# The Changing Angle of the Sun and Its Effect on Temperature

Over the last four centuries, the sun in the northern hemisphere is getting progressively higher in the sky. Based on data from the National Renewable Energy Laboratory (NREL)’s Solar Position Algorithm, the average surface incidence angle—the angle that solar rays intersect with the Earth, or the inverse of the solar zenith—has steadily increased decade over decade with a sharp increase since the 2000s.

The data is based on a single location in Colorado at noon each day since the year 1600 to 2021. Data is algorithmically generated based on established understanding of the sun’s movements.

The increase is small, less than a thousandth of a degree a decade on average, although it increased .02 degrees in the past decade alone. But small changes in the angle can have large effects on solar radiation, which in turn affects temperature.

Based on a similar location in the southern hemisphere, the angle is instead *decreasing* on average, albeit at a significantly slower rate—about half as fast.

## Daily, Annual, Quadrennial, and Octogennial Frequencies

On a daily and yearly basis, the angle at which the sun’s rays hit the Earth are constantly changing. It fluctuates between the time of day and the point of rotation of the Earth’s axis as well as the time of the year and the position of the Earth in its revolution around the sun.

Yet there are even more alterations to the sun’s angle, like the wobble in the Earth’s axis known as the Chandler Wobble or the free precession.

As a result, from one year to the next the angle of the sun on one particular day at the same time will vary. Across four years it can increase slightly only to fall back down and reset the pattern. Then that pattern resets every 80 to 120 years.

But as that pattern progresses, over the course of a century the overall average increases eight-hundredths of a degree (.008).

## Surface Incidence and Insolation Rate

Solar angle is a large determiner of temperature, sometimes more so than the length of exposure to the sun. The angle that the sun’s rays hit the Earth determine how much radiation is absorbed by the surface, and it is integral to maximize solar panel effectiveness.

The larger the angle of incidence, the more a solar ray is spread out over a larger area and therefore transmits less energy. Solar rays hitting near the equator regularly strike close to a complete perpendicular angle (90˚) and lead to hotter, tropical climates. Whereas closer to the north and south pole the angle is lower and little heat is transferred even in the middle of summer.

The amount of radiation transferred, otherwise known as insolation, can be calculated based on the angle of incidence. The ratio of the width of a solar ray to the area affected is equal to the *sine* of the angle of incidence in radians.

Based on that equation, the change in the angle around Colorado would equate to a change in the insolation ratio of .056 percentage points since the 1920s or .0257 since the 2000s.

Those numbers might seem small, but when you consider that the sun delivers 44 quadrillion watts of power to the Earth every year according to the National Aeronautics and Space Administration (NASA), an increase of .0257 percentage points in solar radiation across the surface of the Earth would lead to an additional 11.31 trillion watts of energy radiated each year since 2000.