Models Methods Software

Dan Hughes

Equilibrium, Energy Balances and Budgets, and Stuff

Recently I ran across the following comments on a blog. The comments are followed by my response.


“The physics of the direct warming effects of increased concentrations of CO2 and other infrared-absorbing gasses is completely clear.”

Let me try, “The physics of radiative-energy transport phenomena and processes given changing compositions of CO2 and other infrared-absorbing gasses in a homogeneous mixture of gases is completely clear.”

In fact, I think this can be expanded to include all radiative-energy transport phenomena and processes, ( absorption, transmission, and reflectance ), for both ultra-violet and infrared radiation, so long as homogeneous mixtures of gases are the material.

For me, one question is, How does this relate to the Earth’s atmosphere, oceans, ice, and land, and all the materials in and on these, and all the phenomena and processes occurring within and between these?


“So, yes, one must combine this measurement of anthropogenic CO2 with the simple radiative physics in the atmosphere to get the fact that we expect AGW.”

The radiative-energy transport phenomena and processes occurring in the Earth’s atmosphere are far from ‘simple’. If these were simple, I think the treatment of them in mathematical models could be fairly characterized as being based on the full and complete fundamental equations associated with these, depend solely on properties of the materials of interest free of any parameterizations, accurate numerical solution methods known and fully incorporated into all GCMs, and resolution of all temporal and spatial scales accurately resolved for every calculation.

So far as I am aware, none of these conditions are met. The parameterizations for some of the phenomena and processes associated with radiative-energy transport in the Earth’s atmosphere are in fact used to tune the GCMs when improvements in hindcasts are needed. The properties of materials as they appear in the fundamental equations for any phenomenon or process are never used as tuning knobs.

I’ll add now, that R. D. Cess, V. Ramanathan, G. E. Thomas, K. Stamnes and a few other people might be surprised to learn of the simplicity of radiative-energy transport calculations in the Earth’s atmosphere. The earth’s atmosphere is not a homogeneous mixture of gases; it’s far more complex. Some of the materials that make the Earth’s atmosphere a heterogeneous mixture of gases, vapor, liquid, and solids have critically important interactions with the radiative energy transport.

Recently, I also ran across this statement in an online kind-of textbook:

“To develop this understanding we must discuss various forms of energetic equilibria in which a physical system may reside. Earth (and the other terrestrial planets, Mercury, Venus, and Mars) are said to be in planetary radiative equilibrium because, on an annual timescale the solar energy absorbed by the Earth system balances the thermal energy emitted to space by Earth.”

My bold.

The writer has specified a time scale over which the in-come and out-go of radiative energy for the Earth’s systems are balanced; ‘annually’. In my opinion there is no foundation whatsoever for this statement. By the same token, I think that this is the first time that I’ve seen any temporal scale attached to the radiative-equilibrium hypothesis. This one is clearly unsupported, however. The Earth’s systems both receive and reject energy on all temporal and spatial scales. Yes, the Earth’s systems, at this very instance, are losing energy to deep space and this seems to be frequently overlooked.

1. The Earth’s systems at some time in the past were in a state of radiative-energy balance, and will again be at some time in the future in radiative-energy-transport balance, between the energy supply source from the Sun and the energy sink from Earth into deep space.

2. Experimental measurements and theoretical calculations show that addition of gaseous CO2 into a homogeneous mixture of gases acts solely to change the radiative-energy transport response of the mixture. The sole interactions between the energy and the gaseous mixture are radiative phenomena and processes. There’s nothing else in there.

3. Addition of CO2 into the Earth’s atmosphere will act to decrease the fraction of the incoming radiative energy supply that is returned back to deep space.

4. Some vague average temperature, over grand, but unspecified, temporal and spatial scales, of some part(s) of the Earth’s systems must increase so that the increase in the fraction of retained radiative energy input will be rejected back into deep space.

5. Feedback, primarily (almost exclusively) associated with water vapor, is assigned an important player with respect to the amount of temperature increase associated with the increase in the energy content of the Earth’s systems.

Note, especially, that the change in the radiative energy budget at the outer boundary of the Earth’s systems will highly likely never be subjected to validation. That is, the fundamental hypothesis of the AGW issue will highly likely not ever be validated.

Note, too, that for every hour of every day, some radiative energy is lost from the Earth’s systems back into deep space. The focus seems to always be, without exception, that the energy content of the Earth’s systems is increasing with time. It is not. The energy content of the Earth’s systems is constantly changing at all time and space scales.

I continue to fret over the fundamental hypotheses that have been presented to support the basis of the effects of increased concentrations of CO2 in the Earth’s systems. And, yes, I know this borders on heresy, but I’m an engineer and have a pretty good grasp of several aspects of energy transport, storage, exchange, and associated responses of materials.

