Understanding the W/m^2 of CO2; The Flux Conundrum

The entire foundation CAGW is based upon is that the change in outgoing LWIR “trapped” by manmade CO2 will have catastrophic consequences. There are serious problems with that concept, but to understand the flaws, one must understand the basics.

CO2 absorbs, radiates and “thermalizes” LWIR between 13 and 18µ, that is the only mechanism by which CO2 can affect climate change. CO2, through the “thermalization” or conversion of EM radiation to kinetic/heat energy, warms the atmosphere. Thermometers don’t measure EM radiation, they measure the kinetic energy of the atmosphere.

What then is a Watt? A Watt is a flow of energy, much like a hose may be a 40 gallon/hour hose. Under a certain pressure, a hose may allow 40 gallons to flow through it in an hour. The bigger the hose the greater the flow or “flux.” Using that analogy, a Watt is defined as a unit of Power equal to 1 Joule/second.

What then is Power? Power is the rate at which work can be done or energy per unit of time.

What then in Work? Work, in physics, is a measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. If the force is constant, work may be computed by multiplying the length of the path by the component of the force acting along the path.

What is a Force: Force = MA or Mass x Acceleration, this is Newton’s 2nd Law

What is a Joule? A Joule is a unit of work or energy equal to the work done by a force of one newton acting through a distance of one meter.

Okay, now that we have the basics, let’s go take a look at how all this comes together. We will use MODTRAN to do the calculations. (Source)

We will start with MODTRAN set to:

  1. Looking down from 70km
  2. Tropical Atmosphere
  3. No Clouds or Rain
  4. Ground Temperature of 299.7°K

Using those initial settings, if I change CO2 to 0.00 ppm I get an outgoing Upward IR Heat Flux 329.7 W/m2.

If I then change the CO2 to the Pre-Industrial 270 ppm I get an Upward IR Heat Flux 300.404 W/m2. This means that 29.3 W/m^2 less energy is leaving the atmosphere by the height of 70 km relative to when CO2 was 0.00 ppm.

If I then change the CO2 to the current level of 410 ppm I get an Upward IR Heat Flux 298.394 W/m2. This means that 31.31 W/m^2 less energy is leaving the atmosphere by the height of 70 km relative to when CO2 was 0.00 ppm.

Man’s contribution to the energy balance is therefor the difference between Per-Industrial and current levels of CO2. The net contribution by man, assuming that he is 100% responsible for the additional CO2, is a whopping 2.01 W/m^2. From that, we learn man’s contribution to the energy balance attributed to CO2 is 2.01/31.31, or about 6.4%.

Once again, all those numbers can be checked using MODTRAN (Source)

Now, the argument goes that CO2 is the cause of warming because it is a constant additional 2.01 W/m^2. Because it is a constant amount of additional radiation, and CO2 only increases as long as man continues burning fossil fuels, the climate has no choice but to continue to warm, thus the name CATASTROPHIC ANTHROPOGENIC GLOBAL WARMING.

That sounds really scary until you understand that W/m^2 is a flux. Climate alarmists act as if the energy gets “trapped” in the atmosphere. That is pure nonsense, it is always working its way out to outer space. Energy is like a river flowing from the surface to outer space. Green House Gasses act like small dams in the energy river slowing this flow. The sun heats the earth during the day, energy is inflowing, and then at night, the energy flows back out to outer space.

That is the basic concept, but remember that this is an inflow/outflow model, and many things other than GHGs can alter that dynamic. CO2, as noted above, is responsible for 2.01 W/m^2, but what does that really mean?

The latent heat of fusion of ice is 337 joules/gram

The specific heat of water is = 4.186 joule/gram °C which is higher than any other common substance.

The CO2 provided 2.01 W/m^2 could melt 1 gm of ice every 168 seconds (337/2.01). Every m^2 in the Arctic would have 1 gm of ice melt if the temperature is 0.00°C or above due to anthropogenic CO2. Does that seem very alarming? Considering the period of time the Arctic is ever above 0.00°C is very short. There are 3785.4118 gms in a Gallon. So it would take 168 x 3785.4118 = 634,668.55 seconds, or 10,577.81 minutes, or 176.30 hours for the marginal CO2 to melt a single gallon of ice over a m^2. Trust me, CO2 isn’t going to melt the Arctic at that rate.

