Air Mass Spectrum Overview

Would you prefer a visual guide to the effects of the Air Mass spectrum? Check out our “Explaining the Air Mass (AM) Spectral Influence” chapter from our Solar Simulation and LEDs: Multi-Source Lighting for Advancing Future Technologies presentation on YouTube. To learn more about the Air Mass spectrum in depth, continue reading.

What is Air Mass in the Solar Energy Field?

When you first read the term “air mass,” you might have wondered what relevance the mass of air has to sunlight and the solar spectrum. You’re not alone! This term can definitely cause some confusion, but it is very important to understand how different solar spectra are defined. It’s doubly confusing because there are similar definitions in the disciplines of meteorology and solar energy.

In meteorology, an air mass is defined as a volume of air with a specified temperature and vapour content. Gases and particles in two similar air masses will, therefore, exhibit similar chemical and spectral behaviour. However, this definition is not the most useful in the discipline of solar energy.

In the solar energy field, air mass is better referred to as the “air mass coefficient” and defines the amount of atmosphere between you and the Sun. As we discussed earlier, the atmosphere absorbs and scatters light, so knowing how much of it is vital to knowing and quantifying the spectrum of light. The air mass coefficient tells you the relative distance (or path length) that light has to travel through the atmosphere before it gets to you.

While these two definitions share some similarities, it is important to recognize that they are not interchangeable. Therefore, when you’re in solar energy circles, the term “air mass” really refers to the “air mass coefficient.” We’ll go through some specific examples below.

What is the AM1 Spectrum?

When we measure the solar spectrum on Earth, it is different from the 5800 K black body radiation of AM0 due to scattering (of blue light, for example) and absorption (of red light, for example) by molecules in the Earth’s atmosphere. Overall, the spectrum is going to be attenuated or diminished after passing through air. The more atmosphere sunlight passes through, the greater the light’s attenuation.

We’ve already discussed how air mass (or air mass coefficient) is the path length of a direct sunbeam through the atmosphere. Now we can introduce some definitions and specifics of how to calculate it.

The air mass coefficient defines “1” as the path length light travels through when the Sun is directly overhead at sea level. The spectrum of light after travelling through this path length of the atmosphere is what we call Air Mass 1 or AM1. In this case, the sun’s direct radiation passes vertically through the atmosphere in the shortest possible path.

This point directly above a particular location is known as the zenith. Expressed as a ratio relative to the sun at the zenith (a zenith is an imaginary point directly above a particular location) above a sea-level location. In this case, the sun’s direct radiation passes vertically through the atmosphere in the shortest possible path. This is known as Air Mass 1.

AM1 is the baseline from which the rest of the spectra can be defined. The air mass is expressed as a ratio relative to the sun at the zenith above a sea-level location.

If our path length is twice that of seaside sunlight zenith, then that spectrum is referred to as AM2. If we have four times the path length, that’s AM4, and so on.

What are the AM0.1, AM0.2 … AM0.9 Spectra?

These spectra refer to fractions of the standard path length when the sun is at its zenith, shining on the sea. If you climb up a mountain until you are at half the atmosphere’s height, the light when the sun is directly overhead will be travelling through half the path length, and you’ll be exposed to the AM0.5 spectrum. If you fly a plane until you’re at 90% of the height of the atmosphere’s height, with only 10% remaining, then the plane will be exposed to AM0.1 (i.e. 10% of the path length of AM1).

Because we have topography and don’t spend all our time at sea level, we need spectral definitions for when the sun is directly overhead, and we’re above the sea. These are all the spectra from AM0.1 to AM0.9.

AM1.1 to AM40 Spectra Explained

These spectra correspond to sunlight that has travelled through path lengths much longer than direct overhead sunlight at sea level (1.1 times, 1.5 times, 2 times, 5 times, and 40 times to be specific).

Your next question might be: When does light travel through that path length? We’ll need to do some calculations, but the short answer is that as the sun changes its angle on the horizon, the AM spectrum changes.

When does a Specific AM Spectrum Apply?

Because the air mass coefficient is calculated as the ratio of the sun’s actual path length to that at the sun’s zenith, we can use some basic geometry to start seeing when AM1.1, AM1.5, etc. might apply.

