Stochastic and scaling climate sensitivities: Solar, volcanic and orbital forcings

Climate sensitivity (λ) is usually defined as a deterministic quantity relating climate forcings and responses. While this may be appropriate for evaluating the outputs of (deterministic) GCM's it is problematic for estimating sensitivities from empirical data. We introduce a stochastic definition where it is only a statistical link between the forcing and response, an upper bound on the deterministic sensitivities. Over the range ≈30 yrs to 100 kyrs we estimate this λusing temperature data from instruments, reanalyses, multiproxies and paleo spources; the forcings include several solar, volcanic and orbital series. With the exception of the latter ‐ we find thatλ is roughly a scaling function of resolution Δt: λ ≈ with exponent 0 ≈ < Hλ ≈ < 0.7. Since most have Hλ > 0, the implied feedbacks must generally increase with scale and this may be difficult to achieve with existing GCM's.