Between August and September 2024, the M5 lab captured data on waves at a site of restored mangroves along China’s Zhanjiang coast. When Typhoon Yagi swept through the Philippines and southern China in early September, high-speed winds created waves nearly 0.9 meters (3 feet) high upon meeting the mangroves’ front edge — a record-breaking wave height observed in a mangrove ecosystem.
The team found that even those waves were dissipated by the mangroves, decreasing to 0.36 meters (1.18 feet) high after washing through a football-field length of mangrove forest. Throughout the monitoring period, mangroves at their site reliably decreased wave height from between 44%-70%.
Typically, predicting mangrove attenuation takes a lot of involved math. Field scientists have historically had to juggle a precise set of calculations: The measured density and diameters of individual mangrove plants, along with waves’ drag coefficients, turbulence and friction factors.
“We go into this kind of deep dive into physics,” said Ruth Reef, a professor at Monash University in Melbourne, Australia, who was not involved in the research.
Conversely, this new process is far less complicated: It involves only the waves’ relative heights divided by the number of waves sampled (represented by the variable HLn), and a parameter called the Ursell number that is calculated using wave height, length and water depth (and denoted by the variable Ur). Represented by the acronym HU, this method of calculation was first published in a 2025 study.
With successful data collection from Yagi, the lab had a rare opportunity to see whether the HU method could use wave measurements during calm weather to retroactively predict mangrove attenuation during storms. This second round of data was collected from the same Zhanjiang site during the spring of 2025.
link to open access article https://www.sciencedirect.com/science/article/pii/S2212096326000872?via=ihub
The third method is the newly developed HU method, a non-drag-based predictive framework (Hu et al., 2025). Unlike conventional models that rely on explicit drag parameterization, the HU method was built upon HLn-Ur relations, where HLn is relative wave height (ratio between in-canopy and incident wave height) over n wavelengths and Ur is the Ursell number (= Hs0 L2/D3, where L is wavelength and D is water depth at the seaward edge of the canopy), a common metric for wave nonlinearity (Phan et al., 2019). At each wavelength, a general form of the HLn-Ur relation is as follows:(1)
𝐻𝐿𝑛=1/(1+𝑎·𝑈𝑟𝑏)
....where a and b (varying with n) are calibrated from low-wave measurements. The core premise is that larger wave nonlinearity (higher Ur) enhances energy dissipation within vegetation, leading to lower HLn values [lower relative wave height]. For any given Ur [for any degree of nonlinearity/chaos in wave motion], HLn [relative wave height] can be iteratively determined along the transect as the cumulative number of wavelengths increases (Fig. 3b), thereby quantifying the progressive, distance-dependent wave attenuation induced by the mangroves. For a given wave burst, L is held constant along the transect. This simplification is justified because the transect is short (∼100 m) and the bed slope is mild, so depth variations are limited.

Fig. 3. Prediction of wave reduction in storm conditions using a web-application based on the HU method. (a) Relations of HLn and Ursell number (Ur)
at 1–5 wavelengths (L) in the mangrove forest, as an illustration of the HU method. At each number of wavelengths, a fitted HLn-Ur curve can be derived based on low Hs0 cases (0.1 m < Hs0 < 0.4 m). The data points of high Hs0 cases also fall on these curves. Subsequently, for a given Ur number, the evaluation of HLn along the mangrove (as the number of L increases, dashed lines) can be obtained for both low and high Hs0 cases. The dashed lines are translated into the 2D representation in panel (b), where each line corresponds to a fixed Ur value. (b) Examples of predicted and observed relative wave height with a sequence of L with given Ur numbers. (c) Performance of the three different methods (measured by R2 values) in predicting wave attenuation. For the two methods based on CD relations (analytical and numerical modeling), we show the selected top 3 CD relations that result in highest R2 values in high Hs0 cases. For visual clarity, R2 values below 1 are plotted as 1. A complete summary of the model performance is shown in Table S4. (d) Interface of the web-application based on the HU method (see Method section and Text S1) (Zhao et al., 2025). Z. Hu et al. Climate Risk Management 54 (2026) 10
Building upon the successful validation of the HU method using the highest in situ wave measurements ever recorded in mangrove environments, we developed an interactive web-based application (https://nioz.shinyapps.io/Wave-Decay-Prediction-HU-Method/; Zhao et al., 2025) to allow non-specialists to predict storm wave attenuation by mangroves (Fig. 3). The accompanying web-application, implemented in R language, allows users to upload local wave datasets to automatically compute and visualize attenuation performance under storm conditions (Fig. 2d). The platform provides freely downloadable results and supports real-time assessment of mangrove-based wave attenuation (Zhao et al., 2025). Additional details on the computational algorithms, web-application architecture, and the analytical/numerical wave models are provided in the Supplementary Information (Text S1).
This web application enables wave attenuation assessment in mangrove forests under storm conditions without the need for complex numerical modeling. It features three core interfaces: (a) Data-based Prediction: Users can upload field-measured wave data to automatically calibrate the model and predict wave attenuation under storm scenarios. (b) Custom Prediction: Allows manual entry or batch upload of storm parameters (e.g., wave height, period, depth, and vegetation width) for single or multiple scenario simulations. This allows practitioners to estimate the required mangrove width under the envisioned storm wave conditions in restoration projects. (c) Data Sharing: Serves as a collaborative platform for researchers and practitioners to contribute and access quality wave data, fostering evidence-based mangrove conservation and coastal resilience planning.
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We envision this tool as a catalyst for science-policy integration, empowering coastal communities to design and optimize mangrove-based protection projects through accessible, evidence-based modeling. We therefore recommend the adoption of this web-application as a decision-support tool for promoting mangrove restoration and sustainable coastal resilience worldwide. Through our web-application, we could collect cases for young, mature, and mixed-complexity mangrove forests. Guidance is then provided on estimating the required cross-shore width for a target residual wave height, on the influence of planting density (by scaling width), and on recalibration over time as forests mature. These additions enable practitioners to move beyond assessing existing protection to designing new nature-based solutions.