How about the oceans? The vast oceans are enormous. CO2 can warm 1 gm of ocean 4.186/2.01 =  2.08 seconds. That means CO2 can warm a gallon of ocean 1°C every 1819.91 seconds or 30.33 minutes. There are 264.172 gallons in a m^3, so 1 gallon represents the very top 0.39 cm of the m^3 of ocean. It would take 129.408 hours to warm the entire m^3 by 1°C, and this assumes no cooling due to evaporation.

Now that we have that background, let’s look at other factors. Set MODTRAN to 410 ppm CO2, and change the settings to cumulous clouds. The Upward IR Heat Flux is 269.726 W/m2. The clear sky has Upward IR Heat Flux 298.394 W/m2, so the difference is 28.668 W/m^2, or 14x the radiative impact of Anthropogenic CO2. 1 day of cloud cover is the equivalent of 14 days of Anthropogenic CO2.

That, however, isn’t the biggest problem for the climate alarmists. Remember, W/m^2 is a Flux. Temperatures rise and fall as energy enters and leaves the system. That means once a temperature is reached below a previous low temperature, past energy has been removed. The best analogy I can think of is a safety valve on a boiler. Pressure (temperature) builds to a point to trigger the safety valve, and once triggered, gas is released to lower the pressure. Once the valve is triggered all the previous energy/pressure gets released, then the whole process starts all over again.

Now, imagine the boiler has 2 hoses leading into it, one that has a flow rate of about 40 gallons an hour (Water Vapor) and another that has a flow rate of about 1 gallon per hour (CO2). Both hoses are turned on high, so 41 gallons per hour of water are sent into the boiler. The water boils and reaches a point that triggers the safety valve. Steam leaves the system and the water level drops. Water then flows back into the boiler and the process starts all over again. Temperature is analogous to pressure. The pressure never reaches a level above the trigger point. All the 1 gallon per hour hose does is help speed the cycle up by a slight amount, it does not result in higher pressures.

CO2 and the energy it provides 2.01W/m^2 has well-defined warming rates and energy flow. If it takes 129.408 hours to warm m^3 of water by 1°C, if that water cools by 1°C, it will take another 129.408 hours to get back to where it started. If temperatures fall below a previous temperature bottom, all the previous energy has been lost. That is why these references to Pre-Industrial CO2 are nonsensical, as is average temperature. If one day has a low-temperature of 18°C and the next day is 15°C, all the historic impact of CO2 has been removed.

How is this relevant? Well, the climate system acts like the boiler with a safety valve. The safety valves are called El Niño and La Niña. Incoming visible radiation warms the oceans, the temperatures increase, and eventually, the oceans belch out a bunch of energy in the form of El Niño and the temperatures drop resulting in a La Niña, then the entire cycle starts all over again. From the temperature charts, it is obvious that El Niños drive the climate, not CO2.

How, if CO2 was the cause of the warming, could current temperatures be BELOW the level of temperatures in 1987? How could temperatures ever fall? Clearly, from the above chart, temperatures remained in a range between 1979 and 1997 storing up energy from visible radiation. The oceans then belched out accumulated energy in the 1998 El Niño, and temperatures then remained in a range until the 2016 El Niño. The rates at which CO2 could warm the oceans and replace the energy lost through an El Niño are fixed and quantifiable, and there simply isn’t enough time for CO2 to replace the energy lost through an El Niño.

Now, in reality, looking down from 70km isn’t very useful. What we are really interested in is how CO2 impacts the lower atmosphere where the Arctic Ice and glaciers are. To do that, change the setting on MODTRAN to “Looking Up” from 0.00 km (The Surface). This gives one the reading of the IR Heat Flux coming back to the surface. When you enter those settings, the Downward IR Heat Flux is 369.264 W/m2 for 410 ppm and Downward IR Heat Flux 368.322 W/m2 is for 270 ppm, so in reality, the relevant amount of energy associated with Anthropogenic CO2 isn’t the 2.01W/m^2 used above, it is actually less than 1/2 that value at 0.94 W/m2. Basically, every time period mentioned above should be more than doubled.

