Energy Imbalance Part II – An Addendum – Watts Up With That?

Kevin Kilty

The original essay from February 24 to which this addendum applies had several opportunities for discussion items that could be expanded.

First, there was some question about what a radiometer would see if pointed down at the surface. Figure 1 is educational in several ways. It is from the SURFRAD site at Desert Rock, Nevada on June 22, 2024. The four curves correspond to total downward solar radiation, total upward solar radiation, Upward and downward directed LWIR. I have also included the local wind speed and 10m temperature in the lower diagram.  

Figure 1. A description of the site’s 10m tower where many of these instruments are mounted, and a photo of the area, is available here.

Sunrise is around 6am local time (1300UTC; Local PDT=UTC-7hr). Almost immediately after the sun peeks over the horizon the surface begins to warm and the pyrgeometer detects a rise in upward directed LWIR. Downward directed LWIR rises with about an hour’s delay from the heating of the surface but well before surface convection begins to heat the atmosphere which is quite apparent on the wind speed chart starting at around 10-11 am. The peak of upward directed LWIR occurs a half an hour or so past noon at a value of 658W/m². With an assumed surface emissivity of 0.97 this suggests a surface temperature of 137F – far above the peak temperature at 10m elevation of 100F which occurs late in the day. There is a super adiabatic layer of heated air near the surface. The situation is exactly as I described it, using two atmospheric soundings at Albuquerque, Nex Mexico from August 3, 1993 in this addendum. This also, perhaps, explains why GEOS Band 16 images taken around Winter Solstice sometimes show northern Chile to be 60^oC.

Downward directed LWIR curve, the Greenhouse effect, begins its rise almost coincident with both the rise in upward directed LWIR and the rise in 10m temperature, but reaches its peak value well after the peak in upward LWIR but long before the peak in 10m temperature. The Greenhouse effect results from rising air temperature, but this, in turn, results both from bulk transport from the surface and from absorption and re-emission of LWIR from the surface. It is not exclusively a function of air temperature as was claimed.

That upward directed LWIR remains 80W/m² above the greenhouse effect throughout the night demonstrates how it is that natives in elevated and dry places have traditionally made ice overnight even when temperatures remain far above freezing (20F above) [1] and something I observed while camping overnight at Joshua Tree Monument on March 6 of 1982.

Violations of the Second Law of Thermodynamics

An idea that arises, it seems, in every post about the Greenhouse effect, is that energy cannot flow from the cold atmosphere to the warmer ground without violating the Second Law of Thermodynamics. This argument will simply not go away.

Simply put, molecules and atoms do not have temperature – they have energy. Temperature is assigned by the distribution of kinetic energy in an ensemble of molecules and atoms, as in the Boltzmann distribution, where temperature is the only assignable parameter.  Individual atoms and molecules are not guided by a temperature gradient in any way, but what net heat transport they accomplish is statistically in the direction from hot to cold.

Tom Shula provided a darned good reference to Harde (2013) that states…

“…any back radiation from colder and higher atmospheric layers can be absorbed by the lower and warmer layers, and this back radiation can also be absorbed by a warmer surface of the earth without violating the 2nd law of thermodynamics.”

I might mention that careless application of the Stefan-Boltzmann formula is almost guaranteed to end up with a violation of the Second Law.[2]

Is the radiation field isotropic?

There was some discussion about the radiation field being isotropic, in fact, about the necessity of it being so. The radiation field, meaning the distribution of emitted radiant energy in the atmosphere, cannot be isotropic when there are temperature gradients involved. At each point in space (we call this the field point) there is an emitted field originating at that point. This emitted field is isotropic.[3]

In addition there is also a contribution originating at other points in the domain of the problem and passing through the field point. This field component is not isotropic as it is reflective of whatever is emitted by all objects and material within view of the field point. The total field is a vector integration of the two.  A truly isotropic total field could only occur inside a cavity at uniform temperature, which would be an instance of thermal equilibrium, of a true blackbody, and without net heat transfer in any direction. When heat is transported, the field doing so is not isotropic.

Collision rates being far greater than emission rates

There was a discussion about why the emitted power from a molecule like CO2 is so intense when collisions de-energize the CO2 15u line at a rate of “29,000” times the emission rate. The fact that this collision rate, which redistributes kinetic energy locally and continually, occurs with far greater speed than the emission or absorption rate is responsible for maintaining local thermodynamic equilibrium (LTE).[4] It allows us to use atmospheric temperature in conjunction with the Planck function to calculate emission. It is what connects radiation to local atmospheric temperature.

Radiation annihilated?

Someone made a claim to the effect that “… The surface field is completely annihilated and converted into sensible heat. The thermal atmospheric field is produced exclusively by collisional excitation and exists throughout the atmosphere all the way down to the surface….”

For this to be so, radiation leaving the surface would have to be completely absorbed and through collisions converted completely to kinetic energy. Moreover, once converted completely to kinetic energy, would collisions be effective or not at raising IR active gasses from their ground state to a higher energy state?

The present radiational cooling of Earth involves different transport behavior at different wavelengths. In places the atmosphere is quite transparent and transport is ballistic, in other areas the emission is created locally through collisions. Just to drive this point a bit further, Figure 2 shows an LWIR spectrum measured from satellite over the polar ice cap from the publication by Harde (2013).

Figure 2. From Harde (2013).

Red arrows point to segments of the spectrum from within the atmospheric window where there is little IR active gas to absorb radiation. The spectrum nicely follows a blackbody spectrum (dashed curves) just below the 268K ice surface temperature. There is nothing nearer the satellite with this temperature than the ice cap itself. Meanwhile, blue arrows point to other portions of the spectrum which suggest much lower temperature. These occur over wavelengths where IR active water vapor and CO2 hide the surface from direct view and emit radiation from lower temperature higher in the polar atmosphere.

Even if Earth’s atmosphere were more opaque than it presently is  (greater optical depth), radiation from the surface would still make its way skyward. Photons would “diffuse” through a very opaque atmosphere much like thermal conduction except with a “thermal conductivity” proportional to temperature cubed (the Rosselund approximation).

References:

[1]-My handwritten notes from 45 years ago are not entirely clear, but the report of natives of Bengal making ice overnight is probably: S. Tamara, Monthly Weather Rev., 33; 55, 1905.

[2]-A good example is Q=σ(A₁T₁⁴-A₂T₂⁴), where sigma is the Stefan constant. Just using areas for different radiators can lead to a large cold radiator delivering heat to a small hot one. Generally I don’t make reference to my own work, but this link will bring up a lecture I produced as a guest for a nearby community college nearly a quarter century ago that shows how little a person can accomplish with only the Stefan-Boltzmann formula and what little else is needed to make it useful.

[3]-Any radiation can be considered scattered. A phase function describes how the scattering takes place. For example, the “scattering” phase function of isotropic radiation is 1.0, unlike the phase function of, say, Rayleigh scattering which is 0.5(1+cos²Θ), where the scattering angle is measured from the line connecting the Sun and the scattering object or volume. It explains why the blue of the sky is not uniformly blue.

[4]-LTE is simply a state of being close enough to thermal equilibrium to make reasonable use of results from true thermal equilibrium.