I understand all that. What I don’t understand is the point you’re trying to make. Yes the surface temperature will be very slightly higher than if there weren’t radioactive decay in the core of the planet. But the difference is so small it can be ignored. Other than that, what’s your point?

]]>Hello DeWitt Payne,

Thanks for the answer. I think the fact that we know that U is variable (measured) is somewhat beside the point. Let me try to explain.

Actually, the first sentence of the OP:

“…how a very simple energy balance model with some very basic assumptions provided some insight into how the surface and atmospheric temperatures are determined.”

reminded me of the system as I defined it, except that I included oceans and upper ~10 m of the earth crust. The system is, let’s say, pre-AGW or better pre-anthropogenic.

Internal energy of the system can go up or down slightly (or more when we have natural changes like glacials/interglacials), my point is that there is continuous geothermal flux from the earth interior, which must mean that heat is being added to the system (positive heat flux at the inner boundary, however tiny).

Therefore, at the outer boundary (TOA), to keep the internal energy somewhat constant (not changing too much and not increasing/decreasing continuously), the net flux must be negative (averaged) – the added heat must be lost at TOA.

So, the net flux at TOA is very tiny, negative (earth radiation is greater than insolation) and “almost” equal to the geothermal flux – the difference is dU.

dU = Qgt + Qtoanet = Qgt + Qsol – Qearth-rad

]]>The problem is that we know for a fact that dU ≠ 0. We can measure ocean heat content. It’s been going up. It’s not going up very fast right now but the trend is still up.

1955-2002 (pre-Argo) data as graphed by Bob Tisdale

I doubt that even if you average over millions of years you would find that dU = 0.

Tiny is indeed relative. Teff for 240 W/m² is 255.0683 K. For 240.1 W/m² it’s 255.0952 for a difference of 0.0269 K or 0.01%. That’s tiny in my book and far less than the precision of our current data.

]]>Maybe I am not being clear, sorry.

The system has only two boundaries (inner and outer) and only two NET fluxes:

Inner boundary – geothermal flux (positive – heat is being added to the system continuously),

Outer boundary – net heat flux at TOA (insolation minus earth thermal radiation). This flux is sofar unknown.

Now if we assume dU = 0 (internal energy of the system is constant), the heat entering at the inner boundary must leave the system at the outer boundary (TOA), otherwise U must increase. Therefore, over timescales with dU = 0, averaged net heat flux at TOA must be equal in magnitude to the geothermal flux (but negative).

dU = Q(geothermal) – Q(TOAnet) = 0

]]>I don’t understand what you are trying to say.

If the earth is in approximate energy balance then the energy in = energy out.

So solar absorbed radiation + geothermal heat = energy radiated from TOA

241 + 0.1 = 240.1

However, the earth may not be complete energy balance and may be gaining or losing energy. In any given month or any given year it is likely to be gaining or losing energy.

If the earth is heating up – as the figures from Loeb et al indicate that it may have been from 2000-2005:

241 + 0.1 -240 = 1.1 W/m^{2} gained

And in fact the geothermal energy is negligible.

If there was no sun then the geothermal energy would be making a significant contribution to the few degrees Kelvin experienced on the surface of the earth.

We are not being heated at the bottom and losing heat at the top.

We are being heated at the top (99.95% or greater) and losing heat at the top.

]]>My point is not about the magnitude of geothermal flux vector but rather about its direction.

Its direction is outwards. Assuming dU of the system, as I defined it, is zero, the heat entering the system at the inner boundary (crust, ~10 m under surface), must leave the system at the outer boundary (TOA).

Therefore, the net flux at TOA is outwards (outgoing) and is equal to the geothermal flux (averaged, dU = 0).

Therefore, the system (atmoshere, oceans and upper 10 m of crust) receives heat from earth interior and dissipates it over TOA.

At TOA, the system is losing energy (thermal radiation), despite the insolation!

So back to tiny – it is only tiny because of insolation, without the sun geothermal flux wouldn’t be as tiny.

But tiny or not, it is positive (for my system), contrary to the net heat flux at TOA, which is negative!

We are being heated from the bottom and are losing heat at the top.

]]>Another article to write as many people keep asking about this.

]]>atmosphere, oceans and upper ~10 m of earth crust (including oceanic).

]]>Thank you for the answer.

I think the net flux (averaged) should be outwards (outgoing) and equal to the heat flux from the earth interior.

If we define our system (pre-anthropogenic) with the boundaries:

outside – TOA

inside – earth and oceanic crust, ~10 m under the surface

and neglect any heat generation in the system and assume dU = 0

Then these two heat fluxes should be equal. The heat from the earth interior must be dissipated, otherwise the internal energy (U) must increase.

]]>