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 How do we square this with the ZDEBM we’ve been working with so far? As we noted above, the model as we’ve expressed it suggests that the Earth’s temperature ought to be somewhere around 255K, which is below the freezing point of water. The solution to this puzzle lies in recognizing two facts: first that the effective temperature of the planet—the temperature that the planet appears to be from space—need not be the same as the temperature at the surface, and second that we’ve been neglecting a heat source that’s active on the ground. The second recognition helps explain the first: the greenhouse gasses which re-radiate some of the outgoing energy keep the interior of the atmosphere warmer than the effective surface. If this seems strange, think about the difference between your skin temperature and your core body temperature. While a healthy human body’s internal temperature has to remain very close to 98.6 degrees F, the temperature of the body along its radiative surface—the skin—can vary quite dramatically (indeed, that’s part of what lets the internal temperature remain so constant). At first glance, an external observer might think that a human body is much cooler than it actually is: the surface temperature is much cooler than the core temperature. Precisely the same thing is true in the case of the planet; the model we’ve constructed so far is accurate, but it has succeeded in predicting the effective temperature of the planet—the temperature that the planet appears to be if we look at it from the outside. What we need now is a way to figure out the difference between the planet’s effective temperature T$p$ and the temperature at the surface, which we can call T$s$.

Let’s think about how we might integrate all that into the model we’ve been building. It might be helpful to start with an explicit statement of the physical picture as it stands. We’re still working with an energy balance model, so the most important thing to keep in mind is just the 125