You know from why we have seasons that summer sunlight is stronger because the Sun climbs higher. This lesson shows exactly how much stronger, using sine and the height of the Sun above the horizon. Insolation is the sunlight energy arriving on each square meter of level ground.
🔑 Key idea
A beam of sunlight that strikes the ground at a Sun height $h$ spreads over $1/\sin h$ times as much ground as when the Sun is overhead. So the energy on each square meter of level ground is $$E = E_{\text{beam}} \times \sin h$$ At noon, $h = 90^\circ - |\text{latitude} - \text{Sun's latitude}|$, where the Sun is overhead at 23.4° N on the June solstice, at the equator on the equinoxes and at 23.4° S on the December solstice.
💡 Why it works
Hold a flashlight straight down over a table: it makes a small, bright circle. Tilt it and the same light spreads into a long, dim oval. The beam carries the same energy either way, but tilted it shares that energy among more square centimeters. With the Sun at height $h$, a beam 1 m wide lands on a strip $1/\sin h$ meters long, so each square meter gets $\sin h$ of the overhead amount. At 30°, $\sin 30^\circ = 0.5$: half.
A beam of sunlight at a 30° Sun height spreads over twice the ground it would cover from straight overhead. Drag to change the angle and watch the energy per square meter.
✏️ Worked example: A low winter Sun
At noon the Sun is 30° above the horizon, and the direct beam carries 1000 W for each square meter facing the Sun. How much falls on each square meter of level ground?
The spreading factor is $\sin h = \sin 30^\circ = 0.5$.
$E = 1000 \times 0.5 = 500$ W/m².
Answer: 500 W/m²
✏️ Worked example: Summer and winter at 40° N
Compare noon sunlight on level ground at 40° N on the June and December solstices, for the same beam.
June: the Sun is overhead at 23.4° N, so $h = 90^\circ - (40^\circ - 23.4^\circ) = 73.4^\circ$.
December: the Sun is overhead at 23.4° S, so $h = 90^\circ - (40^\circ + 23.4^\circ) = 26.6^\circ$.
Each square meter gets about twice the energy at noon in June, and the June day is also much longer.
Answer: About 2.1 times as much in June
⚠️ Common mistake
Thinking low sunlight is weak mainly because it passes through more air. A low beam does cross more air, and haze and clouds take a bit more of it, but on a clear day the main effect is geometry: the beam spreads over more ground. Check: at a 30° Sun height the spreading alone cuts each square meter's share in half.
This is the engine of all weather. Near the equator the noon Sun is always high and insolation is large all year. Toward the poles the Sun stays low (and in winter does not rise at all), so far less energy lands on each square meter. That uneven heating drives the winds, the ocean currents and the storms of the rest of this course.
The day's length matters too. On the June solstice the North Pole gets 24 hours of sunlight, so even with a low Sun its total daily insolation tops that of the equator for a few weeks. Over a whole year, the equator still gets far more.
Practice
Pass with 3 right answers, the last 2 in a row. Each right answer earns 2 XP.