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Radiation Physics Laws Give the Effect of CO2 on Earth’s Temperatures – A Primer

Written by Pierre R Latour PhD, PE, Chemical Process Control Engineer

Abstract: A new chemical process control systems engineering model of Earth’s atmosphere quantifies the effect of CO2 on Earth’s surface temperature. It uses the rigorous S-B radiant energy transfer rate law. The Earth’s surface and atmospheric temperatures are given explicitly as linear ordinary differential and algebraic equations; the only system properties needed are absorptivity and emissivity, five of which depend on CO2.

CO2 affects surface temperature by at least four mechanisms, one positive and three negative. CO2 decreases Earth’s global radiating temperature to space slightly. When atmosphere parameters increase by 1% due to CO2, surface temperature changes – 0.762C and atmosphere changes – 0.392C.

Astrophysicists and climatologists have been struggling to quantify the effect of atmospheric CO2 on Earth’s temperature since the 1997 Kyoto Protocol called for control of Earth’s global temperature by human throttling of hydrocarbon combustion, which emits CO2 to the atmosphere. Kyoto called for building a thermostat for the whole Earth. The greenhouse gas theory, GHGT, is not quantitative and not proven.

Chemical process control system engineers agree one needs a valid dynamic process model before designing a feedback controller to hold a desired dependent response variable like temperature about a desirable setpoint target, by adjusting an independent manipulated variable like combustion rate, which strongly affects effects the controlled variable, temperature. Such a control system is called a thermostat. They are in oil refineries, buildings, homes, cars and the human body.

Before designing any control system, engineers analyze four criteria necessary to insure the control system will work at all, even if it is built. There is a rigorous mathematical method for determining the desired setpoint setting, involving optimization of a risky tradeoff1-5. This technology is available, but humanity is not organized properly to use it. (We can’t agree whether it is too hot or too cold.) Further the system must be measurable, observable and controllable. Mathematical criteria6, 7 were developed in 1970’s to verify a priori whether these conditions are satisfied.

Work8-10 in early 1997 indicated the proposed Kyoto thermostat did not satisfy any of these criteria, hence it will never work. (Never. No matter what the global consensus and government research spending may be.) After 20 years the conclusion has been confirmed by the UN and world scientific community. They recently estimated it will take at least 50 years and $4 trillion to build their thermostat. Still won’t work.

There are three main approaches to mathematically describing the atmosphere’s behavior. Two encompass forms of the main laws of physics: conservation of energy (First Law of Thermodynamics), conservation of matter, and Stefan-Boltzmann Law of radiators. These laws incorporate the physical properties of the system and rate law parameters. When an input variable change like CO2 is specified, like a step, ramp, sine wave or arbitrary function, the model can be solved for the output response variables, temperatures.

Rigorous space and time is described by complex coupled nonlinear partial differential equations11, 12. Since the atmosphere varies greatly day to night, from the surface to space, equator to poles, clouds, auroras, storms and lightening, with gases, liquids and solids of different compositions, temperatures and pressures, solving the equations is not practical, even with computers. Weathermen cannot forecast accurately more than a few days in advance. But the forms of these equations falsify the greenhouse gas theory12.

Control system engineers developed lumped parameter model methods to simplify the mathematics by combining spatial effects with effective properties and parameters, retaining the dynamic behavior. The partial differential equations are reduced to ordinary differential equations which are easier to solve and reveal important system characteristics, like stability, measurability, observability and controllability.

A body of control theory for differential equation models was developed since 196013. Multivariable dynamic control systems now model and control complex commercial oil refinery reactors and distillation columns around the world by several businesses. So control system engineering works, adds value.

If only long term steady-state behavior rather than short term dynamic responses is of primary interest, the dynamic terms can be neglected and the system of differential equations reduces to algebraic equations. Over long periods, say years or decades, this steady-state model quantifies output changes caused by input and property changes. This is the scientific cause and effect model missing in climate change studies.

