# Do I get really get solar & visible light transmission? PART 1

…was a question I asked myself at the end of a previous post about a reflection coming off a new tower being built in Auckland.

The answer to my (own) question currently would be:

“Yeah, kind of.”

So, it’s a work in progress. To start with I got tied up with what the sun was doing: what happened between it and eye-frazzling glass in terms of solar radiation, so a more apt title to this post would be:

# (My take on) Solar spectra

## In a sketch

I realized how is irrelevant all this is when I drew the sketch below: but I have started now, so ought to finish.

Something comes out the sun (I), gets to Earth (II), and gets to Auckland (III) at 5ish on an Autumn Friday afternoon.

The graph below shows the 3 solar spectra from ASTM G173 1. It’s pretty similar to a load of other similar graphs you would get if you googled it, except my mine is specific to ASTM G173, which is kind-of relevant (which I will get to at some point).

Oh, and my black body curve is probably wrong.

• In blue: The extraterrestrial spectrum, just outside the earth’s atmosphere. Measured by satellites. I am guessing floating around at the defined ‘1 AU’ from the sun. (Not sure if that’s true).
• In red and yellow: The spectrum at sea level at quite narrowly defined position and atmospheric condition, for Standard’s sake.

And;

• In black: My take (my maths!?!) on the theoretical black body radiation for-the-sun at-the-earth.

### Stuff I learnt (starting from the sun)

#### I. Sun to earth

1. The inner sun emits radiation pretty closely to a black body at ~5800K.
2. The outer parts of the sun are *relatively* cool, and various elements and compounds modified the smooth black body (see below)
3. the radiation travels through space, 14,959,7870,700 km (or more on conveniently 1AU) to earth. Between the two, not a great deal happens, it being space. You might make a cup of tea (it takes 8-and-a-bit minutes).

NOTE We can take this transitory period to make a conceptual switch from Radiance (W/m²/sr) to Irradiance (W/m² ). A moot point but a real brain bender for me. I worked it out, but a post for another time?

#### II. Not quite in Earth’s atmosphere

When Mr Photon arrives (is about to arrive) at the Earth’s atmosphere, he and his photon friends are characterized by the extraterrestrial spectrum (blue):

1. If you calculate the total power in this, you get (as near as dammit) ‘1361’ W/m2 which is, give-and-take some technicalities, the solar constant.
2. The spikey differences between the smooth black-body curve and the blue curve are due to those interactions in the sun’s outer layers mentioned before. They are called Fraunhofer lines.

#### III. The Atmosphere

On goes Mr Photon…

What happens to form the spectra at the earth’s surface is way better explained elsewhere, but best summarised in the diagram below from this Physics Stack Exchange question (which also helped me on the radiance to irradiance conundrum).

In a nutshell, the water vapour, carbon dioxide and oxygen soak up some infrared causing those various valleys in the graphs (and global warming), and ozone soaks up the more nasty UV.

Not quite sure what causes the big difference between the surface and extraterrestrial spectra in the visible part. The ASTM profile I am working to is at a 37° tilt, so that is a ~20% reduction in the direct irradiance power (cos 37° = 0.8) which account for quite a bit of it. I am not sure where cloud cover (reflecting away stuff) comes into the ‘standard atmosphere’ either. For another time.