What if the Sun stayed low in the sky?

In summer the Sun climbs high in the sky. In winter it stays low.

Does it matter how high the Sun is? What if it stayed low all day?

On a winter afternoon the Sun hangs low, shadows stretch long across the ground, and even on a clear day the sunshine feels weak. In summer the noon Sun is high and the light feels strong.

It is the same Sun. So why does a low Sun warm us so much less? In this lab you can keep a town in place, slide the date from June to December, and watch how the Sun's height and the sunlight it delivers change.

Earth's distance from the Sun changes only a little through the year, and NASA Space Place notes that this change does not make much difference to our weather. Yet a mid-latitude town receives far less solar energy per day in winter than in summer.

This lab separates the two causes: the angle at which sunlight strikes the ground and the number of daylight hours. Using London at 51.5°N, how much does each contribute to the drop in daily insolation between the solstices?

In London in June, the Sun climbs high at lunchtime.

It shines for more than 16 hours. The sunshine is strong and warm.

Start in London, at 51.5° north, on June 21. In the model the noon Sun climbs to about 62 degrees and stays up for 16.4 hours. Every square meter at the top of the atmosphere gets an average of 497 watts of sunlight over the whole day.

The Met Office says summer in the UK, June to August, brings the hottest temperatures and sunniest days.

At 51.5°N on day 172 the model gives a noon altitude of 61.9°, 16.4 h of daylight and a daily-mean insolation of 497 W/m², 115 percent of the equator's equinox value.

NASA's energy budget explains that in the summer hemisphere the combination of more direct sunlight and longer days increases the incoming solar energy; the Met Office puts the UK's summer in June to August.

Now Olly moves the date to December. The Sun stays low all day.

It is up for less than 8 hours. The sunshine is much weaker. Brr!

Now move the date to December 21 and keep the town where it is. The noon Sun only reaches about 15 degrees, and it is up for just 7.6 hours.

The daily sunlight falls from 497 to 73 watts per square meter, about one seventh. Watch the chart of the noon Sun through the year: it rises to its highest around June 21 and sinks to its lowest around December 21.

On day 355 at 51.5°N the noon altitude is 15.1° (the year's minimum, 15.06° on day 354), daylight 7.6 h and insolation 73 W/m², 17 percent of the equator's equinox value.

The ratio 497/73 = 6.8 splits into two parts. At noon, the beam-spreading factor 1/sin a rises from 1.13 to 3.84, about 3.4 times; the shorter, lower day accounts for the rest.

Shine a flashlight straight down. You get a small, bright spot.

Tip the flashlight low. The spot gets big and dim. A low Sun is like that!

Imagine shining a flashlight straight down at the floor: you get a small, bright circle. Tip it low and the same light stretches into a big, dim oval. The Bureau of Meteorology explains that in winter, sunlight is spread over a larger area, so the ground receives less heat.

In London in December, each beam of noon sunlight covers almost four times as much ground as it would from straight overhead. And with only 7.6 hours of daylight, there is less time to soak it up.

Irradiance on a horizontal surface is S·sin a, where a is the Sun's altitude. At 61.9° that is 88 percent of the beam; at 15.1° only 26 percent. Integrating over the day gives the model's daily mean Q = (S₀/π)(h₀ sin φ sin δ + cos φ cos δ sin h₀).

The low winter Sun comes from Earth's tilt: in December the Northern Hemisphere leans away from the Sun. NASA Space Place notes that Earth is actually closest to the Sun in January, so distance is not the cause. The model gives sunlight at the top of the atmosphere; air and clouds are not included.

When the Sun is low, your shadow is very long!

In winter, the far north gets even less sunshine than London.

You can see the low Sun in your shadow. Trigonometry gives the noon shadow of a 1-meter stick from the model's Sun heights: about half a meter in London in June, but almost four meters in December.

The Met Office says the UK's winter months, December to February, are the coldest of the year, with the shortest days. Go farther north and it gets more extreme: at 60° north, the model's December noon Sun is under 7 degrees high and the day lasts 5.5 hours.

A vertical stick of height h casts a noon shadow h/tan a: 0.53 h at 61.9° and 3.71 h at 15.1°, a practical way to measure the Sun's altitude.

The Met Office relates the seasons to how directly the Sun's heat reaches the hemisphere tilted toward it, and the Bureau of Meteorology to sunlight spread over a larger area in winter. At 60°N on day 355 the model gives a 6.6° noon Sun, 5.5 h of daylight and 24 W/m².