Why is this research valuable?  

Waves and oscillations carry hidden information about a system — from pressure oscillations rumbling through Earth’s crust to magnetoacoustic waves racing across a sunspot, or even intricate fluctuations in biomedical data. Interpreting these signals, however, depends entirely on the analysis tools we choose. With so many approaches developed for specific goals or tailored datasets, misapplying a technique — or oversimplifying it — can yield incomplete or inaccurate results, and ultimately misinterpret a crucial phenomenon.

During a 2019 discussion meeting in Oslo, our Waves in the Lower Solar Atmosphere (WaLSA) international team — a mix of observers, theorists and modellers — began brainstorming new analysis ideas and set everyone a simple task: run the same analysis on the same solar dataset. Fourteen people, three public codes, three different answers. It turned out that two routines had been fine‑tuned for very specific datasets and quietly failed on our test case; only one produced a correct interpretation.

That uncomfortable moment crystallised a broader problem: one researcher’s “trusted” package or analysis method can be another’s source of systematic error, especially when the underlying assumptions (stationarity, noise level, sampling, linearity, etc.) do not match the data or science goals. Similar pitfalls exist in geophysics, engineering and medicine. We realised the community needed (i) a clear-eyed comparison of methods and (ii) a shared, well‑tested code base.

What did we do?  

1. A cross‑disciplinary team
   Our WaLSA discussions gradually expanded beyond solar physics, as new colleagues with backgrounds in plasma physics, mathematics, astrophysics, environmental science, and engineering joined the team — bringing complementary expertise and fresh cautionary tales.
   
   
2. Systematic head‑to‑head tests
   We built synthetic datasets, serving as ground truth, that mimic real‑world challenges: overlapping modes, transients, non‑stationary trends, noise, missing samples, and more. We then applied popular techniques — FFT, Lomb‑Scargle, wavelets, Hilbert–Huang, Empirical Mode Decomposition (EMD), Welch, k‑ω analysis, Proper Orthogonal Decomposition, among others — and asked two questions:
   ⦿  What can each method reliably recover?
   ⦿  Where does it mislead or lose information?
   Side‑by‑side plots make the trade‑offs stark: FFT excels at evenly sampled, stationary signals but smears transients; wavelets localise bursts but may broaden spectral peaks; EMD captures nonlinearity yet is sensitive to noise; an apparently minor detrending choice can leave residual trends that look like low-frequency power, to name but a few conclusions. Hence, we highlight how, for example, using a tool optimised for simple, stationary signals on non-stationary data can lead to misinterpretations or overlooked phenomena.
   
   
3. WaLSAtools — a living library
   We merged clean, cross-checked implementations into a single open-source repository, WaLSAtools, and tested them against synthetic datasets. Our goal is to provide a one-stop resource for wave analysis across disciplines.
   
   
4. From internal discussions to Nature Reviews
   The journal commissioned us to write a Methods Primer focused on reproducibility — a perfect venue. Tight word and figure limits forced us to pick representative methods and reserve deeper parameter studies for Supplementary Information and, even more so, for the evolving WaLSAtools repository and its living documentation — with further methods and use cases being added over time.
   
   

What are the implications?  

A key message is that no single technique is universally “best”. Every method carries assumptions; ignoring them can hide dozens of wave modes and important information, or invent artefacts. By mapping each tool’s advantages and disadvantages, the Primer helps researchers choose the most appropriate analysis pathway — or combine complementary ones — before drawing conclusions. The few techniques discussed are intended as examples to raise awareness about the importance of matching analysis tools to data characteristics and scientific goals.

For solar physics, this means disentangling more than 30 co‑existing wave modes within a sunspot in the Sun’s lower atmosphere — a finding that sheds new light on energy transport to the solar corona (as shown in a recent Nature Communications study). In geophysics the same logic can improve discrimination between foreshocks and noise. In biomedicine, it can prevent over‑interpreting minor oscillations in EEG or glucose traces.

Equally important, WaLSAtools encourages reproducible science: the repository is open source, test signals are public, and contributions are welcome. We view the library as a starting point that the broader community — across astrophysics, seismology, engineering, economics, life and environmental sciences — can extend. Cross-disciplinary collaboration enables us to refine existing tools, develop new techniques, and harness advancing computational power — ultimately leading to more precise discoveries wherever waves and fluctuations play a fundamental role.

Finally, the work is dedicated to our esteemed colleague and co-author Bernhard Fleck, whose insistence on methodological rigour sparked that pivotal Oslo debate and continues to motivate us.

🔗  Read the Primer: https://www.nature.com/articles/s43586-025-00392-0 

🔗  Free read‑only access: https://WaLSA.tools/nrmp 

🔗  Supplementary Information: https://WaLSA.tools/nrmp‑si 

🔗  WaLSAtools repository: https://WaLSA.tools 

🎬  Short animation (2 min): https://youtu.be/b_rG7Q8fyMU