The three datasets used in this study, shown in Table 1, are bathymetric lidar survey data for three rivers in the United States: the Swan River in Montana, the Snake River in Wyoming, and the Eel River in California. All three datasets were collected by the National Center for Airborne Laser Mapping (NCALM) (ncalm.cive.uh.edu) and the data includes independent ground truth data. The ground truth was created using manual classification, ensuring high accuracy through multiple iterations. The process involved using Terrasolid’s Terrascan software to guarantee precise data labeling, with verification using Google Earth images. The Swan River survey was conducted in 2023, the Snake River in 2012, and the Eel River in 2014. These surveys cover a range of geographical areas, with the Swan River encompassing 53 km 2 , the Snake River 77 km 2 , and the Eel River 57 km 2 . However, only a narrow corridor along each river was selected for analysis to focus the study on only the river itself, significantly reducing the total point count and concentrating solely on river classes as shown in Table 2. The surveyed corridor length of these rivers is 27 km for the Swan River, 44 km for the Snake River, and 204 km for the Eel River. An important aspect of these surveys is the point density, expressed as the number of lidar points per square meter. This metric is used for determining the survey data’s resolution and level of detail. The Swan River survey has a high point density of 28 pts/m 2 , which suggests a very detailed and fine-scale survey. In contrast, the Snake River survey has a much lower point density of 3 pts/m 2 , indicating a coarser resolution. The Eel River survey falls between these two, with a point density of 14 pts/m 2 . The sensor technologies employed for these surveys also differ, reflecting technological advancements and specific sensor capabilities. The Snake River and Eel River surveys were conducted using the Optech AQUARIUS sensor (Guo et al., 2018) and the Swan River survey used the RIEGL VQ-840-G sensor (Pfennigbauer et al., 2022). The datasets used in our study are diverse in terms of river hydrogeomorphology, lidar sensor technologies, and point cloud densities. This diversity enhances the robustness and generalizability of any machine learning model, allowing it to effectively learn and predict river channel evolution in various geographic and environmental contexts.

The data for all three rivers were manually classified into four categories: river surface, riverbed, ground, and other. The river surface class represents the interface between the water and the atmosphere, capturing the mostly specular reflection of laser light on the water surface. The riverbed class encompasses the benthic layer at the bottom of the water, including both the sediment and any submerged vegetation. The riverbed class also accounts for volumetric scattering in the water column. Volumetric scattering occurs when light interacts with suspended particles and water molecules. These interactions cause the lidar signal to scatter in multiple directions, affecting its penetration depth and the peak of the backscatter signal received. The ground class includes terrestrial surfaces, excluding aquatic or vegetative components, clearly differentiated from the marine environment. Lastly, the other class includes all remaining data points that do not fall into the previous three categories and predominantly consist of vegetation. This categorization ensures comprehensive mapping and analysis of the riverine and adjacent environments. To focus on the riverine environment, only a subset of each dataset was used, including points along a 50-m corridor from the centerline of each river. The class distribution for this corridor is given in Table 2. Even after reducing to a narrow along the river, the ground and other classes still comprise the majority of points, whereas the river surface and riverbed classes account for only a small percentage.

To validate our depth corrections on the Snake River, we used the ground truth acquired by Legleiter et al. (2016). They surveyed Rusty Bend (a specific bend in the Snake River) with a SonTek RiverSurveyor S5 Acoustic Doppler Current Profiler (ADCP) mounted on a kayak and tied to an RTK-GPS base station, getting depth soundings with 0.001 m resolution and 1% accuracy over 0.2–15 m. Along the channel margins, they also measured water edge elevations with RTK-GPS to correct for instrument drift and kayak offset. All ADCP returns within 0.5 m of a GPS control point were cross-calibrated to ensure vertical consistency. We used these rigorously corrected and georeferenced ADCP measurements as the bathymetric ground-truth along the Snake River for validating our fully automated depth correction model.

The methodology starts with the data processing steps used to convert light detection and ranging files into uniformly sized blocks suitable for deep learning input. The process continues with data augmentation techniques aimed at increasing the dataset’s size and generalizability for the machine learning model. The model is then discussed with an in-depth analysis of the PointCNN implementation using ESRI’s deep learning module arcgis.learn (Esri, 2024). Different metrics and error rates are then used to evaluate the model’s performance. Finally, the methodology addresses depth and refraction corrections to achieve the desired corrected final riverbed points, as shown in Figure 2.

All of the training was performed on an NVIDIA Quadro P6000 GPU (24 GB VRAM) under Ubuntu 22.04.5 LTS. For both PointCNN and DGCNN, Adam optimizer was used with a learning rate of 0.004 and a dropout rate of 0.25. In PointCNN, we used point-wise cross-entropy loss with a batch size of 6. For DGCNN, cross-entropy loss was used with a batch size of 2. Both setups required approximately 22 GB of GPU memory. Block size and per-block point-sampling configurations were explored in Section 3.2, and then the optimal setting was selected for the final model.

