# The Earth’s Energy Balance.

So with all the sun we’ve been having recently in the UK I’ve been thinking about the role of the sun in our climate. I also need to know this stuff for my project so I’m refreshing my memory!

The sun!

That big ball of light in the sky is responsibly for providing practically all the energy in the Earth’s energy budget.

Here is a shiny diagram I’ve borrowed from wikipedia, you should understand it at the end of this post!

The standard type of diagram you get for the Earth’s energy balance. Publisher: Earth Observatory, part of the EOS Project Science Office, located at NASA Goddard Space Flight Center.

Now what happens to the energy?

Some of it is reflected back from the Earth’s surface or the tops of the clouds. The amount being reflected is called the albedo. White things like ice are highly reflective and have a high albedo.

Some energy goes into heating up the land and sea.

Thinking about it, if the sea is being heated up then there must be evaporation from the surface.

Latent heat- you what?

Now think back to high school, did you ever do the experiment where you stuck a thermometer in a jar of water and heated it over a Bunsen burner? Just me? Ok, well what happens is the water gets hotter and hotter until it starts to boil, and then the thermometer sticks at 100C! Why is this? Well as we know water is H2O, you might not know the molecules are polar. That oxygen atom is way bigger than the Hydrogen ones, and pulls the negative charge to itself, so a molecule of water becomes like a tiny magnet with a negative pole in the middle and two positive ones either side.

So if you stick loads of magnets together, what happens? They stick to one another don’t they? Well this isn’t entirely what happens with water (your cup isn’t full of one massive stuck together water molecule) however you still need energy to pull the separate molecules apart from their mutual attraction. This is supplied by the heat, and that’s why the thermometer gets stuck at 100, as the extra energy is being used to break those bonds of attraction and free the water to be steam!

This energy is known as latent heat of vaporisation, the opposite is called latent heat of freezing, can you imagine that when you freeze it water gives back that extra energy you put in when you boiled it? Well it does! We will call these energy changes latent heat.

So what else happens to the energy?

We got to heating up land and sea didn’t we? So how about heating up the air? This is called the sensible heat as all the energy is doing is making something be warmer. Sensible here means you can feel it. The changes in sensible heat cause convection, air rising as it is warmer and less dense.

Long and Short Wave.

What about the energy that has been absorbed by the surface? Well you’re right to think it goes somewhere, else the planet would just be getting hotter and hotter.

The absorbed energy is given back out, but in a slightly different form, Long wave radiation.

The energy from the sun is Short wave radiation.

This long wave radiation may go back out into space, or be absorbed by clouds, or reflected back by the atmosphere (the greenhouse effect).

Lets get out the maths!

So as the earth doesn’t make any of its own solar energy we can say,

sun’s energy in = energy out + energy used.

So lets call the energy in : $E_{sw}\downarrow$ , short wave coming down.

The short wave radiation being bounced back up is $E_{sw}\uparrow$. This could be expanded further so we’ll come back to it.

The energy used was for the latent and sensible heats, so $H_{l}$ and$H_{s}$ respectively.

So now the Energy coming out of the Earth, $E_{lw}\uparrow$, the long wave radiation upwards, emitted by the surface and atmosphere.

Not forgetting the energy that is absorbed and re-emitted by the atmosphere or reflected back downwards, so we have an $E_{lw}\downarrow$ too.

So we can write the net change in the Earth’s energy as Change = energy in – energy out – energy used.

Lets give the change its proper name, a Flux and call it $F$. So now we have,

$F = E_{sw}\downarrow - E_{sw}\uparrow - H_{l} - H_{s} - E_{lw}\uparrow + E_{lw}\downarrow$.

$F$ will be a positive number if there is more energy in than out, and negative if there is more energy out than in (so at night).

What about the albedo?

We can go back to $E_{sw}\uparrow$ and describe it better. Earlier I said that the amount of energy reflected back was termed the albedo. If the earth had a totally reflective surface (so an albedo of 100%) then everything would be reflected. If the albedo was 0% then everything would be absorbed and emitted as long wave instead.

So we could say that energy out is equal to the albedo, $\alpha$, (as a number between 0 and 1) multiplied by the short wave energy in.

Giving us,

$F = E_{sw}\downarrow - \alpha E_{sw}\downarrow - H_{l} - H_{s} - E_{lw}\uparrow + E_{lw}\downarrow$.

We could keep going, describing things in terms of other things, but I’ll leave it there for now.

Soooo where do the clouds come in?

I’m interested in Arctic clouds (amongst other things) so how do clouds affect the energy balance?

I’ve mentioned above that some of the short wave is reflected back from the top of clouds. The thicker and whiter a cloud the more reflective it is, so lower clouds reflect more than thin high clouds. This would cool the surface. Higher up thinner clouds let shortwave through but help to trap the longwave closer to the surface. Exactly what effect the clouds have is a function of its altitude, size, and the kind of particles that form the cloud. In the arctic the increased albedo from cloud cover isn’t important as much of the surface is covered in highly reflective ice, its the action of trapping energy near the surface that is important, and how much energy they let through.

Clouds also emit long wave radiation that they have absorbed, this is a function of their temperature. In the arctic you can get clouds that are warmer than the surface, which in turns warms the surface more.

Does the ice in cloud reflect more energy? Does a cloud with more ice emit less long wave radiation? These are things I should find out, but you never stop learning!

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