Lesson 13: Total Solar Irradiance

Total Solar Irradiance Composite. From: https://soho.nascom.nasa.gov/gallery/helioseismology/large/vir011.jpg

The Sun, providing almost all the energy we receive, is the driver of our climate. Therefore one of the core parameters needed to understand the climate is a quantity called “total solar irradiance” (TSI). TSI is measured in watts per metre squared and is a measure of the incoming energy from the Sun into a square metre every second. Note that even that definition needs some caveats – the irradiance of the Sun will depend on the angle the ground is to the Sun and will depend on the distance between the Earth and the Sun which changes a little over our year’s orbit. So, it’s defined as the “straight on” area – something like at the Equator at noon – and for the average distance between the Earth and the Sun over the whole year. The “Total” in total solar irradiance means that this is the Sun’s output at any wavelength of light and distinguishes it from “spectral solar irradiance” where we measure how much light there is at each wavelength individually.

The graph at the top represents the satellite observations of total solar irradiance over the last 40 years. Because the Sun is the driver of the Earth’s climate, it is absolutely essential to understand these data. The coloured lines you see represent the daily values – there’s a lot of natural variation. This is because the Sun has something akin to “weather” – the Sun’s activity can vary significantly and it becomes more and less active depending on the exact processes going on in the upper regions of the Sun. The grey line is a rolling average of that weather – akin to a measure of the Sun’s climatic state.

We’ve been monitoring the Sun’s activity since 1611 when the first telescope observations of Sun spots were made. (The Wikipedia article on Sunspots also says that sunspot observations go right back to the Chinese Book of Changes in 800 BC). When the Sun is particularly active there are lots of Sunspots and when the Sun is not very active there are fewer Sunspots.

If you look at Sunspot numbers over the last 400 years, you see there is a regular 11 year cycle for most of this time where Sunspot numbers increase, then go to almost zero and then increase again. This is known as the “solar cycle” and it is also visible in the satellite observations at the top of the page – the total solar irradiance is higher when the number of sunspots is higher.

Sunspot counts since 1610, from Wikipedia article on Sunspots

You can also see from the 400 year record that there were times when the number of sunspots was extremely low. This is especially true in the very early record with a long “Maunder Minimum” with almost no Sunspots observed at all from 1650 to 1700. That time period also corresponds to the “Little Ice Age” which may have had multiple causes, including because of the Sun’s lower total solar irradiance.

Clearly, the total solar irradiance is a variable quantity and therefore it is essential that climate models include TSI in their analyses. The satellite observations that make up the graph at the top are our best estimates of this quantity – mostly because they are measuring the pure sunlight, unfiltered by the atmosphere. Any observations from the ground (and the best of those are made in Davos, Switzerland at the “World Radiometric Reference”) will lose some light to the atmosphere and that loss will depend on the weather conditions.

In my last blog I showed how even with something as simple as “temperature” there needed to be some thinking about how to interpret and analyse the data to give meaningful information that could be used by climate scientists. On my facebook page someone asked me how you can tell if data are “manipulated” and I’ve been meaning to talk about TSI since then because TSI data must be analysed carefully before being used.

The first clue is in the title of the graph at the top of the page. It describes this record as a “composite”. That means that people have combined data from multiple sources and that almost always means that some analysis is required. If you know how to find scientific data, you can relatively quickly find the graph of the “raw” data.

See the source image
Total Solar Irradiance raw data from different satellites. From Kopp (2014): http://dx.doi.org/10.1051/swsc/20140

The colour scale is slightly different from the top graph, but you can see from the names of the satellites that these are the same satellite observations. When you see the raw data you see why analysis is required – there are noticeable step changes between satellites. Furthermore, at times when more than one satellite was observing simultaneously, you can see that some of the detailed shape is also different.

These differences are because the satellites themselves have slightly different methods for measuring the TSI. All of them use a basic “electrical substitution” technique – they have black cavities that absorb the sunlight and heat up and they compare the temperature rise from the sunlight with the temperature rise that they get using an electrical heater. But there are differences in exactly how they absorb the sunlight and in exactly how they compare the solar heating with the electrical heating. Each satellite instrument manufacturer has made the best attempt at getting that heating equivalent – but there are real differences between satellites because there are real differences between approaches. When I first showed this graph in talks in 1999, I used to say “but you can see that more recently the lines are closer together” and then ACRIM3 and TIM V15 were launched. TIM V15 used a far more accurate technique to do the electrical substitution and that showed a step change. Instruments also change once they are in space – the sunlight they are absorbing contains considerable amounts of extreme ultraviolet that is very damaging to the instruments – the black absorber might go a bit grey, the electrical heater might not be as powerful – and they also get hit by solar wind particles which are even more damaging.

