Comment on "Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcing" by S. Lovejoy and C. Varotsos (2016)

Abstract. Lovejoy and Varotsos (2016) (L&V) 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 Goddard Institute for Space Studies (GISS) E2-R model. By using a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on timescales from 50 to 1000 years. Nonlinear response on shorter timescales 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 tests without this approximation which are not able to detect nonlinearity in the response, even without accounting for internal variability. We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. L&V's analysis of intermittencies is based on a mathematical result stating that the intermittencies of forcing and response are the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this result for these data. It is valid only for a power-law response function; it assumes power-law scaling of structure functions of forcing as well as temperature signal; and the internal variability, which is strong at least on the short timescales, will exert an influence on temperature intermittence which is independent of the forcing. We demonstrate by a synthetic example that the differences in intermittencies observed by L&V easily 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 detectable nonlinear response in the global temperature in these climate models.