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Calculate Earth's Expected Surface Temperature
MAY 20, 2008
Expanded May 24, 2008

Unless you have been sealed in a bomb shelter since 1987 you will no doubt have heard about global warming. Sometimes this is embellished with modifiers like "catastrophic" and it is given many names, e.g. "climate change" or "climate interference" but almost never do you hear warming relative to what?

According to Hansen: 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.

NCDC suggest using the mean 1901-2000 of 13.9 °C, both then suggest we should add the anomaly to derive the current mean temperature.

The "trusted model" and 20th Century means, however, are not identical with calculated expected values (or each other, for that matter). Moreover, estimates of Earth's mean temperature change through the year due to continental configuration:

NCDC's Revised Monthly Averages 1961-1990 (°C)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
12.0 12.1 12.7 13.7 14.8 15.5 15.8 15.6 15.0 14.0 12.9 12.2

Note that only annual estimated anomalies and annual means are suggested by these groups for deriving estimated Earth temperature.

To help you get some point of reference we have run up a little global energy balance model with just 3 adjustable parameters (marked (o) to signify "tweakable dials"). The defaults are best-guess current values but allow considerable adjustment with TOA W/m2 valid from 1350-1380, albedo from 20-40% Incoming Solar Radiation and GHE 20-60% of Outgoing Longwave Radiation.

Don't get too excited about calculating Earth's precise mean temperature since radiative balance has yet to measured within a precision of ± ~2 Watts per meter squared and calculations in IPCC's AR4 WG1 are internally inconsistent. Estimated albedo could easily be out by 1-2% and "greenhouse effect" is a rubbery figure used to adjust expected near-blackbody temperature to what we think we have measured.

See, you haven't performed a single calculation yet and already you have an idea why we are unimpressed by claims of n thousandths of one degree warming in any given year.

As you test the effect of minor assumption changes on the expected temperature of the planet give some thought to claims of reconstructing the Earth's temperature within 0.5 K precision over the last 500 or 1,000 years.

The bottom line is that we do not know what the planet's current temperature is, although satellite-mounted instruments and Argo autonomous floats are giving us a better picture than we had before.

We do not know what the planet's temperature was 100 years ago with any meaningful precision.

We have no way of telling whether Earth will be warmer or cooler at the beginning of Solar Cycle 25 (SC24 is just sputtering to a start now and it is reasonable to guess Earth will be slightly warmer in the midst of the roughly 11 year cycle, although there is no guarantee).

Feel free to play with the planet's temperature by adjusting the parameters in our little global energy balance model form below. There are some suggested hypothesis tests below the form.

Incoming solar radiation at top of atmosphere (W/m2) (o)
Albedo (proportion solar radiation reflected) (o)
Greenhouse effect (proportion OLR returned to Earth) (o)
Resulting mean global surface temperature (K)
Resulting mean global surface temperature (C)
Resulting mean global surface temperature (F)

So, what value is a simple model like this? After all, GCMs have dozens, hundreds of tweakable parameters so what is the value of this simplistic thing? Actually, its very simplicity is part of its value. You will note when adjusting the available parameters you can happily freeze or cook the planet without need of a multitude of knobs to twist (just drop planetary albedo to 0.2 (20%) to turn the whole planet tropical, increase it to 0.4 (40%) to create an ice age).

Fair enough, what hypotheses can we test? Try this one for a start:

According to the Solar Irradiance Reconstruction of Lean et al, 2000, TOA TSI fell to about 1363.5 W/m2 from the 1650s through 1690s. Was this change sufficient to cool the globe and cause the Little Ice Age? Not according to our little energy balance calculator.

Now, if the reduction in TSI is insufficient, what could have caused the LIA? It is possible Svensmark provides the answer. along with reduced solar warming a slight increase in bright cloud and albedo acts as a multiplier effect, allowing more persistence of snowfields further increasing albedo and so on. Try adding just 0.5% albedo (.315) from increased cloud and snowfield persistence (a trivial amount given estimates of albedo could easily be out by a percent or two).

Interesting result, isn't it? That's about what the IPCC guesstimate is for net change in mean temperature since, oh, about 1750. Certainly supports the contention TSI is far from the whole story in solar climate coupling.

Consider also such cooling would reduce ocean outgassing, increase ice cover to further reduce atmospheric transfer and suppress biological methane production and so natural greenhouse effect might also drop a few 10ths of a percent (suddenly it's easy to chill the planet, isn't it?).

OK, by twiddling a few knobs we managed to recreate the LIA. What else can we test? How about this:

There are claims carbon dioxide is responsible for 35%[!] of the global greenhouse effect (therefore returning 13.9% OLR to Earth). Carbon dioxide is believed to have increased from 280 to 385ppmv (37.5%) since the Industrial Revolution. All things being equal that should add 4.9% to net greenhouse effect, right? Except making greenhouse .446 and leaving the rest of the values at default says the earth should have warmed to 294.32 K (21.17 °C).

Best guesses from NCDC and GISTEMP put the 2007 planetary mean temperature around 287.6/7 K or about 14.5 °C.

A quick test of CO2's effect suggests 35% GHE overstates estimated warming by a factor of at least 7 and that S.M. Freidenreich and V. Ramaswamy, “Solar Radiation Absorption by Carbon Dioxide, Overlap with Water, and a Parameterization for General Circulation Models,” Journal of Geophysical Research 98 (1993):7255-7264 were likely pretty close to the mark when stating "Given the present composition of the atmosphere, the contribution to the total heating rate in the troposphere is around 5 percent from carbon dioxide and around 95 percent from water vapor."

Of course, even at 5% of the 39.7% returned OLR, increased as it has since the IR, would make net greenhouse 40.4% (if linearly accumulative) and make the planet's temperature higher than it has. Guess that must be that darn logarithmic effect thing meaning increases in atmospheric carbon dioxide do, well, next to nothing as far as planetary temperature goes.

Now, albedo is a fascinating and largely overlooked factor in planetary temperature, notice how small adjustments in that parameter make startling differences in global mean temperature. You will find a response even tweaking 0.01% (0.0001). We know that current albedo estimations could be out by a percent or two and we know Svensmark et al came up with a lab demonstration of a mechanism for solar effects being greatly amplified through GCR manipulation of low, bright cloud development and low, bright clouds have significant effect on albedo. What we don't have evidence of is atmospheric carbon dioxide having a particularly strong influence on global planetary mean temperature. In fact, calculated 'expected' global mean temperatures are higher than current estimated planetary means so we can't be sure the planet is actually warm (it could actually be "global less colding").

Nonetheless, our simple model is here for you to play with. Feel free to send us any hypotheses you test with it that you feel return interesting results.

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