Anthony Watts alerted me to this paper
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.
This is another contribution which documents shortcomings in the ability of multi-decadal global climate models to simulate the real climate. Global climate model projections neglect important low frequency natural climate effects on time scales of decades and longer according to this paper.
The abstract reads [highlight added]
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 λ 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 λ is roughly a scaling function of resolution Δt: λ ≈ ΔtHλ, with exponent 0 ≈ < Hλ ≈ 0, the implied feedbacks must generally increase with scale and this may be difficult to achieve with existing GCM’s.
The conclusions read
After decreasing over several decades of scale, to a minimum of ≈ +/-0.1 K at around 10–100 yrs, temperature fluctuations begin to increase, ultimately reaching +/-3 to +/-5 K at glacial-interglacial scales. In order to understand the origin of this multidecadal, multicentennial and multimillenial variability, we empirically estimated the climate sensitivities of solar and volcanic forcings using several reconstructions. To make this practical, we introduced a stochastic definition of the sensitivity which could be regarded as an upper bound on the usual (deterministic) sensitivity with the two being equal in the case of full (and causal) correlation between the temperature and driver. Although the RMS temperature fluctuations increased with scale, the RMS volcanic and 10Be based solar reconstructions all decreased with scale, in roughly a power law manner. If any of these reconstructions represented dominant forcings, the corresponding feedbacks would have to increase strongly with scale (with exponent Hλ ≈ 0.7), and this is not trivially compatible with existing GCM’s. Only the sunspot based solar reconstructions were consistent with scale independent sensitivities (Hλ ≈ 0), these are of the order 4.5 K/(W per meter squared) (i.e., implying large feedbacks) and would require quite strong solar forcings of ≈1 W per meter squared at scales of 10 kyrs.
A recent analysis of S2Δt1/2 for forced GCM outputs over the past millennium S. Lovejoy et al. (Do GCM’s predict the climate…. Or low frequency weather?, submitted to Nature Climate Change, 2012) showed that they strongly underestimate the low frequency variability – even when for example strong solar forcings were used. Our findings here of the occasionally surprising scale-by-scale forcing variabilities helps explain why they were too weak. It seems likely that GCM’s are a missing an important mechanism of internal variability. A possible “slow dynamics” candidate is land-ice whose fluctuations are plausibly scaling over the appropriate ranges of space-time scales but which is not yet integrated into existing GCM’s.