It’s also important to remember that scientists do put “uncertainty estimates” on their observations. And those “uncertainty estimates” are larger than the differences between satellites.

The TSI composite you see at the top is the best estimate by scientists of how to take all this into account. They choose the most stable satellites, they correct for instrument drifts based on models of how the instruments degrade, they “bias correct” the step changes between instruments, they link to the ground observations from Davos and they make their best composite analysis of what the Sun is doing. Different groups around the world have their own best composite and those different composites disagree – and in meeting rooms all over the world scientists argue about the exact details of this composite.

These are real data and real data are always messy. They always need analysing and interpreting by real experts who understand why those differences exist. I’ll write a separate “opinion blog” about how this is over-interpreted by climate sceptics. However, here I’ll just note that when TIM V15 was launched, the TSI was changed downwards. That was taken into account in the modelling and is part of why the older models showed subtle differences to the newer models. But none of that changed the underlying story that anthropogenic greenhouse gases are the dominant cause of recent warming. (Just because we don’t know everything [e.g. about the exact value of TSI] doesn’t mean we know nothing [e.g. the relative effects of anthropogenic greenhouse gases and solar changes].)



Lesson 5: Atmospheric absorption

So in Lesson 4, we learnt that if the Earth had no atmosphere, but still reflected about the same amount of sunlight as it does now, it would be at about -15 °C to -20 °C on average to be in “thermal equilibrium” where the energy coming in from the sun matched the energy coming out through the Earth’s own, thermal infrared, blackbody radiation.

Of course, we all know from our personal experience that the average temperature of the Earth (averaged over the whole Earth, whole day, whole year) is a lot hotter than that. So what is it that the atmosphere does?

To think about that, let’s start with a revision of Lesson 3 about light being absorbed and emitted by atoms. First, the “electromagnetic spectrum” is what I drew in lesson 1: it is the “rainbow” in the visible, and extends that to other wavelengths of electromagnetic radiation. If you look at the visible spectrum (the rainbow) of the sun, you see black lines in the spectrum. These are known as Fraunhofer Lines after the scientist who first described them (see lesson 3b).

Light coming from inside the sun “excites” an atom in the outer parts of the sun, which means that an electron goes to a higher orbital. Then, when the atom returns to its lower state, it releases light with the same wavelength: but it does so in a random direction. So the amount of light heading towards us decreases at that wavelength and we see a black line in the solar spectrum.

In the Earth’s atmosphere the same thing happens – both on the way down and on the way up. Every atom has its own set of lines where it absorbs. But additionally, molecules can absorb lines too. In the atom case, the absorbed energy from the light is used to move a very light-weight electron up to another orbital inside the atom. With molecules, the absorbed energy from the light makes the molecules vibrate in new ways. Since in molecules the things moving are much heavier atoms (rather than very light electrons), all this happens with a lower frequency – and molecular absorptions are in the thermal infrared.

Incoming light from the Sun reaching the top of the atmosphere is in the UV, visible and near infrared spectral region. The UV is absorbed by atoms (and some molecules like ozone) this light gets re-emitted but in all directions, including out of the atmosphere, and is lost. That’s how our ozone layer protects us from harmful UV. Other visible wavelengths are absorbed by the atmosphere too – some Fraunhofer lines are due to atoms in the Sun, others are due to atoms in our atmosphere. This means that some wavelengths do not make it down to Earth.  But this absorption is only a few lines, and it doesn’t affect the overall amount of energy reaching the surface very much.

The Earth’s emitted radiation is in the thermal infrared. This longer wavelength (lower energy) light gets absorbed by molecules to make them vibrate in lots of ways.

Wikipedia has some great images of water molecules vibrating:

The yellow ball is the oxygen. The blue balls (which should really be much smaller than the yellow ball) are the hydrogen atoms (H2O!). Imagine you were holding a model of this with springs for the bonds and balls for the atoms. You can imagine that there are lots of ways for the molecule to vibrate and rotate. Each transition from one way of vibrating to any other way of vibrating requires just the right amount of energy supplied through light at “just the right wavelength”. So you can imagine there are lots and lots of thermal infrared wavelengths that get absorbed by all the water molecules in the atmosphere. And, while that light can also be re-emitted, that will be in any direction – including straight back down to Earth and into the path of another molecule.

[Actually, because the water molecules aren’t cold themselves, they are already doing some vibrations of their own – this actually leads to even more wavelengths being “just right” to create transitions between different vibrational modes.]

There are some difficult concepts in here, so I’ll stop and add give space for questions. 

