Huang Transform: A Method for Quantifying Nonlinear Interactions in Climate Variability and Change

The invention and usage of trigonometric functions may be traced back to the Hellenistic mathematicians such as Euclid and Archimedes. Many fundamental methods of analysis use trigonometric functions to describe and understand cyclical phenomena. It was Fourier in early 19^th century who pioneered the additive usage of trigonometric functions and first expressed various types of functions in terms of the sum of trigonometric functions of different periods/scales, which is now called Fourier transform. Unfortunately, Fourier’s sum cannot effectively express nonlinear interactions between trigonometric components of different periods, and thereby lacking the capability of quantifying nonlinear interactions in any dynamical system, such as the climate system.

In this talk, a new perspective of using trigonometric functions in quantifying nonlinear interaction is introduced. This perspective was pioneered by Norden Huang and emphasizes the multiplicative usage of trigonometric functions in solving problems. The most recent method resulting from this new perspective is Holo-spectrum, a multi-dimensional spectral expression of a time series that explicitly identifies the interactions among different scales and quantifies nonlinear interactions hidden in a time series.

Various enlightening applications of Holo-spectrum analysis, also called Huang transform, in climate studies will also be discussed. As an atmospheric/climate dynamicist and a data analysis method developer who has sided with Norden Huang in their struggles for novel analysis methods in the last fifteen years, the speaker strong believe the Huang transform will help greatly in understanding the complicated climate system.