In 2009, Professor Zhaohua Wu and his collaborator, Dr. Norden Huang—then a NASA scientist—published a groundbreaking paper titled “Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method” as the inaugural article in the journal Advances in Adaptive Data Analysis. The paper introduced a counterintuitive yet philosophically innovative data analysis method, which has since facilitated numerous discoveries across nearly every field of science, engineering, and medicine.
As of the beginning of this year, the paper has surpassed 10,000 citations on Google Scholar, placing it among the 1,000 most-cited papers out of more than 50 million research articles published across all fields since 1970, as recorded in the Web of Science dataset.
The challenge Professor Wu addressed in his study was making Empirical Mode Decomposition (EMD) practically applicable. Originally developed by Dr. Norden Huang in 1998, EMD is an adaptive data analysis method that operates without a predefined basis function—unlike the Fourier transform, which decomposes data using sinusoidal basis functions, or wavelet analysis, which employs amplitude-modulating and frequency-dilating shape functions.
EMD is an empirical technique based on a single assumption: data consists of amplitude-frequency modulated wavy structures, where waves of different frequencies can be separated layer by layer using local extrema information. This decomposition progresses from the shortest period to the longest until no further oscillatory pattern can be identified
However, a major drawback of EMD is its high sensitivity to extrema distribution within the data. Since real-world datasets inherently contain varying levels of noise, even minor perturbations can alter the extrema distribution, leading to instability in EMD results. This instability raises concerns about the physical interpretability of EMD-based analyses, limiting its reliability in practical applications.
“I was extremely lucky to attend a seminar for a random reason on a Saturday morning in the spring of 2002 at the University of Maryland,” Professor Wu recalled. “At the time, I was struggling to understand the rationale behind the rigid linear fitting method used to detrend data—a fundamental technique in many statistical methods widely applied in climate science.
The EMD method and adaptive data analysis, which Norden pioneered and which has transformed the entire landscape of data analysis, were philosophically captivating to me. In the following weeks, I began programming and testing the method. However, I never expected that this pursuit would lead to a two-decade-long journey of challenges and discoveries in the field.” A crucial intermediate step in Professor Wu’s development of Ensemble Empirical Mode Decomposition (EEMD) was his systematic exploration of EMD’s fundamental characteristics. Since EMD is an empirical method without a formal mathematical foundation, understanding its behavior relied heavily on computational experiments rather than analytical derivations.
Instead of working with real-world data—whose complexities make comprehensive analysis difficult—Professor Wu examined two extreme cases: the delta function, which is nonzero at only one location, and white noise, which consists of completely random values at all locations. To apply EMD to a delta function, he introduced low-amplitude white noise to help define local extrema. His findings revealed that EMD, when applied to either a delta function or white noise, behaves as a local dyadic filter across the data domain, with each extracted component having a mean period roughly double that of the previous one.
In data analysis, noise is typically considered detrimental, as it can hinder the accuracy of interpretation. However, the development of Ensemble Empirical Mode Decomposition (EEMD) leverages the unique properties of white noise under EMD, turning noise into an advantage. By utilizing the adaptive and non-rigid dyadic filter characteristics of EMD, EEMD enhances the stability and reliability of decomposition results.
Counterintuitively, adding low-amplitude white noise to real-world data helps even out extrema distribution across the data domain. When this noise-enhanced data undergoes EMD, the extracted components retain dyadic filter properties and exhibit high stability, even if the original data contains some level of noise.
To eliminate the introduced noise, EEMD follows an ensemble approach: instead of adding noise just once and applying EMD, the process is repeated multiple times, each time with a different white noise realization of the same amplitude. The final decomposition result is obtained by averaging the corresponding components from all EMD decompositions. As the number of repetitions increases, the added noise cancels out, leaving only the intrinsic components of the data.
In this sense, white noise in EEMD acts like a catalyst in a chemical reaction—facilitating the process without becoming part of the final outcome, making EEMD as a true noise-assisted data analysis (NADA) method.
“I am deeply grateful to my mentors, Edward Sarachik of the University of Washington and Edwin Schneider from my time at COLA,” Professor Wu continued. “Their unwavering support and willingness to let me pursue any research that interested me were invaluable. Without their guidance, I might never have ventured beyond the field I was originally expected to work in.
“Norden is a giant in the field who introduced me to data analysis, fundamentally shaping my research career. He has been a beacon of inspiration, and I am fortunate to still collaborate with him.”
“I am also incredibly thankful to my colleagues at FSU. Many subsequent studies, especially those introducing new data analysis constraints and philosophies, were conducted here. These works extended beyond meteorology and climate science, reaching a wide variety of disciplines. Without the recognition and support from leadership at the department, college, and university levels, this long journey would not have been possible.”
