V. MODEL Quantitative calculation is precluded by the complexity of the climate system. These complexities includ processes that are difficult to calculate but understood in principle (such as opacity resulting from a dense comb of infrared vibration-rotation lines) and those not understood (such as cloud formation and greenhouse gas exchange with the ocean, soil and biosphere). Even the most elaborate and sophisticated general circulation models (GCM) contain many uncertain parameters that can only be calibrated at a single measured point: today’s climate. It is not surprising that different GCM disagree in the magnitude of the effect of GHG emission, and it is not evident how to resolve these disagreements. Disagreements among the best state-of-the-art GCM suggest considering the opposite approach, a model na¨ıve almost to the point of triviality. If its workings are transparent, it may provide useful insight, even though it cannot make quantitative predictions. Consider a surface heat reservoir warmed by sunlight with a mean (diurnally and annually averaged) intensity P ⊙ and cooled by black body radiative emission with a (Planck weighted) fraction f$_{b}$ ( T ) of the infrared spectrum blocked by lines of Lorentzian lineshape 9 (Doppler broadening of molecular lines is negligible at atmospheric temperatures). The optical depth at the centers of strong lines τ 0 ≫ 1, and assume an underlying heat capacity (per unit area) C$_{p}$ . The temperature T of the thermal reservoir changes at a rate where σ$_{SB}$ is the Stefan-Boltzmann constant and we approximate the line profile as com- pletely opaque within a blocked fraction f$_{b}$ ( T ) of the spectrum, and completely transparent outside it. C$_{p}$ dT dt = P ⊙ − σ$_{SB}$T $^{4}$(1 − f$_{b}$ ( T )) , (1) 0 = P ⊙ − σ$_{SB}$T 4 0 (1 − f$_{b}$ ( T 0 )) . (2) T = T 0 + δT. (3) We suppose an initial equilibrium temperature T 0 defined by the heat balance condition: Small deviations of temperature are described by 4