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Are we really sure the world is too warm?
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.
  • Eventually its temperature was determined to be 5,770 Kelvins (6,000 C or 11,000 F). [!] (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.)
  • Effective temperature: 5,778 K

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 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."

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 have seen these types of forms here before so you can play to your heart's content deriving "expected" temperatures for planet Earth and since no one knows what it "should be" for sure 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.

Sun temperature in kelvin (o)
Resulting solar "constant" (W/m2)
Resulting mean global surface temperature (K) without albedo or greenhouse
Resulting mean global surface temperature (C) without albedo or greenhouse
Resulting mean global surface temperature (F) without albedo or greenhouse



Albedo (proportion solar radiation reflected) (o)
Resulting mean global surface temperature (K) with albedo but no greenhouse
Resulting mean global surface temperature (C) with albedo but no greenhouse
Resulting mean global surface temperature (F) with albedo but no greenhouse



Greenhouse effect (proportion OLR returned to Earth) (o)
Resulting mean global surface temperature (K) with albedo and greenhouse
Resulting mean global surface temperature (C) with albedo and greenhouse
Resulting mean global surface temperature (F) with albedo and greenhouse

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:

Trenberth, K. E., J. T. Fasullo, and J. Kiehl, 2008: Earth's global energy budget. Bull. Amer. Meteor. Soc., in press.

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.

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?

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