The curious incident of the added heat at the surface
Now, we promised you a corollary from the heat transfer and ice melt calculators and, sure enough, here it is:
If you've just come from the calculator forms then you already know we've been playing around with Earth's surface area in meters squared and heat in Joules (or kilo Joules, kJ), along with the heat necessary to warm the atmosphere 1 °C. Why does this cause us to paraphrase Sir Arthur Conan Doyle's fictional detective character? To understand that we need to provide a little background, for the benefit of those who do not habitually read IPCC technical reports and the full papers of global warming's Grandpa, James Hansen.
The IPCC's Third Assessment Report reduced their estimate of increased atmospheric carbon dioxide's heating effect by about 18% from FAR (the First Assessment Report) and SAR (the Second Assessment Report) and left it so in their AR4 (Assessment Report 4, not 'FAR' lest it be confused with the 1st assessment). Provided by the IPCC then we have the simplified formula for calculating increased or 'excess forcing' due to increased atmospheric CO2, which reads, in part:
What does all that mean? Actually, it's pretty simple, every time you double the amount of atmospheric carbon dioxide you add 3.8 watts per meter squared of Earth's surface and you can work out the change in forcing from origin (say pre-1750, which is where the IPCC bases their pre-Industrial Revolution calculations) by calculating 5.35 x natural log(current year [say 380 for 2006]/280) which resolves as 5.35*ln(380/280) = 1.633792 expressed as Watts per meter squared (W/m2). Your favorite spreadsheet should handle that without difficulty and we are not exercising great precision in this example. We'll include some forms at the end of this item so you can play with atmospheric heating.
So, where does that get us? We're glad you asked because we're going to show you anyway! Since this is "excess forcing" or, as Hansen puts it "Human-made climate forcings, mainly greenhouse gases, heat the earth’s surface at a rate of about two watts per square meter—the equivalent of two tiny one-watt bulbs burning over every square meter of the planet"* we are going to ignore the "natural" heat budget with all its complexities and look only at the additional or "excess" forcing.
One Joule, with which we have been working on heat transfer and ice melt, is the equivalent of one Watt.second. That is, according to the IPCC, increased atmospheric CO2 is applying 'excess' surface heating at the rate of 1.633792 Joules every second over every square meter of the Earth's surface. Now, we already worked out the Earth's surface in square meters (~5.1 x 1014 m2). Over a year (standardized to 365.25 days to account for leap years) that's 1.633792 Watts x 5.1 x 1014 m2 x 3.15576 x 107 seconds = 2.62949 x 1022 Joules (or x 1019 if you are working in kJ).
We also worked out heating the atmosphere 1 K (or 1 °C) required 5.162685 x 1018 kJ or 5.162685 x 1021 J.
Deriving atmospheric warming in 2006 from increased atmospheric CO2 forcing is a snap then as 2.62949 x 1022 J (added forcing) / 5.162685 x 1021 J (heat required to raise atmospheric temp by 1 °C) to see the atmosphere warmed 5.09 °C in 2006. Oh, wait... the atmosphere didn't actually warm 5 °C in 2006, did it? In fact the total net warming estimate 1850-2000 is 0.6 ± 0.2 °C.
Hmm... NOAA gives the figures for annual mean atmospheric carbon dioxide 372.39; 374.94; 376.76; 378.78 ; 380.90 and; 382.67 ppmv for the years 2002-2007 respectively, which means our annual atmospheric temperature increase should have ranged from 4.75 °C in 2002 up to 5.21 °C in 2007 for a total increment of about 30 °C. In the unlikely event half that warming was expended melting ice our sea level calculator tells us we should have seen more than two feet of sea level rise and we certainly didn't get that in the last 6 years. So where did all that heat go?
Perhaps Hansen can tell us:
Um, no... that can't be right because the warming of the oceans from the 1990s up to 2002 did not persist (see, e.g., “Correction to ‘Recent Cooling of the Upper Ocean’” by Josh K. Willis, John M. Lyman, Gregory C. Johnson and John Gilson) -- the oceans may not have cooled but they didn't get any warmer either and the previous warming trend is now believed to be an artifact of measurement. As far as we are aware no one claims ocean heat content increase over the last 7 years, which leaves quite a conundrum.
