Warming Calculator Analysis

It is frequently claimed that adding CO2 to the atmosphere will increase the amount of heat absorbed by the Earth by some amount. In a TED Talk, Jim Hansen said As a result, I created this Radiative Warming Calculator.

The intent was to see if Dr. Hansen's claim made sense and perhaps determine how much warming that would produce.

Before continuing, I suggest watching Dr. Hansen's TED Talk from 6:00 to 8:00 - just to make sure that you hear his comments in context. The transcript of part of that section is included below.

Radiative Warming Calculator | Overview | Agro data | TED Talk Details | Hansen paper | Summary

Radiative Warming Calculator

My Radiative Warming Calculator is pretty straight forward When absorbing radiation, Thickness is used to estimate the thermal conductivity and/or mechanical mixing of the substance. Basically, when heating an insulator (sand or concrete) the heat penetrates only a few millimeters per hour. On the other hand, water may be mechanically mixed (wind and waves) to a depth of several meters. Air is well mixed from one to ten kilometers. When heating via other means (such as electricity), Absorptivity should be set to one and Thickness is used to specify the volume of the substance.

Because the thickness is mainly a guess, the calculator does not give accurate results. Its intent is to provide ball park values and to help understand the effect of changing various properties.


I created the calculator to understand the impact of Dr. Hansen's claim. My analysis (details below) indicates that an imbalance of 0.6 W/m2 adds 51.84 kJ/m2/day - and Dr. Hansen is correct, that's a lot. Over the course of a year, that much extra energy would increase the temperature of a 1 meter thick section of a typical soil by 14.2°C. Over a century, the temperature would increase 100 times that amount. (ouch!!)

Since a typical Global Warming paper suggests a temperature increase of about 4°C/century, something is not right.

The problem is pretty obvious - Dr. Hansen ignores that fact that as the temperature increases, the heat loss via IR radiation also increases. Basically, his assumption that an imbalance of 0.6 W/m2 can persist is simply wrong. It can't happen. Within a few hours, the increased outgoing radiation causes the local net heat gain to decrease to zero and the temperature quits increasing. (This is referred to as steady state or equilibrium.) Granted, the planet might be just a bit warmer, but there can not, and will not, be an imbalance of that magnitude over land for more than a few hours.

Another way to interpret Dr. Hansen's claim is to assume that the energy is being absorbed by the oceans. In that case, the ocean temperature increase should be about 0.5°C/century (depending on the assumptions made) or about the natural temperature increase observed by thermometers over the last century. If that analysis is correct, then there is nothing to be concerned about. (According to Hansen (2011), he is referring to just the oceans. See discussion below.)

If Greenhouse Gases are causing the imbalance, then I expect the increase in extra energy to be the same over land and ocean. By corollary, if the energy increase is different over land and sea, then Greenhouse Gases are not the cause.

There are 2 analyses below

Agro data

Both the TED Talk and the related paper are heavily based on data collected from the Argo array. Each float has a lifetime (battery life) of about 4 years.

Correcting Ocean Cooling discusses various issues with the Argo data. In particular, the 2006 and 2007 data showed that the Atlantic ocean had suddenly cooled at the 500 meter depth. (The water may have cooled over the entire 2,000 meter range that was sampled, but the images specifically show cooling at only the 500 meter level.)

After analysis, it was decided to recalibrate the Argo data - but, apparently, only the data from the Atlantic. (I kid you not - their corrections are considered more accurate than the raw data from over 1,000 sensors!)

To be fair, that adjustment might be fully justified - but I don't have the time to dig into the details. Maybe, once 20 or 30 years of data are available the truth will be obvious. But for now, I am skeptical.

You can obtain and analyze Argo data yourself.

TED Talk Details

I'll quote a bit more of Dr. Hansen's February 2012 TED Talk so you can see that I am not taking this out of context. At this point, I mostly agree with Dr. Hansen. If something blocks the escape of radiation to space, then that would cause an energy imbalance. I don't agree that CO2 will do that, but let's ignore that for this analysis and just assume that "something" is blocking it. What he is saying is that the "measured" energy increase in the oceans means that they are absorbing about 0.6 W/m2 more than they are losing. ("The inferred planetary energy imbalance [is] 0.58 ± 0.15 W m-2 during the 6-yr period 2005-2010" ref)

That may, or may not, be correct. As mentioned above, there is a lot of disagreement about the accuracy (validity) of the Argo float data.

At any rate, we can get a better understanding of that claim by using the calculator. In it,

As you can see, the expected temperature increase is 0.05°C. (Kind of a don't care.) Using 100m, the temperate increases 0.45°C/10yrs - a value that is obviously too high. The computed result should be close to 1.0°C/century, not 4.5°C/century. In the related paper (see the next section), 0.6 W/m2 is over the entire 2 km column and 0.44 W/m2 over just the top 700 meters.

Looking at land,

Now the computed result is 15.7°C/decade, 157°C/century.

Because of its relatively low thermal conductivity, to compute the expected daily effect of an increase in energy over a solid surface, 10 meters is way too thick. Instead, I suggest setting the over land (soil) thickness to 10mm. In this scenario, the claim of "0.6 W/m2" made by Dr. Hansen would generate a temperature increase of about 8°F per day, about 54°F per week - and the temperature would continue to increase linearly as long as the imbalance exists. Values like that are obviously nonsense.

