?
At least, I have yet to find any publications about it that are peer reviewed or preprints.
While some laypeople on Twitter seem quick to suggest climate change is a contributing factor, but I haven’t found any reliable studies and references on it yet. The phenomena is perhaps a year old and so it’ll take time for researchers to study and publish on it. My personal feeling is that climate change might have a role, but there’s lots of other things that could’ve messed with this.
From my (incomplete) reading of what affects rotation, here’s the big list of stuff that needs to be accounted for:
Tidal forces, from Moon, Sun (via Earth’s elliptical orbit bringing us closer/further), and other gravitational effects from the solar system. These tidal pulls affect the oceans AND also the “not water” parts of the Earth (aka, solid rock and molten rock) in various ways.
Sea currents can also mess with things by shuttling mass towards the poles.
The Earth’s internal structure: specifically the solid inner core and the liquid mantle spin at different rates and this has effects that aren’t very well understood.
Earthquakes can shuffle mass around the Earth’s insides, which can affect rotation speed.
Atmospheric forces: wind and weather can actually affect the Earth’s rotation by pushing water around and pushing against mountain ranges. This effect could be seasonal (and thus pretty predictable) as well as more random and transient (a big El Nino event can slow the rotation enough to be measured).
From what I’ve managed to read, climate change can mess with rotation in a couple of ways:
As ice caps melt, the water (and its mass) moves from the poles to the equator. Since the Earth’s an oblate spheroid that bulges further in the equator, this moves the mass further from the axis of rotation, which should slow our rotation down further due to conservation of angular momentum
Oddly enough, when the ice caps melt, there’s a phenomenon called Munk’s Enigma where the Earth wasn’t slowing enough compared to the expected mass shift from water moving to the equator. Apparently at least part of the explanation is when glacier’s melt, the ground underneath rebounds upwards and the Earth becomes slightly less of an oblate spheroid, speeding up rotation to compensate.
As mentioned above, El Nino tends to slow the rotation of the Earth, but La Nina events are associated with a speed up in rotation. More fun, La Nina happened/is happening in 2020 and 2021! Climate change putting more energy into the atmosphere and causing stronger weather events might be exaggerating these and similar effects.
Ocean currents can be affected by climate change, and could have done something there too.
That said, the recent trend of speeding up might have to do with something going on in Earth’s core. I’m not entirely sure what the magnitude of all these various factors are, so one (or some) might dominate the whole situation.
But what’s the practical effect of all this?
Right now? Nothing.
If it keeps continuing for a number of years however… things can get interesting.
If the Earth speeds up enough, we might find ourselves pondering over the possibility of a negative leap second. According to the Time and Date folks, a day in 2021 is averaging about 0.2ms faster than the 84600 atomic seconds per day, ~70ms/year, so at most 14 years of this would put us over the threshold (super unlikely). In reality, we don’t have to speed up a full 1000ms of rotation speed because there was always a fractional difference in UT1-UTC.
The time specs involving leap seconds always included the possibility that a negative leap second could happen, but I don’t think anyone really expected it actually happen. In more practical terms, Either July 31 or December 31 23:59:59 would just… disappear from existence, with clocks ticking from 23:59:58 seconds to 00:00:00.
Unix time doesn’t have any ability to account for leap seconds (it works on a fixed definition of 86400 seconds/day) so I have no idea how that would affect it. Same goes for a lot of other date/time libraries that might need to do arithmetic with time units. I’m pretty confident that plenty of software out in the world would behave unexpectedly in such situations. We already have issues dealing with positive leap seconds…
While I generally dread the potential for chaos with a negative leap second, I do have to admit that a tiny child-like part of me would be amazed if we got to live through an extremely rare and unprecedented event like this.
Resources and cool stuff I found along the way
SciShow YouTube video about this whole thing in April 2021.
A brief explanation of the Earth Orientation Parameters, of which rotation speed and UT1 is one of the parameters.
A brief explanation of Excess Length of Day (LOD) and decomposition of LOD’s components
A tool from the Earth Orientation Center to pull some of the charts I posted in this article. You’ll want to pull UT1-UTC or UT1-TAI, and use the Civil date.
About this newsletter
I’m Randy Au, currently a Quantitative UX researcher, former data analyst, and general-purpose data and tech nerd. The Counting Stuff newsletter is a weekly data/tech blog about the less-than-sexy aspects about data science, UX research and tech. With occasional excursions into other fun topics.
All photos/drawings used are taken/created by Randy unless otherwise noted.
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Due to momentum conservation, you can speed up any free rotating object by pulling its mass closer to rotation axis. Now look at any webservice that shows air traffic live. There you can see a tens of thousands airplanes which are airborne continuously at any given moment. This number was significantly reduced at the beginning of COVID-19 pandemic. The mass of those airplanes in total may look insignificant compared to mass of oceans or various Earth's internal structures. However planes fly high, typically at 12 km of altitude, so the change of altitude at which their mass is located has more prominent effect than if they were objects that basically move around roughly same altitude. Due to pandemic, airplanes were grounded, so Earth sped up to maintain its momentum.