The retrieval of tree height percentiles from satellite lidar waveforms observed over mountainous areas is greatly challenging due to the broadening and overlapping of the ground return and vegetation return. To accurately represent the shape distributions of the vegetation and ground returns, the target response waveform (TRW) is resolved using a Richardson–Lucy deconvolution algorithm with adaptive iteration. Meanwhile, the ground return is identified as the TRW component within a 4.6 m ground signal extent above the end point of the TRW. Based on the cumulative TRW distribution, the height metrics of the energy percentiles of 25%, 50%, 75%, and 95% are determined using their vertical distances relative to the ground elevation in this study. To validate the proposed algorithm, we select the received waveforms of the Global Ecosystem Dynamics Investigation (GEDI) lidar over the Pahvant Mountains of central Utah, USA. The results reveal that the resolved TRWs closely resemble the actual target response waveforms from the coincident airborne lidar data, with the mean values of the coefficient of correlation, total bias, and root-mean-square error (RMSE) taking values of 0.92, 0.0813, and 0.0016, respectively. In addition, the accuracies of the derived height percentiles from the proposed algorithm are greatly improved compared with the conventional Gaussian decomposition method and the slope-adaptive waveform metrics method. The mean bias and RMSE values decrease by the mean values of 1.68 m and 2.32 m and 1.96 m and 2.72 m, respectively. This demonstrates that the proposed algorithm can eliminate the broadening and overlapping of the ground return and vegetation return and presents good potential in the extraction of forest structure parameters over rugged mountainous areas.

Topographic slope is a key parameter for characterizing landscape geomorphology. The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) offers high-resolution along-track slopes based on the ground profiles generated by dense signal photons. However, the across-track slopes are typically derived using the ground photon geolocations from the weak-beam and strong-beam pair, limiting the retrieval accuracy and losing valid results over rugged terrains. The goal of this study is to propose a new method to derive the across-track slope merely using single-track photon data of a strong beam based on the theoretical formula of the received signal pulse width. Based on the ICESat-2 photon data over the Walker Lake area, the specific purposes are to (1) extract the along-track slope and surface roughness from the signal photon data on the ground; (2) generate an elevation frequency histogram (EFH) and calculate its root mean square (RMS) width; and (3) derive the across-track slope from the RMS width of the EFH and evaluate the retrieval accuracy against the across-track slope from the ICESat-2 product and plane fitting method. The results show that the mean absolute error (MAE) obtained by our method is 11.45°, which is comparable to the ICESat-2 method (11.61°) and the plane fitting method (12.51°). Our method produces the least invalid data proportion of ~2.5%, significantly outperforming both the plane fitting method (10.29%) and the ICESat-2 method (32.32%). Specifically, when the reference across-track slope exceeds 30°, our method can consistently yield the optimal across-track slopes, where the absolute median, inter quartile range, and whisker range of the across-track slope residuals have reductions greater than 4.44°, 1.31°, and 0.10°, respectively. Overall, our method is well-suited for the across-track slope estimation over rugged terrains and can provide higher-precision, higher-resolution, and more valid across-track slopes.

The retrieval of tree height percentiles with satellite lidar waveforms over the mountainous ar-eas is greatly challenged due to slanted and rugged topographic relief of underlying ground. A novel algorithm is proposed to extract the height percentiles based on the target response waveform (TRW) that is resolved by using a Richardson–Lucy deconvolution algorithm with an adaptive iterative time. The height metrics of the energy percentiles of 25%, 50%, 75% and 95% for the cumulative TRW distribution are determined by their vertical distances relative to the ground elevation in this study. To validate the proposed algorithm, we select the received waveforms of the Global Ecosystem Dynamics Investigation (GEDI) lidar over the Pahvant Mountains of central Utah, USA. The results reveal that the resolved TRWs resemble closely to the actual target response waveforms from the coincident airborne lidar data, with the mean values of the coefficient of correlation, total bias and root mean square error (RMSE) taking val-ue of 0.92, 0.0813 and 0.0016. In addition, the accuracies of the derived height percentiles from the proposed algorithm have been greatly improved compared with the conventional Gaussian de-composition method and the slope-adaptive waveform metrics method. The RMSE values de-crease by the mean values of 1.96 m and 2.72 m, respectively. It demonstrates that the proposed algorithm has good potential in the extraction of forest structure parameter over rugged moun-tainous areas.