In this video we will travel with the sunlight through the atmosphere to see which effects the atmosphere has on the solar spectrum. This is important because the solar spectrum doesn't only change throughout the year, it changes throughout the day as well. The effects we encounter will explain why the sky is blue and seems more reddish during a sunrise or a sunset. But they're also critical in the context of solar cells, because the performance of our devices depends on the solar spectrum. In the previous video we described the sun as a perfect black body and we modeled the solar spectrum using Planck's law of black body radiation. Here we saw that the best fit of Planck's law to the solar spectrum, as measured outside the atmosphere of Earth, was with an effective surface temperature of 5,777 Kelvin. However, the atmosphere has a huge impact on the solar spectrum and should therefore not be ignored. Just take a look at this spectrum measured from the surface of Earth, called the AM1.5G spectrum. Especially the infrared part of the spectrum seems to be heavily affected by the atmosphere. But what could have happened? Well, light can either be reflected off from the atmosphere. It could also be that light is absorbed in the atmosphere, which is what has happened with these large dips right here. It could also be that light is scattered in a lot of different directions. And here we usually distinguish between Rayleigh scattering and scattering of aerosols and dust particles. The most important factor, however, is the distance that light has to travel through the atmosphere to reach the surface of Earth. The longer this optical path length is, the more atmosphere the light has to travel through, and the more pronounced all of these effects become. The concept of air mass simply describes how long this optical path length is. To describe the concept of air mass it is convenient to know a few basic angles describing the position of the sun in the sky. The first angle is called the solar azimuth angle. It's often denoted gamma subscript s. North of the equator, the angle is defined as the deviation from directly south facing. Now that we know the Sun's deviation from south, we need to know how far above the horizon the Sun is positioned. This is called the solar altitude angle, often denoted alpha subscript s. The horizon is, however, not always that easy to define. Therefore, one could have to use the zenith angle, describing the angle between the sun and the vertical. This is actually complementary to the solar altitude angle, but you will most likely see the zenith angle being used more frequently. Now we're ready to look at the concept of air mass. The spectrum measured outside the atmosphere of Earth from the plot I showed you previously was called AM0. This means that the light travels through no atmosphere and therefore the air mas is 0. Now, let us introduce the Earth and the atmosphere. The shortest path that light could possibly travel would be the vertical distance when the Sun is directly overhead. This distance is defined as an air mass of 1, or simply AM1. But what if the sun is not directly overhead? The optical path is now longer, and in this specific case it is 1.5 times longer than that of the vertical distance. Therefore, we called this new distance AM1.5. And if we look at the angle between these two paths, this is exactly the zenith angle we just defined. We should, therefore, be able to calculate the air mass from the zenith angle using simple trigonometry. More complex equations do exist, where the altitude and air pressure and even the curvature of Earth has been taken into account. But this equation is often sufficient. So let's try to apply it. We have just considered the optical path length, called air mass 1.5. But what is the corresponding zenith angle? We can use the trigonomic equation we have just learned to arrive at 48.19 degrees. Now, this exact air mass is actually rather important in the field of photovoltaics, because it's used as an average optical path for sunlight. The spectrum that results from air mass 1.5 is therefore used as a reference spectrum when measuring solar cells and photovoltaic modules. But how much solar power are we left with after the atmosphere has affected the solar spectrum? In the previous video we saw that on the top of the atmosphere of Earth we received 13,167 watts per square meter. Which could have been found if we just integrated the measured AM0 spectrum. But if we now integrate the AM1.5 spectrum instead, we'd get an irradiance of approximately 1,000 watts per square meter. So we have actually lost approximately 30% of the light in the atmosphere. One of the two main scattering mechanisms in the atmosphere is called Rayleigh scattering, and it is caused by ozone, air molecules, and trace gases. The Rayleigh scattering strength is inversely proportional to the wavelength to the power of 4. But what does that even mean? Consider sunlight impinging onto a single air molecule, as the red light has a longer wavelength than blue light, it is scattered much less efficient. Actually, when comparing to the blue light, it is almost negligible. The blue light is, however, scattered in all directions from the air molecule, and as our atmosphere is full of air molecules, the sky appears to be blue. The same effect explains why sunsets are red. As the optical path becomes greater and greater, the blue light is scattered more and more in the atmosphere, and ultimately you're left with only red light. Another scattering mechanism happens when light impinges onto aerosoles, which are particles less than one micron in diameter. Unlike Rayleigh scattering, the wavelength of light is comparable to the size of the particle, and all wavelengths of visible light are there for scattered efficiently. Let's consider sunlight impinging onto a volume of water droplets in the atmosphere. As all visible wavelengths are scattered efficiently, the droplets appear to be white, which explains why clouds are white. The atmospheric concentration of aerosoles is described by a parameter called the aerosol optical depth, going from 0 to 1. Where 0 is extremely clear, and 1 means that all sunlight is absorbed or scattered by aerosols. In Denmark, the aerosol optical depth is between 0.1 and 0.2, but in by Beijing is between 0.4 and 0.5 as a result of heavy air pollution. We have now looked at how the atmosphere influences the solar spectrum, and it is therefore time for a brief summary. We have seen that sunlight is scattered, reflected, and absorbed in the atmosphere. We have also looked at a few basic angles to describe the position of the sun in the sky. Namely, the solar azimuth angle, the solar altitude angle, and the solar zenith angle. The zenith angle turned out to be super useful when we wanted to describe the optical path length that light travels through the atmosphere before reaching the surface of Earth. We call this optical path length the air mass. We then turned our attention to air mass 1.5, which is considered the average optical path length that light has to travel through the atmosphere. And the resulting spectrum is therefore used as a reference spectrum. In the case of AM1.5, the irradiance received on Earth has been reduced by 30% in the atmosphere, to 1,000 watts per square meter. Finally, we looked at Rayleigh scattering, which makes the sky appear blue, but also Mie scattering, or aerosol scattering, that makes clouds appear white.