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The diagram shows huge flows of long wave radiation through the lower atmosphere. But the lower atmosphere is opaque to long wave radiation. Below 5 km the bulk of the energy transfer upwards is via convection.

So why does Climate Science promote a theory that claims you can shine an IR light through a 5 km thick wall?

The Greenhouse Gas Theory for Global Warming violates the Law of Conservation of Energy

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The Greenhouse Gas theory for global warming is invalid because it violates the Law of Conservation of Energy. This law states that energy can neither be created nor destroyed, but can be changed from one form to another. This applies to energy in all of its forms. This is supported by the First Law of Thermodynamics, although this is principally concerned with sensible heat energy.

This can readily be shown as follows.
The infrared energy radiated to space by the Earth’s surface can be absorbed by the atmospheric greenhouse gases such as carbon dioxide, methane, and water vapour. This is then re-radiated, with half rejoining the flow to space, and half flowing back to the surface. This half will be referred to as the “Earth Return”.
Stage 1. Before anthropogenic activities, the output energy from Earth to space was equal to the input energy from the Sun. This is the fundamental energy balance condition, and is accepted by the Greenhouse Gas (GHG) theory.

Stage 2. Anthropogenic activities caused more carbon dioxide to be emitted into the atmosphere, and so more energy was absorbed. Let this extra amount be A. This is then re-radiated, and the amount going to rejoin the output to space is 0.5A, and the Earth Return is also 0.5A.

This means that there is a shortfall of 0.5A in the output required by the balance condition, and so this must be restored. So far, the GHG theory is in line with this.

Stage 3. The GHG theory says that extra energy is radiated from the surface in order to make up the shortfall, and so restore balance.

If this were so, there would then be more energy than before the extra CO2 emission, because the energy to space would have been restored to its initial value as in Stage 1, and also there is now the Earth Return, 0.5A.

So that violates Conservation of Energy, because energy can neither be created nor destroyed.

The GHG theory explains that the extra energy to make up the shortfall arises from an increase in surface temperature, so more energy is radiated in line with the fourth power temperature dependence of Planck’s Law.

But this explanation is too simple, incomplete and incorrect. Firstly, what would make the temperature higher. More energy, of course, and hence more output radiation as required. But if energy is removed from the surface, it will cool down, and so the extra emission needed to respond to the shortfall fails. Therefore, more energy must be supplied to the surface in order to maintain the required higher temperature. But energy cannot be created, so the GHG theory fails too; is still violating Conservation.

Energy cannot be created, so where does this notional amount come from?

In fact, there is a suitable supply mentioned in passing above. It is the Earth Return, and this has been completely ignored by the GHG theory. It is 0.5A, just the required amount to cope with the shortfall, and it has entered the surface. It cannot remain in the surface, because this would aggravate the problem, as above. But it can be re-radiated to space without any need for increased temperature. It cycles from initial absorption, through re-radiation to the surface where it is absorbed, and then re-radiation to space. This maintains the balance condition. And this process is continually repeated.

Therefore, the Greenhouse Gas theory for global warming is not valid.

It was a fanciful idea based simply upon a correlation between anthropogenic activities and temperature measurements.