The fundamental thing that changes when the air mass coefficient changes is the zenith angle, which is the angle between the sun’s current position and a line directly overhead. The higher the zenith angle, the lower the sun is in the sky, and the more atmosphere sunlight has to travel through.

Knowing when a specific AM spectrum applies is really a question of figuring out the sun’s zenith angle for that AM spectrum.

Air Mass Coefficient: Calculating the Zenith Angle

The easiest way (to first-order) to relate the Zenith angle and the air mass coefficient is to use simple triangles. 

A simple triangle model for calculating the air mass coefficient as a function of the zenith angle, theta-z, and vice-versa.

 In this case, trigonometry gives us our equation:

This equation tells us that we’ll get an Air Mass of 1.1 at a zenith angle of about 25 degrees, an Air Mass of 1.5 at about 48 degrees, AM2 at about 60 degrees, and AM40 at 89 degrees. However, as the diagram below shows, this simple calculation has a few inaccuracies.

The simple triangle model for calculating the air mass coefficient doesn’t account for the curvature of the Earth or its atmosphere, as shown in the dotted line above.

The simple-triangle example doesn’t take into account the curvature of either the Earth or its atmosphere. The simple triangle approximation is reasonably accurate up to around 75 degrees but overestimates air mass at high zenith angles. There are a number of approximations that provide a better estimate of air mass across the full range of zenith angles, some even including the effects of atmospheric refraction (for example, in the open ocean, the sun is visible before it has risen above the horizon because light has been bent by the atmosphere around the curve of the earth).

Unfortunately, these models generally go from zenith angle to air mass and are not easy to solve going in the reverse direction. If you have to go from Air Mass to the zenith angle, we recommend using the simple triangle as a rough estimate, then iteratively finding a more accurate solution using the models we discuss in the next section.

How Do I Calculate the Air Mass Coefficient From Zenith Angle?

The simple triangle model makes it easy to go from the zenith angle to AM or vice versa, interchangeably:

However, as discussed in the previous section, this approximation breaks down for higher angles.

Air mass and solar spectrum calculation using the Kasten & Young Equation

Another model (by Kasten & Young, 1989), more sophisticated than the simple triangle model, provides a more accurate estimation of the air mass coefficient. It is as follows, where theta-z is in degrees. You can plug zenith angle values directly into this model to get an accurate calculation of the relative path length increase.

This will get you an air mass coefficient with high accuracy up to the maximum 90-degree zenith angle, which is far better than the simple triangle model. The disadvantage of this model is that it is difficult to solve the equation in the reverse direction, i.e. going from AM and determining the zenith angle. However, in the majority of applications, this direction of calculation is not needed, and if it is, then using the simple triangle method followed by a few iterations on the above equation will get you the answer you need.

What Spectra is the Most Commonly Used in Testing?

Standard spectra include AM0, AM1.5G, AM1.5D. These are defined by ASTM E490, ASTM G173-03, and other standards bodies to provide standard test conditions so that experiments and results can be compared and a reasonable approximation for real-world performance can be obtained. AM0 and AM1.5G are by far the most commonly used test spectra.

The spectrum generated by sunlight at AM1 (at 0° from the zenith) to AM1.1 (at 25° from the zenith) is a useful range for estimating the performance of solar cells in equatorial and tropical regions.

Other AM values approximate sunlight at regions other than mid-latitudes or higher elevations. AM2 and 3 (z=60° and z=70°, respectively), for example, are useful to determine the solar performance of some devices (e.g., solar cells) at higher latitudes, such as those in northern Europe. An AM value of 40 is typically regarded as the air mass value of the horizontal direction (z=90°) at the equator.

If you are looking to test conditions from AM0 to AM40 and everything in between, check out our Class AAA LED solar simulators. 

Our next chapter will explore the common Air Mass spectrum used for aerospace applications AM0.

Chapter 3: Aerospace and the AM0 Spectrum

Before moving on, we’ve summarized a few examples of air masses and their properties in the table below.

Table of Standard Solar Spectra for Testing

Some examples are Air Mass (AM) spectra and their properties.