Dear all,
We are pleased to invite you to the next WISE Webinar on the topic of Estimating the directional spectrum with incomplete information on 18/09/2025 at **2:00 PM CET (**10 PM Melbourne time).
Join us via https://tudelft.zoom.us/my/wisezoominars on 18th September at 2:00 -3.00 PM CET time!
First speaker: Zain Torres, University of Melbourne
Title: Wavelet-based estimation of directional wave spectra from single-point and spatially distributed measurements.
Abstract:
Wave directional information is crucial for understanding wave dynamics and energy distribution; however, accurately capturing wave directionality remains a significant challenge. Most in situ measurements rely on point-based sensors, and while remote sensing can provide directional information, buoys are more commonly used due to their superior resolution and consistency. Nevertheless, estimating the directional spectrum poses inherent mathematical challenges, as solutions can be non-unique and highly sensitive to sparse input data. Adaptive methods have been developed to address these challenges. Among them, the Maximum Likelihood Method (MLM), the Maximum Entropy Method (MEM), and the Wavelet Direction Method (WDM) are commonly used, yet each relies on simplifying assumptions. MLM and MEM assume the wave field is stationary and follows a statistical model, while WDM depends on the choice of wavelet. We evaluate these methods against a baseline obtained from Fourier processing of numerically simulated sea surfaces. Transfer functions are derived and validated against laboratory measurements in a wave basin. The results reveal systematic biases, with MLM spectra approximately 14 percent broader than the baseline and MEM and WDM approximately 6 and 3 percent narrower, respectively. Performance varies across frequency, with WDM performing best near the spectral peak (0.8–1.15 f/fp) and MEM performing more accurately at higher frequencies above 1.3 f/fp. Stereo-image estimates are slightly broader than probe-based measurements due to geometric corrections applied during image rectification. Quantifying these biases provides a framework for correcting directional estimates and improving the reliability of wave field characterization in both laboratory and field settings.
Second speaker: Daniel Peláez Zapata, École Normale Supérieure Paris-Saclay
Title: Transfer Function for Adaptive Methods of Estimating Directional Spectra Using a Fully Nonlinear Wave Model and Laboratory Measurements
Abstract:
The accurate estimation of directional wave spectra is crucial for understanding ocean wave dynamics, air-sea interactions, and coastal processes. The directional wave spectrum is often computed by resolving the distribution of wave energy as a function of frequency and direction using mathematical methods applied to time series from measuring instruments (e.g., buoys). These time series typically consist of either triplets of variables at a single point (e.g., velocity or acceleration components) or arrays of measurements distributed across multiple spatial locations (e.g., wave staffs). Traditional methods, based on the conventional Fourier cross-spectral analysis, such as the Truncated Fourier Series (TFS), Maximum Likelihood (MLM), or Maximum Entropy (MEM) methods, often suffer from limitations in spectral resolution, inaccurate estimations, and spurious spectral peaks. This disadvantage is generally attributed to certain simplifications on the shape of the directional distribution and assumptions such as stationarity, which may not always capture the complexity of ocean waves. Wavelet-based methods provide a more flexible approach, thanks to their time-frequency decomposition capabilities. This presentation introduces the EWDM (Extended Wavelet Directional Method), a Python toolkit developed to estimate the directional spectrum of ocean waves using a wavelet-based technique. EWDM aims to address the limitations of conventional methods by providing a robust estimation of the directional wave spectrum from both single-point triplets and spatially-distributed arrays. Consequently, EWDM can be used on diverse sources of data, including GPS buoys, pitch-roll buoys, arrays of wave staffs, acoustic Doppler current profilers (ADCP) and sampled points from stereo-videos of the sea surface. Key features of the EWDM include the implementation of wavelet-based algorithms for extracting directional information from wave time series, improved estimation of wave directional distribution using Kernel Density Estimation (KDE), tools for processing and visualising directional wave data, and compatibility with popular data sources, including Spotter buoys and CDIP (Coastal Data Information Program) database.
Please note that WISE Webinars including the Q&A will be recorded and posted on the WISE YouTube Channel afterwards (https://www.youtube.com/@wisezoominars). By participating, you consent to any information you share to be included in the recording and shared.
Best wishes,
Alvise, Qingxiang**, Tripp, Morteza,** Alberto and Bernard**.**
(The WISE Webinar organizing committee)