New paper finds climate change is explained by...fractals

A Mandelbrot multifractal which sorta kinda looks like the blade of a hockey stick, followed by a "pause"

A paper published today in Theoretical and Applied Climatology finds the global monthly temperature anomalies over the past 162 years from 1850-2012 are "surprisingly" "well-described" by a simple mathematical model of fractals with multiple exponents, so-called "multifractals." Multifractals can be used describe complex nonlinear phenomena in the real world, including chaos:

"A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed.^[1] 

Multifractal systems are common in nature, especially geophysics. They include fully developed turbulence, stock market time series, real world scenes, the Sun’s magnetic field time series, heartbeat dynamics, human gait, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed, to mathematical convergence effects related to the central limit theoremthat have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models^[2] as well as the geometric Tweedie models.^[3] The first convergence effect yields monofractal sequences and the second convergence effect is responsible for variation in the fractal dimension of the monofractal sequences.^[4] 

From a practical perspective, multifractal analysis uses the mathematical basis of multifractal theory to investigate datasets, often in conjunction with other methods of fractal analysis and lacunarity analysis. The technique entails distorting datasets extracted from patterns to generate multifractal spectra that illustrate how scaling varies over the dataset. The techniques of multifractal analysis have been applied in a variety of practical situations such as predicting earthquakes and interpreting medical images."

According to the IPCC, only man-made CO2 can possibly explain the global temperature record since 1950. However, IPCC models are unable to model natural variability including ocean oscillations, solar amplification mechanisms, and internal variability, and thus these factors cannot be excluded as possible causes. The fractal model as described in this study might be a potential way to model natural internal variability of the climate system, and suggests that internal variability alone could account for climate change since 1850, without any contribution from man-made CO2. 

Could multifractals be another cause for the "pause?"

Multifractal characterization of global temperature anomalies

• Provash Mali
• 
  

The global monthly temperature anomaly time series for the period 1850–2012 has been investigated in terms of multifractal detrended fluctuation analysis (MF-DFA). Various multifractal observables, such as the generalized Hurst exponent, the multifractal exponent, and the singularity spectrum, are extracted and are fitted to a generalized binomial multifractal model consists of only two free parameters. The results of this analysis give a clear indication of the presence of long-term memory in the global temperature anomaly time series which causes multifractal pattern in the data. We investigate the possible other source(s) of multifractality in the series by random shuffling as well as by surrogating the original series and find that the probability density function also contributes to the observed multifractal pattern along with the long-memory effect. Surprisingly, the temperature anomaly time series are well described by the two-parameter multifractal binomial model.