Lesson 3b: More on the solar spectrum lines

Source: N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF
Published: November 30, 2017


I was asked:

‘In the sun’s spectrum there are black lines at special wavelengths’
This threw me a bit, and so in the continuing paragraph I also got confused. The ‘spectrum’ is the range of light yes? I’m not sure why there are black lines in there. And so then are these black lines acting as blackbody? Are the black lines matter? or more electromagnetic waves?

So let me explore that a little more.

The spectrum is the rainbow – but extending beyond the visible. It’s the light spread out in different wavelengths. Above is the photo NASA took of the spectrum from the top of a mountain in Arizona, USA. Note that really it’s one line going from red to blue, (it’s not 2D – they just made it that way to fit on a page!). The colour you see is the spectrum from about 800 nm (top left) to about 400 nm (bottom right) – the visible part of the solar spectrum. (Note that the solar spectrum actually goes from about 200 nm in the UV to about 3000 nm in the infrared – but we can only see this little bit of it).

You also see black lines in the spectrum. These come from gases either in the outer part of the sun or in our own atmosphere that absorb light with particular wavelengths because that light has exactly the right energy (E = h nu) to make an electron jump from one orbit to another. Later the atom might release that energy going back down again – but, this is the crucial bit, it won’t do so in the same direction that the light was going in in the first place (and sometimes that will then cause another atom’s electron to jump up). So less light gets to us at those wavelengths than should – and we see black lines in our spectrum.

Lesson 2: Blackbody radiation

blackbody radiation

One of the most important bits of physics to understand, before we get to climate, is what blackbody radiation is all about. So this builds on lesson 1 about the electromagnetic spectrum. Here I’ve zoomed in on the middle bit and turned the scale around (so now IR – long wavelengths – are on the right and UV – short wavelengths – are on the left).

When something is perfectly black, it will absorb all energy falling on it (nothing is reflected) but if that were the whole story, things would get hotter and hotter for ever. Of course, that does not happen – because black bodies also radiate energy away as “light”. The blackbody curve (see picture) shows how black objects radiate “light” – and what wavelengths of electromagnetic radiation are radiated. That depends on how hot the object is.  Max Planck wrote down the theory of the blackbody curve back in 1900 and, almost by accident, invented quantum mechanics in the process (but let’s not get side tracked down that interesting alleyway).

As a blackbody gets hotter it emits more light and the spectrum shifts “up and left” (so more light, and the peak moves to shorter wavelengths).

Now that’s all a bit physicy and esoteric so let me link it to things you already know. You already know the idea of “red hot” – as you start heating an electric stove and it gets hotter there comes a point where it starts to glow red. What has happened is that the curve has shifted up and left enough that there’s enough red for you to see it. That’s somewhere around 600 degC (scientists call this ~900 kelvin as we like to start temperatures at absolute zero).

If you keep heating something up it will go orange hot as you start getting orange and red wavelengths too. Your old fashioned tungsten lightbulb (I hope by now replaced by an LED!) had a tungsten filament at around 2500 K – 3000 K (subtract 273.15 to convert to degrees Celsius). That was a yellowy-white. The outside of the sun is about 5500 K and that is “white hot” – the peak of the blackbody curve is in the middle of the visible so all the wavelengths are there and they mix to look “white” (remember Newton splitting white light with a prism to show all the wavelengths are there). There are stars hotter than our sun that are “blue hot” as their peak is in the UV and their spectrum is already dropping in the visible – with blue much higher than red.

But you can see from the graph that the sun also emits plenty of what we call “short wave infrared” (incidentally that was the problem with tungsten lamps – almost all their radiation was actually infrared and thus invisible.).

Of course it doesn’t stop there. Almost everything has a blackbody curve. Blackbodies around room temperature (~300 K) have a peak at wavelengths around 10 micrometres. That’s a wavelength we call “the thermal infrared” and it’s what those thermal imaging cameras you see in science museums (the ones that give people red faces and blue noses and black glasses) measure. Even space itself has a microwave blackbody signal – that represents a temperature of around 3 K (just above absolute zero) – and is the temperature the Big Bang has cooled down to.

Now real objects aren’t perfect blackbodies – they reflect some light – but these basic ideas hold up. And the sun and earth are, to a first approximation, blackbodies at 6000 K and 300 K respectively. And this matters because it’s how the sun heats the Earth up and how the Earth cools back down again.

(Don’t worry, we’ll start getting onto the climate soon! This is the background stuff that makes the explanation meaningful. I know this stuff is hard, so please feel free to ask questions. Lesson three will involve my favourite equation and how atoms and molecules emit and absorb single wavelengths of light rather than blackbodies emitting and absorbing broad spectra … and then we’ll start talking about the temperature of the Earth!).