Some of the Missing Energy

Guest Post by Willis Eschenbach

The canonical equation describing the energy balance of the earth looks like this:

∆Q (energy added) = ∆U (energy lost) + ∆Ocean (energy moving in/out of the ocean)                                                          (Equation 1)

This has been modified in the current climate paradigm (e.g. see Kiehl) by substituting in the following:

∆U (energy lost) = [∆T (change in surface temperature) / S (climate sensitivity)]                                                           (Equation 2)

which gives us

∆Q (energy added) = [∆T (change in surface temperature) / S (climate sensitivity)] + ∆Ocean (energy moving in/out of the ocean) (Equation 3)

As I detailed in “Where Did I Put That Energy“, the problem is that the data doesn’t bear out the substitution. In the real world, ∆U is very different from ∆T/S. There’s a whole lot of energy missing. I think that some of it is here:

Figure 1. Tracing the path of a tiny bit of energy through a simplified climate system.

Why does this count as some of the missing energy?

Note that all of the energy goes into evaporating the molecule of water. As a result, there is no net change in the surface temperature. Since the definition of the climate sensitivity is ∆T/∆Q, and ∆T is zero, that means that for this entire transaction the climate sensitivity is zero.

It is important to remember that Equation 1 is still true, and this situation complies with Equation 1. The amount of energy entering the system equals the amount leaving plus ocean storage (zero in Fig. 1). However, it does not comply with equation 2 or 3.

This certainly qualifies as a possible mechanism for the missing energy. Response time is fast, and it can move huge amounts of energy from the surface to the condensation level and eventually to space. Also, it is outside the ambit of the the climate sensitivity calculation, since the climate sensitivity for this transaction is zero.

Is this all of the missing energy? Can’t be. The missing energy is moving in huge amounts in both directions, both into and out of the system. However, the mechanism above is one-way. It can remove energy from the system, but not add energy. I say the extra energy added in the other direction comes from clouds clearing out when the temperature drops. But that is another story for another post.

My conclusion? Climate sensitivity is not a constant, it is a function of temperature. Note for example that the warmer the water, the larger a percentage of the incoming energy takes the path illustrated in Fig. 1. The formation of the clouds and thunderstorms is also temperature dependent. All of which makes the climate sensitivity strongly temperature dependent.

As always, questions, corrections, and suggestions are more than welcome.

w.

PS – Please don’t say “but you left out the greenhouse gases”. Yes, I did, but in this case they have almost no effect. The transport of the heat to the upper troposphere takes place in the thunderstorm, so it is protected from thermal exchange with the troposphere. At the top of the troposphere, where it leaves the thunderstorm, there is little atmosphere of any kind. From there it is free to radiate to space with little interference.

And in any case, GHGs will only modify rather than rule the effect. Sure, we might end up with a bit of surface warming rather than zero as in the above analysis. But the essence of the transaction is that surface temperature is not directly coupled to radiation. This means that the substitution done to get Equation 3 is not correct.

PPS — In fact, the system above does more than have zero effect on the surface temperature. When the thunderstorm starts, albedo goes up, storm winds increase evaporation, cold wind and rain from aloft chill the surface, and other cooling mechanisms kick into gear. As a result, the surface ends up cooler than when the thunderstorm started, giving negative climate sensitivity. But that is another story for another post as well.