Understanding and modeling the scaling spectrum of climate

Modeling climate dynamics in a comprehensive way and improving its predictability in a warming world requires a better understanding of climate variability across scales. However, fundamental mechanisms governing variability on long timescales are still poorly understood.
The temporal evolution of climate can be inferred from paleoclimate records, such as ice cores or marine sediments. Power spectra serve to quantify changes of variability over time and to identify timescales associated with periodic or quasi-periodic processes. The spectra of surface temperature not only comprise spectral peaks, but also reveal a continuous part. It was shown that the background continuum exhibits a scale break, following different power-laws on monthly to decadal versus millennial to longer periods. It is yet mostly unexplained, how these power-laws arise and whether a coupling between different timescales can be deduced from it. We study these questions by comparing and applying spectral analyses to paleoclimate records and climate model simulations for the Quaternary. The data is used to reconstruct the temperature spectrum on diurnal to astronomical timescales. We extend previous studies by including climate responses, such as δ¹⁸O and temperature records, and climate forcings, for example, insolation and volcanic forcing. The emergence of scaling in temperature variability is analyzed by successively accessing the background continuum. Higher order spectra test for correlations between forcings and responses. In particular, the bispectrum and bicoherence is computed for statistical processes and evaluated for temperature records in order to study whether the scaling properties are related to energy transfers between different states in time. We elaborate the potential of these methods to reveal dynamical processes governing the continuous spectrum of surface temperature.