White rooftops?

Global warming and climate change should really be ever present on the collective minds of our species these days. After all, despite science communicators like Carl Sagan having been beseeching us for decades to curb out use of fossil fuels, we simply haven’t. In fact, our use of fossil fuels has, if anything, increased. So, if you like to take part in such conversations (as I do), you may have heard the question asked in the past – how would it affect global warming if we all painted our rooftops white?

Oooo... shiny!The principle behind this is pretty simple. The amount of solar radiation absorbed by Earth is determined by its albedo. Simply, this is the fraction of light reflected by our planet. All planets (and indeed, all objects) have an albedo, ranging from highly reflective worlds like Venus, to certain comets and asteroids which are only half as reflective as coal. Could painting all rooftops white really affect Earth’s albedo? After all, going by all of the city lights in NASA’s black marble images, there must be quite a lot of rooftops, right? While I’m sure the calculation has been done in the past, I thought it might be interesting to play with…

Unfortunately, this isn’t the easiest of things to estimate, so I’m going to need to make some huge assumptions here. Firstly, I don’t think anyone knows exactly how many buildings are on the surface of Earth. But based on the current world population of around 7 billion, I’m going to assume that there are around 2 billion buildings. I also need to estimate how much roof area they have. A website for a UK building company states that the average rooftop area in the UK is about 55 m2. Well, that’s a good enough estimate for me. Both of these are probably underestimates, but they should suffice.

I was always quite fond of the word "insolation"...As it turns out, that means that roughly 0.02% of Earth’s surface is covered with buildings (a total rooftop area of around 110 billion square metres). Yes, that’s a very small percentage and personally, I’m quite content for it to stay that way. Earth has an albedo varying from 30% to 35% dependent on cloud cover. So could white buildings help reflect back any significant percentage of the 174 petawatts(!) of energy Earth receives every day from the Sun?

Looking up a few values, you can find that matte white paint has a reflectance of around 80% (aluminium foil, for comparison, has a reflectance of 85% or 95% for the dull and shiny sides). Cutting a long story short, if you crunch the numbers it turns out that white rooftops would only increase Earth’s albedo by 0.01%. This may seem slightly disappointing, but don’t forget that most of Earth’s surface isn’t even land! Incidentally, if you calculate it for aluminium foil instead of white paint, the albedo increases by 0.012%. That’s shiny side up, too. Given the extra effort which would be needed, it doesn’t really seem worth the 0.002%, so let’s stick with paint. So how does this affect the temperature? Well there’s rather a convenient equation which we can use for that…

Simplistic, but adequate.

This equation is fairly simplistic. It doesn’t account for greenhouse effect at all, so if you throw in Earth’s average albedo as 35%, it’ll give you a temperature of 250.184 K. Without any carbon dioxide at all, Earth would be a very cold place. Good thing we have an atmosphere to keep us warm. Not too warm, though. One last bit of number crunching…

So it turns out that painting all of our rooftops white would decrease Earth’s average temperature by 0.01 K. Not really much of a difference. Mind you, a change of 1 K is a serious problem on a global scale, and a change of 2 K would be catastrophic. Perhaps such a tiny percentage isn’t quite as insignificant as it might first appear. Sadly though, a full solution to global warming is evidently going to require a little more than just a few billion buckets of white paint…

About invaderxan

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.
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5 Responses to White rooftops?

  1. Pingback: Printed solar cells as easy to produce as t-shirts!

  2. s katz says:

    Light color roofs do reduce heat load, and perhaps electric demand for cooling/ventilating, as pointed out.

    I’d be curious to see what damage could result to weather patterns if a substantial percentage of roads, as well as roofs were painted light colors. Potential unintended consequences of forcing changes to weather patterns could result.

    • invaderxan says:

      They do, as pointed out. Though as was also pointed out, that is not really what this was about. Electric demand is a matter of economics, while the calculations here are about global reflectivity.

      I’m curious. Forced changes to weather patterns? Do you mean to do with local alteration of convection currents, thermals, etc? Please do elaborate…

  3. Wil says:

    I always though the point of painting the roof white was to cut down on the amount of energy needed to cool a house in hotter countries. Less power needing generating meaning less pollution and so on.

    Though it is a nice reminder that we are really tiny.

    • invaderxan says:

      It certainly does serve that purpose in hotter countries, yes. I’m just looking at it from a different angle. This is about the planet as a whole, so individual houses aren’t actually relevant here. :)

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