PW-SDF: a terrain-optimized pseudo-waveform and spatial-distribution-feature method for ground photon extraction from ICESat-2 data in vegetated mountainous regions

Accurate extraction of ground photons from ICESat-2 data is critical for reliable sub-canopy terrain retrieval, yet it remains challenging in mountainous regions characterized by complex topography, dense vegetation, and sparse ground returns. To address these challenges, this study proposes a novel ground photon extraction framework, PW-SDF (Terrain-Optimized Pseudo-Waveform and Spatial-Distribution-Feature), which is designed to mitigate terrain-induced distortions, detect weak ground signals beneath dense canopies, and suppress residual noise. The PW-SDF framework consists of four stages: noise removal, coarse ground photon extraction, fine ground photon extraction, and ground photon densification. The performance of PW-SDF was evaluated across four representative mountainous sites, including three non-rainforest sites (Surry Mountain Preserve [SMP] and Sierra National Forest [SNF] in the United States; Yushan National Forest Park [YNFP] in China) and one rainforest site (El Yunque National Forest [EYNF] in Puerto Rico). Ground photons extracted from raw ATL03 data using PW-SDF were validated against airborne LiDAR-derived digital terrain models (DTMs). The resulting root mean square error (RMSE) values were 1.39 m at SMP, 2.40 m at SNF, 1.50 m at YNFP, and 3.16–3.62 m at EYNF. Across all study sites, PW-SDF consistently outperformed the ATL08 product and the ALCSF algorithm. In non-rainforest regions, PW-SDF achieved RMSE reductions of 0.07–0.36 m relative to ATL08 and 0.03–0.84 m relative to ALCSF. Even under the extremely sparse ground-return conditions of the EYNF rainforest, PW-SDF maintained superior accuracy, reducing RMSE by 0.20–0.44 m relative to ATL08 and 2.77–4.19 m relative to ALCSF. These results demonstrate that PW-SDF is highly resilient to sparse ground photons, interference from near-ground noise, and strong terrain variability. Thus, PW-SDF provides a robust solution for extracting ground photons from ICESat-2 data in complex mountainous forest environments, enhancing the reliability of sub-canopy terrain mapping and related ecological applications.