Review of the greenhouse gas theory (GHGT) literature indicates climate scientists have bypassed the two rigorous engineering methods and opted for an empirical statistical regression input – output modeling approach from atmospheric measurements. These methods can detect possible correlations but never prove causation alone. (Control engineers incorporate this law of science in their work.)

Since scientists cannot specify the type of Earth’s input functions known to better identify the system with experimental testing, they are limited to measured natural input fluctuations which are weak system identifiers. While this approach may give useful interpolations, it cannot give reliable extrapolations beyond the range of its basis data.

This knowhow is often used by engineers, the art of combining science and empiricism to build things. Sadly, UN and university modelers have wasted billions of dollars on this approach, known to be futile, proving it doesn’t work for themselves14. Yet some continue attempting the impossible.

The second method is employed here to draw conclusions. The key is to model Earth’s radiating atmosphere with Martin Hertzberg’s general radiant energy transfer rate law15.

We will derive algebraic expressions that quantify the effect of adding CO2 on temperature. If we assign physical properties correctly to each radiator we should have accurate radiant energy flows, temperatures and the effect of inputs like CO2 on all these dependent variables.

Read the full paper with algebraic equations here:


Speaking to John O’Sullivan (CEO of Principia Scientific International) Dr Latour said:

“I have consolidated my engineering ideas and consider this the most important paper I have ever written; of monumental significance. Probably the most significant paper PSI has posted.

It solves many problems; answers many questions. I used the rigorous law of radiant energy transfer published by Dr Martin Hertzberg and conservation of energy law to rigorously model Earth’s interacting surface and atmosphere energy flows.

This gives algebraic equations for both temperatures without any assumptions or empirical statistical parameters at all, just their physical properties: absorptivity & emissivity. Pure physics + HS algebra + ES arithmetic.

I estimated properties from known flows and predict temperatures to a “T”.  Once the effect of CO2 on atmosphere absorptivity and emissivity is included, we have the only mathematical relationship of CO2 on temperatures. I included an example of 1% increase.”

In the conclusion to the paper Dr Latour makes the astonishing finding that assuming a one percent increase in atmospheric parameters (emissivity and absorptivity) levels gives surface temperature DROP from 14.786C to 14.033C by – 0.763C. Atmosphere temperature drops from – 18.141C to – 18.533C by – 0.392C.

Such a conclusion refutes the claims of government climate scientists  who say ANY rises in levels of atmospheric carbon dioxide must cause warming.


Bio: Dr Pierre Latour: Chemical Process Engineer. Among achievements served as Chief of Simulations Branch for NASA on the Apollo mission at the Manned Spacecraft Center, Houston, Texas. Devised computer simulations of Apollo docking, Lunar Module, separation maneuvers, Saturn V booster wind gust loads. Long and distinguished, award-winning career in engineering; served at senior levels including working at Shell and DuPont. See more at: https://www.linkedin.com/in/pierre-latour-0057a579


Comments (7)

  • Avatar



    Dr Latour.
    It would have been easier if you’d first investigated the relative heat-containing properties of CO2 in a mixture such as the atmosphere. It’s less than 0.04%!

    I’ve shown this in Chapter 1B in my website at pjcarson2105.wordpress.com
    (which has recently been reproduced in PSI).

    • Avatar

      Pierre R Latour


      I viewed your site:

      My model does not call for relative heat, heat capacity of CO2 or air. They enter heat transfer by conduction. I use radiant energy transfer because it dominates the energy flows from/to space and the effect of CO2 on temperatures..

      • Avatar



        Hi Pierre, and thanks for at least glancing at my work.
        However, we are interested in the amount of heating captured by the atmosphere – its greenhouse effect – and that does depend on the amounts of its components; CO2’s is an insignificant 0.04% of the total. How the heat is captured – by radiation, conduction, winds, or convection – is irrelevant.

        That’s easy.

