JunkScience.com
October, 2009
Daily we are bombarded with claims of a catastrophically heating Earth and the need to take drastic action. One thing we don't do, however, is stop to look at the actual numbers.
We are told the Earth is so many hundredths of a degree from specified norms, in the case of NASA's GISTEMP that averages +0.59 °C for the period 1999-2008 (latest available decade and allegedly the hottest on record), to which we are instructed to add 14.0 °C to derive the globe's mean temperature of 14.59 °C (see footnote of linked file). Immediately we have a problem though, because Earth's 33 °C "normal" greenhouse effect is predicated on Earth's mean temperature of 15 °C, i.e., warmer than its current allegedly overheated state. This is a figure with which NASA's Goddard Institute traditionally agrees, making the current panic somewhat mystifying.
Most of us probably remember the derivation like this (your radii and temperatures may not match precisely and so, as they say, your mileage may vary):
The sun behaves approximately like a black body of radius rs=6.955 x 105 Km, at a temperature of Ts=5,783 K. The radiative flux at the sun's surface is given by the expression σTs4, where σ is the Stefan-Boltzmann Constant (5.6704 x 10-8 Wm2K4). Flux refers to radiation per unit area. Thus, at the Earth's distance from the sun, res=1.496 x 108 Km, this flux is reduced by the factor (rs/res)2. The Earth's disk has a cross section, acs=πre2, where re is the Earth's radius (6.371 x 103 Km), and thus intercepts acsσTs4(rs/res)2 radiation from the sun. In order to balance this intercepted radiation, the Earth would warm to a temperature Te, where σTe44πre2 = acsσTs4(rs/res)2. This leads to a solution Te=272 K. Clouds, which obviously require an atmosphere, and other features of the Earth reflect 31% of the incident radiation. Taking this into account reduces Te to 255 K.
Actually it would be surprising if everyone derived the same value due to rounding and base number variations, just look at these potential causes of confusion:
Solar temperature:
- These two methods give a rough temperature for the Sun of about 5800 K. ... You can use the absorption line strengths as an accurate temperature probe to measure a temperature of about 5840 K. http://www.astronomynotes.com/starsun/s2.htm
- Eventually its temperature was determined to be 5,770 Kelvins (6,000 C or 11,000 F). [!] http://sunearthday.gsfc.nasa.gov/2009/TTT/65_surfacetemp.php (No e-mails, please -- NASA has indeed made a major conversion error here: t °C = (t + 273.15) K is still true and 5,770 K remains 5,497 °C or 9,927 °F)
- "Temperatures in the photosphere usually do not exceed 6,000 °C (6,273 K)" (Loble-Murray-Rice. Earth Science.)
"The sun's surface or photosphere is about 340 miles thick and its temperature about 5,500 °C (5,773 K)" (World Book Encyclopedia Vol. 18.)
"The Solar surface is not solid like the earth's, but its high temperature 5,700 °C (5,973 K) …." (Davis, Dan & Anny Levasseur-Regourd. Our Sun.)
"… temperature of the sun is about 6,000 °C (6,273 K)" (Principles Of Science. Columbus, OH: Merrill, 1979.)
"… while the sun's surface (photosphere) is 5,600 °C (5,873 K)" (Dichristina, Mariett. "Our Violent Star." Popular Science. 249, 3 (September 1996): 17.) http://hypertextbook.com/facts/1997/GlyniseFinney.shtml - Effective temperature: 5,778 K http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
So there you go, you have a range of 500 kelvins with apparently credible sources.
NASA says Earth is subjected to a solar irradiance of 1,367.6 W/m2 http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html while Astronomy Notes states: "From the Inverse Square Law of Light Brightness, you find that the solar flux at the Earth's distance = the Sun's surface flux × (Sun's radius/Earth's distance)2 = 1,380 Watts/meter2." http://www.astronomynotes.com/starsun/s2.htm
How much incoming solar radiation is reflected by bright clouds, snow & ice fields, bright deserts, atmospheric dust and other aerosols? Again, we don't know for sure -- commonly this figure (albedo) is cited as 30% (0.3) but it could be anywhere from 28%-32% for an average (it constantly varies with cloud cover, season and regional drought).
