Global temperature shows signs of accelerating. Here I use a simple model of the atmosphere to explore the reason. Assume an earth modeled by a spherical shell, very well insulated on the inner surface, so that its temperature is only determined by the radiant energy entering and leaving its outer surface. A change in temperature of the shell will be proportional to the cumulative change in energy.
ASR is absorbed solar radiation and ETR is emitted thermal radiation. These fluxes have been measured by the NASA CERES program since 2000. The following graph shows the 12-month running average of the energy imbalance (ASR – ETR) by year.
The cumulative energy is the integral of this curve shown in the following graph.
Note that the cumulative energy seems to have a quadratic dependence with time. It is accelerating. As shown in the next graph a plot of the 12-month running average of 2m mean global temperature versus the corresponding cumulative energy shows a reasonable straight-line dependence.
In fact, the least square fit of global temperature with cumulative energy had a smaller standard deviation (0.095) than either a straight line fit of temperature by year (0.101) or a quadratic fit (0.0964).
The next graph shows global temperature and the fit of global temperature with cumulative energy (blue line). The lavender lines show quadratic and straight-line extensions of global temperature. Note that the quadratic extension is essentially the same 2nd order polynomial line as the line of cumulative energy. A green line shows a rise to an equilibrium temperature if albedo and emissivity were to remain constant. Right now, that equilibrium temperature would be slightly above the 1.5-degree Paris goal.
Global temperature is accelerating at a quadratic rate because the earth’s cumulative energy imbalance is increasing at a quadratic rate. In previous posts I showed that the effect of albedo decrease has slightly exceeded the effect of greenhouse gases on emissivity since 2000. Whether linear or quadratic, global temperature is heading toward 2°C above preindustrial levels between 2035 and 2060
hswildman 