  • Avatar

    Jerry L Krause


    Hi Pierre,

    “A new chemical process control systems engineering model of Earth’s atmosphere quantifies the effect of CO2 on Earth’s surface temperature. It uses the rigorous S-B radiant energy transfer rate law. The Earth’s surface and atmospheric temperatures are given explicitly as linear ordinary differential and algebraic equations; the only system properties needed are absorptivity and emissivity, five of which depend on CO2.” (your abstract)

    Carl questioned you about empirical evidence. And your response was: “I claim my model eqn (10) is the correct one; I am not aware of any other one.”

    And you acknowledge that the system to which you refer is a natural system of which is nearly impossible to artificially change to concentration of carbon dioxide to observe what might be observed. I recently wrote the essay about how Galileo proved which ideas were false (http://principia-scientific.org/galileo-proved-ideas-false/). I did this to show that he was always directly observing what happened in the natural world which he could observed and that his reasoning (arguments) were his explanation (interpretation) of what he observed. And of course, we know he did experiments whose results were not compatible with certain accepted false ideas. Maybe, some one could interpret what he did observe, and others could observe it they did the same experiments, differently. But to this point in time, I have not discovered that anyone has.

    Carl has reported that he measured the surface temperature of the soil and found that shortly after midday this temperature was about 21C above the temperature of air as conventionally measured about 1.5m above the surface (http://principia-scientific.org/solar-radiation-sufficient-no-greenhouse-effect-certain-atmospheric-gases/). Does your model take this observation into account? Of course not. Because I doubt any mathematical model can predict the variation of such a fundamental factor as temperature which varies significantly during the day and from one day to the next. So I am really lost on how you can claim that your “model eqn (10) is the correct one” when it seems to disregard many natural factors which are observed to influence the soil’s temperatures at depth as well as the more difficult to directly measure surface temperature. Which is easily observed (or reasoned based upon lower soil temperatures) to not be simply related to the air temperature by any known mathematical relationship. For what Carl observed really surprised me because I had not read about it until he made his observations and brought it to my attention.

    Have a good day, Jerry

    • Avatar

      Pierre R Latour


      My paper defines properties as global averages. I use average surface absorptivity/emissivity to get a corresponding surface radiator average temperature. I account for differences between dirt, grass, concrete, water, ice, forests, and rock with an effective average, which exists but is hard to determine independently. I found it from available temperature and rate data in reference 16. Global results fit available data. Averages over days, seasons. Say period of a decade.

      I have no comment on the difference between surface radiating temperature and the thermal temperature just above it, say at 1 meter altitude. I suspect the average difference is small.

      My physics says any effect of CO2 on temperatures is vanishingly small; hence unmeasurable and undetectable. That seems to agree with the data so far. I am ready to call it a day.

  • Avatar

    Carl Brehmer


    I appreciate the detailed explanation of this counter hypothesis to the more common hypothesis that climate sensitivity to carbon dioxide is positive, i.e., doubling the concentration of carbon dioxide from pre-industrial levels (~270ppm to ~540ppm) will force the average global surface level temperature to increase anywhere from 2-4 C.

    What we are still left with though is two competing hypotheses—to different mathematical models of the hypothetical effect of carbon dioxide on surface level air temperatures. Is there any scientific experiment; is there any empirical data set; is there any method by which the actual effect that carbon dioxide has on surface level air temperatures can be empirically measured? Do you have any empirical data gathered from the open atmosphere that demonstrates that the presence of carbon dioxide in the atmosphere results in surface level air temperatures being cooler than they would otherwise be?

    • Avatar

      Pierre R Latour


      I claim my model eqn (10) is the correct one; I am not aware of any other one.
      Such an experiment you seek requires
      1. Control of CO2 in atmosphere. You must stick with measured change, now increasing.
      2. Accurate measurement of average global surface temperature. Difficult, almost impossible.
      3. Account for all significant energy inputs during test period. Impossible.
      4. Account for time lag between CO2 change and resulting T change. Imprecise.
      5. The physical cause – effect relationship for T from [CO2]. My eqn (10) gives this.
      With three great difficulties, and item 5 showing the effect is vanishingly small, it is not surprising you cannot find anyone who has done what you seek. I doubt you could ever detect the vanishingly small effect. The answers to your questions are no & no.

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