by Judith Curry
By Judith Curry
Here is another attempt at trying to untangle the Skydragons’ misunderstanding about the greenhouse effect and the planetary energy balance.
To clarify the planetary energy balance equation and its (mis) application to interpreting the greenhouse effect, I am posting section 14.3 [planetary energy balance] from my text Thermodynamics of Atmospheres and Oceans. If you have been following the Postma thread, you should be familiar with the starting point in this section.
The planetary energy balance equation has its greatest utility in the context of comparative planetology. It is not needed to prove the existence of the greenhouse effect, although it is conceptually useful in explaining and understanding the greenhouse effect.
With regards to the planetary energy balance equation 12.1:
The temperature Te is not necessarily the actual surface or atmospheric temperature of the planet; it is simply the equivalent blackbody emission temperature a planet requires to balance the solar radiation that it absorbs. Using a value of ap = 0.31, we obtain from (12.1c) a value of Te = 254 K. Note that this temperature is much less than the observed global mean surface temperature T0= 288 K. The difference between Te and T0 arises from the emission of thermal radiation by atmospheric gases and clouds at temperatures colder than T0.
The ratio of Te to T0 provides an indication of the magnitude of the infrared optical depth, which is referred to as n. n includes contributions from both clouds and gases.
So far nothing new. In section 14.3.2 I introduce the concept of planetary time scales, which I think gets to the heart of the problem that Postma has with equation 12.1.
If radiative transfer is the only process occurring in a planetary atmosphere, the surface temperatures of the planets would be determined solely by the net radiation at the top of the atmosphere. Thus, the equatorial regions would be warmest and the poles would be extremely cold. Whereas this is the case on Mars and to a lesser extent on Earth, other planets such as Venus and all of the Jovian planets have little or no equator-to-pole temperature gradients at the surface or deep in their interiors.
Simple arguments allow us to understand why there are differences in horizontal temperature gradients among the planets. There are two fundamental time scales that determine how a planetary atmosphere transfers heat. The radiative timescale, trad, is the time it would take for an atmosphere above some pressure level p0 to reduce its temperature by 1/e of its initial value via radiative cooling if solar radiation were turned off. The dynamic timescale, tdyn, is the time required to move a parcel over a characteristic distance in the atmosphere and, in so doing, transport heat from one location to another.
Introducing a variable e = tdyn / trad . There are several different regimes for e:
(i) If e >> 1, the dynamic time scale is much greater than the radiative time scale, and hence radiative processes dominate. This regime is characteristic of Mars. Consequently, on a planet with e >> 1, the equator-to-pole temperature gradient is very large, in response the latitudinal variations of solar radiation. Also, as the radiative cooling of the atmospheric parcel is so efficient, a very large diurnal variation of temperature is expected.
(ii) If e << 1, the dynamical transports of heat dominate over radiative cooling. This regime, characteristic of Venus, Jupiter, and Saturn. Thus, for e << 1 a very small or negligible equator-to-pole temperature difference is expected. For similar reasons, the diurnal variation of temperature on such a planet would be negligibly small.
(iii) For e ~ 1, there is parity between the two time scales. Such a situation occurs if the mass of the atmosphere is moderate and the velocities on the planet are relatively weak, which is the case for Earth. On such a planet, one would expect a pole-to-equator temperature difference but one where the temperature of a parcel at a particular latitude is not in radiative equilibrium with the net radiative fluxes at the top of the atmosphere. Furthermore, a moderate diurnal temperature is expected.
In this context, equation 12.1 provides a good representation for Venus, with little diurnal variation and pole-to-equator temperature gradient (Jupiter and Saturn have large internal heat sources, so equation 12.1 is not applicable). For Venus, a time integration or spatially varying energy balance model would add nothing.
What Postma proposes (if implemented correctly) might make sense for Mars, with a large diurnal cycle and pole-to-equator gradient, with local thermodynamic balances in a column. However, the fact that equation 12.1 does a good job of simulating the actual surface temperature of Mars (which has an optically thin atmosphere) implies that added complexity is not necessary.
For the Earth, the issue with equation 12.1 is how to interpret Te and n. There is no simple way to deconvolute the gaseous greenhouse effect from the radiative emission from clouds. Postma’s proposed model doesn’t help at all with the Earth, because of the complex coupling between the radiation and dynamics. Which is why a dynamical climate model with interactive radiative transfer, water vapor and clouds is needed to get insights much beyond Equation 12.1. Which is what climate scientists have been doing for several decades.
Note to Skydragons: Exercises such as Postma that use (or misuse) the planetary energy balance equation cannot disprove the existence of the Earth’s greenhouse effect. If you want to disprove the existence of the greenhouse effect, you need some sort of alternative explanation for a whole lot of fundamental physics that explains the infrared emission spectra as measured at the Earth’s surface and high above the emitting portion of the atmosphere (see Pierrehumbert). With regards to the magnitude of the Earth’s greenhouse effect, for a given atmospheric thermodynamic state and gaseous composition, the clear-sky (cloudless) radiative fluxes are accurately calculated using sophisticated radiative transfer models that have been validated extensively by the Atmospheric Radiation Measurement program (see this previous thread).
Trying to take the planetary energy balance equation and torture it into something that it was never intended to do is pointless and misleading at best. The planetary energy balance equation is the simplest possible climate model. On the other hand there are the general circulation global climate models, which are of enormous complexity. In between is a whole class of energy balance climate models, which were very popular in the 1950’s – 1980’s, the Wikipedia gives a good introduction to this class of models, which includes box models, radiative-convective models, higher dimension versions of the zero-dimensional planetary energy balance model, and Earth system models of intermediate complexity (statistical/dynamical models). Different models can be used depending the nature of questions asked and the pertinent time scales.
So starting from the simplest zero-dimensional model (planetary energy balance model) and saying that it does not answer all relevant questions and resolve issues related to the diurnal cycle, and therefore the greenhouse effect doesn’t exist, is well, I can’t even find a word for this. Use a higher dimensional model and play around with it, but if the model has the correct physics, the greenhouse effect is not going to disappear. Trying to demonstrate that the greenhouse effect doesn’t exist with one of these models, particularly by applying a particular model for something that is beyond the assumptions built into the model, makes no sense.