Power-law behavior in millennium climate simulations

Using a method of discrete Fourier transform with varying starting point and length of time window and the long time series provided by millennium Earth System Model simulations, we get good fits to power laws between two characteristic oscillatory timescales of the model climate: multidecadal (50–80 yr) and El Nino (3–6 yr) timescales. For global mean temperature, we fit β ~ 0.35 in a relation S(f) ~ f β in a simulation without external climate forcing and β over 0.7 in a simulation with external forcing included. We also fit a power law with β ~ 8 to the narrow frequency range between El Nino frequencies and the Nyquist frequency. Regional variability in best-fit β is explored and the impact of choosing the frequency range on the result is illustrated. When all resolved frequencies are used, land areas seem to have lower βs than ocean areas on average, but when fits are restricted to frequencies below 1/(6 yr), this difference disappears, while regional differences still remain. Results compare well with measurements both for global mean temperature and for the Central England temperature record.