Although the physics of global warming is complex, the basic mechanism for global warming from anthropogenic greenhouse gases can be explained in relatively simple terms. Sunlight (primarily short-wavelength light) warms the Earth. The warm Earth’s surface then radiates its heat in the form of long-wavelength infrared (IR) light to the sky. Although most short-wavelength sunlight passes through greenhouse gases in the upper atmosphere unattenuated, much of the long-wavelength IR radiation is absorbed by greenhouse gases. Greenhouse gas IR light absorption prevents emission to space from the lower, warmer regions of the atmosphere; hence, IR radiation must be emitted from the colder upper atmosphere, where IR emission is less efficient. Consequently, the atmosphere and the Earth’s surface heats up until the upper atmosphere temperature increase is sufficient to restore the energy balance by IR emission to space.

A very simple model is provided by Hansen et al

for predicting the Earth surface temperature. The model predicts surface temperature Ts from the effective surface temperature Te (the temperature without greenhouse gas effects), the mean altitude for radiative emission to space H, and the atmospheric mean lapse rate G. The mean lapse rate is the temperature gradient between Earth's surface and the mean radiating level; i.e.,

Ts=Te+GH,

where Te = 255 K, G = 5.5 K/km, and H = 6 km. Using this simple model the predicted Earth average surface temperature is 288 K (15 °C), in agreement with Earth's observed temperature. The authors point out that the increased opacity due to increasing CO₂ results in a higher effective elevation for emission to space. Doubling the atmospheric concentration of carbon dioxide results in an increase in the effective emission height of 200 m. Thus, assuming a linear relationship, the change in elevation in km is given by (0.2)Cc/100, where Cc is the change in atmospheric carbon dioxide in percent. Furthermore, the authors calculate the effect of feedback mechanisms due to increased water vapor in the atmosphere, changes in lapse rate, decreased albedo, and changes in cloud cover and cloud height. The net effect of these feedback mechanisms is to increase the temperature change due to carbon dioxide by a factor of f = 2.5. Combining these observations, we can obtain the approximate effect of CO₂ increase on Earth's average surface temperature; i.e.,

Temperature increase (°C) = (f) G (Cc)(0.2)/100 = 2.75 Cc/100

The estimated effect of carbon dioxide emission on Earth's average temperature is shown in the plot below as a function of percent increase in carbon dioxide emission. The prediction is given with and without feedback effects. Observe that the predicted temperature increase for a 35% increase in CO₂ is about 1 °C, in agreement with observation.

The figure below, based on Meehl et al. (2004), compares the global average temperature change predicted by a mathematical models (the DOE PCM [1]) with the observed temperature change [2] from 1900 through 1990. The figure also shows the effect of the five principal forcing factors; i.e., anthropogenic greenhouse gases, solar variability, ozone changes, anthropogenic sulfate emissions, and volcanic emissions. Anthropogenic greenhouse gases are seen to have a domonant effect, although solar variations and ozone changes also contribute to temperature increases. Volcanic emissions and anthropogenic sulfate emissions have a cooling effect. Thus, global temperatures from greenhouse gas emissions would be higher than observed if these cooling effects were not present.

The generally good agreement between the model predictions and the observed temperature changes support the conclusion that anthropogenic greenhouse gas emissions are the principal cause of global warming. A recent IPCC report (Summary for Policy Makers)

has provided additional model comparisons with observations, as shown in the figure below. The continent-by-continent agreement of model predictions with observed temperature changes provides further support for the validity of the predictive models. Model predictions agree with observed temperatures only when anthropogenic effects are included.

References
1. Meehl, G.A., W.M. Washington, C.A. Ammann, J.M. Arblaster, T.M.L. Wigleym and C. Tebaldi (2004). "Combinations of Natural and Anthropogenic Forcings in Twentieth-Century Climate". Journal of Climate 17: 3721-3727.
2. Jones, P.D. and Moberg, A. (2003). "Hemispheric and large-scale surface air temperature variations: An extensive revision and an update to 2001". Journal of Climate 16: 206-2

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