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

Abstract. (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.

Probing the timescale dependency of local and global variations in surface air temperature from climate simulations and reconstructions of the last millennia

“…Our analysis of the spectral gain was limited to global average values and those timescales where linearity can be reasonably assumed [39,40,100]. Nonlinearities are inherent to the climate system, for example, due to the temperature-albedo feedback.…”

“…Mean spectra were calculated by interpolation to the lowest resolution, binning into equally spaced log-frequency intervals, and taking the average with equal weights [23]. This requires the statistical independence of the averaged values [40]. The spectral exponent β is calculated by linear regression to the logarithm of (1) on periods between τ 1 = 10 and τ 2 = 200 years.…”

“…where additivity is a valid assumption and nonlinearities in the global mean temperature are sufficiently small [39,40]. The main practical problem that confronts us is that the gain might be subject to a sampling bias due to our data sets choice.…”

“…Moreover, the differentiation between forced and unforced changes poses a challenge to understanding temperature variability [36,37]. Beyond the analysis of Haar fluctuations of a few forcing reconstructions [38][39][40], spectral analysis of climatic drivers and their frequencydependent linkage to the temperature response remains incomplete.…”

The Structure of Climate Variability Across Scales

“…Scaling of paleo-climate data has received a lot of attention (e.g., Bunde et al, 2014;Huybers & Curry, 2006;Laepple & Huybers, 2013;Lovejoy & Schertzer, 2013;Lovejoy & Varotsos, 2016;Nilsen et al, 2016;Rypdal & Rypdal, 2016a;Schmitt et al, 1995;Zhu et al, 2019) and has been used in evaluating how well climate models reproduce observed long-term climate variability (Blender et al, 2006;Østvand et al, 2014). While global mean temperature variability on interannual to millennial time scales seems to be consistent between climate models and climate reconstructions, the strong discrepancy of slow climate variability at regional scales calls for continued research on the temporal and spatial structures of climate variability and also on improving the interpretation and quality of paleo-climate records.…”