The Azimuth Project
Blog - apologia of profound confusion

This page is a blog article in progress, written by Tim van Beek.

Tim van Beek: I have put off finishing this blog post until the need arises to explain some aspects mentioned in Postma’s paper.

Or: common criticism concering energy balance models

We have not succeeded in answering all our problems. The answers we have found only serve to raise a whole set of new questions. In some ways we feel we are as confused as ever, but we believe we are confused on a higher level and about more important things. — Postend outside the mathematics reading room, Tromsø University, according to Bernt Øksendal: "Stochastic Differential Equations", 5th edition, Springer 2000.

Last time when we talked about a quantum of warmth and refining the most simple energy balance model, reader “Bryan” pointed out the paper

This paper is concerned with a lot of aspects that were covered both in the post a quantum of warmth and its predecessor putting the earth in a box. So I would like to use this opportunity to look back upon the ground we covered and talk about some aspects that may have missed out the discussion to far.

The first thing that met my eye is the need for a…

Separation of Concerns

The principle of separation of concerns is a very important guiding design principle in software engineering: You need to split a complex system into components such that each component does a well defined job, and only that job and nothing else.

Just in case you are thinking “well, that is so obvious, every organisation works this way” all I have to respond is “yes, you are right”. But software developers had to re-discover this principle the hard way nevertheless, after they came to realize that software systems became too complex to be managed otherwise.

The natural sciences have employed this design principle for centuries. Scientists realized that it is necessary to separate

a) the understanding of processes occuring in nature and

b) the inference and implementation of necessary reactions of humans to this knowledge.

Recent human history tells some stories where a mixup of the two points turned out to be unwise; I’m sure you know some.

So here is what I would like to do: I would like to ignore any statments of the paper at hand that - in my opinion - are part of world b), and instead pick some statements of world a) that are connected to our previous discussions and may serve to illuminate some points that deserve more attention.

Is a black body black and how hot is it?

Only a bad lecture is a good lecture. A good lecture tricks you into believing that you got it all. Only a bad lecture forces you to actively think about what you have been told. Horst Holdgrün, professor emeritus of the faculty of mathematics, university of Göttingen

The definition of a black body is that it completely absorbs every photon that hits its surface. This means that no photon is reflected:

Tim van Beek: Definition of absorption and reflection, elastic and inelastic scattering.

But that does not imply that a black body appears to be black to human eyes: This depends on its temperature. But a black body needs a fairly high temperature to emit radiation in the visible range. Most object on Earth are way cooler, so that we only see radiation that is reflected from them, but not radiation that is emitted by them, which is in the infrared range.

Tim van Beek: Background information that may be superfluous:

The principle of detailed balance of quantum statistical mechanics says that

When in thermal equillibrium with a photon gas, the intensity of radiation emitted by an object must be equal to the intensity absorbed at each energy and wavelength.

This means that a black body that is in thermal equillibrium with a photon gas has to emit radiation with the same energy distribution as a gas of photons.

Note that the definition of a black body does not say anything about its heat capacity or heat transport capabilities.

category: blog, climate