In the following form we have plugged in some fairly uncontroversial numbers:
AU (earth's average distance from the sun) = 149,597,870 km;
solar radius = 695,500 km;
pi = 3.1415926535897931 and;
sigma (Stefan–Boltzmann constant) = 0.000000056704.
It was a bit of a toss-up whether we used a solar radius of 696,000 instead as it is very commonly used but this does not materially affect the results below. You've seen these types of forms here before so you can play to your heart's content deriving "expected" temperatures for planet Earth and no one knows what it "should be" for sure so they can't really prove you wrong :-) This form is somewhat more sophisticated than the previous calculator we gave you in that it begins with solar temperatures rather than simply accepting TOA irradiance numbers as provided.
In the past we have shown you this graphic from Earth’s Annual Global Mean Energy Budget (Kiehl and Trenberth, 1997)
They have recently come up with a more politically correct version:
Abstract:
An update is provided on the Earth's global annual mean energy budget in the light of new observations and analyses. In 1997 Kiehl and Trenberth provided a review of past
such estimates and performed a number of radiative computations to better establish the role of clouds and various greenhouse gases in the overall radiative energy flows,
with top-of-atmosphere (TOA) values constrained by Earth Radiation Budget Experiment values form 1985 to 1989, when the TOA values were approximately in balance. The Clouds
and the Earth's Radiant Energy System (CERES) measurements from March 2000 to May 2004 are used to TOA but adjusted to an estimated imbalance from the enhanced
greenhouse effect of 0.9 W m-2. Revised estimates of surface turbulent fluxes are made based on various sources. The partitioning of solar radiation in the
atmosphere is based in part on the International Satellite Cloud Climatology Project (ISCCP) ISCCP-FD computations that utilize the global ISCCP cloud data every 3 hours,
and also accounts for increased atmospheric absorption by water vapor and aerosols. Surface upwards longwave radiation is adjusted to account for spatial and temporal
variability. A lack of closure in the energy balance at the surface is accommodated by making modest changes to surface fluxes, with the downward longwave radiation as the
main residual to ensure a balance. Values are also presented for the land and ocean domains that include a net transport of energy from ocean to land of 2.2 Petawatts (PW)
of which 3.2 PW is from moisture (latent energy) transport, while net dry static energy transport is from land to ocean. Evaluations of atmospheric reanalyses reveal
substantial biases. (em added)
Figure caption: The global annual mean Earth's energy budget for the March 2000 to May 2004 period in W m-2. The broad arrows indicate the schematic flow of energy in proportion to their importance.
Now, we understand their desire to "get with the program" and support their AGW colleagues' claims but we have a real problem with the emphasized portion. We showed you methods here for calculating atmospheric heating, to quote Dr. John Christy: "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 0.9 j/s/m2, then you can calculate the average rate of temperature change as 0.00000009 per second for the whole column.", which yields 0.00000009 x the number of seconds in a year, or a little over 2.8 °C warming per year.
So where is it? We know atmospheric temperatures have flatlined (or "plateaued" in the IPCC's preferred parlance) since 2001 and we know also that there has been no warming of the upper 700 meters of the oceans either. Are they trying to suggest less than 30% of the Earth's surface preferentially absorbed 100% of the planet's alleged radiative imbalance, sharing none with oceans or atmosphere (an atmosphere where enhanced greenhouse is actually supposed to manifest itself)?
Sorry, not buying it. There's a world of difference between not knowing how energy moves through the system and simply declaring a politically correct "imbalance" which can not in reality exist and when empirical measure demonstrates unequivocally that it is not functioning now or over at least half the period they studied.
Their adjustment of albedo from 31% down to 30.5 implied in the new paper simply don't appear justified, any more than their energy imbalance assumption.