What happened to an estimate of surplus heat sufficient to warm the atmosphere some 30+ °C over the last 6 years? It didn't go into the oceans, where researchers have been looking for it. It most certainly didn't warm the atmosphere (where everyone would've noticed) and it for sure didn't all go into melting ice since that much heat would've melted enough ice to raise the oceans by more than 4 feet (something also sure to be noticed).
Now we are left with the other point to which we wish to draw your attention.
It is possible, however unlikely, that heat is being transferred and stored in a manner escaping the multi-billion-dollar annual effort to observe it. It is possible we are entirely wrong about the laws of physics and heat simply disappears. It is significantly more likely that climate models and IPCC assertions are wildly erroneous and the alleged trace gas-driven warming did not exist to begin with, which would explain why we cannot observe it.
Odd that even Hansen's GISTEMP, itself a galloping outlier in the warming stakes, claims a trend hundreds of times smaller than that which the IPCC's simplified formula insists must be... Users will have to decide for themselves whether to believe PlayStation® Climatology or their own lying eyes.
Of course, there is another explanation. It could be that people telling you "human-made climate forcings, mainly greenhouse gases, heat the earth’s surface at a rate of about two watts per square meter—the equivalent of two tiny one-watt bulbs burning over every square meter of the planet" are not providing the right calculation to start with. The above calculations, while perfectly valid in themselves, produce obviously ridiculous answers and must be based on flawed premises, which indeed they are. Alleged radiative imbalance from increased atmospheric carbon dioxide does not and can not produce surface warming at the rate of 1.63 Joules every second. We have examined Earth's climatic sensitivity to increased forcing before and the answers are that a new equilibrium (stable temperature, if you like) is achieved in the range 0.1 - 0.3 °C per additional Watt forcing. This means, over time, Earth will adjust its temperature upwards from 0.16 - 0.48 °C to accommodate the additional 1.63 W/m2 forcing from atmospheric carbon dioxide added since 1750. Just doesn't invoke the same urgency as all those pretty little lights of Hansen's though, does it?
Activists come in many flavors and they all want to tell the story in a manner designed to evoke a specific response from you. As you can see from the above it is really easy to take an expert's statement and, using verifiable physics and math, produce truly alarming results. Only thing is, just as the above, they are nonsense. Hansen knows full well that Top of Atmosphere forcing does not equate to the little light bulb analogy with the attractive imagery, just as he knows that dry and boring facts do not attract grants and lucrative enviro-awards. Imagery of "heat-trapping pollution" also gives the impression that summing incremental rises, as we did with the allegation of +30 °C atmospheric heating over 6 years is appropriate when the fact is significantly less exciting global net temperature adjustment to equilibrium over centuries or millennia.
We hope you'll forgive us our little bit of frivolity waltzing you twice around the mulberry bush but the situation is becoming quite dangerous with politicians of all descriptions promising to visit great harm on the global economy to address the illusion of catastrophic global warming. Everyone needs to wake up and see the situation is not at all as advertised. Restricting energy supplies is not a smart move and will save no one from a mythical threat.
As promised above, here is a form for you play around with atmospheric heating. First a couple of things you should know for background of these simplified models:
Dr John Christy teaches a simplified concept, one of examining a single one meter square column of the atmosphere (saving the necessary arithmetic of total atmospheric mass and number of square meters for Earth's surface area -- there's a reason he's the expert). To quote: "In my classes I make the problem simpler by describing what happens in a single atmospheric column of 1 m square. We have about 10,000 Kg of air in that meter squared, so the calculations are simpler. Change in temperature is simply cp*d(T)*mass = Q where Q is the heating rate and cp = 1004 j/K/Kg or essentially d(T) = Q*0.0000001 for the whole column. So, if you dump heat in at a rate of 1.7 j/s/m2, then you can calculate the average rate of temperature change as 0.00000017 per second for the whole column." For simplicity's sake Christy has rounded the atmospheric heat capacity 1004 down to 1000 Joules per Kilogram per kelvin while our form does not. For those who wish to cut to the chase Christy's columnar calculation comparable to our 2006 calculation above delivers 5.12 °C with the difference due to minor variations in precision and assumptions (e.g., he uses global atmospheric mass; 5.1361 x 1018 Kg: Trenberth, K.E., J.R. Christy and J.G. Olson, 1987: Global atmospheric mass, surface pressure and water vapor variations. J. Geophys. Res. 92, 14,815-14,826). Bottom line, less than 1% difference we can live with.
