THE TEMPERATURE FEEDBACK PROBLEM.

In the past 810 ka, inferred variability of absolute temperature has barely exceeded ±3 K, or ±1 % of the period mean. This thermostatic behavior seems inconsistent with a feedback sum f_t = (Σ_if_t,i) ⪢ 0 over any term of years t. In electronic circuits, as the loop gain g_t exceeds 1, the Bode system-gain relation G_t = (1 -g_t)^-1 models the abrupt transition of the output voltage from V_t → + ∞ to - ∞ ← V_t(G_t,V_t being momentarily undefined at the singularity, where g_t = 1). Yet in the climate, where g_t might plausibly exceed unity owing to, say. the near-exponential Clausius-CIapeyron increase in the water-vapor carrying capacity of the atmospheric space as it warms, +Δf_t⇒ +ΔT_t ⇒ - ΔT_t for all f_t 0. In this and several other material respects the Bode relation, which as clearly specifies a negative dynamical-system response to g_t > 1 as a positive response to g_t < 1, seems inapplicable to the climate. In general-circulation models, the equilibrium system gain G_∞ = (1 -g_∞)^-1=(1-λ₀f_∞)^-1, where λ₀ is the Planck parameter, doubles or triples a direct warming. But if Bode is inapplicable to the climate, what is the appropriate relation between loop gain g_t and system gain G_t, and thus between instantaneous (ΔT₀), transient (ΔT_t), and equilibrium (ΔT_∞) climate sensitivity? What representation of system gain in the climate should replace the inapplicable Bode relation? [ABSTRACT FROM AUTHOR]