American Scientist

To the Editors:

In the Computing Science column “Clarity in Climate Modeling” (November–December), Brian Hayes shows the following equation as the energy balance at the surface of the Earth: Q (1–α)= σT ⁴. He says that the heat radiated into space has to equal the heat absorbed from solar radiation to keep the average temperature of Earth’s surface relatively constant.

This calculation is not exactly true, because Hayes is ignoring what is called the geothermal heat flux, the heat conducted from the molten core of the Earth to the surface, which is also radiated into space. An article on Wikipedia says the estimated total heat loss from the Earth is about 4.42 × 10¹³ watts, which is about 0.03 percent of solar power absorbed by the Earth. For the Earth’s surface temperature to stay relatively constant, the heat radiated must be about 1.0003 times the amount absorbed. This number may not seem like a lot, but another article, “Climate and Earth’s Energy Budget,” from the NASA Earth Observatory website, estimates that the heat imbalance caused by excess carbon dioxide is about 0.8 watts per square meter. The Wikipedia article says the geothermal heat flux is about 0.087 watts per square meter. I do not think it is justifiable to ignore an input that is on the order of 10 percent of the variable one is trying to predict.

W. C. Rust
Wallace, ID

Mr. Hayes responds:

It’s true that the Earth’s surface is warmed from below as well as above, but the magnitudes of these heat flows are very different: We get roughly 4,000 times as much energy from the Sun as from the Earth’s interior. In a model that simply calculates the planet’s overall energy budget, the geothermal contribution is too small to have any noticeable effect. It’s less than the variation in solar output associated with the sunspot cycle. Furthermore, the geothermal flow is constant on a human time scale, and so it is an unlikely contributor to climate change.

On the other hand, one of the important findings of modern climate studies is that small perturbations can have large consequences, especially when they are amplified by feedback effects or other nonlinearities. Accordingly, geothermal flux is taken into account in the detailed computational models that yield quantitative predictions of future climate. For example, the Community Earth System Model includes geothermal flows into the atmosphere, the oceans, and ice on land.

Finally, one detail in Mr. Rust’s letter requires correction. The equation Q(1–α)= σT ⁴ defines the energy balance at the top of the atmosphere, not at the surface of the Earth. The surface is warmer by more than 30 degrees Celsius because of the greenhouse effect.