As you saw in the form above, no one knows for sure exactly what temperature Earth "should be", all we have are a range of values according to assumptions made. Is the Earth currently "too warm" or is it simply adjusting to a previous equilibrium state following the Little Ice Age? We don't know -- and nor does anyone else.
Importantly, we haven't even agreed what we are trying to measure when we talk about surface air temperature:
Q&A with James Hansen: The Elusive Absolute Surface Air Temperature (SAT)
Q. What exactly do we mean by SAT ?
A. I doubt that there is a general agreement how to answer this question. Even at the same location, the temperature near the ground may be very different from the temperature 5 ft above the ground and different again from 10 ft or 50 ft above the ground. Particularly in the presence of vegetation (say in a rain forest), the temperature above the vegetation may be very different from the temperature below the top of the vegetation. A reasonable suggestion might be to use the average temperature of the first 50 ft of air either above ground or above the top of the vegetation. To measure SAT we have to agree on what it is and, as far as I know, no such standard has been suggested or generally adopted. Even if the 50 ft standard were adopted, I cannot imagine that a weather station would build a 50 ft stack of thermometers to be able to find the true SAT at its location.
Q. What do we mean by daily mean SAT ?
A. Again, there is no universally accepted correct answer. Should we note the temperature every 6 hours and report the mean, should we do it every 2 hours, hourly, have a machine record it every second, or simply take the average of the highest and lowest temperature of the day ? On some days the various methods may lead to drastically different results.
...
Q. If SATs cannot be measured, how are SAT maps created ?
A. This can only be done with the help of computer models, the same models that are used to create the daily weather forecasts. We may start out the model with the few observed data that are available and fill in the rest with guesses (also called extrapolations) and then let the model run long enough so that the initial guesses no longer matter, but not too long in order to avoid that the inaccuracies of the model become relevant. This may be done starting from conditions from many years, so that the average (called a 'climatology') hopefully represents a typical map for the particular month or day of the year.
Q. What do I do if I need absolute SATs, not anomalies ?
A. In 99.9% of the cases you'll find that anomalies are exactly what you need, not absolute temperatures. In the remaining cases, you have to pick one of the available climatologies and add the anomalies (with respect to the proper base period) to it. For the global mean, the most trusted models produce a value of roughly 14 Celsius, i.e. 57.2 F, but it may easily be anywhere between 56 and 58 F and regionally, let alone locally, the situation is even worse. (NASA's Goddard Institute for Space Studies)
Hansen is being disingenuous with his claims about models, to say the least. Irrespective of the model flavor used, from the most basic to the multipartite coupled models utilizing each other's output as dynamic input, all models are by necessity overly simplistic and inadequate to represent the chaotic, nonlinear coupled system we call climate. While the average of model representations of global climate suggests Earth's mean temperature is about 14 °C (287 K), the 16 most trusted and 'stable' models tested in the Coupled Model Intercomparison Project (CMIP) (see original .pdf) are not well able to reproduce this result.
This
graphic represents the unforced control runs for the "ensemble" (IPCC-speak for "haven't got a clue if any of these actually represent reality -- throw 'em
all together and say the errors average out"). The range starts out guessing mean Earth surface temperature as anything from 11.5 to 16.5 °C (roughly 285-290 K)
and ends -- without messing with carbon dioxide levels or anything else -- with the guesses even further apart. If they can't agree where they should start in a 5 °C
range how are they supposed to figure out trends an order of magnitude smaller?
Note also that several of these models produce at least as much warming as we think we have measured over the entire Twentieth Century absent any additional forcing whatsoever. Seven of the sixteen controls even suggest the world should be a little (or a lot) warmer than we believe it to be at present (how's that for "consensus"?).
Precipitation results for the various models are similarly erratic, signifying a huge problem in the way models handle the most important greenhouse gas: water vapor. At this time they appear more a disarray of models and we will not be paying attention to model "guesstimations" any time soon.
One thing is for sure: this whole "emergency" is predicated on a few guesses and no real knowledge. Do you really believe it is a good idea to radically change the global energy supply at great expense and certain interruption merely because some people made some scary guesses?