Assuming that the energy imbalance is caused by Greenhouse Gases, it should be the same over land and ocean. To me, this exercise proves (demonstrates) beyond a doubt that the statement of "an excess of 0.6 W/m2/day" due to Greenhouse Gases is complete nonsense.

If a small imbalance continues for more than a few hours, the temperature would become so high that few things would survive.

According to this model, to raise the temperature 1°C in 10 years requires a sustained energy imbalance of only 0.00001 W/m2. Since the consensus is closer to 1°C in 100 years (as determined for the twentieth century), the imbalance is actually one tenth that value. But, Dr. Hansen claims the currently measured imbalance is 0.6 W/m2 (clarified as 0.07 W/m2 over land in the paper).

Based on radiation (using Stefan's equation), an increase of 1°C indicates an increase in emitted radiation of 5.46 W/m2.

Obviously, something is wrong! The solution is simple - if the energy toward the surface was suddenly 5.46 W/m2 larger, based on the calculator, it would take only 3 minutes 39 seconds for the surface to warm up 1°C (assuming soil and a 1mm thickness). At that point, the surface radiation has increased to match the incoming radiation and the system is back in near equilibrium. The small amount of heat conducted thru the soil over the next few meters will keep it from reaching full equilibrium, but the difference will not be significant.

This simple model does not account for the fact all (most) changes follow an exponential curve - I've just used a linear approximation. Also different materials (and different thicknesses) will require different amounts of time to reach equilibrium. For instance, 10 mm of still water will require about 2 hours to increase its temperature 1°C after a 5.46 W/m2 increase in incoming radiation (ie, to reach equilibrium) - assuming that all the energy is absorbed in the top 10 mm and ignoring evaporation.

At any rate, this calculator shows, quite clearly, that any energy imbalance will be fully balanced within about a day and the consensus assumption that the imbalance will continue for years is simply nonsense.

Letting the calculator determine the amount of energy needed to produce a 1°C increase per century can be estimated by

This yields a daily surplus of 0.00423 W/m2 - significantly smaller than the value Dr. Hansen claims.

Of course, my model might be wrong. I might have made a stupid assumption. However, even performing this type of analysis automatically labels me as a despicable anti-science denier. I would much rather have a stringent review of the model and have specific errors pointed out.

This is the difference between religion and science

Hansen paper

Wanting more details, I searched for papers where Dr. Hansen referred to the Argo floats - there are several. The comments on this page refer to Earth’s energy imbalance and implications (Hansen 2011).

In particular, I enjoyed reading the peer review comments and Dr. Hansen's responses. For the 2 "anonymous" reviews, both sides responded very professionally. For the third review, the reviewer was obviously a climate skeptic, and Dr. Hansen just blew him off (as he should have).

At any rate, this paper confirms my analysis that heat absorbed by the ocean is much larger than the heat added to the land. While I seriously disagree with their numbers over land, the large difference still indicates (to me) that the ocean warming is not related in any way to changes in Greenhouse Gases.

In the paper, Figure 9 clearly states that the 0.6 W/m2 imbalance is in the oceans and that the imbalance is only 0.07 W/m2 for land.

For soil and a depth of 10 meters, that would compute an increase of 18.4°C/century - completely unbelievable.

Looking at just the ocean, the paper is pretty clear that the imbalance is 0.44 ± 0.1 W m-2 for the upper 700 meters (page 13432, footnote 3). Using the calculator, that translates into a temperature increase of 0.37 to 0.58°C/century. The rest of the 0.6 W m-2 imbalance is in the ocean to a depth of 2 km and results in a temperature increase of about 0.09°C/century. This is what Dr. Hansen considers "gaining heat at a substantial rate". Sorry, I consider this to be insignificant. And since this is based on only 6 years of data, using this to push his global warming platform is highly unscientific.

These are just a few interesting quotes from the paper.

Willis is the person who detected (and "corrected") the cooling anomaly in the Atlantic mentioned above.

So, we can't trust satellites.


I think my head is about to explode.

All in all, the paper has all the correct caveats - the TED Talk doesn't.


This page discusses how to use my Radiative Warming Calculator to analyze Dr. Hansen's claim of "a continuous energy imbalance".

Over the oceans, I think it is highly likely that there is a significant (or at least detectable) imbalance. Basically, oceans absorb Solar energy over considerable depth (up to 5 km), but can only lose it at the surface. Since there is little vertical motion, this energy (temperature) increase should easily map out the ocean circulation patterns. Because of the long time lags of the ocean circulation (measured in centuries) it is perfectly reasonable for the oceans to still be recovering from the Little Ice Age.

However, it should be clear that the oceans themselves are producing this imbalance, not anything related to the atmosphere.

Basically, if the atmosphere was the cause, I would expect the same results over land - and the results are completely different.

In my opinion, I think I have shown that any claim that "Greenhouse Gases cause the Earth to be in a continuous energy imbalance" is simply non-scientific nonsense.

Author: Robert Clemenzi
URL: http:// questionable-science.com / Global_Warming / MyApplications / WarmingCalcAnalysis.html