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Simple models for Earth's climate sensitivity (i.e. its temperature response to radiative forcing) are developed by combining the time-tested idealization of one-dimensional radiative-convective equilibrium (RCE) with simple yet quantitatively reasonable models for CO2 forcing and the water vapor feedback. Along the way, we introduce key paradigms including the emission level approximation, the forcing-feedback decomposition of climate sensitivity, and “Simpson's law” for water vapor thermal emission. We also discuss climate feedbacks unaccounted for in this RCE framework, as well as differing variants of climate sensitivity, all of which may be ripe for their own chalkboard treatments.
Nadir Jeevanjee (Wed,) studied this question.