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

Climate sensitivity (lambda) 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 approximate to 30 yrs to 100 kyrs we estimate this lambda using 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 that lambda is roughly a scaling function of resolution Delta t: lambda approximate to Delta t(H lambda), with exponent 0 approximate to < H-lambda approximate to < 0.7. Since most have H-lambda > 0, the implied feedbacks must generally increase with scale and this may be difficult to achieve with existing GCM's. Citation: Lovejoy, S., and D. Schertzer (2012), Stochastic and scaling climate sensitivities: Solar, volcanic and orbital forcings, Geophys. Res. Lett., 39, L11702, doi:10.1029/2012GL051871.