29. Lateral thought #1 - suburban heating

Question

How much does the average home heat up its environment?

This is really a question that ties in with what I wrote on Post 14. Surface Heating, but I think it illustrates the point at a level that most people can relate to.
 

Answer

Well, we know from Trenberth et al. that the average power of solar radiation incident on the Earth's surface is approximately 161 W/m² (see Fig. 14.1). We also know that this leads to a mean surface temperature for the Earth of about 288 K. We also know from Post 12 (black body radiation and Planck's law) that the emitted surface radiation density scales as T ⁴, where T is the absolute temperature of the surface measured in kelvins, and the emitted radiation must balance the incoming radiation. In other words, both incoming and outgoing surface radiation densities will be proportional to T ⁴. For the outgoing radiation the constant of proportionality will be the Stefan-Boltzmann constant, while for the incoming radiation it will be the Stefan-Boltzmann constant divided by the feedback amplification factor. It therefore follows that if the mean surface temperature were to increase by 1 K to 289 K, then the quantity T ⁴ must increase by 1.40 %. And there are two main ways that this could be achieved. 

The first is to increase the feedback or radiative forcing through an increase in the strength of the Greenhouse Effect. This is what most climate scientists concentrate on, and what they believe is responsible for any temperature changes. But the second possibility is to increase the radiation power absorbed by the surface before the feedback amplification occurs. This could happen if the strength of the Sun's output changes, but more realistically it will happen whenever extra heat is liberated at the surface of the Earth. The amount of heat required to do this will be 1.40 % of 161 W/m², or 2.25 W/m². So an increase of 2.25 W/m² in the incident surface energy density will result in a 1 °C temperature rise (see Post 13 - Case 2).

As I pointed out in Post 14, a major source for such additional heat liberation at the Earth's surface is energy generation and consumption by humans, often for industrial needs. This leads to direct anthropogenic surface heating (DASH) that can raise the temperature of whole countries by as much as 1 °C. But it is not just industry that can significantly heat the local environment.

Consider a typical home. The average household in the UK uses at least 10,000 kWh of energy per year. That equates to an average rate of usage of energy of 1.14 kW throughout the year.

The average land area of homes in the UK is at most 500 m². Most modern housing developments have more than 30 new homes per hectare (see PPG3 guidance paragraphs 57-58); older suburban developments are generally a lot less dense than this; inner city flats and terraced houses are clearly a lot more.

All of this means that the power density for heat escaping from homes will be at least 2.28 W/m² (i.e 1140 ÷ 500). In other words, the energy used by a typical household is more than sufficient to increase the local surface temperature by more than 1 °C. And remember, all this heating has got nothing to do with CO₂ emissions. Nor does this calculation include the energy consumption of commercial buildings, industry or transport.


Conclusion

The energy used by the average household in the UK each day raises the temperature of their local environment by at least 1 °C compared to pre-industrial levels. That will be true irrespective of the source of the energy. Renewables will not help. Nor will cutting your level of CO₂ emissions. This is all down to heat, entropy and thermodynamics.