First, if I ruled the world, it would not be called Downwelling longwave radiation. Atmospheric potential energy is a much more apt term. Life is what it is though, so here goes.
Anything that contains heat emits radiant energy. Since just about everything is above absolute zero, even space, everything emits radiant energy. How energetic and at what wavelength that radiant energy is depends on the temperature of the object and the fundamentals of black body radiation.
So in our atmosphere where is this down welling infrared radiation? It can be anywhere. Pick a spot and a number and we can work it out. For it to be a meaningful number, the DWLR has to have a source and an intensity. As and energy flow it has to obey the laws of thermodynamics.
The atmosphere as a whole has a temperature greater than absolute zero and contains energy. The energy it absorbs from the surface is the origin of the DWLR and that energy is from the sun.
If we model the DWLR as solely from the surface, then its value is only the value the atmopshere absorbs that originated at the surface. If we model DWLR as the average energy of the atmosphere, the the energy absorbed from the surface and the energy absorbed directly by the atmosphere from the sun is considered the source of the DWLR. The simplest is the energy of the atmosphere.
The point source of the DWLR or energy of the atmosphere would be the point in the atmosphere where the total energy of the atmosphere can be approximated as point or layer of the atmosphere. Since the energy into the Earth/atnmosphere is less than the total energy from the surface and the atmosphere, the difference of the energy from the surface and the energy out at the top of all the atmosphere is by definition the atmospheric effect. That amount of energy is then the maximum value of the DWLR after allowing for the efficiency of energy flow from its source to the surface, which would be the same location as the average accumlation of the energy in the atmosphere by the outgoing surface and atmospheric energy flux.
That is a little complicated, but if DWLR is real, it must be properly defined.
If the only source of the DWLR was the surface, then the DWLR would be located where the average of the energy absorbed from the surface could be approximated. Since the solar absorbed is include in the atmosphreric energy, the the average location of the absorbed energy would be higher than if only the surface was considered.
If we intergrated the energy of the atmosphere from the surface to the TOA, we would find that the average energy content of the atmosphere is close to the surface were the atmospheric pressure produces the higher air density.
Without energy exchanged by radiation, the average energy of the atmosphere would be at the altitude where the dry adiabatic lapse rate resulted in a temperature equal to the temperture of the Earth's surface without an atmospheric effect. Since the Earth is supposed to be 33 degrees C warmer than it would be without an atmospheric effect, the point of no effective DWLR would be 33c colder than the surface.
There is energy exchanged between the outgoing surface flux, and incoming solar energy in the atmosphere. The amount changes with latitude, time of day and season. So only and average value has any physical meaning if we are to determine what impact the DWLR has on surface temperature.
So what makes sense has to be considered when selecting an equivalent point source and intensity of DWLR.
The ideal intensity is simple, with and average surface flux of 390Wm-2 and and Average TOA flux of 240, the ideal value of surface generated DWLR would be 160Wm-2. Since the sun adds energy directly to the atmosphere, approximately 60 Wm-2 on average, the approximate value of the intensity of the DWLR would be 220 Wm-2. Trying to determine the exact value is a little more complicated.
Theoretically, if the DWLR were a point source of energy, its flow would not be ideal. It would require more energy at a distance to produce an equivalent effect. The difference between the surface generated DWLR portion, 160Wm-2 and the total DWLR 220Wm-2 accounts for the loss of energy during transfer from the surface to the point source of the DWLR.
This is theoretical so it has to make sense to be accepted. This value of 220Wm-2 in the atmosphere corresponds to an effective temperature of 249.6 degrees K or -23.4 C. At the point in the atmosphere where the heat of compression would cause a parcel of air at that temperature to rise to 288K, the average surface temperature, that would be the source of the DWLR.
The altitude of this point varies with the surface temperature and local atmospheric conditions. So it is an effective reference value to determine if energy is being added to the atmosphere or transferred from the atmosphere to the surface.
Most of the energy tranferred to the surface is in the form of pressure. Warm air cooled by convection in the lapse rate decends to the surface in another location either adding to or reducing the surface temperature. Near the poles, the average effect is warmer surface temperatures and near the equator the average effect is cooler surface temperatures. The rising and falling air adds energy to the atmosphere in the form of pressure differentials creating atmospheric circulation patterns that distribute heat gained in the atmosphere to other locations.
Rarely does the DWLR have any direct effect on the surface. Due to water in the atmosphere that has a radiant spectrum that is not totally blocked by greenhouse gases, some DWLR in the atmospheric window does impact surface temperature directly. If it were not for this rather small amount of the total energy in the atmosphere being radiant and impacting the surface, the term Down Welling Longwave Radiation would not exist. It would be replaced with barametric pressure.
Downwelling Long wave does physically exist and it has some impact on the surface. It also has impact on water and water vapor in the atmosphere. DWLR warms water in all its phases and being warmed, it reduces local atmospheric density creating convection. This convection cools locally and adds to the heat transfer through pressure of the up welling thermal and down welling cooler denser air after adiabatic cooling. The net result is pressure and temperature migration to the polar regions.
When the water vapor and to a lesser extent greenhouse gases closer to the surface are warmed by DWLR, the an increase in surface temperature occurs. The renews the convection cycle transferring more energy.
So DWLR is the potential energy of the atmosphere in terms of radiant energy that has to obey the laws of physics. Most of the DWLR is converted locally to convective and conductive energy flux, some to latent energy flux and most of the energy is converted into changes in atmospheric pressure which tends to spread the equatorial warmth poleward.
So defined, DWLR is a useful tool for studying the physics of the atmosphere. Any other definition only leads to confusion.