Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcing

Researchers analyse the temperature response to solar, volcanic, and solar plus volcanic, forcing in the Zebiak-Cane (ZC) model, and to solar and solar plus volcanic forcing in the GISS-E2-R model. By a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on time scales from 50 to 1000 yr.

Nonlinear response on shorter time scales is claimed by analysis of intermittencies in the forcing and the temperature signal for both models. The analysis of additivity in the ZC model suffers from a confusing presentation of results based on an invalid approximation, and from ignoring the effect of internal variability. We present a test without this approximation which is not able to reject the linear response hypothesis, even without accounting for internal variability.

We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. The analysis of intermittencies is based on a mathematical corollary stating that the intermittencies of forcing and response is the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this corollary for these data. First, the corollary is valid only for a power-law response function. This implies a strong response on centennial time scales, which the authors claim does not take place in these models. Second, it assumes power-law scaling of structure functions of forcing as well as temperature signal, which is not the case for these data. And third, the internal variability, which is strong at least on the short time scales, will exert an influence temperature intermittence which is independent of the forcing.

We demonstrate by a synthetic example that the differences in intermittencies observed by L&Veasily can be accounted for by these effects under the assumption of a linear response. Our conclusion is that the analysis performed by L&V does not present valid evidence for a nonlinear response in the global temperature in these climate models.

[adapted from source]