Ungermann et al. (2025) JuWavelet – continuous wavelet transform and S transform for wave analysis

Identification

• Journal: Geoscientific model development
• Year: 2025
• Date: 2025-11-17
• Authors: Jörn Ungermann, Robert Reichert
• DOI: 10.5194/gmd-18-8613-2025

Research Groups

• Forschungszentrum Jülich GmbH, Jülich, Germany
• Meteorological Institute Munich, Ludwig-Maximilians-Universität, Munich, Germany
• Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Wessling, Germany

Short Summary

This paper describes JuWavelet, an open-source Python package that implements 1-D, 2-D, and 3-D continuous wavelet transforms (CWT) using the Morlet wavelet and the S transform, providing a comprehensive tool for analyzing and reconstructing localized wave-like phenomena in geosciences.

Objective

• To describe and validate the open-source Python package JuWavelet, which implements 1-D, 2-D, and 3-D continuous wavelet transforms (CWT) using the Morlet wavelet and the S transform, including both analysis and synthesis capabilities, to address a gap in available multi-dimensional wave analysis software.

Study Configuration

• Spatial Scale: 1-D, 2-D, and 3-D data analysis. Examples range from local (e.g., atmospheric gravity waves with wavelengths of tens to hundreds of thousands of meters horizontally, and thousands of meters vertically) to regional (e.g., sea surface temperature index). Specific examples include synthetic fields of 200x200 grid points, ALIMA lidar data covering approximately 50,000 meters vertically and 1,000,000 meters horizontally, and 3-D mountain wave simulations over tens of thousands of meters.
• Temporal Scale: Applicable to time series data, with examples including sea surface temperature index analyzed over periods of several decades (e.g., 504 entries representing a time series). The transforms are general for analysis in either spatial or temporal domains.

Methodology and Data

• Models used:
  • JuWavelet Python package implementing:
    • Continuous Wavelet Transform (CWT) using the Morlet wavelet.
    • S transform (ST).
    • Gabor transform (for 1-D).
    • Fast Fourier Transform (FFT) for efficient computation.
• Data sources:
  • Synthetic 1-D, 2-D, and 3-D data.
  • Sea surface temperature (SST) index (Niño3).
  • Temperature data measured by the ALIMA lidar.
  • Modelled mountain wave field (e.g., vertical displacement for a bell-shaped mountain with height 1000 meters and half-width 25,000 meters).

Main Results

• The JuWavelet Python package successfully implements 1-D, 2-D, and 3-D continuous wavelet transforms (CWT) using the Morlet wavelet and the S transform, including both analysis and reconstruction capabilities.
• Examples demonstrate the package's ability to analyze synthetic data, reproduce established geophysical analyses (e.g., SST index), and separate overlapping wave packets in multi-dimensional fields.
• The software provides consistent implementations for both CWT and S transform across all dimensions, addressing a gap in available software that typically focuses on discrete transforms or lower dimensions.
• The reconstruction functionality allows for manipulation and filtering of coefficients (e.g., separating waves by angle or scale) to extract individual wave packets or features.
• The implementation leverages optimized FFT libraries (Intel MKL, FFTW) for computational efficiency and supports parallelization.

Contributions

• Provides the first readily available, open-source Python package for 1-D, 2-D, and 3-D continuous wavelet transforms (Morlet wavelet) and S transforms, including full analysis and reconstruction capabilities.
• Closes a significant gap in software availability for multi-dimensional geophysical wave analysis, which was previously limited to 1-D or specialized tools.
• Offers a consistent mathematical framework and implementation for both CWT and S transform across all dimensions, facilitating broader application and derivative work.
• Includes features like aspect ratio scaling for anisotropic data (e.g., atmospheric gravity waves in vertical cross-sections) and flexible parameter configuration (e.g., Morlet parameter k).
• Demonstrates practical applications for filtering and separating complex wave phenomena in geophysical data.

Funding

• Forschungszentrum Jülich (covered article processing charges).

Citation

@article{Ungermann2025JuWavelet,
  author = {Ungermann, Jörn and Reichert, Robert},
  title = {JuWavelet – continuous wavelet transform and <i>S</i> transform for wave analysis},
  journal = {Geoscientific model development},
  year = {2025},
  doi = {10.5194/gmd-18-8613-2025},
  url = {https://doi.org/10.5194/gmd-18-8613-2025}
}