Additionally, this form introduces another layer of complexity, that of oceanic absorption. Bear in mind that every 10 meters of water column is equivalent to one entire atmosphere (10 cubic meters of water has a mass of 10,000 Kg), meaning that the oceans are an enormous heat sink. There is a theory that we can not find atmospheric warming because the oceans are absorbing it and 300 atmosphere's worth of oceans make the temperature change far too small to measure.
Now, we have no specific problem with the possibility that Earth's warmth is distributed through the oceans as well as the atmosphere. Our response, however, remains the same. If additional or "excess" warmth is being spread over so many more atmospheres, at least atmosphere's worth of oceans, then we are looking at as little as one-third of one percent of estimated warming to achieve equilibrium temperature with enhanced greenhouse forcing. This would make the IPCC's touted 1.5-6 °C atmospheric warming an immeasurably small 0.005-0.02 °C for a doubling of pre-Industrial atmospheric carbon dioxide -- not a particularly worrisome prospect.
So, recent data acquisition fails to show warming in the top 750 meters of the oceans (equivalent to 75 atmospheres) but there is a suggestion of warming in the deep ocean (below 1,000 meters, although historic data is sparse, to say the least -- the warming of so much of the ocean would be so small from enhanced greenhouse that the figures are of little relevance here). We are providing a field for you to select ocean depth to disperse additional forcing so you can see the effect ocean absorption has. As an exercise try maxing out the atmospheric carbon dioxide at 1200 ppmv (four times pre-IR levels) and share the additional Joules through the full allowable 3,000 meters of ocean depth and see that it would take more than 100 years to raise the temperature of the system just 1 °C. If the assertions that heat is being added to the system at the claimed rate but we can not detect it because it is being "hidden" by dispersal in the oceans then again we are unconcerned -- distributing the additional heat through so many more atmospheres' worth of heat sink makes mean warming trivial.
Note also that none of these scenarios include the slightest increase in emission efficiency. By this we mean slight increase in the evaporation and precipitation cycle, which transports enormous amounts of heat to regions of the atmosphere where it is radiated to space. In addition to evapo-transpiration we have convective columns, the thermals sought by soaring birds and glider pilots alike, a trivial increase in which will bypass significant enhanced greenhouse effect and improve the efficiency of the atmosphere's radiation of heat to space. There are many ways 'excess' energy can vent to space but, regrettably, our current measurement capacity cannot detect. Any adjustment in Earth's radiative efficiency reduces the radiative imbalance (the difference between incoming and outgoing energy) and means that the IPCC's simplified expression for change in radiative forcing will be too large and indeed Hansen's infamous "Smoking Gun" claimed less than 1 Watt per meter squared.
The situation is further complicated by tropospheric warming (sub ~8,500 meters) and stratospheric cooling (>8,500 meters) expected because heat "trapping" would mean Joules retained closer to Earth's surface and therefore unavailable to warm the stratosphere (never mind that there has been no detectable stratospheric cooling over the last decade in conjunction with rising atmospheric carbon dioxide).
Nonetheless, here is the form where you can play with the Earth's thermal balance to your heart's content.
To use the form simply fill in the atmospheric carbon dioxide level in parts per million (ppmv), this can be the current or some future estimated level and the form will accept any value from 280 to 1200. This will determine 'excess' forcing compared with the pre-Industrial Revolution level as per the IPCC's simplified expression, above. Pre-IR atmospheric CO2 is assumed to be 280 ppmv. By default the form will deliver atmospheric heating only but you have the option of including oceanic warming to a depth of your choice (simply enter the depth in meters, the default is zero). Your result is the expected warming over one year provided no increase in radiation efficiency occurs (that is, if all additional Joules are retained in the system rather than any increase in radiation to space, no alteration in specific humidity, precipitation efficiency...).
How much would the atmosphere warm if
* Yes, we know that's not how it works but Hansen explicitly states so and it is the caption of the cute picture (reprinted above) on page 73 of the March 2004 Scientific American reprint of Defusing The Global Warming Timebomb. We are using it to demonstrate how a few misstatements and flawed understanding lead to completely erroneous expectation of catastrophic warming. For a serious examination of climate sensitivity to enhanced greenhouse forcing go here.