Analyzing semantic segmentation performance across various block sizes (S) and number of points (P) reveals crucial insights into how these parameters impact the model’s effectiveness. This analysis focuses exclusively on classifying the primary classes, river surface, and riverbed, as those are needed to apply depth and refraction correction.

We first tested PointCNN’s performance against DGCNN with optimized values for P and S (as defined in Section 3.1). We set P to 8,192 and S to 50 m. Both the training and testing were done using the Swan River data. In Table 4, PointCNN has more balanced results between Precision and Recall, leading to higher F1 scores than DGCNN. This balance suggests that PointCNN is better at identifying the correct points.

DGCNN manages to achieve low CE for the river surface and riverbed classes but struggles with high OE. This indicates a tendency to misclassify points more than PointCNN, which is particularly problematic in classes requiring better scores, like riverbed and river surface for our application. PointCNN’s consistently high performance across both classes reflects its robustness and adaptability to segmentation challenges. The model’s ability to maintain low error rates while achieving high IoU and Kappa scores shows its effectiveness in semantic segmentation tasks.

For the final modeling, 80% of the data from the Swan and Eel Rivers was used to train the model, while the remaining 20% was set aside for testing on seen data. The results of these tests on the seen data are detailed in Supplementary Appendix SA, demonstrating the model’s performance across various metrics for the Swan and Eel Rivers. For the final evaluation and analysis, the focus is on the unseen data from the Snake River. This unseen data serves as a test of the model’s ability to generalize and accurately classify river features in previously unobserved environments, providing insights into its overall performance. On average, the model training took 2 h and 50 min per epoch. Over 30 epochs, the total training time amounted to approximately 85 h. For inference, the classification of the entire Snake River dataset was completed in approximately 12 min.

A detailed analysis of a river segmentation using both a top-down and a cross-section view derived from the lidar data is shown in Figure 8. The top section of the image presents a classified map of the river and its surrounding areas, with different colors representing the classes. The cross-section view compares adjusted and unadjusted riverbed depths from the river surface. The raw data is biased due to the bending and slowing of light as it passes through the water. The adjusted depth from the river surface is measured at 0.86 m, accounting for the refraction and distortion effects caused by the interaction of the laser pulses with the water column. By comparing these two measurements, the image highlights the significant impact of the change in speed of light on the accuracy of bathymetric data. Adjusting for these distortions is crucial for producing reliable maps of underwater features.

To evaluate our automated bathymetry lidar depth correction workflow, we validated our results using 1,595 independent high-accuracy ADCP depth measurements collected from the clear-water Snake River (Legleiter et al., 2016). Metrics used for the depth accuracy validation are based on Pan et al. (2015a) and Legleiter et al. (2016). Mean error was used to quantify the systematic offset between predicted and true depths. The standard deviation of errors measures the variability of individual errors around the mean, reflecting the consistency of predictions. Root mean square error (RMSE) combines both bias and variability into a single metric, giving greater weight to larger errors. Mean absolute error (MAE) captures the typical magnitude of errors without considering their direction. Finally, the coefficient of determination (R²) assessed how well the predicted depths explained the variability in the true depth measurements, with values closer to 1 indicating stronger predictive performance.

Initially, our uncorrected bathymetric data showed a mean bias of 45 cm, indicating systematic overestimation. After refraction correction, this bias was eliminated, reducing the mean bias to 2 cm as shown in Table 6. This improvement highlights the effectiveness of the method in addressing systematic depth overestimation. Compared to previous studies using the same dataset, our bathymetry depth accuracy show improved mean bias. Pan et al. (2015a) and Legleiter et al. (2016) reported mean bias of approximately 6 cm and 8 cm, respectively, both higher than the 2 cm error achieved by our automated method. The RMSE decreased from 0.47 m to 0.16 m after correction, and the MAE decreased from 0.45 m to 0.12 m. We observed a slight increase in the standard deviation of errors, from 0.12 m before correction to 0.15 m. This increase indicates greater variability among corrected measurements rather than persistent systematic errors. The model significantly improves bathymetric accuracy by effectively eliminating bias and achieving precision on par with previously published continuous wavelet transform (CWT) based approaches. These results confirm the reliability and consistency of our workflow for automated bathymetric depth estimation.

The misclassification of the riverbed class as ground can be attributed to several factors. The riverbed and the ground have similar characteristics, especially near the edges of the river where small changes in water level is the only factor governing the difference between ground and riverbed classes. This likely confused classification algorithms, leading to misclassification. Vegetation and debris on the riverbed further complicated classification, as plants, fallen branches, or other debris were mistaken for ground. These misclassifications often occurred around the river’s edges, as shown in Figure 9a. One thing to note is that this occurs in very shallow water regions, where the elevation of the ground and water is nearly the same, and the river surface class is absent because the river surface and benthic layer returns overlap in the lidar response (Pan et al., 2015a).

