Lesson 4b: Further thoughts on the temperature of the Earth

The ideas developed in Lesson 4 are the basic “radiative balance” that make up the Earth’s “energy budget” (look up radiative balance or Earth’s energy balance on Wikipedia as a starting point). This is all based on a very simple concept – if an object has more energy coming in than going out, it will heat up, until the energy in balances the energy out. Similarly, if an object has more energy going out than coming in, it will cool down until the energy out balances the energy in. All physical systems try to maintain an equilibrium. In the Earth system, the energy “in” is coming from the Sun, the energy “out” is coming from the Earth’s own blackbody radiation – and the hotter it is, the more it is radiating out.

I’ve considerably over-simplified the problem in the example in lesson 4 (and not just by ignoring the greenhouse gas effect – which we’ll come onto next).

First, I’ve ignored any heat generated by the Earth’s core, which does work its way up to the surface (hot springs and geysers). This is ok, though, the heat that comes up from the core is about 0.03 % of the energy that comes from the sun. That is much smaller than the size of the approximations I’m giving above.

Second, to improve this calculation you’d have to properly know the average reflectance in the solar reflective spectral region (from UV to short wave infrared). That’s called the “Earth’s albedo” and will vary from something very high (clouds, snow) to something very low (deep ocean, dark forests). It’s generally assumed that the average albedo is somewhere between 0.2 and 0.4 (search it yourself if you want).

You also need to know the Earth’s emissivity in the thermal infrared. Generally natural surfaces have a high emissivity in the thermal infrared – around 0.8 (low end of shiny snow ice) – 0.96 (deep water), with stone and mud around 0.9. (see: https://www.jpl.nasa.gov/spaceimages/details.php?id=PIA18833). So my calculation should be more like 340 × (1 – 0.3) = 0.9 × σT4. That gives a temperature of 261 K, or -12 ºC.

Third, I’ve ignored the effect of atmospheric and ocean circulations that move the energy around the Earth (though that’s ok with my “no atmosphere” approximation).

But my basic premise holds: without greenhouse gases (next lesson we’ll talk about what they do), the Earth would be really, really cold – with average temperatures in negative teens.  

Before we leave this simplification, it’s worth thinking about what you’d do to do this simple calculation better. You’d probably split the Earth up into little boxes. In each box you’d work out what the average energy (over a day, over a year) coming in from the Sun would be (higher at the equator than at the poles). And you’d work out how much was reflected (more over ice and sand than over ocean or forest) and what the thermal infrared “emissivity” is (i.e. how well that type of surface emits thermal infrared radiation). Then you’d do the energy balance equation in each box and then add that all up for the whole Earth. That would be the beginning of a climate model (more later!)


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