First, returning to the results of my previous post, Spencer's model reduces to Eq. 18:
(18) T(t) = Te + A0e-t/τ + β Q(t)/c h
(see the previous post for definitions). Note that since c h/α = τ the factor multiplying Q(t) can also be written as β/τ α. The convoluted PDO index (PDOI) function, Q(t), is defined as (see eq. 16):
(19) Q(t) = ∫-∞t PDOI(s) e- (t - s)/τ ds
and note that it depends on the PDO index going back in time (to negative infinity in the integral) - though values from more than a few multiples of the time constant τ in the past contribute only a minuscule amount to the total. Spencer seems to have used a particular source for the PDO index (downloadable here) which begins in 1900, so at least for the first few decades of the 20th century Q(t) is missing important information about pre-1900 index values
And on and on it goes. Finally reaching the rather ho hum proof that;
It turns out you need to set the starting temperature to negative six trillion degrees in 993, in order to match Spencer's model for the 20th century. 6 trillion degrees. Wow. Now that's global warming!Of course no where does Smith explain why -6 trillion degrees could not be the real world starting point. Show me one peer-reviewed study that categorically rules this out.
(thanks to reader Professor Bob)