In Figure 9b, the histogram (blue bars) shows that the majority of misclassifications occur at shallower depths, with the frequency decreasing as depth increases. A total of 431,225 points are misclassified. The red line represents the depth error, which rises linearly from 0.0 to 0.8 m as the depth ranges from 0.0 to 2.5 m. Misclassifications are more frequent at shallower depths, with the errors increasing with water depth. However, because a majority of the misclassifications are in shallow areas, the overall point cloud errors due to the improper application of refraction and speed of light corrections is minimal for this majority of misclassified points. The misclassification for river-related classes decreases with increasing water depth and shallow river regions are more susceptible to errors. As depicted in Figure 9c, most misclassifications between the riverbed and river surface classes occur within the 0.4 m depth range. The histogram (blue bars) reveals the majority of misclassifications occur at shallower depths, with the frequency decreasing as depth increases. A total of 127,162 points are misclassified. The red line illustrates the depth error, which rises linearly from 0.0 to 0.2 m as the depth increases from 0.0 to 0.6 m. The algorithm struggles to accurately differentiate between the benthic layer and the water surface in extremely shallow areas (below 20 cm), due to the laser pulse width of the bathymetric lidar system (8 ns for Aquarius (Fernandez-Diaz et al., 2014) and 1.5 ns for the Riegl 840-G (Mandlburger et al., 2020). The shallow water lidar returns are normally a convolution of the water surface and benthic layer, and therefore distinguishing these two surfaces from convolved lidar returns is difficult, both for the lidar processing algorithms (e.g., Schwarz et al., 2019) and the machine learning results presented herein. Since most misclassifications occur at very shallow depths where the differences between the riverbed and surface are minimal, the impact due to incorrect application of depth corrections and therefore the accuracy of the final point cloud is minor. Figures 9b,c show that although the algorithm struggles in shallow regions, the depth error caused by misclassification remains relatively small and localized for the majority of the misclassified points. As a result, the overall effect on point cloud accuracy is minimal.

The strong agreement between our corrected lidar depths and independent ADCP measurements on the Snake River demonstrates the robustness of the semantic segmentation results. The high classification accuracy achieved for the river surface and riverbed classes suggests that the model generalized well across different river environments, despite being trained on datasets from geographically distinct rivers. Because accurate river surface and riverbed identification is important for reliable depth estimation, the close match with the ADCP ground truth confirms that the semantic segmentation was precise and can support real-world depth correction applications. These findings indicate that our model effectively transfers across diverse bathymetric conditions, leading to accurate and consistent results even on an unseen river system. Because of the strong generalization performance, we found no need for additional data or further data augmentation techniques for training.

Deep learning models are often computationally intensive, particularly for large-scale 3D point cloud data. This was evident with DGCNN, which required nearly 7 h per epoch with a limited batch size of 2 due to its dynamic graph recomputation at every layer. In contrast, PointCNN demonstrated strong computational efficiency by completing each training epoch in approximately 2 h and 50 min with a larger batch size of 6. This efficiency comes from the fixed neighborhood structure, where local point relationships are established once during initial sampling and reused throughout the network, avoiding the costly repeat of graph construction. During inference, PointCNN further demonstrated scalability by classifying the entire Snake River dataset (approximately 20 million points) in just 12 min. These results show that by integrating an efficient deep learning model like PointCNN into our workflow, we achieve fast, scalable, and practical processing for large-scale bathymetric lidar applications.

Although PointCNN yielded the strongest results in our experiments, the primary aim of this study was not to optimize a specific architecture but to establish a generalizable workflow for automating bathymetric lidar classification and depth correction. The segmentation stage was designed to be modular, allowing for the substitution of any deep learning model capable of distinguishing the river surface from the riverbed points. Numerous point-cloud segmentation architectures have been developed in recent years with varying trade-offs in accuracy, complexity, and computational efficiency. Our workflow demonstrated that such models can be integrated interchangeably without altering the downstream refraction-correction or depth-estimation components. This flexibility enables the method to benefit from future advancements in 3D point-cloud learning and provides a robust foundation for developing fully automated bathymetric processing pipelines.

This study presents an automated workflow specifically aimed at supporting engineering surveys that require accurate bathymetric mapping. By validating our corrected lidar depths against high-accuracy ADCP measurements, we demonstrated that the method reliably captures riverbed topography with minimal bias. The ability to generate precise riverbed digital elevation models (DEMs) or estimate river volumes makes this approach highly suitable for bathymetric engineering surveys. By automating the classification process, the workflow enables large-scale surveys to reduce time, cost, and manual effort traditionally associated with riverine bathymetric surveys.

In PointCNN, X-Conv operations transform local neighborhoods relative to a center point by applying a learned transformation matrix. The effectiveness of classification relies on meaningful spatial differences ( x , y , z ) and feature differences among neighboring points. In shallow water regions, river surface and riverbed points have minimal vertical separation. Similarly, along riverbanks, the horizontal and vertical distances between riverbed and ground points are small, resulting in overlapping local geometries. When such local differences diminish, the learned transformation matrix X cannot effectively distinguish between classes, leading to increased misclassification errors.