This is a follow up to Propane vs Electric Heaters.

I spent more time looking into anthropogenic waste heat and its relationship to climate change the other day. I figured some of it out, but am still a bit confused on the fundamentals and could only find some older sources.

Disclaimer: I think that “waste heat vs CO2” was an argument that climate deniers used to make. That’s obviously not my situation.

# Comparing waste heat to GHGs

## Waste heat

As I understand it, waste heat is measured in W/m2 (= J/sm2): the energy flow per time per area. This makes sense to me, a net outflow of heat.

The Wikipedia article on waste heat says: “Global forcing from waste heat was 0.028 W/m2 in 2005.”

There’s significant local variation but I’ll ignore that for simplicity.

## GHGs

GHG emission are usually measured in GWP or CO2-equivalent tons. For simplicity I’ll ignore non-CO2 GHGs like methane and f-gases – I’d be curious how much this changes the story.

How do we convert this to compare with waste heat? Section 2.2 in Zhang 2015 explains how to convert CO2 concentration to W/m2: “The radiative forcing from CO2 in the atmosphere increases approximately with the logarithm of atmospheric CO2 content, with an increase of about 3.7 W m−2 for a doubling of atmospheric CO2”.

Radiative forcing, then, is also measured in W/m2 – it’s the flow of heat that would have escaped the atmosphere if not for GHGs. So radiative forcing from atmospheric CO2 is `5.34 * ln(CO2)`, where `5.34 = 3.7/ln(2)`.

If we plug a pre-industrial baseline of 280ppm, and a current level of 415ppm, this leads me to find a change in radiative forcing of 2.1 W/m2.

## Comparison:

0.028 / 2.1 = .013, about 1.3%. And indeed, the Wikipedia article says:

“globally [waste heat] accounted for only 1% of the energy flux created by anthropogenic greenhouse gases”.

Okay, this seems to check out.

# Current consensus:

I went digging to understand that 1% claim in the Wikipedia article. It looks like it’s citing Flanner 2009, which in turn cites Crutzen 2004, which in turn looks like its citing publications from 1998 and 2001.

Jin et al 2019 claims that global average AHF flux was 0.05 W/m2 in 1970 and 0.13 W/m2 in 2015.

So if we take this updated number 0.13, and compare to our 2.1 above, it looks like waste heat is now about 6% of radiative forcing.

# Effects over time

There’s something about the comparison that I still don’t quite understand intuitively. When you emit 1 ton of CO2, you are changing its atmospheric concentration and changing the rate at which the earth can radiate heat permanently (or at least for a very long time). When you generate 1 joule of heat, you are adding heat once. In other words, this is like “narrowing the bathtub drain” vs “adding 1 cup of water to the tub”. To draw a direct comparison, don’t we need to understand the time horizon and make some assumptions about future emissions, both heat and CO2? Am I missing that in the Zhang paper?