In our weblog A Serious Problem With The Use Of A Global Average Surface Temperature Anomaly To Diagnose Global Warming - Part I
under the header
“Definition of a Global Average Surface Temperature”
it is written that
“The definition of the global average surface temperature used by the IPCC and others can be expressed as
dH/dt = f -T’/λ
where H is the heat content of the land-ocean-atmosphere system, f is the radiative forcing (i.e. the radiative imbalance), T’ is the change global average surface temperature in response to the change in H, and λ is called the “climate feedback” parameter which defines the rate at which the climate system returns forcing to space as infrared radiation and/or as changes in reflected solar radiation (such as from changes in clouds, sea ice, snow, vegetation, etc).”
One of our conclusions is
“In constructing a global average of T’, its spatial distribution matters since T’ in regions with a baseline colder temperature have a significantly smaller effect on the return of heat energy to space (through infrared emission) than regions with a warmer baseline temperature.”
This weblog follows up on this subject to illustrate why this matters. First, the equation given above for dH/dt is actually only accurate for a homogeneous body which has a uniform temperature. With the Earth, this is obviously not true. Indeed, it is easy to show this.
As an example, assume a region of the Earth with a base temperature of 270K and another region with a base temperature of 300K. The difference in the outgoing long wave radiation (assuming blackbody behavior where the emission is proportional to T**4) results in a 34% greater emission from the warmer location. Adding a temperature increase of 1K to each location results in a 38% greater change when this increase is applied to the warmer temperature (i.e. comparing the difference between the incremental change in outgoing long wave radiation at the cold and warm locations).
Thus, by constructing a global average value of T’ in the equation for dH/dt introduces a significant error in diagnosing the actual global radiative imbalance. A 1C increase in surface temperature in the higher latitudes has less of an effect on the outgoing long wave radiation than a 1C increase in the tropics. This also means that using the mean daily temperature over land, rather than a diurnal cycle where the long wave emission from the surface is substantially larger at the time of maximum daily temperature, introduces yet another error.
Thus when the science assessments and policymakers claim we need to keep the global average temperature change below some threshold (e.g. 2K), they should be questioned on how this number is constructed both in the observations and in the models.