Monday, June 8, 2015

Daylight and Twilight

Did you know that interior Alaska actually receives more sun and twilight than any other place in the U.S. and that the northern hemisphere Arctic latitudes receive more daylight and twilight than their counterparts in the southern hemisphere?

The Northern Hemisphere:

Alaska is known for long summer days and long winter nights. However, if you average all 365 days together, everyone ends up with 12 hours of daylight and 12 hours of darkness throughout the course of the year no matter where in the world you are, right? Actually, that is not correct. 

Looking at Figure 1 below, the red line at the bottom of the chart shows that daylight at the equator averages about 12 hours and 7 minutes per day over the course of the year. Remember that the sun is a circle (not a point) and we receive daylight from the top of the sun's disc before the middle of the disk reaches the horizon. The same is true at sunset. This makes an average day over 12 hours everywhere.


Figure 1. Hours of daylight and daylight plus Civil Twilight by latitude. All data obtained from the U.S. Naval Observatory's Astronomical Observations Department.

At the equator, the sun moves nearly straight up and down with respect to the horizon. This means the sun rises quickly and sets quickly. As we move to higher latitudes, the path of the sun is more oblique; i.e., the sun moves more and more diagonally with respect to the horizon. It therefore takes longer for the entire disk of the sun to make is across the horizon at both sunrise and sunset. 

If the sun were a point and not a circle, the annual average length of a day would be 12 hours everywhere. Since the sun is a 2-dimensional circle from our perspective, the relative speed of the rising and setting dramatically changes the amount of light we receive. This effect is greatest at the Arctic and Antarctic Circles due to the effective ground speed of the sub-solar point near the time of the solstices. The difference in cumulative day lengths between the equator and the Arctic Circle (for all 365 days) is 225 hours per year – or 37 minutes per day on average. 

Figures 2 and 3 show the length of daylight (Figure 2) and the combined length of daylight and Civil Twilight on the summer solstice.

 Figure 2. Length of daylight on the summer solstice.

Figure 3. Combined length of daylight and Civil Twilight on the summer solstice.

If we include Civil Twilight, which is when the entire sun's disk is below the horizon but by no more than 6°, the extra light for Alaska dramatically increases. At 69°N latitude, the 365-day average for daylight plus Civil Twilight is 15 hours and 6 minutes. At the equator, the 365-day average is only 12 hours and 50 minutes. The average difference in light (daylight plus Civil Twilight) is a shocking 2 hours and 16 minutes per day. Places just north of the Brooks Range in Northern Alaska therefore receive the most usable light of any place in the U.S. Table 1 shows the cumulative length of daylight and Civil Twilight for cities at a variety of latitudes.


Table 1. Annual hours of daylight and Civil Twilight for nine cities sorted by latitude.

The final two maps (Figure 4 and 5) show the length of daylight plus Civil Twilight for Alaska and the Lower 48. Again, note how much more light Alaska receives than the Lower 48 over the course of the year.

Figure 4. Average annual length of daylight plus Civil Twilight. The average is for all 365 days of the year. The map perspective is Alaska-centric.

Figure 5. Average annual length of daylight plus Civil Twilight. The average is for all 365 days of the year. The map perspective is Lower 48–centric.

Hemispheres Comparison:

What about our friends in the south? Isn't the southern hemisphere a mirror of the northern hemisphere? The answer is "no." You see, the earth orbits the sun in an ellipse – not a circle. We are actually farthest from the sun on July 3rd and closest on January 4th. When we are farthest from the sun in the summer, we move more slowly (think of a figure skater spinning faster/slower as they move their arms inward/outward). Since the earth moves slower in the northern hemisphere summer, it takes longer for the sun's sub-solar point to approach it's northern most latitude (Tropic of Cancer) and to start its retreat southward.

Figure 6 shows that the earth revolves nearly 1,000 meters per second slower at the summer solstice versus the winter solstice and Figure 7 shows the rate of change of the sub-solar point over the course of the year.


Figure 6. Earth's revolution speed around the sun (fixed point of reference) throughout the course of a single (tropical) year.



Figure 7. Daily change in the position of the sub-solar point throughout the course of the year. Units are (absolute value) of degrees of change per day in latitude. Earth's revolution speed is also shown.

The difference in speed is demonstrated by several easy to describe facts. First, the time from the March Equinox to the September Equinox covers the earth's slow period. The time difference between the March and September equinoxes is 186.4 days. On the other hand, the time difference from the September equinox to the March equinox is only 178.8 days. If we look at Barrow, they have 79 days in summer with no sunset but only 61 days with no sunrise in winter (+18 differential). At the same latitude in the southern hemisphere, there are 75 days with no sunset and 66 days with no sunrise (+9 differential). Therefore, we conclude that summer is longer in the northern hemisphere.


Figure 8. Average number of hours of daylight and daylight+civil twilight by latitude for each hemisphere.

The effect of the slower earth movement in summer is longer periods with daylight and also twilight. Figure 8 shows the average number of hours of daylight and civil twilight by latitude in each hemisphere. As we increase in latitude, the angle of the sun's movement becomes more diagonal. And since the sun is a disc (from our perspective), at high latitudes it takes longer for the center of the sun's disc to cross the horizon after the top can be seen. This is true in both hemispheres. However, since the earth moves more slowly in the summer, there are more days with a high sun angle in the northern hemisphere than in the southern hemisphere. When we add all the hours up, there is about 1.6% more daylight in the northern hemisphere than the southern hemisphere. If we expand to look at daylight plus civil twilight, the hemisphere difference is more dramatic. In fact, ever place in Alaska from Fairbanks to Barrow receives more daylight plus twilight than any place in the southern hemisphere.

Conclusion:

The next time you hear someone say that all the day and night hours even out over the course of the year, remind them that reality is a little more complicated.

1 comment:

  1. does the amount of sunlight time the longest and shortest days of the year change over time -- as the years go by?

    ReplyDelete

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