Some skeptics have suggested that we are not entering a man-made period of global warming but instead are entering a mini ice age (as Earth has done many times before in its 4+ billion year history). Consider this simple block model of the conflicting possibilities:

In this model the calculated warm atmospheric temperatures are subject to a cooling feedback, the result of which is the predicted atmospheric temperature of Earth. Show that

in which G_p1 is the gain for global warming and G_p2 is the gain for global cooling. If K is defined as G_p2/G_p1, plot the Earth’s predicted atmospheric temperature from the years 2000 to 2050 for 

(a) K = 1.001,

(b) K = 1.000, 

(c) K = 0.999.

Assume G_p1 = 0.50012 as in Example 10.6.

Tatm + TCale Tcalc Tatm T alc=Gp1(Tcalc + Tatm) Tcale Tcalc TCalc + TGlobal warming TGlobal warming T Global warming = G,2 (Tcalc+ TGlobal warming I Global warming