I firstly get stuck at the radiative-equilibrium stage. Surely this equilibrium is not the rock-steady equilibrium as used in thermodynamics and other energy-budget and -balance situations. Equilibrium can generally mean different things within different contexts.

The first, within the context of energy budgets and balance, is that all materials that comprise the systems are at a uniform temperature at all spatial locations and for all time. There are no driving gradients in any potentials that could initiate change. Clearly this is not the equilibrium of interest whenever radiative-equilibrium and the Earth’s systems are the subject. Such a state has never been and will never be attained for these systems.

Secondly it can mean ‘steady state’ or ‘stationary state’; what comes out is equal to what goes in. I think this is the meaning for radiative-equilibrium. However, so far as I know the statement cannot be held to mean the same degree of equality that is generally associated with the concept of equilibrium. The radiative-energy exchange for the Earth’s systems is always changing at all temporal and spatial scales. What goes out is seldom, if ever, equal to what comes in.

There are no inherent natural physical phenomena and processes acting so as to produce such a response by the Earth’s systems. None of the natural phenomena and processes can possibly be ensuring that as the period of time over which in-come=out-go is theoretically to obtain, say, “Whoa, we need some corrections here because in-come is not equal to out-go.” All the subsystems, both internally and between systems ring as a function of time. There are no over-damped mechanisms that ensure monotonic approach to a state of equality for in-come and out-go over any spatial or temporal scales. The radiative-energy transport phenomena and processes for all components of the systems vary in both space and time.

Thirdly the phrase can refer to some kind of quasi-equilibrium condition in which departures from a nearly-equilibrium state are small. I think maybe this is the condition whenever radiative-equilibirium of the Earth’s energy budget is the subject. The question now is, What have been the magnitudes, and the temporal and spatial scales, of these departures from an equilibrium state in the past.

The Problem
The thermal state of the Earth’s systems have always rang and will always ring. The significant heterogeneous nature of the thermodynamic states of the systems, in both space and time, plus the extremely wide range of time scales for the important phenomena and processes, ensures this response. Again, true equilibrium is a condition never experienced by the Earth’s systems, so we’re here talking about ringing on top of ringing. Some of the past departures from a more-or-less equilibrium state can be traced to known perturbations on either the in-coming and out-going energy, or both. Some of these perturbations occur at very long intervals as determined primarily by the mechanics of the Earth-Sun system.

There are no inherent natural physical phenomena and processes acting so as to maintain the present state of the radiative-energy balance. Natural events, both external from and internal to, the Earth’s systems are free to cause changes in the state of the systems that can either increase or decrease the amount of energy that reaches the important parts of the Earth’s systems; in-come. Natural events can also act to both increase or decrease the amount of energy leaving the systems; out-go. Very likely, the grand-time-and-space-average albedo is changing all the time and thus changing the in-coming energy. So are the mechanisms that effect loss of infrared energy and changes in the out-going energy.

So, it seems to me that to discern the effects of human activities on the radiative-energy equilibrium balance, we need to determine the delta ( increase or decrease ) in energy content, not from some unattainable equilibrium state, and not from the long-time-scale perturbations in a quasi-equilibrium state, and not from the natural perturbations, but from the perturbations of these latter states.

This is a very confusing description. Let’s try the following. Draw a horizontal line to represent the unattainable equilibrium state. Superimpose along this line the long-time-scales perturbations due to Earth-Sun orbital mechanics. Superimpose on this latter curve the perturbations due to natural variations in the radiative-energy transport properties and characteristics of the systems. And, finally, the effects of human activities are superimposed on this last curve.

Unfortunately, we don’t know the time scales for all the perturbations, so we don’t know which is which. However, some might be better understood than others. Additionally, if we restrict criteria and metrics to planet-wide averages, we don’t know the spatial extent of perturbations that might be of sufficient magnitude to affect the over-all energy balance.

It’s a very tough problem, in my opinion.


March 10, 2010 - Posted by | Uncategorized | , ,


  1. The properties of materials as they appear in the fundamental equations for any phenomenon or process are never used as tuning knobs.

    I touched on this aspect a little in this recent post.

    Comment by jstults | March 11, 2010 | Reply

  2. […] Energy Balance and Budget In this previous post, I mentioned the energy budget / balance for the Earth’s systems. Specifically, the […]

    Pingback by Testing Energy Balance and Budget « Models Methods Software | March 16, 2010 | Reply

  3. Woot, I will ceatirnly put this to good use!

    Comment by Bubbi | August 9, 2011 | Reply

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