Temperature Sensitivity of a Basic Climate Model

We use a simple climate model to assess climate sensitivity as temperature response to heat forcing. How wonderful that we have met with a paradox. Now we have some hope of making progress. (Nils Bohr) Some aspects of climate have not been observed to change. (IPCC Summary for Policymakers 2007) 1 IPCC Climate Sensitivity and Global Warming Climate science as presented by IPCC [2] is based on a postulate of basic climate sensitivity or global warming, without feed back, of about 1 degree Celsius C upon doubling of the concentration of CO2 in the atmosphere corresponding to a 1% perturbation of heat forcing, as a consequence of Stefan-Boltzmann’s Black Body Radiation Law. In this note we argue that the postulate is based on a fundamentally incorrect application of Stefan-Boltzmann’s Radiation Law. We present a model study showing that basic climate sensitivity (without feed back) can be estimated to instead 0.15 C, in accordance to Fourier’s Law. We start with the model and then show in what sense the application of the Radiation Law is incorrect. The basic physics of global warming is presented by IPCC as follows [2]: • The Sun powers Earths climate, radiating energy at very short wavelengths, predominately in the visible or near-visible (e.g., ultraviolet) part of the spectrum. Roughly one-third of the solar energy that reaches the top of Earths atmosphere is reflected directly back to space. The remaining two-thirds is absorbed by the surface and, to a lesser extent, by the atmosphere. To balance the absorbed incoming energy, the Earth must, on average, radiate the same amount of energy back to space. Because the Earth is much colder than the Sun, it radiates at much longer wavelengths, primarily in the infrared part of the spectrum. Much of this thermal radiation emitted by the land and ocean is absorbed by the atmosphere, including clouds, and reradiated back to Earth. This is called the greenhouse effect. Computer Science and Communication, KTH, SE-10044 Stockholm, Sweden.