In the last post was an explanation of the difference between energy and energy flux. Energy is generally a simple static scalar quantity, while flux refers to an instantaneous expenditure of energy.
Physics, i.e. the real world and real-world reactions, occur in real-time. Reality doesn’t wait around for an average of something to build up and then decide to act – reality acts as time flows by, each infinitesimal moment to the next. Reality reacts to instantaneous flux, not the average flux because there is no “average” that reality waits around for to react to.
The standard procedure for “conserving energy” and then creating an energy budget and subsequent greenhouse effect is by numerically equating the terrestrial flux output with the solar flux input. This numerical procedure is done with the justification that “on average, the input and output must equal if the system is in equilibrium”. But this is done numerically on paper, not physically in reality, because the physics of reality reacts instantaneously to forces, and doesn’t wait around for averages.
So what’s the basic thing that we’re actually trying to conserve in regards to solar input and terrestrial output? The real physical quantity we want to conserve is energy, not flux. Energy is a fundamental unit of physics, while flux always depends upon the particular, real-time, local situation. So if we assume that, on average, the input and output energies are equal, which they should be, then we can consider such energies for any particular second. Considering any particular second is convenient since this allows us to directly convert the energy into flux later on.
In any given second, the Earth absorbs 1.22 x 1017 Joules of light energy from the Sun. This is calculated with the Stefan-Boltzmann equation for the Sun, factored for the distance to the Earth and the Earth’s cross-sectional area, and its albedo.
In any given second, this energy, 1.22 x 1017 Joules, falls on one-side of the planet – the day-side hemisphere. So, now that we know the total energy falling on the Earth in one second, and we now also know where the energy falls in one second, we can convert the energy value into the units of the Stefan-Boltzmann equation, which are Joules per second per square meter. Therefore if we take the total energy and divide it by the surface area of a hemisphere of the Earth, you get an (linear) average of 480 Joules per second per square meter, or 480 W/m2. Using the Stefan-Boltzmann equation which equates flux to temperature, this is a temperature of +30 degrees C, which is very nice and warm and will melt ice into water on the day-side, etc. It is a reasonable number.
However, we must again recall that reality reacts to forces instantaneously, and not to averages of those forces after-the-fact. The light energy falling on the day-side hemisphere in one second is not evenly (linearly) distributed because the Earth is round, not flat. That means that there is a locality-dependence on the true, real-time value of the flux density. That is, when the Sun is overhead it is strongest, and when it is near sunrise or sunset it is weakest, and in between it smoothly ranges. When the Sun is directly overhead, and even barely so, the flux density of the energy falling isn’t strong enough to just melt ice into water, but it is also strong enough to evaporate water into vapour. This is what basically creates everything we recognize as the climate, is water vapour rising into the atmosphere from the strength of the Sun, and this occurs in real-time. The greenhouse effect models do not show this, and they actually even contradict it, because they incorrectly average the power of the Sun to where it doesn’t physically exist, and thereby make the solar power far too cold (on paper) to be able to create that water cycle and climate.
This diagram is a representation of real-time reality and the physics that drives the climate on the Earth:
Back to Equating Flux
With an energy input of 1.22 x 1017 Joules over a hemisphere in one second from the Sun, and an energy output from the Earth of 1.22 x 1017 Joules from the entire globe, i.e. both hemisphere’s, it is not physically correct to equate these energy values in terms of flux. These values are true and totally correct in terms of energy. They can not be made to be equal in terms of flux.
For example, if we say that the Earth is in numerical flux equilibrium with the Sun, and mistake this for conserving energy, then that would mean that the Earth must emit the same flux of energy as it receives the Sun. Therefore the Earth must emit 480 W/m2 on average since that is what it receives from the Sun on an instantaneous basis.
Well, the Earth does not emit this flux of energy. That is way too high of value. If you converted that value into total energy emitted per second over the entire globe, it would be more energy than actually comes in. The known and measured value for the flux output from the Earth is 240 W/m2.