But wait, just what does 0.94 W/m2 really mean in the grand scheme of things? Is this amount of energy really material to the system, even over very long periods? Not really. Daylight has a peak irradiance of the surface of around 1,000 W/m^2 on a clear day. This means that 1 hour of peak solar radiance is the equivalent of 1,000 hours of Anthropogenic CO2’s irradiance. (Source) That is actually a low value. Wikipedia places the value at 1,120 W/m^2. Considering just the Northern Hemisphere and various factors, that value can drop to 300 W/m^2 in the winter, 150 on a cloudy Winter day, and 50 on a foggy winter day. (Source) The day to day, hour to hour, season by season variations of energy reaching the surface of the earth are enormous, dwarfing the impact of even a constant 0.94 W/m2. A single sunny HOUR can add more energy to the system than nearly 2 months of Anthropogenic CO2.

That, however, isn’t the important aspect. Remember, W/m2 is a flux. A single cloudy HOUR in the summer, when W/m^2 drops from 1,120 W/m^2 to 600 W/m^2, will release the amount of 21 days of Anthropogenic CO2 back radiation. It would take 21 days for CO2 to replace the energy lost from just 1 HOUR of clouds in the summer. Climate alarmists make it sound as if the energy budget can go nowhere but up, which is complete nonsense. The climate system has release valves, and the rate of energy replacement by Anthropogenic CO2 is so small and slow that it is immaterial in the grand scheme of things.

The oceans control the climate. They are the Earth’s hypothalamus or thermostat. Define the oceans and you define the climate. Our climate models shouldn’t be modeling the atmosphere, they should be modeling the oceans if they truly want to model the climate. As noted above, it takes Anthropogenic CO2 129.408 hours to warm m^3 of water by 1°C using the inflated value of 2.01W/m^2. Daylight can warm that same amount of water in 14 minutes. 14 minutes of clouds can remove the amount of 64 hours of the effect of Anthropogenic CO2. Once again, because the energy replacement rate of CO2 moves at glacial speed, it is like a Tortoise in a race against a Hare. By the time Anthropogenic CO2 even starts to replace the energy lost by a single cloudy day, another one hits. That is why temperatures don’t travel in a straight line like atmospheric CO2 does. Once temperatures drop below the previous low levels, the system resets, and all previous contributions from Anthropogenic CO2 are lost to outer space.

Because of the time rates associated with CO2, Anthropogenic CO2 simply can’t be the cause of temperature volatility, and it certainly can’t be the cause of increasing temperatures. There is nothing about CO2 that regulates the amount of energy lost through an El Niño. Once a previous temperature low is exceeded, the system simply resets, and any impact of historical CO2 is lost.

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4 thoughts on “Understanding the W/m^2 of CO2; The Flux Conundrum”

  1. Very helpful comparisons and details showing how the increased CO2 cannot be the main driver of atmospheric temperature. Your caveat of “The net contribution by man, assuming that he is 100% responsible for the additional CO2, is a whopping 2.01 W/m^2.” is the crux of my recent studies in this field. I have concluded that the increased CO2 is nearly all natural and there is no reasonable argument I have found for it being anthropogenic. So not only is CO2 not causing warming humans are not changing the atmospheric CO2 content enough to matter. Somehow this info never gets past these blogs. My experience is almost no one is aware of these facts outside the “denier” community yet most Montanans think there is something fishy about the climate change hype they are constantly fed by the media.

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    1. DMA, thanks for the comment. If you watch the atmospheric CO2 its trend remains basically unchanged during large forest fires and volcanoes. My bet is that the warming oceans are the cause.

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      1. I think Ole Humlum’s work at Climate4you.com shows you are most likely correct.
        When the warmists say the human CO2 is only partly absorbed and the rest hangs around for 1000 years I like to ask them how nature can tell who started the forest fire lightening or an arsonist so it can choose which molecules to keep. At that point I am usually ridiculed and dismissed.

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      2. Yep, that is the exact same question I ask. CO2 for the most part is CO2, the characteristics of CO2 from a tree is largely the same for oil except for a small fraction of a certain isotope. BTW, that 1,000 is nonsense. Nuclear testing in the 50s and 60s spiked a certain carbon isotope, so the lifecycle of CO2 is easily calculated, and it is more like 5 to 15 years.

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