Friday, December 12, 2014

All Seasons and Times in a Day -OR- Another Ride Along December Sunset Boulevard

Sunset as seen from my apartment overlooking 16th and U Streets and New Hampshire Avenue NW, Washington, D.C., at 4:34PM December 12, 2014.

Actual sunset here in Washington, D.C., this evening was 4:46PM EST. Indeed, that fact is the launching point for this whole entry.


Friday night. The Sun set several hours ago (at the time of actual entry posting). The Sun is setting at its earliest for the whole year. Furthermore, tonight is (was) the last night of the earliest sunset times of the year -- 4:46PM Eastern Standard Time (EST) in Washington, D.C.

Tomorrow, the sunset actually bumps up to 4:47PM EST and continues to do so all the way until early July. (To be clear, I'm not including the seconds in any of this -- if a time is ":46," the assumption is that the seconds are between :00 and 0:59 with no "rounding up.")

On a related note, Earth is quickly approaching its perihelion (closest to the Sun) point on its orbit for the year.

Schematic diagram showing Earth at perihelion and aphelion by approximate date.


Yes, the "shortest day" in terms of daylight is on the winter solstice (Dec. 21, 2014 at 2303UTC) and the "longest day" in terms of daylight is on the summer solstice (June 21, 2015 at 1638UTC) but owing to Keplerian orbital mechanics of Earth's slightly elliptical path about the Sun versus a nearly constant rate of axial rotation[1], the earliest and latest sunset and sunrise times are offset from the solstices just slightly (with the sunrises in the opposite sense of the sunsets and for both times of the year).

No, this isn't sunset in Washington, D.C., in December 2014. It's in Sweden in February 2004. Source: Flickr.


The reason -- as explained in this excellent CWG entry from Dec. 21, 2011 -- is that there are two "competing" forces that determine local sunrise and sunset times: (1) Changes in the Sun's declination, or height above the horizon throughout the year, and 2) the changing time of solar noon. The latter is driven by the Equation of Time.

An analemma helps explain this effect. The above entry contains an animated GIF of the effect. I can only post one sideways still-frame of it.

Above: A sideways still-frame from the above-linked animated GIF showing an analemma for Washington, D.C., for 2011 with the winter solistice spot highlighted.


The latest sunrise this seasons start on Dec. 31st here in D.C. at 7:27AM EST and runs until Jan. 10th before they start moving in tandem with the sunsets in terms of the overall lengthening of daylight.

Conversely for next year, the latest sunsets start on June 26th at 8:38PM Eastern Daylight Time (EDT) (7:38PM EST) here in Washington, D.C. and it runs until June 30th. The earliest sunrises start June 10, 2015 at 5:42AM EDT (4:42AM EST) and stay there until June 18, 2015.

For a quick summary of how these change, here are four links: The first two show the sunrise and sunset times for the months of December 2014 and January 2015 in Washington, D.C., and the latter two show the sunrise and sunset times for the months of June 2015. (I'm not going to get into the issue of astronomical, nautical, and civil twilight times.)

The Earth is at its closest (perihelion) around January 4th every year and at its farthest (aphelion) around July 4th plus or minus a day. It is winter in the Northern Hemisphere simply because this hemisphere is tilted away from the Sun around the time of perigee and vice versa for the summer.

Got it?

Another schematic of the Earth at aphelion and perihelion also showing a highly exaggerated sense of our planet's slightly elliptical orbit. This image came from Danish Meteorological Institute but I had to correct the aphelion date. It originally said June 4th, which is simply incorrect.


About the Length of Day and Seasonal Fluctuations ...

Our Home. Earth.


[1] This "length of day" (LOD) (not length of daylight) varies only by several milliseconds due to angular momentum exchanges between the solid Earth and the atmosphere -- principally through angular momentum exchanges between the atmosphere and the solid Earth as a result of the strengthening or relaxing of the prevailing westerlies or trade easterlies. Furthermore, there are greater seasonal change in the Northern Hemisphere than in the Southern Hemisphere due to greater temperature gradients and much greater topography that acts as a torque.

Hence, there is a net LOD difference during the course of a given year.

Idealized and actual schematics of Earth's atmospheric general circulation.


In short, the seasonal (as in "inter-seasonal") angular momentum exchange between the atmosphere and Earth is greater in the Northern Hemisphere than in the Southern Hemisphere. There is a greater acceleration of the prevailing westerlies in the Northern Hemisphere winter and greater deceleration of the prevailing in the Northern Hemisphere summer than in the Southern Hemisphere winter summer.

Another cartoon schematic of Earth's atmospheric general circulation pattern.


As a result, there is a net LOD difference between the seasons with the LOD decreasing (i.e., the solid Earth slowing down) going into the NH winter and the LOD increasing (i.e., the solid Earth speeding up) going into the NH summer. It is on the order of several milliseconds.

This can be augmented by wholesale reversals such as the monsoonal winds over the Indian subcontinent or in a large warm ENSO event in which the trade easterlies relax and can even become westerlies.

A chart of the observed changes in LOD at different time series including within a season (intra-seasonal), seasonal, interannual, decadal, and total since 1900 as published in a book in 2007. Chart by Richard Gross. The vertical axis scale is the same for each time series.

The topic of this blog portion of the blog entry are the seasonal ("inter-seasonal") changes. The serrated uptick is the NH winter representing a slightly longer LOD (i.e., a slower rotation of the solid Earth).


One way I have found useful to picture this (even if the analogy isn't perfect) is to consider a runner on an east-west facing track.

If the runner accelerates toward the east -- the direction in which the solid Earth is rotating -- the runner's feet are pushing against the Earth and exerting a net negative torque on the solid Earth, causing an imperceptible deceleration of the planet. Conversely, when the runner slows down, she exerts a net positive torque on the Earth, causing it to accelerate imperceptibly.

So, yes, the atmosphere (mass of approximately 5.1 quintillion (10^18) kilograms) can actually slightly change the rotation rate of the solid Earth (mass of about 5.97 septillion (10^24) kilograms) despite the one million times mass differential between the two.

In short, this flea can (imperceptibly) move that elephant.

None of this takes into account other issues such as very long-term lunar tidal drag via the exchange of momentum between the Earth and the Moon or changes within the solid Earth such as massive earthquakes that can redistribute moments of inertia.

For a wild extreme of this, consider the planet Venus, where a "day" is longer than a "year": 243 Earth days versus 224.7 Earth days, to be exact -- and rotating on its axis in the reverse sense of the other eight planets (sorry, Pluto!).

Venus in ultraviolet light.


On Venus, the upper atmosphere is in super-rotation with respect to the ponderously slowly rotating solid planet. The former whips around the planet every four Earth days. By contrast, nearer to the surface, the crushing atmosphere might have actually caused the planet to slow down to a full stop and start rotating in reverse.

Alternatively, that "backwards" rotation was caused by some ancient cataclysm in the early Solar System that flipped Venus upside down -- and perhaps contributed to that runaway greenhouse effect (870F anybody?) in which any early liquid water ocean became a crushing CO2 atmosphere (90 bars at the surface).

All Summer in a Day, indeed.


Well, I had planned a whole entry including about my trip to the doctor and check up (my blood pressure has been only a tad above normal the past week) but I seem to have run out of time. I might try to post one additional entry before I go to No. 9 tonight.

For tomorrow, it's a gym visit and posting a jukebox Saturday night entry before going to Jake's place for a "white elephant" holiday party in Arlington (Crystal City).

That's all for now.


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