One of the critical elements of the Clock of the Long Now to keep good time over ten millennia is the part of the clock that is synchronized to solar noon. We have several schemes that allow this mechanical synch from sunlight, but one of the questions that came up as we designed these systems, was how much we might expect solar noon to drift in 10,000 years. We had already compensated for the earth’s ~26,000 year precessional cycle, and the average rotational dampening of about a second per century, but it was not until Danny Hillis requested this paper from Astrophysicist Michael Busch that we appreciated how much climate change will play a role.
Many people bring up the recent earthquake and tsunami events that have altered the earth’s rotation, or even the filling of the Three Gorges Dam. While those events have a theoretical effect, it is so minute that they are generally not detectable empirically. Polar ice however is the real game changer, it could effect when solar noon is over 10,000 years by weeks not minutes or seconds. Below is the paper by Busch for your reading pleasure…
Climate Change and the Clock
Michael W. Busch
2010 April 9Based on a request from Danny Hillis for a check of the Clock’s accuracy requirements
There is now a consensus that the Earth’s climate is changing and that it can be greatly influenced by human activity. While we can argue about predictions of the particular form climate change will take, any changes in the climate will have important effects on the Clock.
The most direct effect will be power: the Clock’s core oscillator is powered by focused sunlight. Climate changes leading to frequent clouds over the site in the American Southwest would interrupt that supply. This is not likely to be fatal, since the Clock can operate for fifteen years without sunlight and even the cloudiest places on Earth have sunny days more often than that. But climate change will also affect the Clock indirectly, by disrupting its timekeeping.
The Clock keeps the oscillator calibrated by resetting it at local solar noon – the time of day when the sun is directly south as seen from the mountaintop – at the solstice. On cloudy days, the oscillator keeps running without being reset, and begins to drift away from the true time. However, again, unless the weather becomes implausibly bad at some point in the next ten millennia, the errors in the oscillator will not grow to an entire day before it is reset, and the overall count of how many days have passed will be correct. The problem is connecting the number of days the Clock has counted to the true amount of time that has passed. For everyday life, we treat days as being all the same length (86400 seconds from one solar noon to the next), but they are not. In addition to slight changes in the time of noon on each rotation of the planet since the Earth’s orbit is not quite circular, the length of the day is determined by how fast the Earth spins, and that changes slightly all the time (Hide & Dickey 1991). From day to day, some amount of angular momentum is transferred between the solid body of the Earth and the atmosphere. Adding angular momentum to the Earth makes it spin faster and makes the days shorter, and taking angular momentum away makes the days longer. Each year, a large amount of water moves from the equator to the high latitudes as snow and back again as water and water vapor. Moving mass from the equator to the poles means that the same mass can spin faster with the same angular momentum, and the days get shorter. The standard analogy here is a figure skater pulling his arms in to spin faster.
For the Clock, these daily and yearly changes in the length-of-day average out and do not matter too much. But there are longer term and much larger changes in length-of-day. Mountain ranges get raised up and oceanic crust gets subducted, moving mass around. Earthquakes and the emptying and filling of lakes move around much smaller masses, which can also be estimated. The tides from the Moon and the Sun are slowly subtracting angular momentum and spinning the Earth down. These trends can be measured and estimated over millennia by comparing records of solar eclipses. Over the last 3500 years, the length of the day has increased by 84 milliseconds, give or take a few (Stephenson & Morrison 1995).
Having the length of day off by about tenth of a second may not seem like much, but over ten thousand years it adds up to a difference of several hundred thousand seconds (a few current days) between an estimate of the time based on how many days there have been and the true amount of time that has passed. The tide-produced natural change in the length-of-day can be predicted and corrected for in the design of the Clock. The Earth has been spinning down at a roughly constant rate for more than three thousand years. But climate change may change that.
One of the most dramatic climate change predictions is the possibility of large changes in the mass of the ice sheets in Greenland and Antarctica. Doubling the mass of the ice sheets or completely melting them takes many hundreds of years, if the most extreme instances during the last ice age are a guide (Clark & Mix 2000), but that is far less than the lifespan of the Clock. Just as seasonal motions of water change the length-of-day, so does either melting the ice sheets into the ocean or freezing more ice into them (Trupin 1993, Wahr et al. 1993, Nakada & Okuno 2003). The ice sheets are near the poles. Melting the current ice sheets completely would move about 0.001% of the Earth’s mass from near the pole to much nearer to the equator (since the ice goes into the oceans), and increase the length of the day by roughly 1 second. Freezing out ice sheets comparable to the last glacial maximum would put four times that much mass near the poles, making the day about 4 seconds shorter.
The current Clock design calibrates the oscillator at the solstice. The time of the solstice is determined by the direction of the Earth’s rotation axis relative to its orbit around the Sun, and not by the length of the day. If the conversion from the day count to true time is off by more than about 20 days, the Clock won’t be able to connect the oscillator to the Sun, and the accuracy will rapidly decay. This is only of concern if there is a large change in the length-of-day that lasts for most of the Clock’s lifespan.
Since climate change is a chaotic process, and human decisions and actions in the next several centuries are very likely to have a significant effect on it, it is impossible to predict the length of the day to better than a second or so over the next ten thousand years. The inherent uncertainty in the future climate places a limit on the accuracy of the Clock. It can measure time to about ten parts per million, or a few weeks over ten thousand years.
References:
- Clark, P.U., Mix, A.C., 2001, Ice sheets and sea level of the Last Glacial Maximum, Quat. Sci. Rev. 21, 1-7.
- Hide, R., Dickey, J.O., 1991, Earth’s variable rotation, Science 253, 629-637.
- Nakada & Okuno, 2003, Perturbations of the Earth’s rotation and their implications for the present-day mass balance of both polar ice caps, Geophysical Journal International 152, 124-138.
- Stephenson, F.R., Morrison, L.V., 1995, Long-term fluctuations in the Earth’s rotation: 700 BC to AD 1990, Phil. Trans. Phys. Sci. & Eng. 351, 165-202.
- Trupin, A.S., 1993, Effects of polar ice on the Earth’s rotation and gravitational potential. Geophys. J. Int. 113, 273-283.
- Wahr, J., Dazhong, H., Trupin, A., Lindqvist, V., 1993, Secular changes in rotation and gravity: Evidence of post-glacial rebound or of changes in polar ice? Adv. Space Res. 13, 257- 269.
