Using Scaling to Understand, Model and Predict Global Scale Anthropogenic and Natural Climate Change

The atmosphere is variable over twenty orders of magnitude in time (≈10^-3 to 10¹⁷ s) and almost all of the variance is in the spectral “background” which we show can be divided into five scaling regimes: weather, macroweather, climate, macroclimate and megaclimate. We illustrate this with instrumental and paleo data. Based the signs of the fluctuation exponent H, we argue that while the weather is “what you get” (H>0: fluctuations increasing with scale), that it is macroweather (H<0: fluctuations decreasing with scale) – not climate – “that you expect”. The conventional framework that treats the background as close to white noise and focuses on quasi-periodic variability assumes a spectrum that is in error by a factor of a quadrillion (≈ 10¹⁵).

Using this scaling framework, we can quantify the natural variability, distinguish it from anthropogenic variability, test various statistical hypotheses and make stochastic climate forecasts. For example, we estimate the probability that the warming is simply a giant century long natural fluctuation is less than 1%, most likely less than 0.1% and estimate return periods for natural warming events of different strengths and durations, including the slow down (“pause”) in the warming since 1998. The return period for the pause was found to be 20-50 years i.e. not very unusual; however it immediately follows a 6 year “pre-pause” warming event of almost the same magnitude with a similar return period (30 - 40 years).

To improve on these unconditional estimates, we can use scaling models to exploit the long range memory of the climate process to make accurate stochastic forecasts of the climate including the pause. We illustrate stochastic forecasts on monthly and annual scale series of global and northern hemisphere surface temperatures. We obtain forecast skill nearly as high as the theoretical (scaling) predictability limits allow: for example, using hindcasts we find that at 10 year forecast horizons we can still explain ≈ 15% of the anomaly variance. These scaling hindcasts have comparable – or smaller - RMS errors than existing GCM’s. We discuss how these be further improved by going beyond time series forecasts to space-time.