Articles | Volume 7, issue 3
Earth Syst. Dynam., 7, 597–609, 2016
Earth Syst. Dynam., 7, 597–609, 2016

Peer-reviewed comment 13 Jul 2016

Peer-reviewed comment | 13 Jul 2016

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

Kristoffer Rypdal and Martin Rypdal Kristoffer Rypdal and Martin Rypdal
  • Department of Mathematics and Statistics, UiT The Arctic University of Norway, Tromsø, Norway

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.

Short summary
This comment on the paper by Lovejoy and Varotsos demonstrates that their methods for establishing nonlinearity in the global temperature response in climate models are flawed. One of their methods is based on an invalid approximation, which when corrected does not falsify the hypothesis that the response is linear. This conclusion is enforced when internal variability in the models are accounted for. The other results in their paper are also shown to be reproduced by linear-response models.
Final-revised paper